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TEACHER EDITIONMission 1Math1 2 3 4 75 86 9GRADE7GRADE 7Mission 1 Scale DrawingsMission 2 Introducing Proportional RelationshipsMission 3 Measuring CirclesMission 4 Proportional Relationships and PercentagesMission 5 Rational Number ArithmeticMission 6 Expressions, Equations, and InequalitiesMission 7 Angles, Triangles, and PrismsMission 8 Probability and SamplingMission 9 Putting It All TogetherTEACHER EDITIONMathGRADE 7TEACHER EDITIONGrade 7 | Mission 1

GRADE 7Mission 1Scale DrawingsIn this Mission, students learn to understand and use the terms “scaled copy,” “to scale,” “scale factor,” “scale drawing,” and “scale,” and recognize when two pictures or plane gures are or are not scaled copies of each other. They use tables to reason about measurements in scaled copies, and recognize that angle measures are preserved in scaled copies, but lengths are scaled by a scale factor and areas by the square of the scale factor. They make, interpret, and reason about scale drawings. These include maps and oor plans that have scales with and without units.

© 2023 ZearnPortions of this work, Zearn Math, are a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.Zearn is a registered trademark.Printed in the U.S.A.ISBN: 979-8-88868-970-7

Table of ContentsMISSION OVERVIEW viiiASSESSMENTS xiiiTOPIC A: SCALED COPIESLESSON 1 What Are Scaled Copies? 1LESSON 2 Corresponding Parts and Scale Factors 18LESSON 3 Making Scaled Copies 32LESSON 4 Scaled Relationships 47LESSON 5 The Size of the Scale Factor 60LESSON 6 Scaling and Area 72TOPIC B: SCALE DRAWINGSLESSON 7 Scale Drawings 89LESSON 8 Scale Drawings and Maps 105LESSON 9 Creating Scale Drawings 116LESSON 10 Changing Scales in Scale Drawings 127LESSON 11 Scales without Units 142LESSON 12 Units in Scale Drawings 155TOPIC C: LET’S PUT IT TO WORKLESSON 13 Draw It to Scale 164© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. iii

ZEARN MATH MISSION OVERVIEW G7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.M3Comparison of Length, Weight, Capacity, & Numbers to 10WEEK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36KG1G2G3G4G5G6G7G8M1Numbers to 10M4Number Pairs, Addition, & Subtraction to 10M6Analyzing,Comparing, & Composing ShapesM1Add & Subtract Friendly NumbersM2Meet Place ValueM3Measure LengthM2Explore LengthM3Counting & Place ValueM1Add, Subtract, & RoundM1Multiply & Divide Friendly NumbersM2Measure ItM4Add & Subtract Big NumbersM5Work with ShapesM4Find the AreaM1Area and Surface AreaM1Scale DrawingsM3Measuring CirclesM6Add & Subtract to 100M4Add, Subtract, & SolveM5Add & Subtract Big NumbersM6EqualGroupsM7Length, Money, & DataM3Multiply & Divide Tricky NumbersM5Fractions as NumbersM6Display DataM7Shapes & MeasurementM3Multiply & Divide Big NumbersM5Equivalent FractionsM6Decimal FractionsM1Place Value with Decimal FractionsM7Multiply & MeasureM2Base Ten OperationsM3Add & Subtract FractionsM4Dividing FractionsM5Arithmetic in Base TenM4Multiply and Divide Fractions & DecimalsM5Volume, Area, & ShapesM6The Coordinate PlaneM2Introducing RatiosM2Introducing Proportional RelationshipsM1Rigid Transformations and CongruenceM4Proportional Relationships and PercentagesM4Linear Equations and Linear SystemsM3Rates and PercentagesM6Expressions and EquationsM6Associations in DataM3Linear RelationshipsM5Functions and VolumeM7Exponents and Scientific NotationM7Rational NumbersM8Data Sets and DistributionsM7Angles, Triangles, and PrismsM8Pythagorean Theorem and Irrational NumbersM6Expressions, Equations, and InequalitiesM5Rational Number ArithmeticM8Probability and SamplingM9Putting It ALL TogetherM4Construct Lines, Angles, & ShapesM2Measure & SolveM9Putting It ALL TogetherM9Putting It ALL TogetherM22D & 3D ShapesM5Numbers 10–20; Count to 100 by Ones and TensM8Shapes, Time, & FractionsM2Dilations, Similarity, and Introducing SlopeWhole Numbers and OperationsExpanding Whole Numbers and Operations to Fractions and DecimalsAlgebraic Thinking and Reasoning Leading to FunctionsGeometry Measurement, Statistics and ProbabilityM1Add & Subtract Small NumbersKeyCURRICULUM MAPv

ZEARN MATH MISSION OVERVIEWG7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.Overview of Topics and Lesson ObjectivesEach mission is broken down into topics. A topic is a group of lessons that teach the same concept. There is a balance of Independent Digital Lessons and Concept Explorations in each topic of a mission to ensure every student learns with a mix of modalities, feedback, and support while engaging in grade-level content. Throughout each mission, students work on grade-level content with embedded remediation to address unnished learnings.ObjectiveTopic A Scaled CopiesLesson 1 Dierentiate between scaled and non-scaled copies of a gure. Lesson 2 Identify corresponding parts and determine the scale factor between two gures. Lesson 3 Draw a scaled copy of a given gure using a given scale factor.Lesson 4Use corresponding sides, corresponding distances and corresponding angles to tell whether one gure is a scaled copy of another.Lesson 5Describe how scale factors of 1, less than 1, and greater than 1 aect the size of a scaled copy, and explain how scaling can be reversed using reciprocal scale factors.Lesson 6Describe how the area of a scaled copy is related to the area of the original gure and the scale factor that was used.Topic B Scale DrawingsLesson 7 Use a scale drawing and its scale to calculate actual distances.Lesson 8 Use scale drawings to estimate distance traveled, speed, and elapsed time.Lesson 9Determine the scale and the dimensions of a scale drawing when given the actual dimensions of an object.Lesson 10Reproduce a scale drawing at a dierent scale and determine how much actual area is represented by one square unit in a scale drawing.Lesson 11 Explain (orally and in writing) how to use scales without units to determine scaled or actual distances.Lesson 12 Use dierent scales, with or without units, to describe the same drawings.vi

ZEARN MATH MISSION OVERVIEW G7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.ObjectiveTopic C Let’s Put It to WorkLesson 13 Create scale drawings using an appropriate scale.End-of-Mission Assessment: Topics A-CNote on Pacing for DierentiationIf you are using the Zearn Math recommended weekly schedule that consists of four “Core Days” when students learn grade-level content and one “Flex Day” that can be tailored to meet students’ needs, we recommend omitting the optional lessons in this mission during the Core Days. Students who demonstrate a need for further support can explore these concepts with you and peers as part of a ex day as needed. This schedule ensures students have suicient time each week to work through grade-level content and includes built-in weekly time you can use to dierentiate instruction to meet student needs.Optional lessons for G7M1:Lesson 6, Lessons 8, and Lesson 13.vii

ZEARN MATH MISSION OVERVIEWG7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.Mission OverviewWork with scale drawings in grade 7 draws on earlier work with geometry and geometric measurement. Students began to learn about two- and three-dimensional shapes in kindergarten, and continued this work in grades 1 and 2, composing, decomposing, and identifying shapes. Students’ work with geometric measurement began with length and continued with area. Students learned to “structure two-dimensional space,” that is, to see a rectangle with whole-number side lengths as an array of unit squares, or rows or columns of unit squares. In grade 3, students distinguished between perimeter and area. They connected rectangle area with multiplication, understanding why (for whole-number side lengths) multiplying the side lengths of a rectangle yields the number of unit squares that tile the rectangle. They used area diagrams to represent instances of the distributive property. In grade 4, students applied area and perimeter formulas for rectangles to solve real-world and mathematical problems, and learned to use protractors. In grade 5, students extended the formula for the area of a rectangle to include rectangles with fractional side lengths. In grade 6, students built on their knowledge of geometry and geometric measurement to produce formulas for the areas of parallelograms and triangles, using these formulas to nd surface areas of polyhedra.In this mission, students study scaled copies of pictures and plane gures, then apply what they have learned to scale drawings, e.g., maps and oor plans. This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity.Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what dierentiates scaled and non-scaled copies of a picture. As the mission progresses, students learn that all lengths in a scaled copy are multiplied by a scale factor and all angles stay the same. They draw scaled copies of gures. They learn that if the scale factor is greater than 1, the copy will be larger, and if the scale factor is less than 1, the copy will be smaller. They study how area changes in scaled copies of an image.Next, students study scale drawings. They see that the principles and strategies that they used to reason about scaled copies of gures can be used with scale drawings. They interpret and draw maps and oor plans. They work with scales that involve units (e.g., “1 cm represents 10 km”), and scales that do not include units (e.g., “the scale is 1 to 100”). They learn to express scales with units as scales without units, and vice versa. They understand that actual lengths are products of a scale factor and corresponding lengths in the scale drawing, thus lengths in the drawing are the product of the actual lengths and the reciprocal of that scale factor. They study the relationship between regions and lengths in scale drawings. Throughout the mission, they discuss their mathematical ideas and respond to the ideas of others. In the culminating lesson of this mission, students make a oor plan of their classroom or some other room or space at their school. This is an opportunity for them to apply what they have learned in the mission to everyday life.In the mission, several lesson plans suggest that each student have access to a geometry toolkit. Each toolkit contains tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor (clear protractors with no holes that show radial lines are recommended), and an index card to use as a straightedge or to mark right angles. Providing students with these toolkits gives opportunities for students to develop abilities to select appropriate tools and use them strategically to solve problems. Note that even students in a digitally enhanced classroom should have access to such tools; apps and simulations should be considered additions to their toolkits, not replacements for physical tools.Note that the study of scaled copies is limited to pairs of gures that have the same rotation and mirror orientation (i.e. that are not rotations or reections of each other), because the mission focuses on scaling, scale factors, and scale drawings. In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reections, and dilations.Progression of Disciplinary LanguageIn this mission, teachers can anticipate students using language for mathematical purposes such as representing, generalizing, and explaining. Throughout the mission, students will benet from routines designed to grow robust disciplinary language, both for their own sense-making and for building shared understanding with peers. Teachers can formatively assess how students are using language in these ways, particularly when students are using language to:viii

ZEARN MATH MISSION OVERVIEW G7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.Represent• a scaled copy for a given scale factor (Lessons 3 and 5)• distances using dierent scales (Lesson 11)• relevant features of a classroom with a scale drawing (Lesson 13)Generalize• about corresponding distances and angles in scaled copies (Lesson 4)• about scale factors greater than, less than, and equal to 1 (Lesson 5)• about scale factors and area (Lessons 6 and 10)• about scale factors with and without units (Lesson 12)Explain• how to use scale drawings to nd actual distances (Lessons 7 and 11)• how to use scale drawings to nd actual distances, speed, and elapsed time (Lesson 8)• how to use scale drawings to nd actual areas (Lesson 12)In addition, students are expected to describe features of scaled copies, justify and critique reasoning about scaled copies, and compare how dierent scales aect drawings. Over the course of the mission, teachers can support students’ mathematical understandings by amplifying (not simplifying) language used for all of these purposes as students demonstrate and develop ideas.The table shows lessons where new terminology is rst introduced, including when students are expected to understand the word or phrase receptively and when students are expected to produce the word or phrase in their own speaking or writing. Terms from the glossary appear bolded. Teachers should continue to support students’ use of a new term in the lessons that follow where it was rst introduced.New TerminologyLesson Receptive Productive1 scaled copyoriginalpolygon2 correspondingscale factorguresegmentix

ZEARN MATH MISSION OVERVIEWG7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.New TerminologyLesson Receptive Productive4 quadrilateralmeasurementldistancecorrespondingscale factororiginal5 reciprocal6 areaone-dimensionaltwo-dimensionalsquared7 scale drawingscalerepresentactualthree-dimensionalscaled copy8 estimatetravelconstant speedscale9 oorplan10 appropriatedimensionactual represent11 scale without units to scale drawing12 equivalent scales to Digital LessonsStudents also learn the concepts from this mission in their Independent Digital Lessons. There are 9 Digital Lessons for Mission 1. It’s important to connect teacher instruction and digital instruction at the mission level. So when you start teaching Mission 1, set students to the rst digital lesson of Mission 1. The intentional balance of learning with teachers and peers and learning independently in digital lessons ensures every student has multiple opportunities to represent, engage with, and express their math reasoning. In the digital lessons, students explore the concepts through interactive problem solving with embedded support that launches at the moment of misconception. As students complete digital lessons, they will automatically progress to the next lesson. Go online to Zearn.org to explore more of the digital lessons for this mission.x

ZEARN MATH MISSION OVERVIEW G7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.TerminologyCorrespondingWhen part of an original gure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.For example, point B in the rst triangle corresponds to point E in the second triangle.Segment AC corresponds to segment DF.ScaleA scale tells how the measurements in a scale drawing represent the actual measurements of the object.For example, the scale on this oor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and 12 inch would represent 4 feet.Scale drawingA scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.For example, this map is a scale drawing. The scale shows that 1 cm on the map represents 30 miles on land.Scale factorTo create a scaled copy, we multiply all the lengths in the original gure by the same number. This number is called the scale factor.In this example, the scale factor is 1.5, because 4 ∙ 1.5 = 6, 5 ∙ 1.5 = 7.5, and 6 ∙ 1.5 = 9.Scaled copyA scaled copy is a copy of an gure where every length in the original gure is multiplied by the same number.For example, triangle DEF is a scaled copy of triangle ABC. Each side length on triangle ABC was multiplied by 1.5 to get the corresponding side length on triangle DEF.A C DEFB1 inch8 feetA4 56 7.56C D9EFBA4 56 7.56C D9EFB“Map of Texas and Oklahoma” by United States Census Bureau via American Fact Finder. Public Domain.xi

ZEARN MATH MISSION OVERVIEWG7M1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.Required MaterialsBlank paperGeometry toolkitsTracing paper, graph paper, colored pencils, scissors, and an index card to use as a straightedge or to mark right angles.Graph paperMeasuring toolsMetric and customary unit conversion chartsPattern blocksRulersTemplateCopies of templatePre-printed slips, cut from copies of the templatexii

PAGE 1Name: Date: GRADE 7 / MISSION 1End-of-Mission Assessment1. Polygon WXYZ is a scaled copy of polygon ABCD.a. Record which angles in the scaled copy correspond to angles in the original polygon.AB CDWX YZAngles in Original PolygonCorresponding Angles in Scaled CopyAngle ABCAngle BADAngle DCBAngle CDAb. Record which segments in the scaled copy correspond to segments in the original polygon.Segments in Original PolygonCorresponding Segments in Scaled CopySegment ABSegment ADSegment CBSegment DC© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.

© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.G7M1 End-of-Mission Assessment2. Polygon B is a scaled copy of Polygon A.Complete the table to identify the scale factor.AB54312159PAGE 2Side Length in Original PolygonCorresponding Length in Scaled CopyScale Factor5 5 ∙ = 3 3 ∙ = 4 4 ∙ = The scale factor is .3. Create a scaled copy of the given rectangle using a scale factor of 4 and identify the dimensions of your scaled copy.The scaled rectangle is units wide and units tall.

G7M1 End-of-Mission AssessmentA scale drawing of a football field has a scale of 1 inch to 40 feet.4. reasoning.5 05 09 in4 in5. PAGE 3© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.

© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.G7M1 End-of-Mission Assessment a. Label the dimensions of the given scale drawing b. Make a scale drawing of the pool where each unit on the grid represents 5 meters and label all dimensions.PAGE 4

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 1What Are Scaled Copies?LEARNING GOALSDescribe (orally) characteristics of scaled and non-scaled copies.Identify scaled copies of a figure and justify (orally and in writing) that the copy is a scaled copy.STUDENT LEARNING GOALS Let’s explore scaled copies.LEARNING TARGETS(STUDENT FACING)I can describe some characteristics of a scaled copy.I can tell whether or not a figure is a scaled copy of another figure.REQUIRED MATERIALSTemplate for Concept Exploration: Activity 2pre-printed slips, cut from copies of the templateREQUIRED PREPARATIONYou will need the Pairs of Scaled Polygons template for this lesson. Print and cut slips A–J for the Pairs of Scaled Polygons activity. Prepare 1 copy for every 2 students. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 1

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:This lesson introduces students to the idea of a scaled copy of a picture or a gure. Students learn to distinguish scaled copies from those that are not—rst informally, and later, with increasing precision. They may start by saying that scaled copies have the same shape as the original gure, or that they do not appear to be distorted in any way, though they may have a dierent size. Next, they notice that the lengths of segments in a scaled copy vary from the lengths in the original gure in a uniform way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. Students work toward articulating the characteristics of scaled copies quantitatively (e.g., “all the segments are twice as long,” “all the lengths have shrunk by one third,” or “all the segments are one-fourth the size of the segments in the original”), articulating the relationships carefully along the way.The lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them from the very beginning of the course.Warm-UpPRINTING PORTRAITSInstructional Routines: Think Pair Share, MLR2: Collect and DisplayThis opening task introduces the term scaled copy. It prompts students to observe several copies of a picture, visually distinguish scaled and unscaled copies, and articulate the dierences in their own words. Besides allowing students to have a mathematical conversation about properties of gures, it provides an accessible entry into the concept and gives an opportunity to hear the language and ideas students associate with scaled gures.Students are likely to have some intuition about the term “to scale,” either from previous work in grade 6 (e.g., scaling a recipe, or scaling a quantity up or down on a double number line) or from outside the classroom. This intuition can help them identify scaled copies.Expect them to use adjectives such as “stretched,” “squished,” “skewed,” “reduced,” etc., in imprecise ways. This is ne, as students’ intuitive denition of scaled copies will be rened over the course of the lesson. As students discuss, note the range of descriptions used. Monitor for students whose descriptions are particularly supportive of the idea that lengths in a scaled copy are found by multiplying the original lengths by the same value. Invite them to share their responses later.LAUNCHArrange students in groups of 2. Give students quiet think time and time to share their response with their partner.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.2

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASKHere is a picture of a bird. 1. Look at pictures A-E. How is each one the same as or dierent from the original picture of the bird?2. Some of the pictures A-E are scaled copies of the original picture. Which ones do you think are scaled copies? Explain your reasoning.3. What do you think “scaled copy” means?STUDENT RESPONSE1. Answers vary. Sample response:• Similarities: Pictures A-E are all based on the same original picture. They all show the same bird. They all have the same white background.• Dierences: They all have dierent sizes; some have dierent shapes. Pictures A, B, and E have been stretched or somehow distorted. C and D are not stretched or distorted but are each of a dierent size than the original.2. C and D are scaled copies. Sample explanation:• A, B, and E are not scaled copies because they have changed in shape compared to the original picture. Picture A is stretched vertically, so the vertical side is now 1A B C D E© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 3

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:much longer than the horizontal side. B is stretched out sideways, so the horizontal sides are now longer than the vertical. E seems to have its upper le and lower right corners stretched out in opposite directions.• C and D are smaller copies of the original, but their shapes remain the same.3. Answers vary. Sample denitions:• A scaled copy is a copy of a picture that changes in size but does not change in shape.• A scaled copy is a duplicate of a picture with no parts of it distorted, though it could be larger, smaller, or the same size.• A scaled copy is a copy of a picture that has been enlarged or reduced in size but nothing else changes.DISCUSSION GUIDANCESelect a few students to share their observations. Record and display students’ explanations for the second question. Consider organizing the observations in terms of how certain pictures are or are not distorted. For example, students may say that C and D are scaled copies because each is a smaller version of the picture, but the head (or the feet, or the body of the bird) has not changed in shape. They may say that A, B, and E are not scaled copies because something other than size has changed. If not already mentioned in the discussion, guide students in seeing features of C and D that distinguish them from A, B, and E.Invite a couple of students to share their working denition of scaled copies. Some of students’ descriptions may not be completely accurate. That is appropriate for this lesson, as the goal is to build on and rene this language over the course of the next few lessons until students have a more precise notion of what it means for a picture or gure to be a scaled copy.Concept Exploration: Activity 1SCALING FInstructional Routines: MLR1: Stronger and Clearer Each Time, Think Pair ShareThis task enables students to describe more precisely the characteristics of scaled copies and to rene the meaning of the term. Students observe copies of a line drawing on a grid and notice how the lengths of line segments and the angles formed by them compare to those in the original drawing.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.4

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Students identify distinguishing features of the scaled copies, which means nding similarities and dierences in the shapes. In addition, the fact that corresponding parts increase by the same scale factor is a vital structural property of scaled copies.For the rst question, expect students to explain their choices of scaled copies in intuitive, qualitative terms. For the second question, students should begin to distinguish scaled and unscaled copies in more specic and quantiable ways. If it does not occur to students to look at lengths of segments, suggest they do so.As students work, monitor for students who notice the following aspects of the gures. Students are not expected to use these mathematical terms at this point, however.• The original drawing of the letter F and its scaled copies have equivalent width-to-height ratios.• We can use a scale factor (or a multiplier) to compare the lengths of dierent gures and see if they are scaled copies of the original.• The original gure and scaled copies have corresponding angles that have the same measure.LAUNCHKeep students in the same groups. Give them quiet work time, and time to share their responses with their partner. Tell students that how they decide whether each of the seven drawings is a scaled copy may be very dierent than how their partner decides. Encourage students to listen carefully to each other’s approach and to be prepared to share their strategies. Use gestures to elicit from students the words “horizontal” and “vertical” and ask groups to agree internally on common terms to refer to the parts of the F (e.g., “horizontal stems”).ACTIVITY 1 TASK 1On the top le is the original drawing of the letter F. There are also several other drawings.2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 5

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:1. Original Drawing 1 Drawing 2 Drawing 3Drawing 4Drawing 5 Drawing 6Drawing 7Identify all the drawings that are scaled copies of the original letter F drawing. Explain how you know.2. Examine all the scaled copies more closely, specically the lengths of each part of the letter F. How do they compare to the original? What do you notice?STUDENT RESPONSE1. Drawings 1, 2, and 7 are scaled copies of the original drawing. Explanations vary. Sample explanation: I know because they are not stretched dierently in one direction. They are enlarged evenly in both vertical and horizontal directions.2. Answers vary. Sample responses:• In the scaled copies, every segment is the same number of times as long as the matching segment in the original drawing.• In the scaled copies, all segments keep the same relationships as in the original. The original drawing of F is 4 units tall. Its top horizontal segment is 2 units wide and the shorter horizontal segment is 1 unit. In Drawing 1, the F is 6 units tall and 3 units wide; in Drawing 2, it is 8 units tall and 4 units wide, and in Drawing 7, it is 8 units tall and 4 units wide. In each scaled copy, the width is half of the height, just as in the original drawing of F, and the shorter horizontal segment is half of the longer one.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.6

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 2On the grid, draw a dierent scaled copy of the original letter F. STUDENT RESPONSEDrawings vary. Sample response:DISCUSSION GUIDANCEDisplay the seven copies of the letter F for all to see. For each copy, ask students to indicate whether they think each one is a scaled copy of the original F. Record and display the results for all to see. For contested drawings, ask 1–2 students to briey say why they ruled these out.Discuss the identied scaled and unscaled copies.• What features do the scaled copies have in common? (Be sure to invite students who were thinking along the lines of scale factors and angle measures to share.)33© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 7

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• How do the other copies fail to show these features? (Sometimes lengths of sides in the copy use dierent multipliers for dierent sides. Sometimes the angles in the copy do not match the angles in the original.)If there is a misconception that scaled copies must have vertices on intersections of grid lines, use Drawing 1 (or a relevant drawing by a student) to discuss how that is not the case.Some students may not be familiar with words such as “twice,” “double,” or “triple.” Clarify the meanings by saying “two times as long” or “three times as long.”ANTICIPATED MISCONCEPTIONSStudents may make decisions by “eyeballing” rather than observing side lengths and angles. Encourage them to look for quantiable evidence and notice lengths and angles.Some may think vertices must land at intersections of grid lines (e.g., they may say Drawing 4 is not a scaled copy because the endpoints of the shorter horizontal segment are not on grid crossings). Address this during the discussion, aer students have a chance to share their observations about segment lengths.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: Math Language Routine 1 Stronger and Clearer Each Time.This is the rst time Math Language Routine 1 is suggested as a support in this course. In this routine, students are given a thought-provoking question or prompt and asked to create a rst dra response in writing. Students meet with 2–3 partners to share and rene their response through conversation. While meeting, listeners ask questions such as, “What did you mean by . . .?” and “Can you say that another way?” Finally, students write a second dra of their response reecting ideas from partners, and improvements on their initial ideas. The purpose of this routine is to provide a structured and interactive opportunity for students to revise and rene their ideas through verbal and written means.Design Principle(s): Optimize output (for explanation)How It Happens1. Use this routine to provide students a structured opportunity to rene their explanations for the rst question: “Identify all the drawings that are scaled copies of the original letter F drawing. Explain how you know.” Allow students time to individually create rst dra responses in writing.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.8

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. Invite students to meet with 2–3 other partners for feedback. Instruct the speaker to begin by sharing their ideas without looking at their written dra, if possible. Provide the listener with these prompts for feedback that will help their partner strengthen their ideas and clarify their language: “What do you mean when you say….?”, “Can you describe that another way?”, “How do you know that is a scaled copy?”, “Could you justify that dierently?” Be sure to have the partners switch roles. Allow time to discuss3. Signal for students to move on to their next partner and repeat this structured meeting. Close the partner conversations and invite students to revise and rene their writing in a second dra. Provide these sentence frames to help students organize their thoughts in a clear, precise way: “Drawing is a scaled copy of the original, and I know this because.…”, “When I look at the lengths, I notice that.…”, and “When I look at the angles, I notice that.…” Here is an example of a second dra: “Drawing 7 is a scaled copy of the original, and I know this because it is enlarged evenly in both the horizontal and vertical directions. It does not seem lopsided or stretched dierently in one direction. When I look at the length of the top segment, it is 3 times as large as the original one, and the other segments do the same thing. Also, when I look at the angles, I notice that they are all right angles in both the original and scaled copy.”4. If time allows, have students compare their rst and second dras. If not, have the students move on by working on the following problems.SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills:Peer Tutors. Pair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate drawing scaled copies as needed.Concept Exploration: Activity 2PAIRS OF SCALED POLYGONSMATERIALS: TEMPLATE FOR CONCEPT EXPLORATION: ACTIVITY 2Instructional Routines: Take Turns, MLR8: Discussion SupportsIn this activity, students hone their understanding of scaled copies by working with more complex gures. Students work with a partner to match pairs of polygons that are scaled copies. The polygons appear comparable to one another, so students need to look very closely at all side lengths of the polygons to tell if they are scaled copies.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 9

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:As students confer with one another, notice how they go about looking for a match. Monitor for students who use precise language to articulate their reasoning (e.g., “The top side of A is half the length of the top side of G, but the vertical sides of A are a third of the lengths of those in G.”).You will need the Pairs of Scaled Polygons template for this activity.LAUNCHIn this activity, students hone their understanding of scaled copies by working with more complex gures. Students work with a partner to match pairs of polygons that are scaled copies. The polygons appear comparable to one another, so students need to look very closely at all side lengths of the polygons to tell if they are scaled copies.As students confer with one another, notice how they go about looking for a match. Monitor for students who use precise language to articulate their reasoning (e.g., “The top side of A is half the length of the top side of G, but the vertical sides of A are a third of the lengths of those in G.”).You will need the Pairs of Scaled Polygons template for this activity.ACTIVITY 2 TASK 1Your teacher will give you a set of cards that have polygons drawn on a grid. Mix up the cards and place them all face up.1. Take turns with your partner to match a pair of polygons that are scaled copies of one another.a) For each match you nd, explain to your partner how you know it’s a match.AEI JF G HB CD34© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.10

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:b) For each match your partner nds, listen carefully to their explanation, and if you disagree, explain your thinking.2. When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.3. Select one pair of polygons to examine further. Draw both polygons on the grid. Explain how you know that one polygon is a scaled copy of the other.STUDENT RESPONSE1. The following polygons are scaled versions of one another:• A and C• B and D• E and I• F and G• H and J2. No answer needed.3. Answers vary. Sample explanation for A and C: All the side lengths in C are twice as long as the lengths of the matching sides in A.ACTIVITY 2 RECAPThe purpose of this discussion is to draw out concrete methods for deciding whether or not two polygons are scaled copies of one another, and in particular, to understand that just eyeballing © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 11

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:to see whether they look roughly the same is not enough to determine that they are scaled copies.Display the image of all the polygons. Ask students to share their pairings and guide a discussion about how students went about nding the scaled copies. Ask questions such as:• When you look at another polygon, what exactly did you check or look for? (General shape, side lengths)• How many sides did you compare before you decided that the polygon was or was not a scaled copy? (Two sides can be enough to tell that polygons are not scaled copies; all sides are needed to make sure a polygon is a scaled copy.)• Did anyone check the angles of the polygons? Why or why not? (No; the sides of the polygons all follow grid lines.)If students do not agree about some pairings aer the discussion, ask the groups to explain their case and discuss which of the pairings is correct. Highlight the use of quantitative descriptors such as “half as long” or “three times as long” in the discussion. Ensure that students see that when a gure is a scaled copy of another, all of its segments are the same number of times as long as the corresponding segments in the other.ANTICIPATED MISCONCEPTIONSSome students may think a gure has more than one match. Remind them that there is only one scaled copy for each polygon and ask them to recheck all the side lengths.Some students may think that vertices must land at intersections of grid lines and conclude that, e.g., G cannot be a copy of F because not all vertices on F are on such intersections. Ask them to consider how a 1-unit-long segment would change if scaled to be half its original size. Where must one or both of its vertices land?SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion Supports.Use this routine to support conversation when students match pairs of polygons that are scaled copies of one another. Display the following sentence frames: “ matches because .” and “I agree/disagree because .”Design Principle(s): Support sense-making; Optimize output (for explanation)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.12

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing Time.Begin with a demonstration of one match, which will provide access for students who benet from clear and explicit instructions.Fine Motor Skills:Peer Tutors. Pair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate drawing scaled copies as needed.Digital LessonWhich is a scaled copy? Explain how you know.The scaled copy is .I know this becauseSTUDENT RESPONSE1. The scaled copy is Figure A.ABoriginal© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 13

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. I know this because in gure A, the length of each segment is twice the length of the matching segment in the original copy. Also, there is no consistent relationship between the length of the segments in the original gure and the length of the segments in gure B.Wrap-UpLESSON SYNTHESISIn this lesson, we encountered copies of a gure that are both scaled and not scaled. We saw dierent versions of a picture of a bird and of a letter F, as well as a variety of polygons that had some things in common.In each case, we decided that some were scaled copies of one another and some were not. Consider asking students:• What is a scaled copy?• What are some characteristics of scaled copies? How are they dierent from gures that are not scaled copies?• What specic information did you look for when determining if something was a scaled copy of an original?While initial answers need not be particularly precise at this stage of the mission (for example, “scaled copies look the same but are a dierent size”), guide the discussion toward making careful statements that one could test. The lengths of segments in a scaled copy are related to the lengths in the original gure in a consistent way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. We might say, “All the segments are twice as long,” or “All the segments are one-third the size of the segments in the original.”TERMINOLOGYscaled copy A scaled copy is a copy of an gure where every length in the original gure is multiplied by the same number.ABC D FE56 97.564© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.14

G7M1 | LESSON 1ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:For example, triangle DEF is a scaled copy of triangle ABC. Each side length on triangle ABC was multiplied by 1.5 to get the corresponding side length on triangle DEF.EXIT TICKETAre any of the gures B, C, or D scaled copies of gure A? Explain how you know.STUDENT RESPONSEOnly gure C is a scaled copy of gure A. Sample explanation: In gure C, the length of each segment of the letter L is twice the length of the matching segment in A. In B, none of the segments are double the length. In gure D, some segments are double in length and some are not. So the block letters in B and D are not enlarged evenly.AC DBOriginal© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 15

TEMPLATE FOR LESSON 1 CONCEPT EXPLORATION: ACTIVITY 2 (PAGE 1 OF 2)PairsofScaledPolygons PairsofScaledPolygonsPairsofScaledPolygons PairsofScaledPolygons© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.16

TEMPLATE FOR LESSON 1 CONCEPT EXPLORATION: ACTIVITY 2 (PAGE 2 OF 2)PairsofScaledPolygons PairsofScaledPolygonsPairsofScaledPolygons PairsofScaledPolygonsPairsofScaledPolygons PairsofScaledPolygons© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 17

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 2Corresponding Parts and Scale FactorsLEARNING GOALSComprehend the phrase “scale factor” and explain (orally) how it relates corresponding lengths of a figure and its scaled copy.Explain (orally) what it means to say one part in a figure “corresponds” to a part in another figure.Identify and describe (orally and in writing) corresponding points, corresponding segments, or corresponding angles in a pair of figures.LEARNING GOALS(STUDENT FACING)Let’s describe features of scaled copies.LEARNING TARGETS(STUDENT FACING)I can describe what the scale factor has to do with a figure and its scaled copy.In a pair of figures, I can identify corresponding points, corresponding segments, and corresponding angles.REQUIRED MATERIALSGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATIONPrepare to display the images of the railroad crossing sign for the Corresponding Parts activity. Make sure students have access to their geometry toolkits, especially tracing paper and graph paper.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.18

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:This lesson develops the vocabulary for talking about scaling and scaled copies more precisely, and identifying the structures in common between two gures.Specically, students learn to use the term corresponding to refer to a pair of points, segments, or angles in two gures that are scaled copies. Students also begin to describe the numerical relationship between the corresponding lengths in two gures using a scale factor. They see that when two gures are scaled copies of one another, the same scale factor relates their corresponding lengths. They practice identifying scale factors.A look at the angles of scaled copies also begins here. Students use tracing paper to trace and compare angles in an original gure and its copies. They observe that in scaled copies the measures of corresponding angles are equal.Warm-UpNUMBER TALK: MULTIPLYING BY A UNIT FRACTIONInstructional Routines: MLR8: Discussion Supports, Number TalkThis number talk allows students to review multiplication strategies, refreshing the idea that multiplying by a unit fraction is the same as dividing by its whole number reciprocal. It encourages students to use the structure of base ten numbers and the properties of operations to nd the product of two whole numbers. For example, a student might nd 72 ∙ 19 (or 72 ÷ 9) and then shi the decimal one place to the right in order to evaluate (7.2) ∙ 19. Each problem was chosen to elicit dierent approaches, so as students share theirs, ask how the factors in each problem impacted their strategies.Before students begin, consider establishing a small, discreet hand signal (such as a thumbs-up) students can display to indicate they have an answer that they can support by reasoning. Discreet signaling is a quick way for teachers to gather feedback about timing. It also keeps students from being distracted or rushed by raised hands around the class.LAUNCHDisplay one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Follow with a brief whole-class discussion.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 19

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASKFind each product mentally. 1. 14 ∙ 322. (7.2) ∙ 193. 14 ∙ (5.6)STUDENT RESPONSE1. 14 ∙ 32 = 8. Possible strategy: 32 ÷ 4 = 82. (7.2) ∙ 19 = 0.8. Possible strategy: 72 ÷ 9 = 8 so (7.2) ÷ 9 = 0.83. 14 ∙ (5.6) = 1.4. Possible strategy: (5.6) ÷ 4 = 1.4DISCUSSION GUIDANCEAsk students to share their strategies for each problem. Record and display their explanations for all to see. If students express strategies in terms of division, ask if that strategy would work for any multiplication problem involving fractions. Highlight that these problems only involve unit fractions and division by the denominator is a strategy that works when multiplying by a unit fraction.To involve more students in the conversation, consider asking:• Who can restate ’s reasoning in a dierent way?• Did anyone solve the problem the same way but would explain it dierently?• Did anyone solve the problem in a dierent way?• Does anyone want to add on to ’s strategy?• Do you agree or disagree? Why?1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.20

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR STUDENTS WITH DISABILITIESMemory: Processing TimeProvide sticky notes or mini whiteboards to aid students with working memory challenges.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsProvide sentence frames to support students with explaining their strategies. For example, “I noticed that , so I .” or “First, I because .” When students share their answers with a partner, prompt them to rehearse what they will say when they share with the full group. Rehearsing provides opportunities to clarify their thinking.Design Principle(s): Optimize output (for explanation)Concept Exploration: Activity 1CORRESPONDING PARTSInstructional Routines: Notice and Wonder, MLR8: Discussion SupportsThis activity introduces important language students will apply to describe scaled copies. In particular, it introduces the important idea of corresponding parts. Students have previously analyzed corresponding sides in gures. Here they will begin to examine angles explicitly as well, understanding that corresponding angles in a gure and its scaled copy have the same measure.LAUNCHTell students that in this lesson, they will look more closely at copies of gures and describe specic parts in them.Display the designs (the three images in the activity statement) and the following descriptions for all to see. Ask students what they notice and what they wonder. Aer discussion, explain that the original design and its two copies have parts that correspond to one another. Point out some of their corresponding parts:• The X-pattern going across each gure• The curved outline of each gure© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 21

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• The points K in the original sign, A in Copy 1, and U in Copy 2Arrange students in groups of 2 and provide access to their geometry toolkits (especially tracing paper). Give students time to complete the rst two questions and time to discuss their responses with their partner. Ask students to pause their work for a quick group discussion aerwards.Have a few students name a set of corresponding points, segments, and angles. Then, ask students to indicate whether they think either copy is a scaled copy. Invite a couple of students to share their reasoning. When the group reaches an agreement that Copy 1 is a scaled copy and Copy 2 is not, ask students to complete the remaining questions individually and to use tracing paper as a tool.Consider demonstrating to the group how to use tracing paper to compare angles. Tell or show students that the line segments forming an angle could be extended for easier tracing and comparison.ACTIVITY 1 TASK 1Here is a gure and two copies, each with some points labeled. 1. Complete this table to show corresponding parts in the three gures.Original Copy 1 Copy 2Point PSegment LMSegment EFPoint WAngle KLMAngle XYZ2OriginalOPNMKLCopy 1 Copy 2YZVXWUEFDCAB© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.22

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. Is either copy a scaled copy of the original gure? Explain your reasoning.3. Use tracing paper to compare angle KLM with its corresponding angles in Copy 1 and Copy 2. What do you notice?4. Use tracing paper to compare angle NOP with its corresponding angles in Copy 1 and Copy 2. What do you notice?STUDENT RESPONSE1. Original Copy 1 Copy 2Point P Point F Point ZSegment LM Segment BC Segment VWSegment OP Segment EF Segment YZPoint M Point C Point WAngle KLM Angle ABC Angle UVWAngle NOP Angle DEF Angle XYZ2. Copy 1 is a scaled copy, but Copy 2 is not. Sample explanation: The original sign is a circle. Copy 1 is also a circle, only smaller. Copy 2 has been stretched sideways and shrunken vertically; its shape has changed into an oval, so it is not a scaled copy.3. Angle ABC in Copy 1 corresponds to and has the same size as angle KLM. Angle UVW in Copy 2 also corresponds to angle KLM but is smaller in size than the original angle.4. Angle DEF in Copy 1 corresponds to and has the same size as angle NOP. Angle XYZ in Copy 2 also corresponds to angle NOP but is larger in size than the original angle.DISCUSSION GUIDANCESelect a few students to share their observations about angles. Discuss the size of corresponding angles in gures that are scaled copies and those that are not. Ask questions such as:• In the scaled copy, Copy 1, did the size of any angle change compared to its corresponding angle in the original sign? (No)• In Copy 2, did the size of any angle change relative to its corresponding angle in the original sign? (Yes) Which ones? (Angle UVW has a dierent measure than angle KLM, for example.)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 23

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• What can you say about corresponding angles in two gures that are scaled copies of one another? (They have the same measure.)• What can you say about corresponding angles in two gures that are not scaled copies? (They might not have the same measure.)SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsUse this routine to amplify mathematical uses of language to communicate about corresponding points, segments, and angles. As students share what they noticed between the three images, revoice their statements using the term “corresponding.” Then, invite students to use the term “corresponding” when describing what they noticed. Some students may benet from chorally repeating the phrases that include the word “corresponding” in context.Design Principle(s): Optimize output (for explanation)SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Executive Functioning: Visual AidsCreate an anchor chart (i.e., examples of corresponding points, line segments, and angles) publicly displaying important denitions, rules, formulas, or concepts for future reference.Concept Exploration: Activity 2SCALED TRIANGLESInstructional Routines: Think Pair Share, MLR3: Clarify, Critique, CorrectIn this activity, students continue to practice identifying corresponding parts of scaled copies. By organizing corresponding lengths in a table, students see that there is a single factor that relates each length in the original triangle to its corresponding length in a copy. They learn that this number is called a scale factor.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.24

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:As students work on the rst question, listen to how they reason about which triangles are scaled copies. Identify groups who use side lengths and angles as the basis for deciding. (Students are not expected to reason formally yet, but should begin to look to lengths and angles for clues.)As students identify corresponding sides and their measures in the second and third questions, look out for confusion about corresponding parts. Notice how students decide which sides of the right triangles correspond.If students still have access to tracing paper, monitor for students who use this tool strategically.LAUNCHArrange students into groups of 4. Assign each student one of the following pairs of triangles in the rst question.• A and E• B and F• C and G• D and HGive students quiet think time to determine if their assigned triangles are scaled copies of the original triangle. Give some time to discuss their responses and complete the rst question in groups.Discuss briey as a group which triangles are scaled copies and select a couple of groups who reasoned in terms of lengths and angles to explain their reasoning. Some guiding questions:• What information did you use to tell scaled copies from those that are not?• How were you able to tell right away that some gures are not scaled copies?Give students quiet work time to complete the rest of the task aer the group recognizes that A, C, F, and H are not scaled copies.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 25

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1Here is Triangle O, followed by a number of other triangles. Your teacher will assign you two of the triangles to look at.1. For each of your assigned triangles, is it a scaled copy of Triangle O? Be prepared to explain your reasoning.2. As a group, identify all the scaled copies of Triangle O in the collection. Discuss your thinking. If you disagree, work to reach an agreement.3. List all the triangles that are scaled copies in the table. Record the side lengths that correspond to the side lengths of Triangle O listed in each column.Triangle O 3 4 54. Explain or show how each copy has been scaled from the original (Triangle O).33O A42528827106622.83245555.3933326.08 6.32B CDHE F G8310332© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.26

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. Answers vary depending on the pair of triangles students have. Triangles B, D, E, and G are scaled copies.2. Triangles B, D, E, and G are scaled copies. Sample reasoning: B, D, E, and G have not changed in shape (they are still right triangles). Each of their sides are the same number of times as long as the corresponding sides in the original triangle. Triangles A and F do not have the same shape as Triangle O (their angles are all dierent), so they are not scaled copies. Triangles C, G, and H are right triangles but their sides are not the same number of times as long as the corresponding sides in the original triangle.3. Triangle O 3 4 5Triangle B 3 4 5Triangle D32252Triangle E 6 8 10Triangle G 2831034. Explanations vary. Sample explanations:• Triangle B is a same-size copy of the original. All the lengths stay the same.• In Triangle D, all the lengths are half of the original ones.• In Triangle E, all sides double in length.• In Triangle G, the lengths are 23 times the corresponding lengths in the original triangle.ACTIVITY 2 RECAPDisplay the image of all triangles and invite a couple of students to share how they knew which sides of the triangles correspond. Then, display a completed table in the third question for all to see. Ask each group to present its observations about one triangle and how the triangle has been scaled from the original. Encourage the use of “corresponding” in their explanations. As students present, record or illustrate their reasoning on the table, e.g., by drawing arrows between rows and annotating with the operation students are describing, as shown here.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 27

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Triangle O 3 4 5Triangle B ∙ 1 3 4 5Triangle D ∙ 1232252Triangle E ∙ 2 6 8 10Triangle G ∙ 23283103Use the language that students use to describe the side lengths and the numerical relationships in the table to guide students toward scale factor. For example: “You explained that the lengths in Triangle F are all twice those in the original triangle, so we can write those as “2 times” the original numbers. Lengths in Triangle A are half of those in the original; we can write “12 times” the original numbers. We call those multipliers—the 2 and the 12-scale factors. We say that scaling Triangle O by a scale factor of 2 produces Triangle F, and that scaling Triangle O by 12 produces Triangle A.”ANTICIPATED MISCONCEPTIONSStudents may think that Triangle F is a scaled copy because just like the 3-4-5 triangle, the sides are also three consecutive whole numbers. Point out that corresponding angles are not equal.SUPPORT FOR ENGLISH LANGUAGE LEARNERSWriting: MLR 3 Clarify, Critique, CorrectCirculate and listen as students discuss their assigned triangles, then present an incorrect explanation that reects a common misconception. For example, “Triangle B cannot be a scaled copy of Triangle O, because the side lengths are the same as the original.” or “Triangle F is a scaled copy of Triangle O, because each side length is increased by 3.” Prompt students to identify the error (e.g., ask students, “Do you agree with the statement? Why or why not?”), and then write a correct version of the statement. This helps students evaluate, and improve on, the written mathematical arguments of others.Design Principle(s): Maximize meta-awarenessSUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Visual AidsCreate an anchor chart (i.e., information needed to determine scaled copies) publicly displaying important denitions, rules, formulas, or concepts for future reference.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.28

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Conceptual Processing: Processing TimeBegin with a demonstration of one scaled copy match, which will provide access for students who benet from clear and explicit instructions.Digital Lesson1. What do we mean by corresponding parts? Use the triangles to identify at least 1 pair of corresponding parts.Corresponding parts refers toIn these two triangles, the sides measuring and are corresponding parts.2. What is a scale factor? How can you create scaled copies using a scale factor?A scale factor isTo create scaled copiesSTUDENT RESPONSESample response:1. Corresponding parts refers to parts in an original gure and a scaled copy that have the same position.15 cm, 45 cm2. A scale factor is a single factor that relates each length in the original triangle to its corresponding length in a copy. To create scaled copies, multiply all the lengths in the original gure by the scale factor.Original Triangle15 cm12 cm36 cm45 cm21 cm7 cm© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 29

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Wrap-UpLESSON SYNTHESIS• What do we mean by corresponding parts?• What is a scale factor? How does it work?Students can use informal language to describe corresponding parts, and recognize a scale factor as a common ratio between the lengths of corresponding side lengths. In the gure, triangle DEF is a scaled copy of triangle ABC. We call parts that have the same position within each gure corresponding parts. For example, we refer to vertex E in triangle DEF and vertex B in triangle ABC as corresponding points; segment BC and segment EF as corresponding segments; and angle C (or angle BCA) and angle F (or angle EFD) as corresponding angles.The segments in a scaled copy are always a certain number of times as long as the corresponding segments in the original gure. We call that number the scale factor. For example, the scale factor between ABC and its copy triangle DEF is 32 or 1.5 because all lengths in triangle DEF are 1.5 times as long as the corresponding lengths in triangle ABC.TERMINOLOGYCorresponding When part of an original gure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.For example, point B in the rst triangle corresponds to point E in the second triangle.Segment AC corresponds to segment DF.Scale factor To create a scaled copy, we multiply all the lengths in the original gure by the same number. This number is called the scale factor.In this example, the scale factor is 1.5, because 4 ∙ 1.5 = 6, 5 ∙ 1.5 = 7.5, and 6 ∙ 1.5 = 9.A4 56 7.56C D9EFBA C DEFBA4 56 7.56C D9EFB© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.30

G7M1 | LESSON 2ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:EXIT TICKETPolygon PQRS is a scaled copy of polygon ABCD.1. Name the angle in the scaled copy that corresponds to angle ABC.2. Name the segment in the scaled copy that corresponds to segment AD.3. What is the scale factor from polygon ABCD to polygon PQRS?STUDENT RESPONSE1. Angle PQR corresponds to angle ABC.2. Segment PS corresponds to segment AD. 3. The scale factor is 32 since PS = 3 and AD = 2. ACDBPRSQ© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 31

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 3Making Scaled CopiesLEARNING GOALS Critique (orally and in writing) different strategies (expressed in words and through other representations) for creating scaled copies of a figure.Draw a scaled copy of a given figure using a given scale factor.Generalize (orally and in writing) that the relationship between the side lengths of a figure and its scaled copy is multiplicative, not additive.LEARNING GOALS(STUDENT FACING)Let’s draw scaled copies.LEARNING TARGETS(STUDENT FACING)I can draw a scaled copy of a figure using a given scale factor.I know what operation to use on the side lengths of a figure to produce a scaled copy.REQUIRED MATERIALSGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATIONMake sure students have access to their geometry toolkits, especially tracing paper and index cards.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.32

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In the previous lesson, students learned that we can use scale factors to describe the relationship between corresponding lengths in scaled gures. Here they apply this idea to draw scaled copies of simple shapes on and o a grid. They also strengthen their understanding that the relationship between scaled copies is multiplicative, not additive. Students make careful arguments about the scaling process, and have opportunities to use tools like tracing paper or index cards strategically.As students draw scaled copies and analyze scaled relationships more closely, encourage them to continue using the terms scale factor and corresponding in their reasoning.Warm-UpMORE OR LESS?This warm-up prompts students to use what they know about numbers and multiplication to reason about decimal computations. The problems are designed to result in an answer very close to the given choices, so students must be more precise in their reasoning than simply rounding and calculating. Whereas a number talk typically presents a numerical expression and asks students to explain strategies for evaluating it, this activity asks a slightly dierent question because students don’t necessarily need to evaluate the expression. Rather, they are asked to judge whether the expression is greater than or less than a given value. Although this activity is not quite the same thing as a number talk, the discussion might sound quite similar.LAUNCHDisplay the problems for all to see. Give students quiet think time. Tell students they may not have to calculate, but could instead reason using what they know about the numbers and operation in each problem. Ask students to give a signal when they have an answer and a strategy for every problem.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 33

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASK For each problem, select the answer from the two choices. 1. The value of 25 · (8.5) is:a) More than 205b) Less than 2052. The value of (9.93) · (0.984) is:a) More than 10b) Less than 103. The value of (0.24) · (0.67) is:a) More than 0.2b) Less than 0.2STUDENT RESPONSE1. More than 205. Since 8 · 25 = 200 and 0.5 · 25 = 12.5, then the product must be more than 205.2. Less than 10. Since 9.93 · 1 = 9.93 and 0.984 is less than 1, then the product must be less than 10.3. Less than 0.2. Since 0.24 is less than 14 and 0.67 is less than 0.8, the product must be less than 0.2 which is 14 of 0.8.DISCUSSION GUIDANCEDiscuss each problem one at a time with this structure:• Ask students to indicate which option they agree with.• If everyone agrees on one answer, ask a few students to share their reasoning, recording it for all to see.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.34

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• If there is disagreement on an answer, ask students with diering answers to explain their reasoning and come to an agreement on an answer.ANTICIPATED MISCONCEPTIONSStudents may attempt to solve each problem instead of reasoning about the numbers and operations. If a student is calculating an exact solution to each problem, ask them to look closely at the characteristics of the numbers and how an operation would aect those numbers.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Visual AidsInclude images depicting “more” and “less” (e.g., up and down arrows), which would aid students who benet from multiple pathways for language processing.Concept Exploration: Activity 1WHICH OPERATIONS? (PART 1)Instructional Routines: MLR3: Clarify, Critique, Correct; Think Pair Share; Anticipate, Monitor, Select, Sequence, ConnectThe purpose of this activity is to contrast the eects of multiplying side lengths versus adding to side lengths when creating copies of a polygon. To nd the corresponding side lengths on a scaled copy, the side lengths of a gure are all multiplied (or divided) by the same number. However, students oen mistakenly think that adding or subtracting the same number to all the side lengths will also create a scaled copy. When students recognize that there is a multiplicative relationship between the side lengths rather than an additive one, they are looking for and making use of structure.Monitor for students who:• notice that Diego’s copy is no longer a polygon while Jada’s still is• notice that the relationships between side lengths in Diego’s copy have changed (e.g., Side 1 is twice as long as Side 2 in the original but is not twice as long as Side 2 in the copy.) while in Jada’s copy they have not• notice that all the corresponding angles have equal measures (i.e., 90 or 270 degrees)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 35

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• describe Jada’s copy as having all side lengths divided by 3• describe Jada’s copy as having all side lengths a third as long as their original lengths• describe Jada’s copy as having a scale factor of 13LAUNCHGive students quiet think time, and then a few minutes to share their thinking with a partner.ACTIVITY 1 TASK 1 Diego and Jada want to scale this polygon so the side that corresponds to 15 units in the original is 5 units in the scaled copy.Diego and Jada each use a dierent operation to nd the new side lengths. Here are their nished drawings.2363021121518202681125Diego’s Drawing12106574Jada’s Drawing© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.36

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:1. What operation do you think Diego used to calculate the lengths for his drawing?2. What operation do you think Jada used to calculate the lengths for her drawing?3. Did each method produce a scaled copy of the polygon? Explain your reasoning.STUDENT RESPONSE1. Since we can get from 15 to 5 by subtracting 10, Diego may have subtracted 10 units from the length of every side. Subtracting 10 from each side length in the original gives Diego’s picture.2. Jada went from 15 to 5 by multiplying by 13 or dividing by 3. Multiplying each side by 13 in the original gives Jada’s picture.3. No, only Jada’s method produces a scaled copy. Sample explanation: Subtracting 10 from each length did not work because now the gure is no longer a polygon. There is a big gap between the two sides that should meet. To create a scaled copy, every length needs to be multiplied (or divided) by the same number.DISCUSSION GUIDANCEInvite previously-selected students to share their answers and reasoning. Sequence their explanations from most general to most technical.Before moving to the next activity, consider asking questions like these:• What is the scale factor used to create Jada’s drawing? What about for Diego’s drawing? (13 for Jada’s; there isn’t one for Diego’s, because it is not a scaled copy.)• What can you say about the corresponding angles in Jada and Diego’s drawings? (They are all equal, even though one is a scaled copy and one is not.)• Subtraction of side lengths does not (usually) produce scaled copies. Do you think addition would work? (Answers vary.)Note: There are rare cases when adding or subtracting the same length from each side of a polygon (and keeping the angles the same) will produce a scaled copy, namely if all side lengths are the same. If not mentioned by students, it is not important to discuss this at this point.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 37

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSRepresenting, writing, and speaking: Math Language Routine 3 Clarify, Critique, CorrectThis is the rst time Math Language Routine 3 is suggested as a support in this course. In this routine, students are given an incorrect or incomplete piece of mathematical work. This may be in the form of a written statement, drawing, problem-solving steps, or another mathematical representation. Students analyze, reect on, and improve the written work by correcting errors and clarifying meaning. Typical prompts are: “Is anything unclear?” and/or “Are there any reasoning errors?” The purpose of this routine is to engage students in analyzing mathematical thinking that is not their own, and to solidify their knowledge through communicating about conceptual errors and ambiguities in language.Design Principle(s): Support sense-making; Optimize output (for reasoning)How It Happens:1. Play the role of Diego and present the following statement along with his awed drawing to the class. “I used a scale factor of minus 10, and Jada used a scale factor of one third. So my drawing is a dierent kind of scaled copy from Jada’s.” Ask students, “What steps did Diego take to make the drawing?” and “Did he create a scaled copy? How do you know?”2. Give students quiet think time to analyze the statement, and then a few minutes to work on improving the statement with a partner. As pairs discuss, provide these sentence frames for scaolding: “I believe Diego created the drawing by because .”, “Diego created/did not create a scaled copy. I know this because .”, “You can’t because .” Encourage the listener to ask clarifying questions by referring to the statement and the drawings. Allow each partner to take a turn as the speaker and listener.3. Invite 3 or 4 pairs to present their improved statement to the small group, both orally and in writing. . Ask students to listen for order/time transition words (rst, next, then, etc.), and any elements of justications (e.g., First, because ). Here are two sample improved statements: “I subtracted 10 from each side length and Jada used a scale factor of one third. So my drawing is not a scaled copy and Jada’s is. Jada’s is a scaled copy because I know that multiplying—not subtracting—creates a scaled copy. Her drawing created a polygon with no gaps.” or “I minused 10 from each side, but I should have realized that in order to scale 15 units in the original down to 5 units in the copy, you have to divide by 3. Jada used a scale factor of one third, which is the same as dividing by 3. My drawing is not a scaled copy and Jada’s is because hers is not a polygon with no gaps, and minusing 10 is not a scale factor.” Call attention to statements that generalize that the method for nding the side lengths of a scaled copy is by multiplying or dividing, not adding or subtracting. Revoice student thoughts with an emphasis on knowing whether or not they created a scaled polygon.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.38

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:4. Close the conversation on Diego’s drawing, discuss the accuracy of Jada’s scaled copy, and then move on to the next lesson activity.Concept Exploration: Activity 2WHICH OPERATIONS? (PART 2)Instructional Routines: Think Pair Share; MLR2: Collect and Display; MLR7: Compare and ConnectIn the previous activity, students saw that subtracting the same value from all side lengths of a polygon did not produce a (smaller) scaled copy. This activity makes the case that adding the same value to all lengths also does not produce a (larger) scaled copy, reinforcing the idea that scaling involves multiplication.This activity gives students a chance to draw a scaled copy without a grid and to use paper as a measuring tool. To create a copy using a scale factor of 2, students need to mark the length of each original segment and transfer it twice onto their drawing surface, reinforcing—in a tactile way—the meaning of scale factor. The angles in the polygon are right angles (and a 270 degree angle in one case) and can be made using the corner of an index card.Some students may struggle to gure out how to use an index card or a sheet of paper to measure lengths. Before demonstrating, encourage them to think about how a length in the given polygon could be copied onto an index card and used as an increment for measuring. If needed, show how to mark the 4-unit length along the edge of a card and to use the mark to determine the needed lengths for the copy.LAUNCHHave students read the activity and check that they understand which side of the polygon Andre would like to be 8 units long on his drawing. Provide access to index cards, so that students can use it as a measuring tool. Consider not explicitly directing students as to its use to give them a chance to use tools strategically. Give students quiet work time, then time to share their work with a partner.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 39

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1Andre wants to make a scaled copy of Jada’s drawing so the side that corresponds to 4 units in Jada’s polygon is 8 units in his scaled copy.1. Andre says “I wonder if I should add 4 units to the lengths of all of the segments?” What would you say in response to Andre? Explain or show your reasoning.2. Create the scaled copy that Andre wants. If you get stuck, consider using the edge of an index card or paper to measure the lengths needed to draw the copy.STUDENT RESPONSE1. Answers vary. Sample reasoning: Adding 4 units would not work because the shape of the copy would be dierent than the shape of the original. For example, in the original drawing, the top horizontal segment is 12 units and the two bottom horizontal segments (5 units and 7 units) also add up to 12 units. If we add 4 units to each segment, the top horizontal segment will be 16 units long, and the two bottom horizontal segments will be 9 units and 11 units, or a total of 20 units. There will be a gap where two segments should meet, or if we make the two ends meet, the angles will no longer be right angles. See the gure below on the le.2. See the gure on the right.3312106574Jada’s DrawingAdding 4 units to each side A correctly drawn figure142420108121416101189© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.40

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ANTICIPATED MISCONCEPTIONSSome students might not be convinced that making each segment 4 units longer will not work. To show that adding 4 units would work, they might simply redraw the polygon and write side lengths that are 4 units longer, regardless of whether the numbers match the actual lengths. Urge them to check the side lengths by measuring. Tell them (or show, if needed) how the 4-unit length in Jada’s drawing could be used as a measuring unit and added to all sides.Other students might add 4 units to all sides and manage to make a polygon but change the angles along the way. If students do so to make the case that the copy will not be scaled, consider sharing their illustrations with the class, as these can help to counter the idea that “scaling involves adding.” If, however, students do this to show that adding 4 units all around does work, address the misconception. Ask them to recall the size of corresponding angles in scaled copies, or remind them that angles in a scaled copy are the same size as their counterparts in the original gure.DISCUSSION GUIDANCEThe purpose of the activity is to explicitly call out a potential misunderstanding of how scale factors work, emphasizing that scale factors work by multiplying existing side lengths by a common factor, rather than adding a common length to each. Invite a couple of students to share their explanations or illustrations that adding 4 units to the length of each segment would not work (e.g. the copy is no longer a polygon, or the copy has angles that are dierent than in the original gure). Then, select a couple of other students to show their scaled copies and share how they created the copies. Consider asking:• What scale factor did you use to create your copy? Why?• How did you use an index card (or a sheet of paper) to measure the lengths for the copy?• How did you measure the angles for the copy?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 41

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: Math Language Routine 7 Compare and ConnectThis is the rst time Math Language Routine 7 is suggested as a support in this course. In this routine, students are given a problem that can be approached using multiple strategies or representations, and are asked to prepare a visual display of their method. Students then engage in investigating the strategies (by means of a teacher-led gallery walk, partner exchange, group presentation, etc.), compare approaches, and identify correspondences between dierent representations. A typical discussion prompt is “What is the same and what is dierent?”, comparing their own strategy to the others. The purpose of this routine is to allow students to make sense of mathematical strategies by identifying, comparing, contrasting, and connecting other approaches to their own, and to develop students’ awareness of the language used through constructive conversations.Design Principle(s): Maximize meta-awarenessHow It Happens:1. Use this routine to compare and contrast dierent methods for creating scaled copies of Jada’s drawing. Before selecting students to share a display of their method with the small group, rst give students an opportunity to do this in a group of 3–4. Invite students to quietly investigate each other’s work. Ask students to consider what is the same and what is dierent about each display. Invite students to give a step-by-step explanation of their method using this sentence frame: “In order to create the copy, rst I…. Next,…. Then, …. Finally,….”. Allow a couple minutes for each display and signal when it is time to switch.2. Next, give each student the opportunity to add detail to their own display for a couple minutes. As students work on their displays, circulate the room to identify at least two dierent methods or two dierent ways of representing a method. Also look for methods that were only partially successful.3. Consider selecting 1–2 students to share methods that were only partially successful in producing scaled copies. Then, select a couple of students to share displays of methods that did produce scaled copies. Draw students’ attention to the approaches used in each drawing (e.g., adding the same value to each side length, not attending to the angles, multiplying by a common factor, not creating a polygon, etc.). Ask students, “Did this approach create a scaled copy? Why or why not?”4. Aer the pre-selected students have nished sharing with the small group, lead a discussion comparing, contrasting, and connecting the dierent approaches and representations. In this discussion, demonstrate using the mathematical language “scale factor”, “corresponding”, and “multiplicative” to amplify student language. Consider using these prompts:• “How did the scale factor show up in each method?”,© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.42

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• “Why did the dierent approaches lead to the same outcome?”,• “What worked well in ’s approach/representation? What did not work well?”, and• “What role does multiplication play in each approach?”5. Close the discussion by inviting 3 students to revoice the incorrect method for creating a scaled drawing, and then invite 3 dierent students to revoice the correct method for creating a scaled drawing. Then, transition back to the Lesson Synthesis and Exit Ticket.SUPPORT FOR STUDENTS WITH DISABILITIESReceptive/Expressive Language: Processing TimeStudents who benet from extra processing time would also be aided by MLR 8 (Discussion Supports).Receptive/Expressive Language: Processing TimeStudents who benet from extra processing time would also be aided by MLR 2 (Collect and Display).Digital LessonOn the right of this grid is one side of a scaled copy of the rectangle. The side that corresponds to 5 units in the original rectangle is 15 units in the scaled copy. What is the scale factor used? Explain how you found the scale factor. Then complete the rest of the scaled copy.The scale factor is .I know this becauseOriginal RectangleScaled Copy© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 43

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSEThe scale factor is 3. I know this because 5 is the length in the original rectangle and 15 is the length of the corresponding side in the scaled copy. 5 times 3 is 15, so this means the scale factor is 3.Wrap-UpLESSON SYNTHESIS• How do we draw a scaled copy of a gure?• Can we create scaled copies by adding or subtracting the same value from all lengths? Why or why not?Scaling is a multiplicative process. To draw a scaled copy of a gure, we need to multiply all of the lengths by the scale factor. We saw in the lesson that adding or subtracting the same value to all lengths will not create scaled copies.Original RectangleScaled Copy© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.44

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:EXIT TICKET1. Create a scaled copy of ABCD using a scale factor of 4.2. Triangle Z is a scaled copy of Triangle M.Select all the sets of values that could be the side lengths of Triangle Z.a) 8, 11, and 14.b) 10, 17.5, and 25.c) 6, 9, and 11.d) 6, 10.5, and 15.e) 8, 14, and 20.BCAD4710M© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 45

G7M1 | LESSON 3ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. 2. B, D, and E.BCAD© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.46

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 4Scaled RelationshipsLEARNING GOALSExplain (orally and in writing) that corresponding angles in a figure and its scaled copies have the same measure.Identify (orally and in writing) corresponding distances or angles that can show that a figure is not a scaled copy of another.Recognize that corresponding distances in a figure and its scaled copy are related by the same scale factor as corresponding sides.LEARNING GOALS(STUDENT FACING)Let’s find relationships between scaled copies.LEARNING TARGETS(STUDENT FACING)I can use corresponding distances and corresponding angles to tell whether one figure is a scaled copy of another.When I see a figure and its scaled copy, I can explain what is true about corresponding angles.When I see a figure and its scaled copy, I can explain what is true about corresponding distances.REQUIRED MATERIALSGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right angles.REQUIRED PREPARATIONMake sure students have access to their geometry toolkits, especially rulers and protractors.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 47

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In previous lessons, students looked at the relationship between a gure and a scaled copy by nding the scale factor that relates the side lengths and by using tracing paper to compare the angles. This lesson takes both of these comparisons a step further.Students study corresponding distances between points that are not connected by segments, in both scaled and unscaled copies. They notice that when a gure is a scaled copy of another, corresponding distances that are not connected by a segment are also related by the same scale factor as corresponding sides.Students use protractors to test their observations about corresponding angles. They verify in several sets of examples that corresponding angles in a gure and its scaled copies are the same size.Students use both insights—about angles and distances between points—to make a case for whether a gure is or is not a scaled copy of another. Practice with the use of protractors will help develop a sense for measurement accuracy, and how to draw conclusions from said measurements, when determining whether or not two angles are the same.Warm-UpTHREE QUADRILATERALS (PART 1)Instructional Routine: Notice and WonderThis warm-up gives students a chance to practice identifying corresponding angles of scaled copies, measure angles using a protractor, and test their earlier conjecture that corresponding angles have the same measure.LAUNCHHave students look at the gures in the activity, and ask “What do you notice? What do you wonder?” Call out in particular questions about the angles in the gures (e.g., whether corresponding ones have the same measure). Tell students that they will test their previous observation about the angles of scaled gures, this time by using protractors instead of tracing paper.Provide access to protractors. Clear protractors with no holes and with radial lines printed on them are recommended here. Some angles may be challenging to measure because of the size of the polygons. If students nd the sides of a polygon not long enough to accommodate angle measurements, suggest that they extend the lines, or demonstrate how to do so (especially if available protractors are opaque with holes in the middle).© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.48

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASKEach of these polygons is a scaled copy of the others. 1. Name two pairs of corresponding angles. What can you say about the sizes of these angles?2. Check your prediction by measuring at least one pair of corresponding angles using a protractor. Record your measurements to the nearest 5°.STUDENT RESPONSE1. Answers vary. Sample response:• Angles ABC and EFG (a.k.a. angles B and F)• Angles LIJ and HEF (a.k.a. angles I and E)The corresponding angles of the polygons will be the same size.2. At least two angles from one of these lists:• Angles A, E, and I each measure about 50°.• Angles B, F, and J each measure about 95°.• Angles C, G, and K each measure about 90°.• Angles D, H, and L each measure about 125°.1cBADGFHEKLJI© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 49

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:DISCUSSION GUIDANCESelect a few students to share their angle measurements and poll the class briey for agreement and disagreement. Discuss major discrepancies, if any. Students should be able to conrm that all corresponding angles in the scaled polygons are equal.If desired, ask students whether recording the angles to the nearest 1 degree would be appropriate: in general, the thickness of the line segments and the markings on the protractor limit accuracy, so reporting to the nearest 5 degrees is appropriate (as long as none of the angles are too close to halfway between two increments).ANTICIPATED MISCONCEPTIONSSome students may read the wrong number on the protractor, moving down from the 180° mark instead of up from the 0° mark, or reading the measurement outside of one of the lines forming the angle instead of between the two lines. Clarify the angle being measured, how to line up the protractor, or how to read the markings correctly.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Concept Exploration: Activity 1THREE QUADRILATERALS (PART 2)Instructional Routine: MLR7: Compare and ConnectStudents have seen that the lengths of corresponding segments in a gure and its scaled copy vary by the same scale factor. Here, they learn that in such a pair of gures, any corresponding distances—not limited to lengths of sides or segments—are related by the same scale factor. The side lengths of the polygons in this task cannot be easily determined, so students must look to other distances to compare.Students must take care when they identify corresponding vertices and distances. As students work, urge them to attend to the order in which points or segments are listed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.50

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:If students are not sure what to make out of the values in the table (for the second question), encourage them to consider the corresponding distances of two gures at a time. For example, ask: What do you notice about the corresponding vertical distances in IJKL and EFGH? What about the corresponding horizontal distances in those two gures?LAUNCHArrange students in groups of 2. Ask if they can tell the lengths of segments GF or DC from the grid (without using rulers). Explain that they will explore another way to compare length measurements in scaled copies.Give students quiet work time for the rst two questions, and time to discuss their responses with a partner before continuing on to the last question.ACTIVITY 1 TASK 1Each of these polygons is a scaled copy of the others. You already checked their corresponding angles.1. The side lengths of the polygons are hard to tell from the grid, but there are other corresponding distances that are easier to compare. Identify the distances in the other two polygons that correspond to DB and AC, and record them in the table.Quadrilateral Distance that corresponds to DBDistance that corresponds to ACABCD DB = 4 AC = 6EFGHIJKL2cBADGFHEKLJI© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 51

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. Look at the values in the table. What do you notice?Pause here so your teacher can review your work.3. The larger gure is a scaled copy of the smaller gure.a) If AE = 4, how long is the corresponding distance in the second gure? Explain or show your reasoning.b) If IK = 5, how long is the corresponding distance in the rst gure? Explain or show your reasoning.STUDENT RESPONSE1. Quadrilateral Distance that corresponds to DBDistance that corresponds to ACABCD DB = 4 AC = 6EFGH HF = 6 EG = 9IJKL LJ = 2 IK = 32. These corresponding distances are related by the same scale factor even though they are not side lengths.3. a) HL = 10. Sample explanation: 15 ÷ 6 = 2.5, so the second gure is related to the rst gure by a scale factor of 2.5. HL is the corresponding distance to AE and is also related by a factor of 2.5. (2.5) ∙ 4 = 10.BADE HLJI K15C6© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.52

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:b) BD = 2. Sample explanation: The scale factor from the small gure to the larger copy is 2.5, so dividing KI by 2.5 gives the corresponding distance in the original gure. 5 ÷ 2.5 = 2.ACTIVITY RECAPDisplay the completed tables for all to see. To highlight how all distances in a scaled copy (not just the side lengths of the gure) are related by the same scale factor, discuss:• How does the vertical distance in ABCD compare to that in EFGH? How do the horizontal distances in the two polygons compare? Do the pairs of vertical and horizontal distances share the same scale factor?• How do the vertical distances in EFGH and IJKL compare? What about the horizontal distances? Is there a common scale factor? What is that scale factor?• What scale factor relates the corresponding lengths and distances in the two drawings of the letter W?ANTICIPATED MISCONCEPTIONSStudents may list the corresponding vertices for distances in the wrong order. For example, instead of writing LJ as the distance corresponding to DB, they may write JL. Remind students of the corresponding points by asking, “Which vertex in IJKL corresponds to D? Which corresponds to B?” and have them match the order of the vertices accordingly.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Executive Functioning: Eliminate BarriersChunk this task into more manageable parts (e.g., presenting one question at a time), which will aid students who benet from support with organizational skills in problem solving.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 53

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 7 Compare and ConnectUse this routine to call attention to the dierent ways students may identify scale factors. Display the following statements: “The scale factor from EFGH to IJKL is 3,” and “The scale factor from EFGH to IJKL is 13”. Give students quiet think time to read and consider whether either or both of the statements are correct. Invite students to share their initial thinking with a partner before selecting 2–3 students to share with the small group. In this discussion, listen for and amplify any comments that refer to the order of the original gure and its scaled copy, as well as those who identify corresponding vertices and distances. Draw students’ attention to the dierent ways to describe the relationships between scaled copies and the original gure.Design Principle(s): Maximize meta-awarenessConcept Exploration: Activity 2SCALED OR NOT SCALED?Instructional Routine: MLR1: Stronger and Clearer Each TimeThe purpose of this activity is for students to determine that gures are not scaled copies, even though they have either corresponding angles with equal measures or corresponding distances multiplied by the same scale factor. This shows that to determine whether one gure is a scaled copy of another, we have to check both the corresponding angles and the corresponding distances.As students work, monitor for convincing arguments about why one polygon is or is not a scaled copy of the other. Ask them to present their cases during the discussion. Students construct arguments and critique the reasoning of others as they present and analyze dierent arguments about the gures in the discussion.LAUNCHKeep students in the same groups. Provide access to geometry toolkits. Give students quiet work time.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.54

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1Here are two more pairs of quadrilaterals. 1. Mai says that Polygon ZSCH is a scaled copy of Polygon XJYN, but Noah disagrees. Do you agree with either of them? Explain or show your reasoning.2. Record the corresponding distances in the table. What do you notice?Quadrilateral Horizontal distance Vertical distanceXJYN XY = JN = ZSCH ZC = SH = 3. Measure at least three pairs of corresponding angles in XJYN and ZSCH using a protractor. Record your measurements to the nearest 5°. What do you notice?4. Do these results change your answer to the rst question? Explain.Here are two more quadrilaterals.5. Kiran says that Polygon EFGH is a scaled copy of ABCD, but Lin disagrees. Do you agree with either of them? Explain or show your reasoning.33NYXJHZCSNYXJHZCSA6B60°60°60° 60°120° 120°120° 120°4 42D CH13 3GFE4© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 55

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. Answers vary. Sample response: Noah is correct, because the corresponding angles are not equal. Mai may have noticed that the corresponding distances are multiplied by 32 and thought this meant the polygons are similar.2. Quadrilateral Horizontal distance Vertical distanceXJYN XY = 6 JN = 9ZSCH ZC = 4 SH = 63. The corresponding angles are not all the same size. Rounded to the nearest 5°, the measures are:XJYN ZSCHangle X measures 100° angle Z measures 125°angle J measures 40° angle S measures 40°angle Y measures 75° angle C measures 75°angle N measures 140° angle H measures 115°4. Since the corresponding angles are not equal, the polygons are denitely not scaled copies of one another.5. Answers vary. Sample response: Lin is correct, because the corresponding distances are not multiplied by the same number (compared to ABCD, the top side in EFGH is half as long, while the bottom side is two-thirds as long). Kiran may have noticed that the corresponding angles are equal and thought this meant the polygons are similar. I noticed that the scale factors for the corresponding sides are not the same. AB and EF are related by a scale factor of 23, but DC and HG are related by a scale factor of 12.DISCUSSION GUIDANCEThe goal of this discussion is to make clear that angle measurements and distances are both important when deciding whether two polygons are scaled copies. To highlight the dierent arguments about whether one polygon is a scaled copy of another, consider debrieng with a role play. Ask four students to take on the roles of the four characters—Mai and Noah in the rst question, and Kiran and Lin in the second—and make a brief argument about why they believe © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.56

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:one gure is a scaled copy of the other in each case. Poll the class aer each pair of cases are presented and nd out with whom students agree.ANTICIPATED MISCONCEPTIONSStudents may rely on the appearance of the gures rather than analyze given information to draw conclusions about scaling. Urge them to look for information about distances and angles (and to think about which tools could help them nd such information) to support their argument.Some students may struggle with comparing the corresponding angles in the rst pair of gures. Remind students of the tools that are at their disposal, and that they could extend the sides of the polygons, if needed, to make it easier to measure the angles.SUPPORT FOR ENGLISH LANGUAGE LEARNERSWriting, speaking, and representing: MLR 1 Stronger and Clearer Each TimeUse this routine to help students rene their justications of whether they agree with Mai or Noah. Give students time to meet with 2-3 partners, sharing their responses. Encourage listeners to press for details and clarity as appropriate based on what each speaker produces. Provide students with prompts for feedback that will help individuals strengthen their ideas and clarify their language (e.g., “Why did you...?,” “Can you clarify how...?,” etc.). Students can borrow ideas and language from each partner to strengthen their nal product.Design Principle(s): Optimize output (for justication)SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Executive Functioning: Eliminate BarriersChunk this task into more manageable parts (e.g., presenting one question at a time), which will aid students who benet from support with organizational skills in problem solving.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 57

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Digital LessonFigure 2 is a scaled copy of Figure 1.AFigure 1Figure 2CUS1. Identify the points in Figure 2 that correspond to the points A and C in Figure 1. Label them R and T. What is the distance between R and T?2. Identify the points in Figure 1 that correspond to the points S and U in Figure 2. Label them B and D. What is the distance between B and D?3. What is the scale factor that takes Figure 1 to Figure 2?STUDENT RESPONSEAFigure 1Figure 2CRTUSDB1. See graph for points R and T. 8 units.2. See graph for points B and D. 3 units.3. 2 because distances between points in Figure 2 are 2 times the corresponding distances in Figure 1.Wrap-UpLESSON SYNTHESIS• Does a scale factor aect any other measurements other than segment lengths?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.58

G7M1 | LESSON 4ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• How can we be sure that a gure is a scaled copy? What features do we check?When a scaled copy is created from a gure, we know that:• The distances between any two points in the original gure, even those not connected by segments, are scaled by the same scale factor.• The corresponding angles in the original gure and scaled copies are congruent.Polygons are a perfect context in which to apply these two ideas, being made up of line segments meeting at angles. So we can use these observations to check whether a polygon is actually a scaled copy of another. If all the corresponding angles are the same size and all corresponding distances are all scaled by the same factor, then we can conclude that it is a scaled copy of the other.EXIT TICKETHere are two polygons on a grid.Is PQRST a scaled copy of ABCDE? Explain your reasoning.STUDENT RESPONSENo. Sample explanation: PQRST is not a scaled copy of ABCDE because we need to use dierent scale factors when comparing corresponding lengths (1 for corresponding segments BC and QR and 2 for corresponding segments CD and RS). Also, not all of their corresponding angles are the same size. Angle A and angle P are not the same size.AEDBCPQRTS© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 59

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 5The Size of the Scale FactorLEARNING GOALSDescribe (orally and in writing) how scale factors of 1, less than 1, and greater than 1 affect the size of scaled copies.Explain and show (orally and in writing) how to recreate the original figure given a scaled copy and its scale factor.Recognize (orally and in writing) the relationship between a scale factor of a scaled copy to its original figure is the “reciprocal” of the scale factor of the original figure to its scaled copy.LEARNING GOALS(STUDENT FACING)Let’s look at the effects of different scale factors.LEARNING TARGETS(STUDENT FACING)I can describe the effect on a scaled copy when I use a scale factor that is greater than 1, less than 1, or equal to 1.I can explain how the scale factor that takes Figure A to its copy Figure B is related to the scale factor that takes Figure B to Figure A.REQUIRED MATERIALSTemplate for Concept Exploration: Activity 1Geometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesPre-printed slips, cut from copies of the templateREQUIRED PREPARATIONPrint and cut sets of slips for the sorting activity from the Scaled Copies Card Sort template. Make enough copies so that each group of 3–4 students has a set. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.Make sure students have access to their geometry toolkits—especially rulers and protractors.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.60

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In this lesson, students deepen their understanding of scale factors in two ways:1. They classify scale factors by size (less than 1, exactly 1, and greater than 1) and notice how each class of factors aects the scaled copies, and2. They see that the scale factor that takes an original gure to its copy and the one that takes the copy to the original are reciprocals. This means that the scaling process is reversible, and that if Figure B is a scaled copy of Figure A, then Figure A is also a scaled copy of Figure B.Students also continue to apply scale factors and what they learned about corresponding distances and angles to draw scaled copies without a grid. Warm-UpNUMBER TALK: MISSING FACTORInstructional Routines: MLR8: Discussion Supports, Number TalkThis number talk encourages students to use structure and the relationship between multiplication and division to mentally solve problems involving fractions. It prompts students to think about how the size of factors impacts the size of the product. It reviews the idea of reciprocal factors in preparation for the work in the lesson.LAUNCHAsk students what operation is meant when a number and a variable are placed right next to each other in an equation. (Multiplication)Display one problem at a time. Give students some quiet think time for each problem and ask them to signal when they have an answer and a strategy.WARM-UP TASKSolve each equation mentally. 1. 16x = 1761© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 61

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. 16x = 83. 16x = 14. 15x = 15. 25x = 1STUDENT RESPONSE1. 11. Possible strategy: 16 x 10 = 160 and 16 x 1 = 16, so 16 x 11 =176.2. 12 or equivalent. Possible strategy: 16 divided by 2 is 8, and dividing by 2 is the same as multiplying by 12.3. 116. Possible strategy: It takes 16 of 116 to make 1.4. 5. Possible strategy: There are 5 copies of 15 in 1, so 5 x 15 = 1.5. 52 or equivalent. Possible strategy: 5 groups of 25 make 2, so 52 of 25 make 1. DISCUSSION GUIDANCEAsk students to share their strategies for each problem. Record and display their explanations for all to see. To involve more students in the conversation, consider asking:• Who can restate ___’s reasoning in a dierent way?• Did anyone solve the problem the same way but would explain it dierently?• Did anyone solve the problem in a dierent way?• Does anyone want to add on to _____’s strategy?• Do you agree or disagree? Why?Highlight that multiplying a factor by a fraction less than 1 results in a product that is less than one of the factors, and that two factors that multiply to be 1 are reciprocals.ANTICIPATED MISCONCEPTIONSStudents might think that a product cannot be less than one of the factors, not realizing that one of the factors can be a fraction. Use examples involving smaller and familiar numbers to remind them that it is possible. Ask, for example, “What times 10 is 5?”© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.62

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion Supports.Provide sentence frames to support students with explaining their strategies. For example, “I noticed that , so I .” or, “First, I because .” When students share their answers with a partner, prompt them to rehearse what they will say when they share with the full group. Rehearsing provides opportunities to clarify their thinking.Design Principle(s): Optimize output (for explanation)Concept Exploration: Activity 1SCALED COPIES CARD SORTMATERIALS: TEMPLATE FOR CONCEPT EXPLORATION: ACTIVITY 1Instructional Routines: Anticipate, Monitor, Select, Sequence, Connect; MLR3: Clarify, Critique, CorrectStudents have studied many examples of scaled copies and know that corresponding lengths in a gure and its scaled copy are related by the same scale factor. The purpose of this activity is for students to examine how the size of the scale factor is related to the original gure and the scaled copy. The activity serves several purposes:1. To reinforce students’ awareness of scale factors2. To draw attention to how scaled copies behave when the scale factor is 1, less than 1, and greater than 1; and3. To help students notice that reciprocal scale factors reverse the scaling.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 63

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:You will need the Scaled Copies Card Sort template for this activity. Here is an image of the cards for your reference and planning.Monitor for students who group the cards in terms of:• Specic scale factors (e.g., 2, 3,12, etc.)• Ranges of scale factors producing certain eects (e.g., factors producing larger, unchanged, or smaller copies)• Reciprocal scale factors (e.g., one factor scales Figure A to B, and its reciprocal reverses the scaling)Select groups who use each of these approaches (and any others) and ask them to share during the discussion.LAUNCHArrange students in groups of 3-4. Distribute one set of slips to each group. Give students some group work time, followed by a discussion with the entire small group.ACTIVITY 1 LAUNCHYou will receive a set of cards. On each card, Figure A is the original and Figure B is a scaled copy.Scaled Copies Card Sort - Card 9 Scaled Copies Card Sort - Card 10 Scaled Copies Card Sort - Card 11 Scaled Copies Card Sort - Card 12 Scaled Copies Card Sort - Card 13 Scaled Copies Card Sort - Card 1 Scaled Copies Card Sort - Card 2 Scaled Copies Card Sort - Card 3 Scaled Copies Card Sort - Card 4 Scaled Copies Card Sort - Card 5 Scaled Copies Card Sort - Card 6 Scaled Copies Card Sort - Card 7 Scaled Copies Card Sort - Card 8 2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.64

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:1. Sort the cards based on their scale factors. Be prepared to explain your reasoning.2. Examine cards 10 and 13 more closely. What do you notice about the shapes and sizes of the gures? What do you notice about the scale factors?3. Examine cards 8 and 12 more closely. What do you notice about the gures? What do you notice about the scale factors?STUDENT RESPONSE1. Grouping categories vary. Sample categories:• Scale factor of 2: Cards 1 and 9.• Scale factor of 12: Cards 3, 7, and 11.• Scale factor of 3: Cards 2, 5, and 10.• Scale factor of 13: Cards 4, 6, and 13.• Scale factor of 1: Cards 8 and 12.2. Answers vary. Sample response: The shapes on both cards are the same, but on Card 10, the scaled copy is larger and the scale factor is 3. On Card 13, the scaled copy is smaller and the scale factor is 13.3. Answers vary. Sample response: The original and the copy are the same size on Cards 8 and 12. The copy is identical to the original. The scale factor is 1.ACTIVITY RECAPDuring the discussion, reference the following two slides.Activity 1 Recap 1Card 10A ACard 13B B© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 65

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY RECAPActivity 1 Recap 2Select groups to explain their sorting decisions following the sequence listed in the activity description above. If no groups sorted in terms of ranges of scale factors (less than 1, exactly 1, and greater than 1) or reciprocal scaling, ask:• What can we say about the scale factors that produce larger copies? Smaller copies? Same-size copies?• Some cards had the same pair of gures on them, just in a reversed order (i.e., pairs #1 and 7, #10 and 13). What do you notice about their scale factors?Highlight the two main ideas of the lesson: 1) the eects of scale factors that are greater than 1, exactly 1, and less than 1; and 2) the reversibility of scaling. Point out that if Figure B is a scaled copy of Figure A, then A is also a scaled copy of B. In other words, A and B are scaled copies of one another, and their scale factors are reciprocals.Suggest students add these observations to their answer for the last question.ANTICIPATED MISCONCEPTIONSStudents may sort by the types of gures rather than by how the second gure in each pair is scaled from the rst. Remind students to sort based on how Figure A is scaled to create Figure B.Students may think of the change in lengths between Figures A and B in terms of addition or subtraction, rather than multiplication or division. Remind students of an earlier lesson in which they explored the eect of subtracting the same length from each side of a polygon in order to scale it. What happened to the copy? (It did not end up being a polygon and was not a scaled copy of the original one.)Students may be unclear as to how to describe how much larger or smaller a gure is, or may not recall the meaning of scale factor. Have them compare the lengths of each side of the gure. What is the common factor by which each side is multiplied?Card 12Card 8ABA B© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.66

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSWriting: MLR 3 Clarify, Critique, CorrectPresent an incorrect statement that reects a possible misunderstanding from the class for the last prompt. For example, “The scale factor of cards 8 and 12 is 0 because the shapes are the same and there was no change.” Prompt students to identify the error (e.g., ask students to consider whether they agree or disagree with the statement and why), and then write a correct version. In this discussion, highlight the use of disciplinary language by revoicing student ideas. This helps students evaluate, and improve on, the written mathematical arguments of others.Design Principle(s): Maximize meta-awarenessSUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Eliminate BarriersDemonstrate the steps for the activity or game by having a group of students and sta play an example round while the rest of the small group observes. Digital LessonRectangles B, C, and D are all scaled copies of Rectangle A.• Which scaled copy has a scale factor greater than 1?• Which scaled copy has a scale factor equal to 1?• Which scaled copy has a scale factor less than 1?Explain how you know.ABCD© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 67

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE Rectangle C has a scale factor larger than one. When the scale factor is larger than 1, the scaled copy is larger than the original, and Rectangle C is greater than Rectangle A. Rectangle D has a scale factor equal to one. When the scale factor is equal to 1, the scaled copy is the same size as the original, and Rectangle D is the same size as Rectangle A. Rectangle B has a scale factor less than one. When the scale factor is less than 1, the scaled copy is smaller than the original, and Rectangle B is smaller than Rectangle A. Wrap-UpLESSON SYNTHESIS• What happens to the copy when it is created with a scale factor greater than 1? Less than 1? Exactly 1?• How can we reverse the scaling to get back to the original gure when we have a scaled copy?When the scale factor is greater than 1, the scaled copy is larger than the original. When it is less than 1, the copy is smaller than the original. A scale factor of exactly 1 produces a same-size copy.Scaling can be reversed by using reciprocal factors. If we scale Figure A by a factor of 4 to obtain Figure B, we can scale B back to A using a factor of 14. This means that if B is a scaled copy of A, A is also a scaled copy of B; they are scaled copies of each other.EXIT TICKETA rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.1. What are the side lengths of the scaled copy?2. Suppose you want to scale the copy back to its original size. What scale factor should you use?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.68

G7M1 | LESSON 5ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. 14 inches by 21 inches, because 2 x 7 = 14 and 3 x 7 = 21.2. 17, because it is the reciprocal of 7.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 69

TEMPLATE FOR LESSON 5 CONCEPT EXPLORATION: ACTIVITY 1 (PAGE 1 OF 2)Scaled Copies Card Sort - Card 1 Scaled Copies Card Sort - Card 2 Scaled Copies Card Sort - Card 3 Scaled Copies Card Sort - Card 4 Scaled Copies Card Sort - Card 5 Scaled Copies Card Sort - Card 6 Scaled Copies Card Sort - Card 7 Scaled Copies Card Sort - Card 8 © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.70

TEMPLATE FOR LESSON 5 CONCEPT EXPLORATION: ACTIVITY 1 (PAGE 2 OF 2)Scaled Copies Card Sort - Card 9 Scaled Copies Card Sort - Card 10 Scaled Copies Card Sort - Card 11 Scaled Copies Card Sort - Card 12 Scaled Copies Card Sort - Card 13 © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 71

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 6Scaling and AreaLEARNING GOALSCalculate and compare (orally and in writing) the areas of multiple scaled copies of the same shape.Generalize (orally) that the area of a scaled copy is the product of the area of the original figure and the “square” of the scale factor.Recognize that a two-dimensional attribute, like area, scales at a different rate than one-dimensional attributes, like length and distance.LEARNING GOALS(STUDENT FACING)Let’s build scaled shapes and investigate their areas.LEARNING TARGETS(STUDENT FACING)I can describe how the area of a scaled copy is related to the area of the original figure and the scale factor that was used.REQUIRED MATERIALSTemplate for Lesson: Activity 2Geometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesPattern blocksPre-printed slips, cut from copies of the templateREQUIRED PREPARATIONPrepare to distribute the pattern blocks, at least 16 blue rhombuses, 16 green triangles, 10 red trapezoids, and 7 yellow hexagons per group of 3–4 students.Copy and cut up the Area of Scaled Parallelograms and Triangles template so each group of 2 students can get 1 of the 2 shapes.ZEARN MATH TIPThis lesson is optional, and there is no Independent Digital Lesson included. If you choose to use this lesson, we recommend teaching this whole group with your students. OPTIONAL LESSON© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.72

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:This lesson is optional. In this lesson, students are introduced to how the area of a scaled copy relates to the area of the original shape. Students build on their grade 6 work with exponents to recognize that the area increases by the square of the scale factor by which the sides increased. Students will continue to work with the area of scaled shapes later in this mission and in later missions in this course. Although the lesson is optional, it will be particularly helpful for students to have already had this introduction when they study the area of circles in a later mission.In two of the activities in this lesson, students build scaled copies using pattern blocks as units of area. This work with manipulatives helps accustom students to a pattern that many nd counterintuitive at rst. (It is a common but false assumption that the area of scaled copies increases by the same scale factor as the sides.) Aer that, students calculate the area of scaled copies of parallelograms and triangles to apply the patterns they discovered in the hands-on activities.Warm-UpSCALING A PATTERN BLOCKBy now, students understand that lengths in a scaled copy are related to the original lengths by the scale factor. Here they see that the area of a scaled copy is related to the original area by the square of the scale factor.Students build scaled copies of a single pattern block, using blocks of the same shape to do so. They determine how many blocks are needed to create a copy at each specied scale factor. Each pattern block serves as an informal unit of area. Because each original shape has an area of 1 block, the (scale factor)2 pattern for the area of a scaled copy is easier to recognize.Students use the same set of scale factors to build copies of three dierent shapes (a rhombus, a triangle, and a hexagon). They notice regularity in their repeated reasoning and use their observations to predict the number of blocks needed to build other scaled copies.LAUNCHArrange students in groups of 3–4. Distribute pattern blocks and ask students to use them to build scaled copies of each shape as described in the task. Each group would need at most 16 blocks each of the green triangle, the blue rhombus, and the red trapezoid. If there are not enough for each group to have a full set with 16 each of the green, blue, and red blocks, consider rotating the blocks of each color through the groups, or having students start with 10 blocks of each and ask for more as needed.Give students time to collaborate on the task and follow with a whole-class discussion. Make sure all students understand that “twice as long” means “2 times as long.”© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 73

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASKWork with your group to build the scaled copies described in each question.1. How many blue rhombus blocks does it take to build a scaled copy of Figure A:a) Where each side is twice as long?b) Where each side is 3 times as long?c) Where each side is 4 times as long?2. How many green triangle blocks does it take to build a scaled copy of Figure B:a) Where each side is twice as long?b) Where each side is 3 times as long?c) Using a scale factor of 4?3. How many red trapezoid blocks does it take to build a scaled copy of Figure C:a) Using a scale factor of 2?b) Using a scale factor of 3?c) Using a scale factor of 4?4. Make a prediction: How many blocks would it take to build scaled copies of these shapes using a scale factor of 5? Using a scale factor of 6? Be prepared to explain your reasoning.STUDENT RESPONSE1. 1ABC4 blocks 9 blocks 16 blocks© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.74

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. 3. 4. 25 blocks and 36 blocksWARM-UP RECAPDisplay a table with only the column headings lled in. For the rst four rows, ask dierent students to share how many blocks it took them to build each shape and record their answers in the table.Scale factor Number of blocks to build Figure ANumber of blocks to build Figure BNumber of blocks to build Figure C1234510s124 blocks 9 blocks16 blocks4 blocks 9 blocks 16 blocks© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 75

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:To help students notice, extend, and generalize the pattern in the table, guide a discussion using questions such as these: • In the table, how is the number of blocks related to the scale factor? Is there a pattern?• How many blocks are needed to build scaled copies using scale factors of 5 or 10? How do you know?• How many blocks are needed to build a scaled copy using any scale factor s?• If we want a scaled copy where each side is half as long, how much of a block would it take? How do you know? Does the same rule still apply?If not brought up by students, highlight the fact that the number of blocks it took to build each scaled shape equals the scale factor times itself, regardless of the shape (look at the table row for s). This rule applies to any factor, including those that are less than 1.ANTICIPATED MISCONCEPTIONSSome students may come up with one of these arrangements for the rst question, because they assume the answer will take 2 blocks to build:You could use one pattern block to demonstrate measuring the lengths of the sides of their shape, to show them which side they have not doubled.Students may also come up with:for tripling the trapezoid, because they triple the height of the scaled copy but they do not triple the length. You could use the process described above to show that not all side lengths have tripled.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.76

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 1SCALING MORE PATTERN BLOCKSInstructional Routines: MLR8: Discussion Supports; Anticipate, Monitor, Select, Sequence, ConnectThis activity extends the conceptual work of the previous one by adding a layer of complexity. Here, the original shapes are comprised of more than 1 block, so the number of blocks needed to build their scaled copies is not simply (scale factor)2, but rather n ∙ (scale factor)2, where n is the number of blocks in the original shape. Students begin to think about how the scaled area relates to the original area, which is no longer 1 area unit. They notice that the pattern (scale factor)2 presents itself in the factor by which the original number of blocks has changed, rather than in the total number of blocks in the copy.As in the previous task, students observe regularity in repeated reasoning, noticing that regardless of the shapes, starting with n pattern blocks and scaling by s uses ns2 pattern blocks.Also as in the previous task, the shape composed of trapezoids might be more challenging to scale than those composed of rhombuses and triangles. Prepare to support students scaling the red shape by oering some direction or additional time, if feasible. As students work, monitor for groups who notice that the pattern of squared scale factors still occurs here, and that it is apparent if the original number of blocks is taken into account. Select them to share during class discussion. LAUNCHKeep students in the same groups, or form combined groups if there are not enough blocks. Assign one shape for each group to build (or let groups choose a shape, as long as all 3 shapes are equally represented). To build a copy of each given shape using a scale factor of 2, groups will need 12 blue rhombuses, 8 red trapezoids, or 16 green triangles. To completely build a copy of each given shape with a scale factor of 3, they would need 27 blue rhombuses, 18 red trapezoids, and 36 green triangles; however, the task prompts them to stop building when they know what the answer will be. Give students time to build their shapes and complete the task. Remind them to use the same blocks as those in the original shape and to check the side lengths of each built shape to make sure they are properly scaled.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 77

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 1 Follow the directions and answer the questions about your group’s assigned gure.1. Build a scaled copy of your assigned shape using a scale factor of 2. Use the same shape of blocks as in the original gure. How many blocks did it take?2. Your classmate thinks that the scaled copies in the previous problem will each take 4 blocks to build. Do you agree or disagree? Explain your reasoning.3. Start building a scaled copy of your assigned gure using a scale factor of 3. Stop when you can tell for sure how many blocks it would take. Record your answer.4. How many blocks would it take to build scaled copies of your gure using scale factors 4, 5, and 6? Explain or show your reasoning.5. How is the pattern in this activity the same as the pattern you saw in the previous activity? How is it dierent?STUDENT RESPONSE1. Answers vary based on the original gure: 12 blue rhombuses, 8 red trapezoids, or 16 green triangles.2. Each block in the pattern is replaced by 4 blocks in the scaled copy. There is more than one block in each pattern so the scaled copies of the patterns require more than 4 blocks.3. Answers vary based on the original gure: 27 blue rhombuses, 18 red trapezoids, or 36 green triangles.4. Blue rhombuses needed for scaled copies of Figure D: 3 ∙ 42 = 48, 3 ∙ 52 = 75, 3 ∙ 62 = 108. Red trapezoids needed for scaled copies of Figure E: 2 ∙ 42 = 32, 2 ∙ 52 = 50, 2 ∙ 62 = 72. Green triangles needed for scaled copies of Figure F: 4 ∙ 42 = 64, 4 ∙ 52 = 100, 4 ∙ 62 = 144.5. At rst glance, the pattern does not seem the same because the answers are not 4 and 9. However, each individual block still scales by 4 and then 9, so you have to multiply that 2DEF© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.78

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:by the number of blocks in the original shape to get the number of blocks in the scaled copy.ACTIVITY RECAPThe goal of this discussion is to ensure that students understand that the pattern for the number of blocks in the scaled copies depends on both the scale factor and the number of blocks in the pattern.Display a table with only the column headings lled in. Poll the class on how many blocks it took them to build each scaled copy using the factors of 2 and 3. Record their answers in the table.Scale factor Number of blocks to build Figure DNumber of blocks to build Figure ENumber of blocks to build Figure F1 3 2 423456s© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 79

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY RECAPConsider displaying the built shapes or pictures of them for all to see.Invite selected students to share the pattern that their groups noticed and used to predict the number of blocks needed for copies with scale factors 4, 5, and 6. Record their predictions in the table. Discuss:• How does the pattern for the number of blocks in this activity compare to the pattern in the previous activity? Are they related? How?• For each gure, how many blocks does it take to build a copy using any scale factor s?ANTICIPATED MISCONCEPTIONSStudents may forget to check that the lengths of all sides of their shape have been scaled and end with an inaccurate count of the pattern blocks. Remind them that all segments must be scaled by the same factor.SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate building scaled copies as needed.Executive Functioning: Graphic OrganizersProvide a Venn diagram with which to compare the similarities and dierences between patterns in the previous activity and this one.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.80

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsGive students additional time to make sure that everyone in the group can describe the patterns they noticed and the ways they predicted the number of blocks needed for copies with scale factors 4, 5, and 6. Vary who is called on to represent the ideas of each group. This routine will provide students additional opportunities to prepare for and share their thinking publicly.Design Principle(s): Optimize output (for explanation)Concept Exploration: Activity 2AREA OF SCALED PARALLELOGRAMS AND TRIANGLESMATERIALS: TEMPLATE FOR LESSON: ACTIVITY 2Instructional Routines: Think Pair Share; Anticipate, Monitor, Select, Sequence, Connect; MLR7: Compare and ConnectIn this activity, students transfer what they learned with the pattern blocks to calculate the area of other scaled shapes. In groups of 2, students draw scaled copies of either a parallelogram or a triangle and calculate the areas. Then, each group compares their results with those of a group that worked on the other shape. They nd that the scaled areas of two shapes are the same (even though the starting shapes are dierent and have dierent measurements) and attribute this to the fact that the two shapes had the same original area and were scaled using the same scale factors.While students are not asked to reason about scaled areas by tiling (as they had done in the previous activities), each scaled copy can be tiled to illustrate how length measurements have scaled and how the original area has changed. Some students may choose to draw scaled copies and think about scaled areas this way.52545555225 545454© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 81

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:As students nd the areas of copies with scale factors 5 and 35 without drawing (for the last question), monitor for these methods, depending on their understanding of or comfort with the (scale factor)2 pattern:• Scaling the original base and height and then multiplying to nd the area• Multiplying the original area by the square of the scale factorSelect students using each approach. Invite them to share their reasoning, sequenced in this order, during the discussion.You will need the Area of Scaled Parallelograms and Triangles template for this activity.LAUNCHArrange students in groups of 2. Provide access to geometry toolkits.Distribute slips showing the parallelogram to half the groups and the triangle to the others. Give students quiet work time for the rst question, and then time to complete the rest of the task with their partner.ACTIVITY 2 TASK 1 Answer the questions about your shape. 1. Your teacher will give you a gure with measurements in centimeters. What is the area of your gure? How do you know?2. Work with your partner to draw scaled copies of your gure, using each scale factor in the table. Complete the table with the measurements of your scaled copies.Scale factor Base (cm) Height (cm) Area (cm2)123121333© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.82

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:3. Compare your results with a group that worked with a dierent gure. What is the same about your answers? What is dierent?4. If you drew scaled copies of your gure with the following scale factors, what would their areas be? Discuss your thinking. If you disagree, work to reach an agreement. Be prepared to explain your reasoning.Scale factor Area (cm2)535STUDENT RESPONSE1. The area of either shape is 10 units, because 5 ∙ 2 = 10 and 12 ∙ 4 ∙ 5 = 10. 2. For the parallelogram:Scale factor Base (cm) Height (cm) Area (cm2)1 5 2 102 10 4 403 15 6 90122.5 1 2.51353231091042.5123531082.5253431561512© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 83

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:For the triangle:Scale factor Base (cm) Height (cm) Area (cm2)1 4 5 102 8 10 403 12 15 90122 2.5 2.51343531093. The areas are the same for each scale factor, even though the dimensions are dierent. Specically, the bases of the parallelograms are equal to the heights of the triangles.4. Scale factor Area (cm2)5 250353.6ACTIVITY RECAPScale factor Base (cm) Height (cm) Area (cm2)1231213Invite selected students to share their solutions. Then focus class discussion on two themes: how the values in the tables for the two shapes compare, and how students determined the scaled areas for the scale factors 5 and 35. Ask questions such as: © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.84

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• What did you notice when you compared your answers with another group that worked with the other gure? (When the scale factors are the same, the scaled areas are the same, though the bases and heights are dierent.)• How did you nd the scaled areas for scale factors of 5 and 35? (By scaling the original base and height and multiplying the scaled measurements; by multiplying the original area by (scale factor)2.)• How is the process for nding scaled area here the same as and dierent than that in the previous activities with pattern blocks? (The area units are dierent; the pattern of squaring the scale factor is the same.)Highlight the connection between the two ways of nding scaled areas. Point out that when we multiply the base and height each by the scale factor and then multiply the results, we are essentially multiplying the original lengths by the scale factor two times. The eect of this process is the same as multiplying the original area by (scale factor)2.ANTICIPATED MISCONCEPTIONSStudents may not remember how to calculate the area of parallelograms and triangles. Make sure that they have the correct area of 10 square units for their original shape before they calculate the area of their scaled copies.When drawing their scaled copies, some students might not focus on making corresponding angles equal. As long as they scale the base and height of their polygon correctly, this will not impact their area calculations. If time permits, however, prompt them to check their angles using tracing paper or a protractor.Some students might focus unnecessarily on measuring other side lengths of their polygon, instead of attending only to base and height. If time is limited, encourage them to scale the base and height carefully and check or measure the angles instead.SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate drawing scaled copies as needed.Executive Functioning: Graphic OrganizersProvide a Venn diagram with which to compare the similarities and dierences between student-scaled drawings.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 85

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSRepresenting, Speaking, and Listening: MLR 7 Compare and ConnectInvite students to prepare a visual that shows their approach to nding the areas for scale factors of 5 and 35. Ask students to research how other students approached the problem, in search of a method that is dierent from their own. Challenge students to describe why the dierent approaches result in the same answers. During the whole-class discussion, emphasize the language used to explain the dierent strategies, especially phrases related to “squaring” and “multiplying a number by itself.” This will strengthen students' mathematical language use and reasoning based on the relationship between scale factors and area. Design Principle(s): Maximize meta-awarenessWrap-UpLESSON SYNTHESIS• If all the dimensions of a scaled copy are twice as long as in the original shape, will the area of the scaled copy be twice as large? (No)• Why not? (Both the length and the width get multiplied by 2, so the area gets multiplied by 4.)• If the scale factor is 5, how many times larger will the scaled copy’s area be? (25 times larger)EXIT TICKETThe rst question gives students only the area of the original shape—but not the dimensions—to encourage them to nd the area of the scaled copy by multiplying by the (scale factor)2; however, students can also choose a length and a width for the rectangle that would give the correct original area, and then scale those dimensions by the scale factor to calculate the area. The second question only asks students to nd the (scale factor)2, but not to multiply by it.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.86

G7M1 | LESSON 6OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT TASK1. Lin has a drawing with an area of 20 in2. If she increases all the sides by a scale factor of 4, what will the new area be?2. Noah enlarged a photograph by a scale factor of 6. The area of the enlarged photo is how many times as large as the area of the original?STUDENT RESPONSE1. 320 in2. Possible strategies:• 20 ∙ 42 = 320• If the rectangle is 4 inches by 5 inches, the scaled copy will be 4 ∙ 4 inches by 4 ∙ 5 inches and (4 ∙ 4) ∙ (4 ∙ 5) = 16 ∙ 20 = 320.• If the rectangle is 2 inches by 10 inches, the scaled copy will be 4 ∙ 2 inches by 4 ∙ 10 inches and (4 ∙ 2) ∙ (4 ∙ 10) = 8 ∙ 40 = 320.2. 36 times as large, because 62 = 36.ANTICIPATED MISCONCEPTIONSSome students may multiply the original shape’s area by just the scale factor, instead of by the (scale factor)2, getting 80 in2. Students who do not understand the generalized rule for how scaling aects area might still be able to answer the rst question correctly. They could assume some dimensions for the original rectangle that would give it an area of 20 in2, scale those dimensions by the given scale factor, and then multiply those scaled dimensions to nd the new area.20 in2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 87

TEMPLATE FOR LESSON 6 LESSON: ACTIVITY 2 (PAGE 1 OF 1)Area of Scaled Parallelograms and Triangles Area of Scaled Parallelograms and Triangles Area of Scaled Parallelograms and Triangles Area of Scaled Parallelograms and Triangles Area of Scaled Parallelograms and Triangles Area of Scaled Parallelograms and Triangles © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.88

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 7Scale DrawingsLEARNING GOALS Describe (orally) what a “scale drawing” is.Explain (orally and in writing) how to use scales and scale drawings to calculate actual and scaled distances.Interpret the “scale” of a scale drawing.LEARNING GOALS(STUDENT FACING)Let’s explore scale drawings.LEARNING TARGETS(STUDENT FACING)I can explain what a scale drawing is, and I can explain what its scale means.I can use a scale drawing and its scale to find actual distances.I can use actual distances and a scale to find scaled distances.REQUIRED MATERIALSTemplate for Concept Exploration: Activity 1Copies of the templateGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATIONPrepare to display the examples and non-examples of scale drawings for all to see. Consider adding to the collection a local map showing the actual route of a train or bus line (example of scale drawing) and a diagrammatic transit map (non-example).Ensure students have access to geometry toolkits, especially centimeter rulers and index cards or paper to use as a measuring tool.You will need the Sizing Up a Basketball Court template for this lesson. Prepare one copy per student.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 89

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Up to this point, students have been exploring scaled copies, or two-dimensional images that have been recreated at certain scale factors. In this lesson, they begin to look at scale drawings, or scaled two-dimensional representations of actual objects or places. Students see that although scale drawings capture three-dimensional objects or places, they show scaled measurements in only two of the dimensions, and that all information is projected onto a plane.In this and upcoming lessons, students see that the principles and strategies they used to reason about scaled copies are applicable to scale drawings. For example, previously they saw scale factor as a number that describes how lengths in a gure correspond to lengths in a copy of the gure (and vice versa). Now they see that scale serves a similar purpose: it describes how the lengths in an actual object are related to the lengths on a drawn representation of it. They learn that scale can be expressed in a number of ways, and use scale and scale drawings to nd actual and scaled lengths.Students begin by interpreting given scale drawings. In subsequent lessons, they will create or reproduce scale drawings at specied scales, as well as determine appropriate scales to use, given restrictions in the size of drawing.Warm-UpWHAT IS A SCALE DRAWING?This activity encourages students to notice characteristics of scale drawings by observing examples and counterexamples, and to articulate what a scale drawing is. Though students are not expected to come up with precise denitions, they are likely able to intuit that scale drawings are accurate two-dimensional depictions of what they represent, in the sense that all shapes, arrangements of parts, and relative sizes match those of the actual objects. Expect student observations about scale drawings to be informal and not mathematical. For example, they might say that a scale drawing looks just like the object it is portraying, with the parts shown having the right size and being in the right places in the drawing. Or that in a scale drawing, a smaller part in the actual object does not end up being larger in the drawing.Like any mathematical model of a real situation, a scale drawing captures some important aspects of the real object and ignores other aspects. It may not be apparent to students that scale drawings prioritize features of one plane of the object (and sometimes features of other planes parallel to it) and ignore other surfaces and dimensions. Notice students who show insights around this idea so they can share later.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.90

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:LAUNCHArrange students in groups of 2. Before students look at the materials, poll the class to nd out who has seen scale drawings. Ask a few students who are familiar with them to give a couple of examples of scale drawings they have seen. Then, give students a couple of minutes to observe the examples and counterexamples of scale drawings and discuss in groups what they think a scale drawing is.WARM-UP TASK Here are some drawings of a school bus, a quarter, and the subway lines around Boston. The rst three drawings are scale drawings of these objects. The next three drawings are not scale drawings of these objects. Discuss with your partner what a scale drawing is.STUDENT RESPONSEAnswers vary. Sample descriptions:• A scale drawing is a drawing that shows the object accurately and all parts in the drawing match the parts in the actual object.• No parts in a scale drawing are distorted.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 91

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• A scale drawing is like a scaled copy of a real object, but it is a drawing that shows one at surface of the object.DISCUSSION GUIDANCEAsk a few students to share what they noticed about characteristics of scale drawings and to compare and contrast scaled copies and scale drawings. Discuss questions such as the following. Record common themes and helpful descriptions.• What do the examples have or show that the counterexamples do not?• How are scale drawings like scaled copies you saw in earlier lessons? How are they dierent than scaled copies?• What aspects of the bus, coin, and the city of Boston do the scale drawings show? What aspects of the actual objects do scale drawings not show?Notice misconceptions, but it is not necessary to address them right away, as students’ understanding will be shaped in this and upcoming lessons. Tell students that they will continue to analyze scale drawings and revise their denitions in upcoming activities.ANTICIPATED MISCONCEPTIONSIf students struggle to characterize scale drawings, oer prompts to encourage them to look closer. For example, ask: “How do the shapes and sizes of the objects in the drawings compare to those of the actual objects?” Students may say that sizes of the objects in the scale drawings are smaller than those of the actual objects. Ask them if any parts of the scale drawings are distorted, compared to the actual object—ask them to focus on the two images of the quarter, one of which is circular in shape while the other is not.SUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Visual Aids Create an anchor chart (i.e., word wall) publicly displaying important denitions, rules, formulas, or concepts for future reference.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.92

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 1SIZING UP A BASKETBALL COURTMATERIALS: TEMPLATE FOR CONCEPT EXPLORATION: ACTIVITY 1Instructional Routine: MLR1: Stronger and Clearer Each TimeIn this introductory activity, students explore the meaning of scale. They begin to see that a scale communicates the relationship between lengths on a drawing and corresponding lengths in the objects they represent, and they learn some ways to express this relationship:• “ a units on the drawing represent b units of actual length”• “at a scale of a units (on the drawing) to b units (actual)”• “ a units (on the drawing) for every b units (actual)”Students measure lengths on a scale drawing and use a given scale to nd corresponding lengths on a basketball court. Because students are measuring to the nearest tenth of a centimeter, some of the actual measurements they calculate will not have the precision of the oicial measurements. For example, the oicial measurement for d is 0.9 m.You will need the Sizing Up a Basketball Court template for this activity.LAUNCHAsk students if they have ever played basketball or seen a basketball court. If so, where? If some students have played basketball or seen a basketball court, ask them if they could throw a basketball across the width of a basketball court. What about across the full length of the court? Arrange students in groups of 2. Distribute a copy of the template and a ruler to each student. Give students some quiet work time to complete the rst three questions. Ask them to share their responses with their partner before completing the remaining questions.acbd© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 93

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 1 You will receive a scale drawing of a basketball court. The drawing does not have any measurements labeled, but it says that 1 cm represents 2 meters. Answer the questions in your notes.1. Measure the distances on the scale drawing that are labeled a–d to the nearest tenth of a centimeter. Record your results in the rst row of the table.2. The statement “1 cm represents 2 m” is the scale of the drawing. It can also be expressed as “1 cm to 2 m,” or “1 cm for every 2 m.” What do you think the scale tells us?3. How long would each measurement from the rst question be on an actual basketball court? Explain or show your reasoning.Measurement (a) length of court(b) width of court(c) hoop to hoop(d) 3 point line to sidelineScale drawingActual court4. On an actual basketball court, the bench area is typically 9 meters long.a) Without measuring, determine how long the bench area should be on the scale drawing.b) Check your answer by measuring the bench area on the scale drawing. Did your prediction match your measurement?STUDENT RESPONSE1. 14 cm, 7.5 cm, 12.4 cm, 0.5 cm, although students may round measurements dierently.2. Answers vary. Sample responses:• The scale tells us how the lengths on the drawing compare to actual lengths.• The scale tells us how to use the measurements on the drawing to nd actual measurements.2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.94

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:3. Sample reasoning: Since every centimeter represents 2 meters, I multiplied each measurement from the drawing by 2 to nd the actual measurement in meters.Measurement (a) length of court(b) width of court(c) hoop to hoop(d) 3 point line to sidelineScale drawing 14 cm 7.5 cm 12.4 cm 0.5 cmActual court 28 m 15 m 24.8 m 1 m4. 4.5 cm. Answers vary.ACTIVITY 1 RECAPBefore debrieng as a small group, display the table showing only the scaled distances so students can do a quick check of their measurements (which they may round dierently). Explain to students that the distances on a scale drawing are oen referred to as “scaled distances.” The distances on the basketball court, in this case, are called actual distances.Focus the discussion on the meaning of scale and how students used the given scale to nd actual distances. Invite a few students to share their response to the second and third questions. To further students’ understanding of scale, discuss:• Does “1 cm for every 2 m” mean that the actual distance is twice that on the drawing? Why or why not?• Which parts of the court should be drawn by using “1 cm for every 2 m” rule?• Can we reverse the order in which we list the scaled and actual distances? For example, can we say “2 m of actual distance to 1 cm on the drawing” or “2 m to 1 cm”?Note that the scaled distance is conventionally stated rst, but the actual distance represented could also come rst as long as it is clear from the context.If needed, a short discussion about accuracy of measurements on the scale drawing might highlight some possible sources of measurement error including:• Not measuring in a straight line.• The lines on the scale drawing have width, and this could contribute a small error depending on whether the measurement is from the inside or the outside of the lines.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 95

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ANTICIPATED MISCONCEPTIONSInstead of using the scale to nd actual measurements, students might try to convert distances in centimeters to meters (14 cm is 0.14 m). Explain that the distances they measured on paper could be converted to meters, but then the results are still lengths on paper, just expressed in meters, rather than the measurements of the actual basketball court. Draw students’ attention to the statement “1 cm represents 2 m” on the scale drawing and ask them to think about how to use it to nd actual measurements.SUPPORT FOR ENGLISH LANGUAGE LEARNERSWriting, Speaking, Listening: MLR 1 Stronger and Clearer Each TimeAer students have completed the rst three questions, provide them an opportunity to rene their reasoning for the third question. Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help them strengthen their ideas and clarify their language (e.g.,“How did you use the scale in your calculations?”, “Why did you multiply each measurement from the drawing by 2?”, etc.). Students can borrow ideas and language from each partner to rene and clarify their original explanation. This will help students rene their own explanation and learn about other ways to nd actual measurements by using the measurements from a scale drawing.Design Principles(s): Optimize output (for explanation); Maximize meta-awarenessSUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Fine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate measurements as needed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.96

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 2TALL STRUCTURESInstructional Routines: Anticipate, Monitor, Select, Sequence, Connect; MLR8: Discussion SupportsThis activity introduces students to graphic scales. Students interpret them, use them to nd actual measurements (heights of tall buildings), and express them non-graphically. In earlier lessons, students used markings on an index card or sheet of paper to measure a drawing and create scaled copies. Here, they use non-standard measuring tools again to solve problems. Students make markings on an unmarked straightedge to measure scaled lengths on a drawing, and then use the given scale to determine actual lengths. This measuring strategy builds on students’ work with measurement in grades 1 and 2 (i.e., placing multiple copies of a shorter object end to end and expressing lengths in terms of the number of objects).As students work, encourage them to be as precise as possible in making their marks and in estimating lengths that are less than 1 scale-segment long. Most distances students are measuring here are not line segments but rather distances between a point (the tip of a building) and a line (the ground). Monitor the dierent ways students reason about scaled and actual distances. Here are two likely approaches for nding the dierence between the Burj Khalifa and the Eiel Tower (the second question):• Find the actual height of each tower and then nd their dierence.• Find the dierence in scaled heights, and then use the scale to nd the dierence in actual heights.Select students who use these approaches to share during the discussion in this sequence.LAUNCHDisplay the scale drawing of the structures. Before beginning the work of the task, students may be interested in or eager to share the locations of the structures. Consider taking a few minutes to elicit what they know, or display a world map showing the locations of the structures.Ask students what the segment labeled with “0 m” and “100 m” might mean. Some students are likely to say that it also conveys a scale. Verify that a scale can indeed be communicated graphically; an actual distance is not represented by a numerical measurement, but rather, by the length of the segment.Provide access to index cards or sheets of paper students can use to measure. Tell students to check their answers to the rst question with a partner. Tell them to discuss as necessary until © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 97

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:they reach an agreement before proceeding to work on the rest of the problems. Give students some quiet work time and partner discussion.ACTIVITY 2 TASK 1Here is a scale drawing of some of the world’s tallest structures. Answer the questions in your notes.1. About how tall is the actual Willis Tower? About how tall is the actual Great Pyramid? Be prepared to explain your reasoning.2. About how much taller is the Burj Khalifa than the Eiel Tower? Explain or show your reasoning.3. Measure the line segment that shows the scale to the nearest tenth of a centimeter. Express the scale of the drawing using numbers and words.STUDENT RESPONSE1. The Willis Tower is a bit more than 500 m tall. It takes about 5 of the segment lengths to measure the height. The Great Pyramid is approximately 150 m. Its height is about 112 segments long.2. The Burj Khalifa is approximately 550 m taller than the Eiel Tower. Sample explanations:• It takes about 3 of the 100-m segments to measure the Eiel Tower, so it is about 300 m tall. It takes about 812of the 100-m segments to measure the Burj Khalifa, so it is about 850 meters tall. 850 – 300 = 55033© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.98

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• It takes about 3 of the 100-m segments to measure the Eiel Tower and about 812 segments to measure the Burj Khalifa. This is a dierence of 512 segments on the scale drawing, which would be an actual dierence of about 550 m.• The Burj Khalifa looks almost 3 times as tall as the Eiel Tower, which would be a dierence of between 500 and 600 m.3. Answers vary depending on the printed size of the scale. Sample responses:• 0.7 cm on the drawing represents 100 m.• 0.7 cm to 100 m.• 0.7 cm for every 100 m in actual height.ACTIVITY 2 RECAP Poll the small group for their answers to the rst question. Ask what might be some sources of discrepancies. The main issue here is measurement error, but there are also dierent methods to make the measurements and estimate the heights of the buildings. Two methods to estimate the heights of the buildings (and their limitations) are:• Estimate how many times “taller” each building is compared to the line segment giving the scale. Then multiply this number by 100 m. The accuracy here is not very good unless, for example, the height of the building is very close to being a whole number times the length of the scale.• Measure the segment giving the scale (in centimeters, for example), and then express the scale using centimeters (for example, 0.7 cm represents 100 m). Then measure each building and use the scale to nd the actual height. Estimating and rounding will be necessary when measuring the scale and when measuring the buildings.Ask previously selected and sequenced students to highlight the dierent approaches for comparing the heights of the Burj Khalifa and the Eiel Tower. The main dierence between the two strategies is the order of arithmetic. Taking the dierence of the actual building heights means multiplying scaled heights rst and then subtracting. Taking the dierence of the scaled heights and then applying the scale factor means subtracting scaled heights rst and then multiplying by the scale factor.If time permits, discuss the scale drawing of the towers more broadly. Consider asking:• Besides height information, what other information about the towers does the drawing show? (Widths of the buildings and their overall shapes.)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 99

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• What information does it not show? (The depth of each building, any projections or protrusions, shapes of dierent parts of the buildings, etc.)• How is this scale drawing the same as that of the basketball court? (They both show information on a single plane and are drawn using a scale.) How are they dierent? (The basketball court is a at surface, like the drawing of the court. The drawing of the towers is a side view or front view; the actual objects represented are not actually at objects.)ANTICIPATED MISCONCEPTIONSStudents may not measure heights of the buildings at a right angle from the ground line. Remind students that heights are to be measured perpendicular to the ground or base line.If needed, demonstrate how to use the edge of a sheet of paper or an index card to measure lengths on a scale drawing with a graphic scale.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsUse this routine to support the discussion. For each response or observation that is shared, ask students to restate and/or revoice what they heard using precise mathematical language. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the small group. Ask the original speaker if their peer was accurately able to restate their thinking. Call students’ attention to any words or phrases that helped to clarify the original statement. This will provide more students with an opportunity to produce language as they interpret the reasoning of others.Design Principle(s): Support sense-makingSUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Fine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate measurements as needed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.100

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Digital LessonBelow are scale drawings of the Statue of Liberty, Golden Gate Bridge, and Washington Monument. Use the scale drawings below to answer the following questions in your Zearn notes:1. About how tall is the actual Golden Gate Bridge? Explain or show your reasoning.2. About how tall is the actual Washington Monument? Explain or show your reasoning.3. About how much taller is the actual Washington Monument than the actual Statue of Liberty? Explain or show your reasoning.STUDENT RESPONSE1. The Golden Gate Bridge is about 220 meters tall. It takes a little over two of the 100-m segments to measure to the top of the bridge.2. The Washington Monument is about 150 meters tall. It takes about 1.5 of the 100-m segments to measure its height.3. The Washington Monument is about 50 meters taller than the Statue of Liberty. In the scale drawing, the Washington Monument is about half of a 100-m segment taller than the Statue of Liberty, which is about 50 meters.100 m0© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 101

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Wrap-UpLESSON SYNTHESIS Let’s discuss what a scale drawing is, and how we can use a scale drawing and its scale to nd actual distances.• What is a scale drawing?• How can we describe the scale for a scale drawing?• How do we nd distances using a scale drawing?A scale drawing is a scaled representation of an object. The scale tells us how lengths on the drawing relate to lengths on the actual object. For example, in the basketball court activity, we saw that 1 centimeter on the drawing represented 2 meters of actual distance on the actual court.If we have a scale drawing, we can use the scale to nd lengths on the actual object. For example, if a line segment in the scale drawing of the basketball court is 5 cm, then it represents a 10 m line segment on a real court, because 2 · 5 = 10. It is important to remember that a scale drawing shows scaled measurements in only two dimensions, i.e., measurements of a particular surface of an object and those that have been projected onto a particular plane. For example, the drawing of the basketball court did not show the height of the basketball hoops.TERMINOLOGYscale A scale tells how the measurements in a scale drawing represent the actual measurements of the object.For example, the scale on this oor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and 12 inch would represent 4 feet.scale drawing A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.1 inch8 feet© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.102

G7M1 | LESSON 7ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:For example, this map is a scale drawing. The scale shows that 1 cm on the map represents 30 miles on land.“Map of Texas and Oklahoma” by United States Census Bureau via American Fact Finder. Public Domain.EXIT TICKET 1. A scale drawing of a school bus has a scale of 12 inch to 5 feet. If the length of the school bus is 412 inches on the scale drawing, what is the actual length of the bus? Explain or show your reasoning.2. A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing? Explain or show your reasoning.STUDENT RESPONSE1. 45 . Sample explanation: There are 9 groups of 12 in 412. If 12 inch represents 5 feet, then 412 inches represents 9 · 5 or 45 feet.2. 12.5 cm. Sample reasoning: Since every 80 m is represented by 1 cm, 1,000 m is represented by 1,000 ÷ 80 or 12.5 cm.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 103

TEMPLATE FOR LESSON 7 CONCEPT EXPLORATION: ACTIVITY 1 (PAGE 1 OF 1)1 cm represents 2 m © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.104

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 8Scale Drawings and MapsLEARNING GOALSJustify (orally and in writing) which of two objects was moving faster.Use a scale drawing to estimate the distance an object traveled, as well as its speed or elapsed time, and explain (orally and in writing) the solution method.LEARNING GOALS(STUDENT FACING)Let’s use scale drawings to solve problems.LEARNING TARGETS(STUDENT FACING)I can use a map and its scale to solve problems about traveling.REQUIRED MATERIALSGeometry toolkits : tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATION Ensure students have access to geometry toolkits.OPTIONAL LESSONZEARN MATH TIPThis lesson is optional, and there is no Independent Digital Lesson included. If students felt comfortable with Lesson 7, you should be encouraged to move to Lesson 9. If you choose to use this lesson, we recommend teaching this whole group with your students.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 105

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:This lesson is optional. In this lesson, students apply what they have learned about scale drawings to solve problems involving constant speed. Students are given a map with scale as well as a starting and ending point. In addition, they are either given the time the trip takes and are asked to estimate the speed or they are given the speed and asked to estimate how long the trip takes. In both cases, they need to make strategic use of the map and scale and they will need to estimate distances because the roads are not straight.In the sixth grade, students have examined many contexts involving travel at constant speed. If a car travels at 30 mph, there is a ratio between the time of travel and the distance traveled. This can be represented in a ratio table, or on a graph, or with an equation. If d is the distance traveled in miles, and t is the amount of time in hours, then traveling at 30 mph can be represented by the equation d = 30t. Students may or may not use this representation as they work on the activities in this lesson. But they will gain further familiarity with this important context which they will examine in greater depth when they study ratios and proportional reasoning in grade 7, starting in the next mission.Warm-UpA TRAIN AND A CARThis warm-up serves two purposes. It refreshes the concept of distance, rate, and time of travel from grade 6, preparing students to use scale drawings to solve speed-related problems. It also allows students to estimate decimal calculations.Students are likely to approach the question in a few dierent ways. As students work, notice students using each strategy.• By nding or estimating the speed of the train in miles per hour and comparing this to the speed of the car• By nding the distance the car travels in 4 hours and comparing it to the distance the train travels in 4 hoursLAUNCHGive students quiet think time. Ask students to calculate the answer mentally and to give a signal when they have an answer and explanation. Follow with a whole-class discussion.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.106

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASK Use the information below to determine which vehicle is traveling faster.Two cities are 243 miles apart.• It takes a train 4 hours to travel between the two cities at a constant speed.• A car travels between the two cities at a constant speed of 65 miles per hour.Which is traveling faster, the car or the train? Be prepared to explain your reasoning.STUDENT RESPONSEThe car is traveling faster. Sample strategy: the speed of the train in miles per hour is 243 ÷ 4. This is (240 ÷ 4) + (3 ÷ 4) = 6034, and that’s slower than the car. Alternatively, in 4 hours, the car would travel or 260 miles, and that’s farther than the distance between the cities. So again, the conclusion is that the car is traveling faster.DISCUSSION GUIDANCEInvite students to share their strategies. Make sure to highlight dierent strategies, such as calculating the train’s speed from the information and calculating how far the car would travel in 4 hours.Record and display student explanations for all to see. To involve more students in the conversation, consider asking:• Did anyone solve the problem in a dierent way?• Does anyone want to add on to ’s strategy?• Do you agree or disagree? Why?SUPPORT FOR STUDENTS WITH DISABILITIESMemory: Processing TimeAer calculating mentally, provide sticky notes or mini whiteboards to aid students with working memory challenges.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 107

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 1DRIVING ON I-90Instructional Routines: Anticipate, Monitor, Select, Sequence, Connect MLR7: Compare and ConnectHere, students use a scale and a scale drawing to answer a speed-related question. The task involves at least a couple of steps beyond nding the distance of travel and can be approached in several ways. Minimal scaolding is given here, allowing students to model with mathematics more independently.As students work, notice the dierent approaches they use to nd the actual distance and to determine if the driver was speeding. Some likely variations:• Comparing the speed in miles per minute (calculating the car’s speed in miles per minute and converting the speed limit to miles per minute).• Comparing the speed in miles per hour (nding the car’s speed in miles per minute and converting it to miles per hour so it can be compared to the speed limit in miles per hour).• Comparing the time it would take to travel the same distance at two dierent speeds (the car’s and the limit).• Comparing the distance traveled in the same amount of time at two dierent speeds (the car’s and the limit).Identify students using each method so they can share later.LAUNCHTell students that they will now use a scale drawing (a map) to solve a problem about speed of travel. Survey the class on their familiarity with highway travel and speed limits. If some students are not familiar with speed limits, ask those who are to explain.Arrange students in groups of 2 and provide access to geometry toolkits. Give students time to work on the problem either individually or with their partner.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.108

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 1 Use the map of Interstate 90 outside of Chicago to answer the following questions.1. A driver is traveling at a constant speed on Interstate 90 outside Chicago. If she traveled from Point A to Point B in 8 minutes, did she obey the speed limit of 55 miles per hour? Explain your reasoning.2. A traic helicopter ew directly from Point A to Point B in 8 minutes. Did the helicopter travel faster or slower than the driver? Explain your reasoning.STUDENT RESPONSE1. No, she did not. Sample explanations:• Using the scale and paper, I found the distance from Point A to Point B to be about 8.5 times the scale representing 1 mile, or 8.5 miles. If she traveled at 55 miles per hour, it would take about 0.15 hour or 9 minutes to travel 8.5 miles, since 8.5 ÷ 55 ≈ 0.15. Since she got from A to B in 8 minutes, she must have been going faster than the speed limit.• The distance between A and B is about 8.5 times the length of the segment representing 1 mile, so the distance is about 8.5 miles. She traveled 8.5 miles in 8 minutes, so her speed was about 1.06 miles per minute. The speed of 55 miles per hour is about 0.917 mile per minute, so the driver did not obey the speed limit.2. The helicopter traveled slower, since the direct (straight-line) distance is shorter than the distance along the highway. Since it took the same amount of time to travel a shorter distance, the helicopter traveled more slowly.DISCUSSION GUIDANCEAsk students to indicate whether they believe the driver was speeding or not. Invite students who approached the task in dierent ways to share, highlighting methods that focus on:2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 109

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• Calculating or estimating the speed the driver is traveling (in miles per minute or miles per hour)• Finding how long it would take to make the trip at the speed limit• Finding how far the driver would travel in 8 minutes going at the speed limitDisplay their work or record or summarize it for all to see.Ask students if they thought any method seems more eicient than others and why. Highlight that all the methods involved nding the distance traveled, and that the scale drawing and scale enabled us to nd that distance.One method for solving this problem which avoids the decimals that approximate fractional quantities is to observe that 55 miles per hour is the same as 55 miles in 60 minutes, so that is less than one mile per minute. So it will take more than 8.5 minutes to travel 8.5 miles at 55 miles per hour, and the driver must have been speeding.ANTICIPATED MISCONCEPTIONSStudents might not realize that they need to compare two quantities (either two speeds, two distances traveled in the same amount of time, or two durations of travel) in order to answer the question about speeding. Remind them that there are two potential scenarios here: the driver is obeying the speed limit or the driver is not obeying it.Once students have found the distance between A and B to be about 8.5 miles, they might be inclined to divide 55 by 8.5 simply because 55 is a larger number. Using double number lines or a table to show the relationship between miles traveled and number of hours might be helpful, as might using friendlier examples of distances (e.g., “How long would it take to travel 110 miles? 11 miles?”).SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate measurements as needed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.110

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking, Representing : MLR 7 Compare and ConnectUse this routine as students share visual displays of dierent approaches for determining whether the driver was speeding. Invite students to create and then share their displays with a partner before selecting 2–3 students to share with the class. In this discussion, listen for and amplify dierent ways of making comparisons (e.g., comparing the driver’s speed with the speed limit using miles per minute or miles per hour; comparing the time it would take to travel the same distance at two dierent speeds; comparing the distance traveled in the same amount of time at two dierent speeds, using miles per minute or miles per hour; and comparing how long it would take to make the trip at the speed limit with how far the driver would travel in 8 minutes traveling at the speed limit).Design Principle(s): Maximize meta-awareness; Optimize output (comparison)Concept Exploration: Activity 2BIKING THROUGH KANSASInstructional Routines: Think Pair Share, MLR7: Compare and ConnectIn the previous activity, students were given a map with a scale and the amount of time it took to get from one place to another. They used this to estimate the speed of the trip. In this activity, students work with the speed and a map with scale to nd the amount of time a trip will take.The main strategy to expect is to measure the distance between the two locations on the map and use the scale to convert this to the distance between the actual cities. Then students can calculate how long it will take at 15 mph.LAUNCHTell students that they will now use a scale drawing (a map) to solve a dierent problem about travel, this time focusing on how long it will take. Ask students what is the farthest they have ever biked. How long did it take? Do they know someone who has biked farther or for longer? If so, how far and how long?Keep students in the same groups. Give students quiet work time followed by partner and whole-class discussion.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 111

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1 A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from Garden City to Dodge City, Kansas?STUDENT RESPONSEAnswers vary. Sample responses:• Using the scale, it appears to be about 50 miles from Garden City. In 3 hours, the cyclist would ride 45 miles, and the remaining 5 miles would take 13 of an hour or 20 minutes. It would take the cyclist about 3 hours and 20 minutes.• 15 mph is 15 miles in 60 minutes or 1 mile every 4 minutes. So 4 miles take 16 minutes. The (4 mile) scale t a little more than 12 times, so that means the trip will take a little more than 12 ∙ 16 minutes. That’s 192 minutes or 3 hours and 12 minutes.DISCUSSION GUIDANCEFirst, have students compare answers with a partner and discuss their reasoning until they reach an agreement.Next, invite students to share how they estimated the distance between the two cities (and how long it takes the cyclist to travel this distance). Ask students to consider the dierent distances students estimated the trip to be. What are some reasons for the dierences? Possible explanations include:• Measurement error33“Map of Kansas” by United States Census Bureau via American Fact Finder. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.112

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• The road is not straight and so needs to be approximated• For students who lay out the scale over and over again to cover the distance, it is diicult to estimate the fraction of the scale at the last stepBecause of these dierent sources of inaccuracy, reporting the distance as 50 miles is reasonable; reporting it as 52 miles would require a lot of time and measurements; and reporting it as 51.6 miles is not reasonable with the given scale and map.ANTICIPATED MISCONCEPTIONSThe road from Garden City to Dodge City has many twists and bends. Students may not be sure how to treat these. Tell them to make their best estimate. Measuring many small segments of the road will have the advantage that those short segments are straight but it is time consuming. A good estimate will be suicient here.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the map image to students who benet from extra processing time to review prior to implementation of this activity.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking, Listening: MLR 7 Compare and ConnectAs students work to determine the duration of the trip from Garden City to Dodge City, look for students with dierent strategies for estimating the distance between the two cities. As students investigate each other’s work, ask students to share what worked well in a particular approach. During this discussion, listen for any comments that make the estimation of the distance more precise. Then encourage students to make connections between the various uses of constant speed to calculate the duration of the trip. Amplify language students use to make sense of the cyclist’s constant speed and how it could be represented in the map. This will support constructive conversations as students compare strategies for calculating the duration of a trip and make connections between the quantity and visual representations of constant speed on the map.Design Principle(s): Cultivate conversation; Maximize meta-awareness© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 113

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Wrap-UpLESSON SYNTHESIS A map with a scale helps estimate the distance between two places by measuring the distance on the map and using the scale to nd the actual distance. Once the distance between two places is known:• If we know how long the trip takes, we can calculate the speed by nding the quotient of the distance and the time.• If we know the speed, we can calculate how long the trip takes by nding the quotient of the distance and the speed.In both cases, care has to be taken regarding units. For example, if a 130-mile trip at a constant speed takes two hours, then the speed is 65 miles per hour, because 130 ÷ 2 = 65. A 35-mile trip at 70 miles per hour takes 12 hour, because 35 ÷ 70 = 12.EXIT TICKET LAUNCHProvide access to geometry toolkits. Make sure students know where the boundaries of the Botanical Garden are on the map.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.114

G7M1 | LESSON 8OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT-FACING TASK STATEMENTHere is a map of the Missouri Botanical Garden. Clare walked all the way around the garden.1. What is the actual distance around the garden? Show your reasoning.2. It took Clare 30 minutes to walk around the garden at a constant speed. At what speed was she walking? Show your reasoning.STUDENT RESPONSE1. It takes about 14 segments of the scale to measure the perimeter of the garden, and 14 ∙ 600 = 8,400. So the distance around is about 8,400 feet.2. If she walks for 30 minutes, that means she was traveling at about 280 feet per minute (8,400 ÷ 30 = 280), or about 16,800 feet per hour (280 ∙ 60 ≈ 16,800).“Map of Missouri Botanical Garden” by United States Census Bureau via American Fact Finder. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 115

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 9Creating Scale DrawingsLEARNING GOALSCompare and contrast (orally) different scale drawings of the same object, and describe (orally) how the scale affects the size of the drawing.Create a scale drawing, given the actual dimensions of the object and the scale.Determine the scale used to create a scale drawing and generate multiple ways to express it (in writing).LEARNING GOALS(STUDENT FACING)Let’s create our own scale drawings.LEARNING TARGETS(STUDENT FACING)I can determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths.I know how different scales affect the lengths in the scale drawing.When I know the actual measurements, I can create a scale drawing at a given scale.REQUIRED MATERIALSGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATION Ensure students have access to geometry toolkits.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.116

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In previous lessons, students have used scale drawings to calculate actual distances. This is the rst lesson where students use the actual distance to calculate the scaled distance and create their own scale drawings. They see how dierent scale drawings can be created of the same actual thing, using dierent scales. They also see how the choice of scale inuences the drawing. For example, a scale drawing with a scale of 1 cm to 5 m will be smaller than a scale drawing of the same object with a scale of 1 cm to 2 m (since each cm represents a larger distance, it takes fewer cm to represent the object). This prepares them for future lessons where they will recreate a given scale drawing at a dierent scale. Noticing how scaled drawings change with the choice of scale develops important structural understanding of scale drawings.Warm-UpNUMBER TALK: WHICH IS GREATER?Instructional Routines: MLR8: Discussion Supports, Number TalkIn this number talk, students compare quantities involving division with whole numbers, decimals, and fractions. In each case, a strategy is available that does not require calculating the quantities. When the quantities are complex, there is motivation for using the structure of the expressions to compare since the actual calculations would be more time-consuming.LAUNCHDisplay one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Follow with a whole-class discussion.WARM-UP TASKWithout calculating, decide which quotient is larger. 1. 11 ÷ 23 or 7 ÷ 132. 0.63 ÷ 2 or 0.55 ÷ 33. 15 ÷ 13 or 15 ÷ 141© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 117

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE 1. 7 ÷ 13 is greater, because it is greater than 12 while 1123 is less than 12.2. 0.63 ÷ 2 is greater than 0.55 ÷ 3 since 0.63 > 0.55 and 0.63 is being divided by 2, whereas 0.55 is being divided into more equal parts (3).3. 15 ÷ 14 is greater than 15 ÷ 13 since 14 is less than 13, and dividing by a smaller (unit) fraction gives a larger quotient.DISCUSSION GUIDANCEMake sure to bring out dierent approaches for comparing the quantities, avoiding direct calculation where possible:• 713 and 1123 can both be compared with 12, or students can nd a common numerator or denominator, but this requires more calculations.• 0.63 is greater than 0.55, and 2 is less than 3, or students might notice that 0.63 ÷ 2 is greater than 0.3 while 0.55 ÷ 3 is less than 0.2.• Dividing by 14 is equivalent to multiplying by 4 while dividing by 13 is equivalent to multiplying by 3, so 15 ÷ 14 is greater than 15 ÷ 13.ANTICIPATED MISCONCEPTIONSStudents may misinterpret the last question as 15 ∙ 13 or 15 ∙ 14. Point out that one way to interpret the rst expression is “How many one-thirds are there in 15?”SUPPORT FOR STUDENTS WITH DISABILITIESMemory: Processing TimeProvide sticky notes or mini whiteboards to aid students with working memory challenges.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.118

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsProvide sentence frames to support students with explaining their strategies. For example, “I noticed that , so I .” or “First, I because .” When students share their answers with a partner, prompt them to rehearse what they will say when they share with the full group. Rehearsing provides opportunities to clarify their thinking.Design Principle(s): Optimize output (for explanation)Concept Exploration: Activity 1BEDROOM FLOOR PLANInstructional Routines: MLR7: Compare and Connect, Think Pair ShareIn previous lessons in this mission, students have investigated the meaning of scale drawings and have used them to solve problems. The purpose of this activity is to prepare students for creating their own scale drawing. The discussion highlights that a scale can be expressed in dierent ways, or that dierent pairs of numbers may be used to show the same relationship. For example, a scale of 4 cm to 1 m is equivalent to a scale of 1 cm to 0.25 m. As students work, notice those who use the language of scale appropriately, e.g., by saying that “every 4 cm on the drawing represents 1 m,” or “every 0.25 m shows up as 1 cm on the drawing.” Also notice those who do and do not attend to the relationship between actual and scaled lengths in nding missing measurements.LAUNCHTell students that a oor plan is a top-view drawing that shows a layout of a room or a building. Floor plans are usually scale drawings. Explain that sometimes the scale of a drawing is not specied, but we can still tell the scale if we know both the scaled and actual lengths.Arrange students in groups of 2. Give students quiet work time and time for partner discussion.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 119

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 1 Here is a rough sketch of Noah’s bedroom (not a scale drawing). Noah wants to create a oor plan that is a scale drawing.1. The actual length of Wall C is 4 m. To represent Wall C, Noah draws a segment 16 cm long. What scale is he using? Explain your reasoning.2. Find another way to express the scale. 3. Discuss your thinking with your partner. How do your scales compare?4. The actual lengths of Wall A and Wall D are 2.5 m and 3.75 m. Determine how long these walls will be on Noah’s scale oor plan. Explain your reasoning.STUDENT RESPONSE1. 4 cm to 1 m; 1 cm to 0.25 m; or 16 cm to 4 m. Sample explanation: Since 16 cm represents an actual length of 4 m, then 1 cm must represent 116 of 4 m, which is 0.25 m.2. Answers vary depending on response to the rst question.3. Answers vary.4. Wall A: 10 cm. Wall D: 15 cm. Sample explanations:• Since every 1 m is shown as 4 cm on the drawing, I multiplied the actual lengths, in meters, by 4 to nd how many centimeters long the scale drawing should be.• Since every 1 cm represents 0.25 m, I divided the actual lengths, in meters, by 0.25 to nd how many centimeters long the scale drawing should be.2Wall EWall AWall BWall CWall D© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.120

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:DISCUSSION GUIDANCEFocus the discussion on two things:• Dierent ways to express the same scale• The relationship between scaled and actual lengthsInvite a couple of students to share how they determined the scale of the drawing. Students are likely to come up with several variations, e.g., 4 cm to 1 m, 1 cm to 0.25 m, 16 cm to 4 m, etc. Discuss how all of these express the same relationship and are therefore equivalent, especially how 4 cm to 1 m is equivalent to 1 cm to 0.25 m (or 1 cm to 14 m).Explain that although we can express a scale in multiple but equivalent ways, 1) scales are oen simplied to show the actual distance for 1 scaled unit, and 2) it is common to express at least one distance (usually the scaled distance) as a whole number or a benchmark fraction (e.g., 14, 12) or a benchmark decimal (e.g., 0.25, 0.5, 0.75).Given their work on scaled copies, students may be inclined to say that the scaled and actual lengths are related by a scale factor of 4. Ask: “Are the actual lengths four times the lengths on the drawing? Why or why not?” Point out that because the units for the two quantities are dierent, multiplying a scaled length in centimeters (e.g., 2.5 cm) by 4 will yield another length in centimeters (10 cm), which is not the actual length. It is not essential for students to know that the scale factor here is 250. That work will be explored in an upcoming lesson.ANTICIPATED MISCONCEPTIONSStudents may see that one value is 4 times the other and write the scale backwards, as “1 cm to 4 m.” Prompt students to pay attention to the units and the meaning of each number.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the image to students who benet from extra processing time to review prior to implementation of this activity.Expressive Language: Visual AidsReview anchor chart (i.e., word wall) which publicly displays important denitions, rules, formulas, or concepts to aid in explanations and reasoning.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 121

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking, Listening: MLR 7 Compare and ConnectAs students prepare a visual display of how they created the oor plan, look for students who expressed the scale in dierent ways. As students investigate each other’s work, ask them to share what is especially clear about a particular approach. Then encourage students to explain why there are various yet equivalent ways to express the scale, such as 4 cm to 1 m and 1 cm to 0.25 m. Emphasize the language used to make sense of the dierent ways to express the same scale (e.g., Since 4 cm on the oor plan represents 1 m in the actual room, then 1 cm on the oor plan represents 14 of 1 m, which is 0.25 m). This will reinforce students’ use of mathematical language related to equivalent scales.Design Principle(s): Cultivate conversation; Maximize meta-awarenessConcept Exploration: Activity 2TWO MAPS OF UTAHInstructional Routines: MLR3: Clarify, Critique, Correct, Notice and WonderIn the previous activity, students calculated the scaled distances they would need to create a scale drawing, but did not actually create the scale drawing. In this activity, they create two dierent scale drawings of the state of Utah and notice how the scale impacts the drawing. One of the reasons choice of a scale is important is that we want to see the appropriate level of detail within a xed space.ACTIVITY 2 LAUNCHDisplay the outline of Utah and ask students “What do you notice? What do you wonder?”Ask students to describe the shape: a rectangle with a smaller rectangle removed in the upper right corner.Give students quiet work time to answer the questions followed by discussion.Utah© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.122

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1A rectangle around Utah is about 270 miles wide and about 350 miles tall. The upper right corner that is missing is about 110 miles wide and about 70 miles tall. Make two scale drawings of Utah.333. How do the two drawings compare? How does the choice of scale inuence the drawing?STUDENT RESPONSE1. A rectangle approximately 5.4 centimeters wide and 7 centimeters tall, missing an upper right corner which is approximately 2.2 centimeters wide and 1.4 centimeters tall.2. A rectangle approximately 3.6 centimeters wide and 4.7 centimeters tall, missing an upper right corner which is approximately 1.5 centimeters wide and 1 centimeter tall.3. The measurements in the 1 cm to 50 mile scale drawings are larger than the measurements in the 1 cm to 75 mile scale drawing. This makes sense because when 1 centimeter represents 50 miles, it takes 1.5 centimeters to represent 75 miles.DISCUSSION GUIDANCEAsk students what the two scale drawings share in common. Answers include: they both represent Utah, they both have the same shape, and they both can be used to measure distances in the actual state of Utah.Ask students how the two scale drawings dier. The one at a scale of 1 centimeter to 50 miles is larger than the one at a scale of 1 centimeter to 75 miles.Some students may notice that the scale drawing at a scale of 1 centimeter to 75 miles is actually a scaled copy of the other drawing, with a scale factor of 1.5. If so, ask them to share their observation linking scale drawings with scale copies.ANTICIPATED MISCONCEPTIONSSome students may get a shape that is not closed or does not have right angles if they did not measure carefully enough. Prompt them to double-check their measurement for a particular side of the state if you can easily tell which side is drawn incorrectly.1. Make a scale drawing of Utah where 1 centimeter represents 50 miles.2. Make a scale drawing of Utah where 1 centimeter represents 75 miles.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 123

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Students may think that a scale of 1 centimeter to 50 miles will produce a smaller scale drawing than a scale of 1 centimeter to 75 miles (because 50 is less than 75). Ask them how many centimeters it takes to represent 75 miles if 1 centimeter represents 50 miles (1.5) and how many centimeters it takes to represent 75 miles if 1 centimeter represents 75 miles (1).SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate scale drawing as needed.SUPPORT FOR ENGLISH LANGUAGE LEARNERSReading, Speaking: MLR 3 Clarify, Critique, CorrectBefore presenting the correct scale drawings of Utah, present an incorrect drawing and written explanation. For example, present a rectangle approximately 5.4 cm wide and 7 cm tall that is missing an upper right corner which is approximately 1.4 cm wide and 2.2 cm tall, and provide the statement: “Since 1 cm represents 50 miles, I divided 110 and 70 each by 50, and got 2.2 and 1.4. The small rectangle that is missing is 2.2 cm tall and 1.4 cm wide.” Ask students to identify the error, critique the reasoning, and revise the statement so that the drawing is a scale drawing of Utah. This will remind students about the characteristics of scale drawings discussed in previous lessons and how to determine whether a drawing qualies as a scale drawing of an actual object.Design Principle(s): Optimize output (for explanation); Maximize meta-awarenessDigital LessonThe actual dimensions for a handball court are 24 feet by 36 feet. Below is a scale drawing of the court. What is the scale? You could think about what you can multiply the dimensions of the scale drawing by to nd the dimensions of the actual court.8 inches12 inches© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.124

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSEThe scale is 1 inch = 3 feet. I can divide the actual dimensions by the dimensions of the scale drawing. 36 ÷ 12 is 3, and 24 ÷ 8 is 3.Wrap-UpLESSON SYNTHESIS The size of the scale determines the size of the drawing. You can have dierent-sized scale drawings of the same actual object, but the size of the actual object doesn’t change.• “Suppose there are two scale drawings of the same house. One uses the scale of 1 cm to 2 m, and the other uses the scale 1 cm to 4 m. Which drawing is larger? Why?” (The one with the 1 cm to 2 m scale is larger, because it takes 2 cm on the drawing to represent 4 m of actual length.)• “Another scale drawing of the house uses the scale of 5 cm to 10 m. How does its size compare to the other two?” (It is the same size as the drawing with the 1 cm to 2 m scale.)Sometimes two dierent scales are actually equivalent, such as 5 cm to 10 m and 1 cm to 2 m. It is common to write a scale so that it tells you what one unit on the scale drawing represents (for example, 1 cm to 2 m).EXIT TICKETA rectangular swimming pool measures 50 meters in length and 25 meters in width.1. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.2. What are the length and width of your scale drawing?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 125

G7M1 | LESSON 9ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE5 cm10 cm© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.126

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 10Changing Scales in Scale DrawingsLEARNING GOALSDetermine how much actual area is represented by one square unit in a scale drawing.Generalize (orally) that as the actual distance represented by one unit on the drawing increases, the size of the scale drawing decreases.Reproduce a scale drawing at a different scale and explain (orally) the solution method.LEARNING GOALS(STUDENT FACING)Let’s explore different scale drawings of the same actual thing.LEARNING TARGETS(STUDENT FACING)Given a scale drawing, I can create another scale drawing that shows the same thing at a different scale.I can use a scale drawing to find actual areas.REQUIRED MATERIALSTemplate for Concept Exploration: Activity 1Geometry toolkits-tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesPre-printed slips, cut from copies of the templateREQUIRED PREPARATIONPrint and cut the scales for the Same Plot, Different Drawings activity from the template (1 set of scales per group of 5–6 students).Ensure students have access to their geometry toolkits, especially centimeter rulers.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 127

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In the previous lesson, students created multiple scale drawings using dierent scales. In this lesson, students are given a scale drawing and asked to recreate it at a dierent scale. Two possible strategies to produce these drawings are:• Calculating the actual lengths and then using the new scale to nd lengths on the new scale drawing.• Relating the two scales and calculating the lengths for the new scale drawing using corresponding lengths on the given drawing.In addition, students previously saw that the area of a scaled copy can be found by multiplying the area of the original gure by (scale factor)2. In this lesson, they extend this work in two ways:• They compare areas of scale drawings of the same object with dierent scales.• They examine how much area, on the actual object, is represented by 1 square centimeter on the scale drawing. For example, if the scale is 1 cm to 50 m, then 1 cm2 represents 50 · 50 or 2,500 m2.Throughout this lesson, students observe and explain structure, both when they reproduce a scale drawing at a dierent scale and when they study how the area of a scale drawing depends on the scale.Warm-UpAPPROPRIATE MEASUREMENTSThis warm-up prompts students to attend to precision in measurements, which will be important in upcoming work.LAUNCHArrange students in groups of 2. Give students quiet think time to estimate the size of their own foot in centimeters or inches, and a moment to share their estimate with a partner. Then, ask them to complete the task. © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.128

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASK 1If a student uses a ruler like this to measure the length of their foot, which choices would be appropriate measurements? Select all that apply. Be prepared to explain your reasoning.a) 914 inchesb) 9564 inchesc) 23.47659 centimetersd) 23.5 centimeterse) 23.48 centimetersSTUDENT RESPONSEA and D would be the only appropriate measurements based on the markings on the given ruler. Since the ruler is only marked in 18 inches and 110 centimeter, we could not get measurements as precise as B, C, or E.WARM-UP TASK 2Here is a scale drawing of an average seventh-grade student’s foot next to a scale drawing of a foot belonging to the person with the largest feet in the world. Estimate the length of the larger foot.111 2 32 3 4 5 6 7 8 9 10InchesCentimeters2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 129

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSEThe largest foot in the world is about 1.5 times as long as the average seventh grader’s foot. My foot is about 10 inches long, so the largest foot is about 15 inches or 1 foot and 3 inches long.DISCUSSION GUIDANCESelect a few students to share the measurements they think would be appropriate based on the given ruler. Consider displaying the picture of the ruler for all to see and recording students’ responses on it. Aer each response, poll the class on whether they agree or disagree.If students consider B, C, or E to be an appropriate measurement, ask them to share how to get such a level of precision on the ruler. Make sure students understand that reporting measurements to the nearest 164 of an inch or to the hundred-thousandths of a centimeter would not be appropriate (i.e., show that the ruler does not allow for these levels of precision).Choice E of 23.48 cm may merit specic attention. With the ruler, it is possible to guess that the hundredths place is an 8. This may even be correct. The problem with reporting the measurement in this way is that someone who sees this might misinterpret it and imagine that an extremely accurate measuring device was used to measure the foot, rather than this ruler. The way a measurement is reported reects how the measurement was taken.Next, invite students to share their estimates for the length of the large foot. Since it is diicult to measure the length of these feet very precisely, these measurements should not be reported with a high level of precision; the nearest centimeter would be appropriate.ANTICIPATED MISCONCEPTIONSSome students may say the large foot is about 312 inches or about 9 centimeters long, because they assume the ruler shown in the rst question is at the same scale as the feet shown in the second question. Explain that the images are drawn at dierent scales.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing Time.Provide the image to students who benet from extra processing time to review prior to implementation of this activity.Expressive Language: Eliminate BarriersProvide sentence frames for students to explain their reasoning (i.e., is an appropriate measurement because .).© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.130

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 1SAME PLOT, DIFFERENT DRAWINGSMATERIALS: TEMPLATE FOR CONCEPT EXPLORATION: ACTIVITY 1MLR2: Collect and DisplayThis activity serves several purposes: to allow students to practice creating scale drawings at given scales, to draw attention to the size of the scale drawing as one of the values in the scale changes, and to explore more fully the relationship between scaled area and actual area.Each group member uses a dierent scale to calculate scaled lengths of the same plot of land, draw a scale drawing, and calculate its scaled area. The group then orders the dierent drawings and analyzes them. They think about how many square meters of actual area are represented by one square centimeter on each drawing. Students are likely to determine this value in two ways:• By visualizing what a 1 x 1 centimeter square represents at a given scale (e.g., at a scale of 1 cm to 5 m, each 1 cm2 represents 5 · 5, or 25 m2 ).• By dividing the actual area represented by the scale drawing by the area of their scale drawings.The relationships between scale, lengths in scale drawings, and area in scale drawings are all important examples of the mathematical structure of scale drawings.You will need the Same Plot, Dierent Drawings template for this activity.LAUNCHDisplay this map of a neighborhood in Philadelphia for all to see. Tell students that they are going to reproduce a map of the triangular piece of land at a dierent scale.“Logan Square map” by United States Census Bureau via American Fact Finder. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 131

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Tell students that the actual base of the triangle is 120 m and its actual height is 90 m. Ask, “What is the area of the plot of land?” (5400 square meters—one half the base times the height of the triangle.)Arrange students in groups of and provide access to centimeter graph paper. Assign each student in a group a dierent scale (from the template) to use to create a scale drawing. Give students quiet work time to answer the rst 3 questions, and then time to work on the last question in their groups. Remind students to include the units in their measurements.ACTIVITY 1 TASK 1 Here is a map showing a plot of land in the shape of a right triangle. Use the map to answer the questions.1. Your teacher will assign you a scale to use. On centimeter graph paper, make a scale drawing of the plot of land. Make sure to write your scale on your drawing.2. What is the area of the triangle you drew? Explain or show your reasoning.3. How many square meters are represented by 1 square centimeter in your drawing?4. Aer everyone in your group is nished, order the scale drawings from largest to smallest. What do you notice about the scales when your drawings are placed in this order?33“Logan Square map” by United States Census Bureau via American Fact Finder. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.132

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. Right triangles of various sizes:2. Answers vary depending on the assigned scale. Possible solutions:• 216 cm2, because 12 · 24 · 18 = 216.• 54 cm2, because 12 · 12 · 9 = 54.• 24 cm2, because 12 · 8 · 6 = 24.• 13.5 cm2, because 12 · 6 · (4.5) = 13.5.• 6 cm2, because 12 · 4 · 3 = 6.• 2.16 cm2, because 12 · (2.4) · (1.8) = 2.16.3. Answers vary depending on the assigned scale. Possible solutions:• 25 m2, because 5400 ÷ 216 = 25.• 100 m2, because 5400 ÷ 54 = 100.• 225 m2, because 5400 ÷ 24 = 225.• 400 m2, because 5400 ÷ 13.5 = 400.• 900 m2, because 5400 ÷ 6 = 900.• 2,500 m2, because 5400 ÷ 2.16 = 2500.4. The smaller the number of meters represented by one centimeter, the larger the scale drawing is.1 cm to 50 m1 cm to 30 m1 cm to 20 m1 cm to 15 m1 cm to 10 m1 cm to 5 m© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 133

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:DISCUSSION GUIDANCEFocus the discussion on patterns or features students noticed in the dierent scale drawings. Ask questions such as:• How does a change in the scale inuence the size of the drawings? (As the length being represented by 1 cm gets larger, the size of the drawing decreases.)• How do the lengths of the scale drawing where 1 cm represents 5 meters compare to the lengths of the drawing where 1 cm represents 15 meters? (They are three times as long.)• How do the lengths of the scale drawing where 1 cm represents 5 meters compare to the lengths of the drawing where 1 cm represents 50 meters? (They are ten times as long.)• How does the area of the scale drawing where 1 cm represents 5 meters compare to the area of the drawing where 1 cm represents 15 meters? (It is 9 times as great.)• How does the area of the scale drawing where 1 cm represents 5 meters compare to the area of the drawing where 1 cm represents 50 meters? (It is 100 times as great.)Help students to observe and formulate these patterns:• As the number of meters represented by one centimeter increases, the lengths in the scale drawing decrease.• As the number of meters represented by one centimeter increases, the area of the scale drawing also decreases, but it decreases by the square of the factor for the lengths (because nding the area means multiplying the length and width, both of which decrease by the same factor).SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer Tutors.Pair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate scale drawing as needed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.134

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSConversing, Reading: Math Language Routine 2 Collect and Display.This is the rst time Math Language Routine 2 is suggested as a support in this course. In this routine, the teacher circulates and listens to student talk while jotting down words, phrases, drawings, or writing students use. The language collected is displayed visually for the whole class to use throughout the lesson and mission. Generally, the display contains dierent examples of students using features of the disciplinary language functions, such as interpreting, justifying, or comparing. The purpose of this routine is to capture a variety of students’ words and phrases in a display that students can refer to, build on, or make connections with during future discussions, and to increase students’ awareness of language used in mathematics conversations.Design Principle(s): Support sense-making; Maximize meta-awarenessHow It Happens:1. As students share their ideas in their groups about what they notice in the scale drawings, write down the language they use to describe how the scale aects the size of the scale drawing. Listen for the language students use to compare the lengths and areas of scale drawings with dierent scales. To support the discussion, provide these sentence frames: “As the value of the scale increases, the size of the drawing because ”, “When I compare the lengths of (choose two scale drawings), I notice that .”, and “When I compare the areas of (choose two scale drawings), I notice that .”2. As groups close their conversation, display the language collected for all to reference.3. Next, facilitate a whole-class discussion encouraging students to ask and respond to clarifying questions about the meaning of a word or phrase on the display. To prompt discussion, ask students, “What word or phrase is unclear? From the language I collected, what part does not make sense to you?”Here is an example:Student A: The phrase ‘the triangle is 9 times greater’ is unclear to me. I’m not sure what 9 times greater means.Teacher: [Point to the phrase on the display] Can someone clarify this phrase with specic details?Student B: The area of the triangle with a 1 cm to 5 m scale is 9 times greater than the area of the triangle with a 1 cm to 15 m scale.Teacher: (pressing for more detail) Why is it 9 times greater? Can someone dierent explain or illustrate what 9 times greater means in this case?Student C: [Student adds a sketch of both triangles to the display next to the phrase; teacher adds labels/arrows/calculations to the sketch while Student C explains] It’s 9 times greater because 15 m divided by 5 m is 3, and since we’re talking about area, you then calculate 3 times 3 to give you 9.4. As time permits, continue this discussion until all questions have been addressed. If it did not arise through student-led questions and responses, help students generalize that as the number of meters represented by one centimeter increases, the lengths and areas of the scale drawing decreases.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 135

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:If students are having diiculty, consider using multiple examples from the activity to build up to the generalization. You may say, “Let’s look at the case where we are comparing….” or “Can someone demonstrate the steps they took to compare…?”5. Close this conversation by posting the display in the front of the classroom for students to reference for the remainder of the lesson, and then have students move on to the next activity.Concept Exploration: Activity 2A NEW DRAWING OF THE PLAYGROUNDInstructional Routines: Anticipate, Monitor, Select, Sequence, Connect; MLR7: Compare and ConnectEarlier, students created scale drawings given the actual dimensions and dierent scales. In this activity, instead of being given the actual dimensions, they are given a scale drawing to reproduce at a dierent scale.There are two dierent types of reasoning students may apply. Monitor for students who:• Use the scale drawing to nd the dimensions of the actual school playground and then use those measurements to nd the dimensions of the new scale drawing.• Notice that in the given drawing, 1 centimeter represents 30 m, and in the new drawing, 1 centimeter represents 20 m. That means that each centimeter in the new drawing represents 23 centimeters in the given one. So in the new drawing, the length of each side needs to be multiplied by a factor of 32.Select students using each strategy to share during the discussion, sequenced in this order.LAUNCHTell students that they are going to reproduce a scale drawing using a dierent scale. The scale for the given drawing is 1 cm to 30 meters, and they are going to make a new scale drawing at a scale of 1 cm to 20 meters. Ask them if they think the new drawing will be larger or smaller than the given one.Arrange students in groups. Make sure students have access to their geometry toolkits. Give students quiet work time, followed by a group discussion.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.136

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 TASK 1Here is a scale drawing of a playground. The scale is 1 centimeter to 30 meters. Answer the questions.1. Make another scale drawing of the same playground at a scale of 1 centimeter to 20 meters.2. How do the two scale drawings compare?STUDENT RESPONSE1. Scaled copy of the drawing where each edge is 1.5 times as long as in the drawing.2. The new drawing is larger. Sample explanation: When 1 cm represents 20 m, it takes 1.5 cm to represent 30 m. So the length measurements on the 1 cm to 20 m scale are 1.5 times as long as they are with the 1 cm to 30 m scale. The area measurements are 2.25 (1.5 · 1.5) times as large.DISCUSSION GUIDANCEInvite selected students to share their work producing the new scale drawing. Ask students how the two scale drawings compare. Make sure that they recognize the shapes are the same (both represent the same playground) but the sizes are dierent.Ask students if their prediction about which scale drawing would be larger was correct. Ask them to explain why the drawing at a scale of 1 cm to 20 m is larger than the drawing at a scale of 1 cm to 30 m. The important idea here is that when 1 cm on the scale drawing represents a greater distance, it takes fewer of those centimeters to describe the object. So the scale drawing at a scale of 1 cm to 30 m is smaller than the scale drawing at a scale of 1 cm to 20 m. Consider doing a demonstration in which you zoom in on a map with the scale showing.To encourage students to think about the areas of the scale drawings like they did in the previous activity, consider asking questions like the following:34ABCD© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 137

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• “On the original map with the scale of 1 cm to 30 m, how much area does one square centimeter represent?” (900 cm2)• “On the new map with the scale of 1 cm to 20 m, how much area does one square centimeter represent?” (400 cm2)• “How many times as large as the original map is the new map?” (1.5 times for side lengths; 1.5 · 1.5, or 2.25, times for area)SUPPORT FOR STUDENTS WITH DISABILITIESFine Motor Skills: Peer Tutors.Pair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate measurements as needed.Conceptual Processing: Eliminate Barriers.Allow students to use calculators to ensure inclusive participation in the activity.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking, Listening: MLR 7 Compare and Connect.Ask students to make connections between the various strategies for producing the new scale drawing of the playground. Some students may nd the dimensions of the actual playground and then use those measurements to nd the dimensions of the new scale drawing. Others may reason that when 1 cm represents 20 m, it takes 1.5 cm to represent 30 m. So the length measurements on the 1 cm to 20 m scale are 1.5 times as long as they are with the 1 cm to 30 m scale. Encourage students to think about why both methods result in the same scale drawing. This will promote students’ use of mathematical language as they make connections between the various ways to reproduce a scale drawing at a dierent scale.Design Principles(s): Cultivate conversation; Maximize meta-awarenessDigital LessonIf all the dimensions of a scale drawing are twice as long as in the original shape, will the area of the scaled copy be twice as large? Use an example to explain your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.138

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSEIf all the dimensions of a scale drawing are twice as long as in the original shape, the area of the scaled copy will be four times as large, not twice as large. The scale factor would be 2, since the dimensions of the scale drawing are twice as long as the original shape. I know the area of the scaled copy will be 4 times as large as the original, or 22 times as large. I found how many times larger the area of the scale copy is by taking the scale factor and squaring it.Wrap-UpLESSON SYNTHESISSometimes we have a scale drawing and want to reproduce it at a dierent scale. Two common approaches are:1. Using the original scale drawing to calculate the actual lengths and then using the actual lengths and the new scale to calculate the corresponding lengths on the new drawing.2. Scaling lengths in the original scale drawing by a factor that relates the scales of the two drawings.Suppose you have a map that uses the scale 1 cm to 200 m. You draw a new map of the same place using the scale 1 cm to 20 m.• How does your new map compare to your original map? (The lengths are 10 times as long and the area is 100 times as large.)• How much actual area does 1 cm2 on your new map represent? (400 m2)• How much actual area did 1 cm2 on your original map represent? (40,000 m2)EXIT TICKETHere is a scale drawing of a window frame that uses a scale of 1 cm to 6 inches.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 139

G7M1 | LESSON 10ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Create another scale drawing of the window frame that uses a scale of 1 cm to 12 inches.STUDENT RESPONSEScaled copy of the drawing where each length is half as long as in the original.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.140

TEMPLATE FOR LESSON 10 CONCEPT EXPLORATION: ACTIVITY 1 (PAGE 1 OF 1)SamePlot,DifferentDrawings1cmto5mSamePlot,DifferentDrawings1cmto10mSamePlot,DifferentDrawings1cmto15mSamePlot,DifferentDrawings1cmto20mSamePlot,DifferentDrawings1cmto30mSamePlot,DifferentDrawings1cmto50mSamePlot,DifferentDrawings1cmto5mSamePlot,DifferentDrawings1cmto10mSamePlot,DifferentDrawings1cmto15mSamePlot,DifferentDrawings1cmto20mSamePlot,DifferentDrawings1cmto30mSamePlot,DifferentDrawings1cmto50mSamePlot,DifferentDrawings1cmto5mSamePlot,DifferentDrawings1cmto10mSamePlot,DifferentDrawings1cmto15mSamePlot,DifferentDrawings1cmto20mSamePlot,DifferentDrawings1cmto30mSamePlot,DifferentDrawings1cmto50mSamePlot,DifferentDrawings1cmto5mSamePlot,DifferentDrawings1cmto10mSamePlot,DifferentDrawings1cmto15mSamePlot,DifferentDrawings1cmto20mSamePlot,DifferentDrawings1cmto30mSamePlot,DifferentDrawings1cmto50m© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 141

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 11Scales without UnitsLEARNING GOALSExplain (orally and in writing) how to use scales without units to determine scaled or actual distances.Interpret scales expressed without units, e.g., “1 to 50,” (in spoken and written language).LEARNING GOALS(STUDENT FACING)Let’s explore a different way to express scales.LEARNING TARGETS(STUDENT FACING)I can explain the meaning of scales expressed without units.I can use scales without units to find scaled distances or actual distances.REQUIRED MATERIALSTemplate for Lesson: Activity 1Copies of the templateRulersGeometry toolkit: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesREQUIRED PREPARATIONYou will need the Apollo Lunar Module template for this lesson. Prepare one copy per student.Ensure students have access to geometry toolkits, especially rulers and graph paper.TEACHER INSTRUCTION ONLYZEARN MATH TIPThere is no Independent Digital Lesson for this Lesson. We recommend teaching this lesson whole group with your students.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.142

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In previous lessons, students worked with scales that associated two distinct measurements—one for the distance on a drawing and one for actual distance. The units used in the two measurements are oen dierent (centimeter and meter, inch and foot, etc.). In this lesson, students see that a scale can be expressed without units. For example, consider the scale 1 to 60. This means that every unit of length on the scale drawing represents an actual length that is 60 times its size, whatever the unit may be (inches, centimeters, etc.).Expressing the scale as 1 to 60 highlights the scale factor relating the scale drawing to the actual object. Each measurement on the scale drawing is multiplied by 60 to nd the corresponding measurement on the actual object. This relates closely to the scaled copies that were examined earlier in the mission in which each copy was related to the original by a scale factor. Students gain a better understanding of both scaled copies and scale drawings as they understanding the common underlying structure.Warm-UpONE TO ONE HUNDREDInstructional Routine: Think Pair ShareThis warm-up introduces students to a scale without units and invites them to interpret it using what they have learned about scales so far.As students work and discuss, notice those who interpret the unitless scale as numbers having the same units, as well as those who see “1 to 100” as comparable to using a scale factor of 100. Invite them to share their thinking later.LAUNCHRemind students that, until now, we have worked with scales that each specify two units—one for the drawing and one for the object it represents. Tell students that sometimes scales are given without units.Arrange students in groups of 2. Give students quiet think time and a moment to discuss their thinking with a partner.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 143

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASK A map of a park says its scale is 1 to 100. 1. What do you think that means?2. Give an example of how this scale could tell us about measurements in the park.STUDENT RESPONSE1. Answers vary. Sample responses:• Distances in the park are 100 times bigger than corresponding distances in the map.• One unit on the map represents 100 units of distance in the park.2. Answers vary. Sample responses:• If a path is 6 inches long on the map, then we could tell that the actual path is 600 inches long.• We could use the scale to tell the size of the park. For example, if the park is 20 inches wide on the map, we can tell the actual park is 2,000 inches wide.DISCUSSION GUIDANCESolicit students’ ideas about what the scale means and ask for a few examples of how it could tell us about measurements in the park. If not already mentioned by students, point out that a scale written without units simply tells us how many times larger or smaller an actual measurement is compared to what is on the drawing. In this example, a distance in the park would be 100 times the corresponding distance on the map, so a distance of 12 cm on the map would mean 1,200 cm or 12 m in the park.Explain that the distances could be in any unit, but because one is expressed as a number times the other, the unit is the same for both. Tell students that we will explore this kind of scale in this lesson.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.144

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ANTICIPATED MISCONCEPTIONSStudents might think that when no units are given, we can choose our own units, using dierent units for the 1 and the 100. This is a natural interpretation given students’ work so far. Make note of this misconception, but address it only if it persists beyond the lesson.SUPPORT FOR STUDENTS WITH DISABILITIESSocial-Emotional Functioning: Peer TutorsPair students with their previously identied peer tutors.Concept Exploration: Activity 1APOLLO LUNAR MODULEMATERIALS: TEMPLATE FOR LESSON: ACTIVITY 1Instructional Routines: MLR8: Discussion Supports; Anticipate, Monitor, Select, Sequence, ConnectIn this activity, students use a scale drawing and a scale expressed without units to calculate actual lengths. Students will need to make a choice about which units to use, and some choices make the work easier than others.Monitor for several paths students may take to determine actual heights of the objects in the drawing. Their choice of units could inuence the number of conversions needed and the eiciency of their paths (as shown in the sample student responses). Select students with the following approaches, sequenced in this order, to share during the discussion.Measure in cm, nd cm for actual spacecra, then convert to mMeasure in cm, convert to m for scale drawing, then nd spacecra measurement in mOne other approach students may use is to measure the scale drawing using an inch ruler. This leads to an extra conversion from inches to centimeters or meters. Ask them to consider the unit of interest. Discuss and highlight strategic choices of units during whole-class debrieng.You will need the Apollo Lunar Module template for this activity.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 145

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 LAUNCHTell students that Neil Armstrong and Buzz Aldrin were the rst people to walk on the surface of the moon. The Apollo Lunar Module was the spacecra used by the astronauts when they landed on the Moon in 1969. Consider displaying a picture of the landing module such as this one. Tell students that the landing module was one part of a larger spacecra that was launched from Earth.Solicit some guesses about the size of the spacecra and about how the height of a person might compare to it. Explain to students that they will use a scale drawing of the Apollo Lunar Module to nd out.Arrange students in groups of 2. Give each student a scale drawing of the Apollo Lunar Module (from the template). Provide access to centimeter and inch rulers. Give students time to complete the rst two questions. Ask them to pause briey and discuss their responses with their partner before completing the rest of the questions.Students are asked to nd heights of people if they are drawn “to scale.” Explain that the phrase means “at the same scale” or “at the specied scale.”ACTIVITY 1 TASK 1 Your teacher will give you a drawing of the Apollo Lunar Module. It is drawn at a scale of 1 to 50.1. The “legs” of the spacecra are its landing gear. Use the drawing to estimate the actual length of each leg on the sides. Write your answer to the nearest 10 centimeters. Explain or show your reasoning.2. Use the drawing to estimate the actual height of the Apollo Lunar Module to the nearest 10 centimeters. Explain or show your reasoning.3. Neil Armstrong was 71 inches tall when he went to the surface of the moon in the Apollo Lunar Module. How tall would he be in the drawing if he were drawn with his height to scale? Show your reasoning.4. Sketch a stick gure to represent yourself standing next to the Apollo Lunar Module. Make sure the height of your stick gure is to scale. Show how you determined your height on the drawing.“Apollo 11 Lunar Module Eagle in landing configuration in lunar orbit from the Command and Service Module Columbia” by NASA via Wikimedia Commons. Public Domain.2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.146

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. The leg of the spacecra is about 350 cm if you just include one straight segment. Sample reasoning:• The leg is about 7 cm on the drawing, so the actual length is 7 ∙ 50 or 350 cm.• The leg is about 2.75 inches on the drawing, so the actual length is 137.5 inches.(2.75) ∙ 50 = 137.5 . Multiplying 137.5 by 2.54 gives the length in centimeters.(137.5) ∙ (2.54) = 349.5 ; this is 350 cm rounded to the nearest 10 cm.2. The Lunar Module was about 7 meters tall. Sample explanations:• The spacecra is about 14 cm tall on the drawing. The actual height is 50 times 14 cm, which is 700 cm. 700 cm is 7 m.• 14 cm is 0.14 m, because 14 ÷ 100 = 0.14, and (0.14) ∙ 50 = 7, so the spacecra is about 7 m tall.• The spacecra is about 5.5 inches on the drawing.(5.5) ∙ 50 = 275 . The actual height is about 275 inches, which is 698.5 cm. 275 ∙ (2.54) = 698.5. 698.5 cm is 6.985 m, or about 7 m. (Do not highlight this solution in class discussion.)3. Neil Armstrong would be about 1.4 inches tall in the scale drawing. Sample reasoning: 71 ÷ 50 ≈ 1.4.4. Drawings vary depending on a student’s height. Sample reasoning:• My height is 5 feet and 2 inches, which equals 62 inches. (5 ∙ 12) + 2 = 62. My height on the drawing is about 114 inches, since 62 ÷ 50 ≈ 1.24.• I am 155 cm tall.155 ÷ 50 = 3.1. My height is 3.1 cm on the drawing.DISCUSSION GUIDANCEInvite selected students who measured using a centimeter ruler to share their strategies and solutions for the rst two questions. Consider recording their reasoning for all to see. Highlight the multiplication of scaled measurements by 50 to nd actual measurements. For example, the height of each leg is about 350 cm because 50 ∙ 7 = 350.Discuss whether or how units matter in problems involving unitless scales:Does it matter what unit we use to measure the drawing? Why or why not?Which unit is more eicient for measuring the height of the lunar module on the drawing—inches or centimeters? (Since the question asks for a height in meters, centimeters would be © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 147

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:more eicient since it means fewer conversions. If the question asks for actual height in feet, inches would be a more strategic unit to use.)Ask a few other students to share their responses to the last two questions. Select those who gave their heights in dierent units to share their solutions to the last problem. Highlight that, regardless of the starting unit, nding the length on the scale drawing involves dividing the actual measurement by 50. In other words, actual measurements can be translated to scaled measurements with a scale factor of 150.If time permits, consider displaying a photograph of one of the astronauts next to the Lunar Module, such as shown here, as a way to visually check the reasonableness of students’ solutions.ANTICIPATED MISCONCEPTIONSIf students are unsure how to begin nding the actual length of the landing gear or actual height of the spacecra, suggest that they rst nd out the length on the drawing.Students may measure the height of the spacecra in centimeters and then simply convert it to meters without using the scale. Ask students to consider the reasonableness of their answer (which is likely around 0.14 m) and remind them to take the scale into account.SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Processing TimeProvide the template image to students who benet from extra processing time to review prior to implementation of this activity.Fine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate scale drawing as needed.“AS11-40-5931, Aldrin unpacks experiments” by NASA via the Apollo 11 Image Gallery. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.148

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsUse this routine to support whole-class discussion. For each response or observation that is shared, ask students to restate and/or revoice what they heard using precise mathematical language. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer was accurately able to restate their thinking. Call students’ attention to any words or phrases that helped to clarify the original statement. This will provide more students with an opportunity to produce language as they interpret the reasoning of others.Design Principle(s): Support sense-makingConcept Exploration: Activity 2SAME DRAWING, DIFFERENT SCALESInstructional Routine: MLR8: Discussion SupportsIn this activity, students explore the connection between a scale with units and one without units. Students are given two equivalent scales (one with units and the other without) and are asked to make sense of how the two could yield the same scaled measurements of an actual object. They also learn to rewrite a scale with units as a scale without units.Students will need to attend to precision as they work simultaneously with scales with units and without units. A scale of 1 inch to 16 feet is very dierent than a scale of 1 to 16, and students have multiple opportunities to address this subtlety in the activity.As students work, identify groups that are able to reason clearly about why the two scales produce the same scale drawing. Two dierent types of reasoning to expect are:Using the two scales and the given dimensions of the parking lot to calculate and verify the student calculations.Thinking about the meaning of the scales, that is, in each case, the actual measurements are 180 times the measurements on the scale drawing.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 149

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 2 LAUNCHAsk students: “Is it possible to express the 1 to 50 scale of the Lunar Module as a scale with units? If so, what units would we use?” Solicit some ideas. Students are likely to say “1 inch to 50 inches,” and “1 cm to 50 cm.” Other units might also come up. Without resolving the questions, explain to students that their next task is to explore how a scale without units and one with units could express the same relationship between scaled lengths and actual lengths.Keep students in the same groups. Provide access to rulers. Give partners time to complete the rst question and quiet work time for the last two questions.ACTIVITY 2 TASK 1A rectangular parking lot is 120 feet long and 75 feet wide. Lin and Diego both made scale drawings of the parking lot.• Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches.• Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches.1. Explain or show how each scale would produce an 8 inch by 5 inch drawing.2. Make another scale drawing of the same parking lot at a scale of 1 inch to 20 feet. Be prepared to explain your reasoning.3. Express the scale of 1 inch to 20 feet as a scale without units. Explain your reasoning.STUDENT RESPONSE1. Answers vary. Sample explanations:• In Lin’s case, 1 in represents 15 , so 120  is 8 in (120 ÷ 15 = 8) and 75  is 5 in (75 ÷ 15 = 5). In Diego’s case, 1 unit on the drawing represents 180 of the same unit in the actual distance, so 1 in represents 180 in. 180 in is equal to 15  (180 ÷ 12 = 15). Since the scale here is also 1 in to 15 , the drawing will also be 8 in by 5 in.• 120  is 1,440 in (120 ∙ 12 = 1,440) and 75  is 900 in (75 ∙ 12 = 900). If the scale is 1 to 180, the sides of the parking lot will be 1,440 ÷ 180 and 900 ÷ 180, or 8 in and 5 in, respectively.33© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.150

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:2. Drawing should show a 6 inch by 334 inch rectangle. Sample reasoning: 120 ÷ 20 = 6. 75 ÷ 20 = 334.3. 1 to 240. Sample explanation: 20  is 240 in, so 1 in on the drawing represents 240 in of actual distance.DISCUSSION GUIDANCESelect a couple of previously identied groups to share their responses to the rst question and a couple of other groups for the other questions.Highlight how scaled lengths and actual lengths are related by a factor of 180 in both scales, and that this factor is shown explicitly in one scale but not in the other.• In the case of 1 to 180, we know that actual lengths are 180 times as long as scaled lengths (or scaled lengths are 1801 of actual lengths). If the scaled lengths are given in inches, we can use scaled lengths to nd actual lengths in inches and, if desired, convert to feet aerward, and vice versa.• In the case of 1 in to 15 , though we know that actual measurements are not 15 times longer than their corresponding measurements on a drawing (because 15 feet is not 15 times larger than 1 inch), it is not immediately apparent what factor relates the two measurements. Converting the units helps us see the scale factor. Since 1 foot equals 12 inches and 15 ∙ 12 = 180, the scale of 1 in to 15 feet is equivalent to the scale of 1 in to 180 in, or 1 to 180.ANTICIPATED MISCONCEPTIONSSome students may have trouble getting started. Suggest that they begin by treating each scale separately and nd out, for instance, how a scale of 1 inch to 15 feet produces a drawing that is 8 inches by 5 inches.SUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Eliminate BarriersChunk this task into more manageable parts (e.g., presenting one person’s situation at a time), which will aid students who benet from support with organizational skills in problem solving.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 151

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsProvide sentence frames to support students in producing statements about how scaled lengths and actual lengths are related. Examples include; “When the scale factor is to , the actual lengths are times as long as scaled lengths,” or “If the scale factor is to , you can nd the scaled/actual length by .”Design Principle(s): Support sense-making, Optimize output (for explanation)Wrap-UpLESSON SYNTHESIS• What does it mean when the scale on a scale drawing does not indicate any units?• How is a scale without units the same as or dierent from a scale with units?• How can a scale without units be used to calculate scaled or actual distances?When a scale does not show units, the same unit is used for both the scaled distance and the actual distance. For instance, a scale of 1 to 500 means that 1 inch on the drawing represents 500 inches in actual distance, and 10 mm on a drawing represents 5,000 mm in actual distance. In other words, the actual distance is 500 times the distance on the drawing, and the scaled distance is 5001 of the actual distance. To calculate actual distances, we can multiply all distances on the drawing by the factor 500, regardless of the unit we choose or are given. Likewise, to nd scaled distances, we multiply actual distances by 5001, regardless of the unit used. 500 and 5001 are scale factors that relate the two measurements (actual and scaled).EXIT TICKETAndre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.152

G7M1 | LESSON 11ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:1. What is the actual measurement of that side of the courtyard? Express your answer in inches and then in feet.2. If Andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the rst drawing? Explain your reasoning.STUDENT RESPONSE1. 165 in, which is 13.75 . Sample reasoning: 275 ∙ 60 = 165. 165 ÷ 12 = 13.75.2. It would be larger. Sample explanation: A scale of 1 to 12 means the length on paper is 112 of the original length (or 10 inches by 13.75 inches), so the drawing would be larger than one drawn at 160 the original length.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 153

TEMPLATE FOR LESSON 11 LESSON: ACTIVITY 1 (PAGE 1 OF 1)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.154

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 12Units in Scale DrawingsLEARNING GOALSComprehend that the phrase “equivalent scales” refers to different scales that relate scaled and actual measurements by the same scale factor.Generate a scale without units that is equivalent to a given scale with units, or vice versa.Justify (orally and in writing) that scales are equivalent, including scales with and without units.LEARNING GOALS(STUDENT FACING)Let’s use different scales to describe the same drawing.LEARNING TARGETS(STUDENT FACING)I can tell whether two scales are equivalent.I can write scales with units as scales without units.REQUIRED MATERIALSGeometry toolkits: tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor, and an index card to use as a straightedge or to mark right anglesMetric and customary unit conversion chartsREQUIRED PREPARATIONNote: This lesson contains optional activities. Decide which activities you will do before preparing the materials!Ensure students have access to geometry toolkits. It is also recommended that a conversion chart for metric and customary units of length be provided while students are working on the activities in this lesson.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 155

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:In previous lessons, students learned to express scales with or without units that can be the same or dierent. In this lesson, they analyze various scales and nd that sometimes it is helpful to rewrite scales with units as scales without units in order to compare them. They see that equivalent scales relate scaled and actual measurements by the same scale factor, even though the scales may be expressed dierently. For example, the scale 1 inch to 2.5 feet is equivalent to the scale 5 m to 150 m, because they are both at a scale of 1 to 30.This lesson is also the culmination of students’ work on scaling and area. Students have seen many examples of the relationship between scaled area and actual area, and now they must use this realization to nd the area of an irregularly-shaped pool.Here are some conversion factors that students may want to refer to during these activities.Measures of lengthsCustomary units Metric units1 foot () = 12 inches (in)1 yard (yd) = 36 inches1 yard = 3 feet1 mile (mi) = 5,280 feet1 mile = 1,760 yards1 meter (m) = 1,000 millimeters (mm)1 meter = 100 centimeters (cm)1 kilometer (km) = 1,000 meters1 decimeter (dm) = 0.1 meterCustomary to metric Metric to customary1 inch ≈ 2.54 centimeters1 foot ≈ 0.30 meter1 mile ≈ 1.61 kilometers11 centimeter ≈ 0.39 inch1 meter ≈ 39.97 inches1 kilometer ≈ 0.62 mileWarm-UpCENTIMETERS IN A MILEThe goal of this warm-up is to review expressions in the context of conversions. This lesson will examine in depth equivalent scales, that is, scales that lead to the same size scale drawing. Checking whether or not two scales are equivalent oen involves converting quantities to common units.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.156

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:WARM-UP TASKThere are 2.54 cm in an inch, 12 inches in a foot, and 5,280 feet in a mile. Which expression gives the number of centimeters in a mile? Explain your reasoning.a) 12 · 5,2802.54b) 5,280 · 12 · (2.54)c) 5,280 · 12 (2.54)1d) 5,280 + 12 + 2.54e) 2.5412 · 5,280STUDENT RESPONSEBDISCUSSION GUIDANCEAsk one or more students to explain their reasoning for the correct choice 5,280 · 12 · (2.54). There are 2.54 centimeters in an inch and 12 inches in a foot, so that means there are 12 · (2.54) centimeters in a foot. Then there are 5,280 feet in a mile, so that makes 5,280 · 12 · (2.54) centimeters in a mile. Students can also use common sense about measurements. A centimeter is a small unit of measure while a mile is quite large, so there have to be many centimeters in a mile.Make sure to ask students what option C, (2.54) · 12 · 5,2801, represents in this setting. (The scale factor to convert from miles to centimeters.)SUPPORT FOR STUDENTS WITH DISABILITIESConceptual Processing: Eliminate BarriersAllow students to use calculators to ensure inclusive participation in the activity.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 157

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Concept Exploration: Activity 1THE WORLD’S LARGEST FLAGInstructional Routines: Think Pair Share; MLR8: Discussion SupportsIn this activity, students use a scale without units to nd actual and scaled distances that involve a wider range of numbers, from 0.02 to 2,000. They also return to thinking about how the area of a scale drawing relates to the area of the actual thing.Students are likely to nd scaled lengths in one of two ways: 1) by rst converting the measurement in meters to centimeters and then dividing by 2,000; or 2) by dividing the measurement by 2,000 and then converting the result to centimeters. To nd actual lengths, the same paths are likely, except that students will multiply by 2,000 and reverse the unit conversion. Identify students who use dierent approaches so they can share later.LAUNCHHave students close their books or devices. Display an image of Tunisia’s ag. Explain that Tunisia holds the world record for the largest version of a country ag. The record-breaking ag is nearly four soccer elds in length. Solicit from students a few guesses for a scale that would be appropriate to create a scale drawing of the ag on a sheet of paper. If asked, provide the length of the ag (396 m) and the size of the paper (letter size: 821 inches by 11 inches, or about 21.5 cm by 28 cm).Aer hearing some guesses, explain to students that they will now solve problems about the scale and scale drawing of the giant Tunisian ag.Arrange students in groups of 3–4. Provide access to a metric unit conversion chart. Give students quiet work time, and then more work time to collaborate and discuss their work in groups.During work time, assign one sub-problem from the second question for each group to present.Pre-1999 Flag of Tunisia” by Orange Tuesday via Wikimedia Commons. Public Domain.“Pre-1999 Flag of Tunisia” by Orange Tuesday via Wikimedia Commons. Public Domain.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.158

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:ACTIVITY 1 TASK 1As of 2016, Tunisia holds the world record for the largest version of a national ag. It was almost as long as four soccer elds. The ag has a circle in the center, a crescent moon inside the circle, and a star inside the crescent moon.1. Complete the table. Explain or show your reasoning.Flag Length Flag Height Height of crescent moonActual 396 m 99 mAt 1 to 2,000 scale 13.2 cm2. Complete each scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain or show your reasoning.a) 1 cm to cmb) 1 cm to mc) 1 cm to kmd) 2 m to me) 5 m to mf) cm to 1,000 mg) mm to 20 m3. a) What is the area of the large ag?b) What is the area of the smaller ag?c) The area of the large ag is how many times the area of the smaller ag?2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 159

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:STUDENT RESPONSE1. Flag Length Flag Height Height of crescent moonActual 396 m 264 m 99 mAt 1 to 2,000 scale 19.8 cm 13.2 cm 4.95 cmSample reasoning:• • • 2.  1 cm to 2,000 cm. 2,000 times 1 cm is 2,000 cm. 1 cm to 20 1 cm to 0.02 2 m to 4,000 m. 2,000 times 2 m is 4,000 m. 100f) 50g) 10 mm to 20 m. I know that 1 cm represents 20 m and 1 cm is 10 mm, so 10 mm represents 20 m.3.  . . The scale factor for the height is 2,000 and the scale factor for the length is 2,000, drawing.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.160

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:DISCUSSION GUIDANCEStudents may be confused about whether to multiply or divide by 2,000 (or to multiply by 2,000 or by 2,0001) when nding the missing lengths. Encourage students to articulate what a scale of 1 to 2,000 means, or remind them that it is a shorthand for saying “1 unit on a scale drawing represents 2,000 of the same units in the object it represents.” Ask them to now think about which of the two—actual or scaled lengths—is 2,000 times the other and which is 2,0001 of the other.For the third question relating the area of the real ag to the scale model, if students are stuck, encourage them to work out the dimensions of each explicitly and to use this to calculate the scale factor between the areas.ANTICIPATED MISCONCEPTIONSSelect a few students with diering solution paths to share their responses to the rst question. Record and display their reasoning for all to see. Highlight two dierent ways for dealing with unit conversions. For example, in nding scaled lengths, one can either rst convert the actual length in meters to centimeters and then multiply by 2,0001 , or multiply by 2,0001 rst, and then convert the quotient into centimeters.Invite previously identied students to display and share their responses for the sub-problems in the second question. Aer each person shares, solicit questions or comments from the class. Emphasize that all of the scales are equivalent because in each scale, a factor of 2,000 relates scaled distances to actual distances.Reiterate the fact that a scale does not have to be expressed in terms of 1 scaled unit, as is shown in the last three sub-questions, but that 1 is oen chosen because it makes the scale factor easier to see and can make calculations more eicient.Make sure students understand why the scale factor for the area of the two ags is 4,000,000. (Both the length and the height of the large ag are 2,000 times the length and height of the small ag. So the area of the large ag is 2,000 · 2,000 times the area of the small ag. Alternatively, there are 10,000 square centimeters in a square meter, so in square centimeters, the area of the large ag is 1,053,360,000. Dividing this by the area of the small ag in square centimeters, 261.36, also gives 4,000,000.)SUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Visual AidsCreate an anchor chart (i.e., a unit conversion chart) publicly displaying important denitions, rules, formulas, or concepts for future reference.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 161

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Conceptual Processing: Eliminate BarriersAllow students to use calculators to ensure inclusive participation in the activity.SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsDuring the explanation of their solution paths, provide students a sentence frame such as: “First I , because ”. This will strengthen students’ mathematical language use and reasoning when describing strategies to use a scale without units to nd actual and scaled distances.Design Principle(s): Maximize meta-awareness; Optimize output (for explanation)Digital LessonWhat does it mean when the scale on a scale drawing does not indicate any units?STUDENT RESPONSEWhen there are no units given in a scale it means the units measuring the scaled drawing are the Wrap-UpLESSON SYNTHESIS Scales can be expressed in many dierent ways, including using dierent units or not using any units.• How can we express the scale 1 inch to 5 miles without units? (Since there are 12 inches in a foot and 5,280 feet in a mile, this is the same as 1 inch to 63,360 inches, or 1 to 63,360.)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.162

G7M1 | LESSON 12ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:A scale tells us how a distance on a scale drawing corresponds to an actual distance, and it can also tell us how an area on a drawing corresponds to an actual area.If a map uses the scale 1 inch to 5 miles:• How can we nd the actual area of a region represented on the map? (Find the area on the map in square inches and multiply by 25, because 1 square inch represents 25 square miles.)• How can we nd a region’s scaled area if we know its actual area? (Multiply the area of the actual region by 251.)EXIT TICKETLin and her brother each created a scale drawing of their backyard, but at dierent scales. Lin used a scale of 1 inch to 1 foot. Her brother used a scale of 1 inch to 1 yard.1. Express the scales for the drawings without units.2. Whose drawing is larger? How many times as large is it? Explain or show your reasoning.STUDENT RESPONSE1. Lin’s scale of 1 inch to 1 foot can be written as 1 to 12. Her brother’s scale of 1 inch to 1 yard can be written as 1 to 36.2. Lin’s drawing is larger. Sample explanations:• The lengths on Lin’s plan are 3 times the corresponding lengths on her brother’s • Since 1 yard equals 3 feet, the scale of Lin’s brother’s drawing is equivalent to 1 inch to 3 feet. Each inch on his drawing represents a longer distance than on Lin’s drawing, so his drawing will require less space on paper.• At 1 inch to 1 foot, Lin’s drawing will show 121 of actual the distances. At 1 inch to 1 yard, or 1 inch to 3 feet, her brother’s drawing will show 361 of the actual distances. Since 121 is larger than 361 her drawing will be larger.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 163

G7M1 | LESSON 13ZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:GRADE 7 / MISSION 1 / LESSON 13Draw It to ScaleLEARNING GOALSCompare, contrast, and critique (orally) scale drawings of the classroom.Generate an appropriate scale to represent an actual distance on a limited drawing size, and explain (orally) the reasoning.Make simplifying assumptions and determine what information is needed to create a scale drawing of the classroom.LEARNING GOALS(STUDENT FACING)Let’s draw a floor plan.LEARNING TARGETS(STUDENT FACING)I can create a scale drawing of my classroom.When given requirements on drawing size, I can choose an appropriate scale to represent an actual object.REQUIRED MATERIALS Blank paper, graph paper, and measuring toolsREQUIRED PREPARATIONMake any available linear measuring tools available, which might include rulers, yardsticks, meter sticks, and tape measures, in centimeters and inches.Prepare at least three different types of paper for each group, which could include:812 × 11 printer paper11 × 17 printer paperCentimeter graph paper14-inch graph paper15-inch graph paperOPTIONAL LESSONZEARN MATH TIPThis lesson is optional, and there is no Independent Digital Lesson included. If you choose to use this lesson, we recommend teaching this whole group with your students. © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.164

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:This culminating lesson is optional. Students use what they have learned in this mission to create a scale oor plan of their classroom.The lesson is organized into three main parts:• Part 1: Plan and measure. Each student sketches a rough oor plan of the classroom. In groups, they decide on necessary measurements to take, plan the steps and the tools for measuring, and carry out their plan.• Part 2: Calculate and draw. Students select the paper to use for drawing, decide on a scale, and work individually to create their drawings. They choose their scale and method strategically, given their measurements and the constraints of their paper.• Part 3: Reect and discuss. In small groups, students explain their work, discuss and compare their oor plans, and evaluate the decisions they made in creating the scale drawing. As a class, they reect on how the choice of scale, units, and paper aected the drawing process and the oor plans created.Depending on the instructional choices made, this lesson could take one or more class meetings. The amount of time needed for each part might vary depending on factors such as:• The size and complexity of the classroom, and whether measuring requires additional preparation or steps (e.g., moving furniture, taking turns, etc.).• What the class or individual students decide to include in the oor plans.• How much organizational support is given to students.• How student work is ultimately shared with the class (not at all, informally, or with formal presentations).Consider further dening the scope of work for students and setting a time limit for each part of the activity to focus students’ work and optimize class time.This activity can be modied so that students draw oor plans for dierent parts of the school—the cafeteria, the gym, the school grounds, and so on—and their drawings could later be assembled as a scale oor plan of the school. If this version is chosen, coordinate the scale used by all students before they begin to draw.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 165

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:Warm-UpWHICH MEASUREMENTS MATTER?This warm-up prepares students to create a scale oor plan of the classroom. Students brainstorm and make a list of the aspects of the classroom to include in a oor plan and the measurements to take.Students are likely to note built-in xtures, like walls, windows, and doors, as important components to measure. They may also include movable objects like furniture. As students work, identify those who list positions of objects (e.g., where a blackboard is on a wall, how far away the teacher’s desk is from the door, etc.). Invite them to share later.LAUNCHTell students they will be creating a scale drawing of the classroom. Their rst job is to think about what parts of the classroom to measure for the drawing. Give students quiet think time to make a list, followed by whole-class discussion. Ask students to be specic about the measurements they would include on the list.WARM-UP TASK Which measurements would you need in order to draw a scale oor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specic as possible.STUDENT RESPONSEAnswers vary. Sample responses:• The lengths of walls• The size and location of windows and doors• The size and location of xed and movable furniture• The measurements of dierent oor materials in the classroomDISCUSSION GUIDANCEInvite students to share their responses with the class, especially those who included measurements between objects in their lists. Record and display students’ responses for all © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.166

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:to see and to serve as a reference during the main activity. Consider organizing students’ responses by type rather than by items (e.g., listing “furniture” instead of “chairs,” “desks,” etc.). Some guiding questions:• Which parts of the classroom must be included in a scale oor plan? Which parts are less important?• What measurements do we need?• Besides lengths of walls and objects, what else would be helpful? (If no one mentioned the positions of objects, ask how we know where to place certain objects on the drawing.)• Should we include vertical measurements? Why or why not?SUPPORT FOR STUDENTS WITH DISABILITIESStrengths-based Approach:This activity leverages many natural strengths of students with ADHD, LD, and other concrete learners in terms of its integration of real-world context and personal student interest. This may be an opportunity for the teacher to highlight this strength in class and allow an individual with disability to lead peer interactions/discussions, increasing buy-in.Executive Functioning: Visual AidsCreate an anchor chart (i.e., classroom measurements) publicly displaying important denitions, rules, formulas, or concepts for future reference.Concept Exploration: Activity 1CREATING A FLOOR PLAN (PART 1)Instructional Routines: MLR8: Discussion Supports, Think Pair ShareThe purpose of this activity is for students to make preparations to create their scale drawings. They sketch a rough oor plan of the classroom. In groups, they plan the steps for making measurements and then carry out their plan.Some things to notice as students work:• As they draw their sketches, encourage them to focus on big-picture elements and not on details. It is not important that the sketch is neat or elaborate. What matters more is that it does not omit important features like the door.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 167

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:• As they make plans for measuring and recording, encourage them to work systematically to minimize omissions and errors.• Urge students to measure twice and record once. It is better to take a little more time to double check the measurements than to nd out during drawing that they are o.LAUNCHGive students time to read the task statement individually and to ask any clarifying questions. Consider displaying a oor plan sketch of another room in the school. Emphasize that the sketch serves a similar purpose as an outline in writing. It does not need to be to scale, accurate, or elaborate, but it should show all the important pieces in the right places so it can be a reference in creating the scale drawing.Arrange students in groups of 2–4. Smaller groups means that each individual student can be more involved in the measuring process, which is a benet, but consider that it might also make the measuring process more time consuming (as it would mean more groups moving about in a conned space). Distribute blank paper and give students time to draw a sketch and to share it with a partner. Provide access to measuring tools. Give students time to plan in groups, and then time to measure (which may vary depending on size of classroom and other factors).ACTIVITY 1 TASK 1 On a blank sheet of paper, make a rough sketch of a oor plan of the classroom.1. Include parts of the room that the class has decided to include or that you would like to include. Accuracy is not important for this rough sketch, but be careful not to omit important features like a door.2. Trade sketches with a partner and check each other’s work. Specically, check if any parts are missing or incorrectly placed. Return their work and revise your sketch as needed.3. Discuss with your group a plan for measuring. Work to reach an agreement on:a) Which classroom features must be measured and which are optional.b) The units to be used.1© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.168

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:c) How to record and organize the measurements (on the sketch, in a list, in a table, etc.).d) How to share the measuring and recording work (or the role each group member will play).3. Gather your tools, take your measurements, and record them as planned. Be sure to double-check your measurements.4. Make your own copy of all the measurements that your group has gathered, if you haven’t already done so. You will need them for the next activity.STUDENT RESPONSEAnswers vary.DISCUSSION GUIDANCEAer groups nish measuring, ask them to make sure that every group member has a copy of the measurements before moving on to the next part.Consider briey discussing what was challenging about doing the measuring. A few important issues which may come up include:• Making sure that the measuring device stays in a straight line.• It is hard to be accurate when the measuring device needs to be used multiple times in order to nd the length of something long, such as a wall.• Taking turns with other groups that are trying to measure the same thing.• The measurements are not exact and need to be rounded.SUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Eliminate BarriersProvide a task checklist that makes all the required components of the activity explicit.Fine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allowing students who struggle with ne motor skills to dictate drawing or sketching as needed.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 169

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR ENGLISH LANGUAGE LEARNERSSpeaking: MLR 8 Discussion SupportsAs students describe their process for measuring features of the room, press for details in students’ explanations by requesting that students challenge an idea, elaborate on an idea, or give an example of their measuring process. Provide a sentence frame such as: “It was challenging to measure because .” This will help students to produce and make sense of the language needed to communicate their own ideas.Design Principle(s): Support sense-making; Optimize output (for explanation)Concept Exploration: Activity 2CREATING A FLOOR PLAN (PART 2)Instructional Routine: MLR2: Collect and DisplayIn this activity, students use the measurements they just gathered to create their scale oor plans. Each student selects one of the paper options, decides on a scale to use, and works individually to create their drawings.Support students as they reason about scale, scaled lengths, and how to go about creating the drawing. Encourage all to pay attention to units as they calculate scaled lengths. Ask students to think about the dierent ways that we can write a scale. If they struggle, remind students that a scale can be written in dierent units or written without units.LAUNCHDistribute at least three dierent types of paper for each group, which could include:• 812 × 11 printer paper• 11 × 17 printer paper• Centimeter graph paper• 14-inch graph paper• 15-inch graph paperAsk each group member to select a paper for their drawing. Encourage variation in paper selections. Explain that they should choose an appropriate scale based on the size of their © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.170

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:paper, the size of the classroom, and their chosen units of measurement. This means that the oor plan must t on the paper and not end up too small (e.g., if the paper is 11 × 17 inches, the oor plan should not be the size of a postcard).Give students quiet time to create their oor plan. If the classroom layout is fairly complex, consider asking students to pause aer they have completed a certain portion of the drawing (e.g., the main walls of the classroom) so their work may be checked. Alternatively, give them a minute to share their drawing-in-progress with a partner and discuss any issues.ACTIVITY 2 TASK 1 Determine an appropriate scale for your drawing based on your measurements and your paper choice. Your oor plan should t on the paper and not end up too small.1. Use the scale and the measurements your group has taken to draw a scale oor plan of the classroom. Make sure to:a) Show the scale of your drawing.b) Label the key parts of your drawing (the walls, main openings, etc.) with their actual measurements.c) Show your thinking and organize it so it can be followed by others.STUDENT RESPONSEAnswers vary.DISCUSSION GUIDANCESmall-group and whole-class reections will occur in the next activityANTICIPATED MISCONCEPTIONSSome students may pick a scale and start drawing without considering how large their completed oor plan will be. Encourage students to consider the size of their paper in order to determine an appropriate scale before they start drawing.2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 171

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:SUPPORT FOR STUDENTS WITH DISABILITIESExecutive Functioning: Eliminate BarriersChunk this task into more manageable parts (e.g., one section of the room at a time), which will aid students who benet from support with organizational skills in problem solving.Fine Motor Skills: Peer TutorsPair students with their previously identied peer tutors and allow students who struggle with ne motor skills to dictate drawing or sketching as needed.SUPPORT FOR ENGLISH LANGUAGE LEARNERSConversing, Representing: MLR 2 Collect and DisplayAs students work, circulate and listen to students talk, and jot notes about common or important phrases (e.g., scale, size, units, etc.), together with helpful sketches or diagrams. Pay particular attention to how students are determining scales for their oor plans. Scribe students’ words and sketches on a visual display to refer back to during whole-class discussions throughout this lesson and the rest of the mission. This will help students use mathematical language during their group and whole-class discussions.Design Principle(s): Support sense-making; Optimize output (for explanation)Concept Exploration: Activity 3CREATING A FLOOR PLAN (PART 3)Instructional Routines: MLR1: Stronger and Clearer Each Time, Group PresentationsIn the nal phase of the drawing project, students reect on and revise their work. Students who chose the same paper option confer in small groups to analyze and compare their oor plans. They discuss their decisions, evaluate the accuracy of their drawings, and then revise them as needed.Aer revision, students debrief as a class and discuss how the choice of scale, units, and paper aected the drawing process and the oor plans they created.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.172

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:LAUNCHArrange students who use the same type and size of paper into small groups. Give them time to share and explain their drawings. Display and read aloud questions such as the following. Ask students to use them to guide their discussion.• What scale did you use? How did you decide on the scale?• Do the scaled measurements in each drawing seem accurate? Do they represent actual measurements correctly?• Did the scale seem appropriate for the chosen paper? Why or why not?• What was the rst thing you drew in your drawing? Why?• How did you decide on the objects to show in your drawing?• What aspects of your drawings are dierent?• How could each oor plan be revised to better represent the classroom?ACTIVITY 3 TASK 1 Compare oor plans with other students, then record ideas for how your oor plan could be improved.1. Trade oor plans with another student who used the same paper size as you. Discuss your observations and thinking.2. Trade oor plans with another student who used a dierent paper size than you. Discuss your observations and thinking.3. Based on your discussions, name some ways your oor plan could be improved.STUDENT RESPONSEAnswers vary.33© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license. 173

G7M1 | LESSON 13OPTIONAL LESSONZEARN MATH TEACHERLESSON MATERIALSYOUR NOTES:LESSON SYNTHESIS Before debrieng as a class, give students quiet time to reect. Ask them to write down ideas for revising their oor plan and strategies for creating accurate scale drawings based on their conversation.Though much of the discussion will take place within the groups, debrief as a class so students can see oor plans created at a variety of scales and on dierent paper types or sizes. Display a range of scale drawings for all to see and discuss the following questions. (Alternatively, consider posting all students’ work for a gallery walk and ask students to reect on these questions.)• What are the dierences in these drawings?• How did dierent scales impact the nal drawing?• How did the size of paper impact the choice of scale?• What choices were really important when creating the scale drawing?• Would these choices be the same if you were doing a dierent room in the school? Or some other building?SUPPORT FOR STUDENTS WITH DISABILITIESReceptive/Expressive Language: Processing TimeStudents who benet from extra processing time would also be aided by MLR 1 (Stronger and Clearer Each Time).© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.174

TEACHER EDITIONMission 1Math1 2 3 4 75 86 9GRADE7GRADE 7Mission 1 Scale DrawingsMission 2 Introducing Proportional RelationshipsMission 3 Measuring CirclesMission 4 Proportional Relationships and PercentagesMission 5 Rational Number ArithmeticMission 6 Expressions, Equations, and InequalitiesMission 7 Angles, Triangles, and PrismsMission 8 Probability and SamplingMission 9 Putting It All TogetherTEACHER EDITIONMathGRADE 7TEACHER EDITIONGrade 7 | Mission 1