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STUDENT EDITION Grade 6 VOLUME 1 Mission 1 Area And Surface Area Mission 2 Introducing Ratios Mission 3 Unit Rates And Percentages NAME

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Table of Contents Mission 1 LESSON 1 Tiling the Plane 3 LESSON 2 Finding Area by Decomposing and Rearranging 9 LESSON 3 Reasoning to Find Area 15 LESSON 4 Parallelograms 21 LESSON 5 Bases and Heights of Parallelograms 27 LESSON 6 Area of Parallelograms 33 LESSON 7 From Parallelograms to Triangles 39 LESSON 8 Area of Triangles 45 LESSON 9 Formula for the Area of a Triangle 51 LESSON 10 Bases and Heights of Triangles 59 LESSON 11 Polygons 65 LESSON 12 What Is Surface Area 73 LESSON 13 Polyhedra 79 LESSON 14 Nets and Surface Area 85 LESSON 15 More Nets More Surface Area 91 LESSON 16 Distinguishing Between Surface Area and Volume 97 LESSON 17 Squares and Cubes 103 LESSON 18 Surface Area of a Cube 109 LESSON 19 Designing a Tent 115 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

Mission 2 iv LESSON 1 Introducing Ratios and Ratio Language 121 LESSON 2 Representing Ratios with Diagrams 127 LESSON 3 Recipes 133 LESSON 4 Color Mixtures 139 LESSON 5 Defining Equivalent Ratios 145 LESSON 6 Introducing Double Number Line Diagrams 151 LESSON 7 Creating Double Number Line Diagrams 157 LESSON 8 How Much for One 163 LESSON 9 Constant Speed 169 LESSON 10 Comparing Situations by Examining Ratios 175 LESSON 11 Representing Ratios with Tables 181 LESSON 12 Navigating a Table of Equivalent Ratios 187 LESSON 13 Tables and Double Number Line Diagrams 193 LESSON 14 Solving Equivalent Ratio Problems 199 LESSON 15 Part Part Whole Ratios 203 LESSON 16 Solving More Ratio Problems 209 LESSON 17 A Fermi Problem 215 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 3 LESSON 1 Using Unit Rate to Solve Problems 221 LESSON 2 Anchoring Units of Measurement 227 LESSON 3 Measuring with Different Sized Units 231 LESSON 4 Converting Units 237 LESSON 5 Comparing Speeds and Prices 243 LESSON 6 Interpreting Rates 249 LESSON 7 Equivalent Ratios Have the Same Unit Rates 255 LESSON 8 More about Constant Speed 261 LESSON 9 Solving Rate Problems 267 LESSON 10 What Are Percentages 273 LESSON 11 Percentages and Double Number Lines 279 LESSON 12 Percentages and Tape Diagrams 285 LESSON 13 Benchmark Percentages 291 LESSON 14 Solving Percentage Problems 297 LESSON 15 Finding This Percent of That 301 LESSON 16 Finding the Percentage 307 LESSON 17 Painting a Room 313 TERMINOLOGY 317 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 v

vi 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

Grade 6 Mission 1 Area And Surface Area

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ZEARN MATH STUDENT EDITION G6M1 LESSON 1 Lesson 1 Tiling the Plane Let s look at tiling patterns and think about area Warm Up 1 Your teacher will show you 4 patterns Which pattern doesn t belong 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

G6M1 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Your teacher will assign you to look at Pattern A or Pattern B In your pattern which shape covers more of the plane gray rhombuses black trapezoids or white triangles Explain how you know Pattern A Pattern B 4 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 1 Lesson Summary In this lesson we learned about tiling the plane which means covering a two dimensional region with copies of the same shape or shapes such that there are no gaps or overlaps Then we compared tiling patterns and the shapes in them In thinking about which patterns and shapes cover more of the plane we have started to reason about area We will continue this work and to learn how to use mathematical tools strategically to help us do mathematics TERMINOLOGY Area Region 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

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ZEARN MATH STUDENT EDITION Name G6M1 LESSON 1 Date GRADE 6 MISSION 1 LESSON 1 Exit Ticket Think about your work today and write your best definition of area 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 2 Lesson 2 Finding Area by Decomposing and Rearranging Let s create shapes and find their areas Warm Up 1 You may recall that the term area tells us something about the number of squares inside a two dimensional shape Which drawings show squares that could be used to find the area of the shape A B C D 1 Select all drawings whose squares could be used to find the area of the shape Be prepared to explain your reasoning 2 Write a definition of area that includes all the information that you think is important 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

G6M1 LESSON 2 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 10 Use the shapes in front of you to make new shapes 1 Notice that you can put together two small triangles to make a square What is the area of the square composed of two small triangles Be prepared to explain your reasoning 2 Use your shapes to create a new shape with an area of 1 square unit that is not a square Trace your shape 3 Use your shapes to create a new shape with an area of 2 square units Trace your shape 4 Use your shapes to create a different shape with an area of 2 square units Trace your shape 5 Use your shapes to create a new shape with an area of 4 square units Trace your shape 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 2 Lesson Summary Here are two important principles for finding area If two figures can be placed one on top of the other so that they match up exactly then they have the same area We can decompose a figure break a figure into pieces and rearrange the pieces move the pieces around to find its area Here are illustrations of the two principles Each square on the left can be decomposed into 2 triangles These triangles can be rearranged into a large triangle So the large triangle has the same area as the 2 squares Similarly the large triangle on the right can be decomposed into 4 equal triangles The triangles can be rearranged to form 2 squares If each square has an area of 1 square unit then the area of the large triangle is 2 square units We also can say that each small triangle has an area of 12 square unit TERMINOLOGY Area Compose Decompose 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

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ZEARN MATH STUDENT EDITION Name G6M1 LESSON 2 Date GRADE 6 MISSION 1 LESSON 2 Exit Ticket The square in the middle has an area of 1 square unit What is the area of the entire rectangle in square units Explain your 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 13

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ZEARN MATH STUDENT EDITION G6M1 LESSON 3 Lesson 3 Reasoning to Find Area Let s decompose and rearrange shapes to find their areas Warm Up 1 Is the area of Figure A greater than less than or equal to the area of the shaded region in Figure B Be prepared to explain your reasoning A B Concept Exploration ACTIVITY 1 2 Each grid square is 1 square unit Find the area in square units of each shaded region without counting every square Be prepared to explain your reasoning A B C 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 15

G6M1 LESSON 3 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Find the area of the shaded region s of each figure Explain or show your reasoning A B 3 cm 4 cm 5 cm 5 cm 2 cm C 2 cm 3 cm 5 cm 2 cm 5 cm 2 cm 4 cm 2 cm 4 cm 16 4 cm 2 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 3 Lesson Summary There are different strategies we can use to find the area of a region We can Decompose it into shapes whose areas you know how to calculate find the area of each of those shapes and then add the areas Decompose it and rearrange the pieces into shapes whose areas you know how to calculate find the area of each of those shapes and then add the areas Consider it as a shape with a missing piece calculate the area of the shape and the missing piece and then subtract the area of the piece from the area of the shape The area of a figure is always measured in square units When both side lengths of a rectangle are given in centimeters then the area is given in square centimeters 8 cm 4 cm The area of this rectangle is 32 square centimeters 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

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ZEARN MATH STUDENT EDITION Name G6M1 LESSON 3 Date GRADE 6 MISSION 1 LESSON 3 Exit Ticket A maritime flag is shown What is the area of the shaded part of the flag Explain or show your reasoning 8 in 6 in 6 in 4 in 4 in 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 4 Lesson 4 Parallelograms Let s investigate the features and area of parallelograms Warm Up 1 Figures A B and C are parallelograms Figures D E and F are not parallelograms A D B E C F Study the examples and non examples What do you notice about 1 the number of sides that a parallelogram has 2 opposite sides of a parallelogram 3 opposite angles of a parallelogram 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

G6M1 LESSON 4 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Find the area of each parallelogram Show your reasoning a b ACTIVITY 2 3 a Find the area of the following parallelograms Show your reasoning b c 4 cm 4 5 cm 6 cm 22 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 4 Lesson Summary A parallelogram is a quadrilateral it has four sides The opposite sides of a parallelogram are parallel It is also true that The opposite sides of a parallelogram have equal length 5 4 24 45 45 135 27 2 4 24 135 4 9 34 152 8 152 8 5 9 34 4 27 2 The opposite angles of a parallelogram have equal measure There are several strategies for finding the area of a parallelogram We can decompose and rearrange a parallelogram to form a rectangle Here are three ways We can enclose the parallelogram and then subtract the area of the two triangles in the corner Both of these ways will work for any parallelogram For some parallelograms however the process of decomposing and rearranging requires a lot more steps than if we enclose the parallelogram with a rectangle and subtract the combined area of the two triangles in the corners Here is an example TERMINOLOGY Parallelogram 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

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ZEARN MATH STUDENT EDITION Name G6M1 LESSON 4 Date GRADE 6 MISSION 1 LESSON 4 Exit Ticket How would you find the area of this parallelogram Describe your strategy 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 5 Lesson 5 Bases and Heights of Parallelograms Let s investigate the area of parallelograms some more Warm Up 1 Use the diagrams below to answer the questions Elena found the area of a parallelogram like this Tyler found the area of the same parallelogram like this How are the two strategies for finding the area of a parallelogram the same How are they different 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

G6M1 LESSON 5 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Each parallelogram has a side that is labeled base Study the examples and nonexamples of bases and heights of parallelograms Then answer the questions Examples The dashed segment in each drawing represents the corresponding height for the given base Non examples The dashed segment in each drawing does not represent the corresponding height for the given base Base Base Base Base Base Base Base Base Select all statements that are true about bases and heights in a parallelogram a Only a horizontal side of a parallelogram can be a base b Any side of a parallelogram can be a base c A height can be drawn at any angle to the side chosen as the base d A base and its corresponding height must be perpendicular to each other e A height can only be drawn inside a parallelogram f A height can be drawn outside of the parallelogram as long as it is drawn at a 90 degree angle to the base g A base cannot be extended to meet a height 28 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

ZEARN MATH STUDENT EDITION 3 G6M1 LESSON 5 Five students labeled a base b and a corresponding height h for each of these parallelograms Are all drawings correctly labeled Explain how you know b A C B h h h b D b E b h h b ACTIVITY 2 43 Find the base height and area of these parallelograms For each parallelogram Identify a base and a corresponding height and record their lengths in the table that follows Find the area and record it in the right most column In the last row write an expression using b and h for the area of any parallelogram A Parallelogram B C D Base units Height units b h Area sq units A B C D Any parallelogram 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

G6M1 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary We can choose any of the four sides of a parallelogram as the base Both the side the segment and its length the measurement are called the base If we draw any perpendicular segment from a point on the base to the opposite side of the parallelogram that segment will always have the same length We call that value the height There are infinitely many line segments that can represent the height 4 4 4 6 4 8 Here are two copies of the same parallelogram On the top right the side that is the base is 6 units long Its corresponding height is 4 units In the next copy the side that is the base is 5 units long Its height is 4 8 units For both three different segments are shown to represent the height We could draw in many more 4 8 5 4 8 No matter which side is chosen as the base the area of the parallelogram is the product of that base and its corresponding height We can check it 4 6 24 and 4 8 5 24 We can see why this is true by decomposing and rearranging the parallelograms into rectangles Notice that the side lengths of each rectangle are the base and height of the parallelogram Even though the two rectangles have different side lengths the products of the side lengths are equal so they have the same area And both rectangles have the same area as the parallelogram 4 4 6 4 8 We often use letters to stand for numbers If b is the base of a parallelogram in units and h is the corresponding height in units then the area of the parallelogram in square units is the product of these two numbers 4 8 5 b h Notice that we write the multiplication symbol with a small dot instead of a symbol This is so that we don t get confused about whether means multiply or whether the letter x is standing in for a number In high school you will be able to prove that a perpendicular segment from a point on one side of a parallelogram to the opposite side will always have the same length h h h h h You can see this most easily when you draw a parallelogram on graph paper For now we will just use this as a fact TERMINOLOGY Base of a parallelogram or triangle Height of a parallelogram or triangle 30 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 5 Name Date GRADE 6 MISSION 1 LESSON 5 Exit Ticket Parallelograms S and T are each labeled with a base and a corresponding height S T h b 1 2 h b What are the values of b and h for each parallelogram Parallelogram S b h Parallelogram T b h Use the values of b and h to find the area of each parallelogram Area of Parallelogram S Area of Parallelogram T 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 6 Lesson 6 Area of Parallelograms Let s practice finding the area of parallelograms Warm Up 1 How many dots are in the image How do you see them 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

G6M1 LESSON 6 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Find the area of each parallelogram Show your reasoning 2 a b 6 cm 8 cm 10 cm 15 cm 10 cm c d 1 cm 1 cm 9 cm 7 cm 8 cm 34 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

ZEARN MATH STUDENT EDITION 3 43 G6M1 LESSON 6 In Parallelogram B what is the corresponding height for the base that is 10 cm long Explain or show your reasoning Two different parallelograms P and Q both have an area of 20 square units Neither of the parallelograms are rectangles On the grid draw two parallelograms that could be P and Q 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

G6M1 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary Any pair of base and corresponding height can help us find the area of a parallelogram but some baseheight pairs are more easily identified than others When a parallelogram is drawn on a grid and has horizontal sides we can use a horizontal side as the base When it has vertical sides we can use a vertical side as the base The grid can help us find or estimate the lengths of the base and of the corresponding height b h b h When a parallelogram is not drawn on a grid we can still find its area if a base and a corresponding height are known In this parallelogram the corresponding height for the side that is 10 units long is not given but the height for the side that is 8 units long is given This base height pair can help us find the area 8 10 8 Regardless of their shape parallelograms that have the same base and the same height will have the same area the product of the base and height will be equal Here are some parallelograms with the same pair of base height measurements 4 4 4 4 3 3 36 3 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 6 Date GRADE 6 MISSION 1 LESSON 6 Exit Ticket 1 Find the area of the parallelogram Explain or show your reasoning 6 cm 9 cm 7 5 cm 2 Was there a length measurement you did not use to find the area If so explain why it was not used 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 7 Lesson 7 From Parallelograms to Triangles Let s compare parallelograms and triangles Warm Up 1 Here are two copies of a parallelogram Each copy has one side labeled as the base b and a segment drawn for its corresponding height and labeled h h b b h 1 The base of the parallelogram on the left is 2 4 meters its corresponding height is 1 meter Find its area in square meters 2 The height of the parallelogram on the right is 2 meters How long is the base of that parallelogram Explain your 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 39

G6M1 LESSON 7 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 40 Two polygons are identical if they match up exactly when placed one on top of the other 1 Draw one line to decompose each of the following polygons into two identical triangles if possible Use a straightedge to draw your line 2 Which quadrilaterals can be decomposed into two identical triangles 3 Study the quadrilaterals that can in fact be decomposed into two identical triangles What do you notice about them Write a couple of observations about what these quadrilaterals have in common 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 7 ACTIVITY 2 3 Your teacher will give your group several pairs of triangles Each group member should take 1 2 pairs 1 a Which pair s of triangles do you have b Can each pair be composed into a rectangle A parallelogram 2 Discuss with your group your responses to the first question Then complete each of the following statements with all some or none Sketch 1 2 examples to illustrate each completed statement a of these pairs of identical triangles can be composed into a rectangle b of these pairs of identical triangles can be composed into a parallelogram 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

G6M1 LESSON 7 ZEARN MATH STUDENT EDITION Lesson Summary A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices identical triangles identical triangles identical triangles Going the other way around two identical copies of a triangle can always be arranged to form a parallelogram regardless of the type of triangle being used To produce a parallelogram we can join a triangle and its copy along any of the three sides so the same pair of triangles can make different parallelograms Here are examples of how two copies of both Triangle A and Triangle F can be composed into three different parallelograms This special relationship between triangles and parallelograms can help us reason about the area of any triangle 42 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 7 Date GRADE 6 MISSION 1 LESSON 7 Exit Ticket 1 Here are some quadrilaterals a Circle all quadrilaterals that you think can be decomposed into two identical triangles using only one line b What characteristics do the quadrilaterals that you circled have in common 2 Here is a right triangle Show or briefly describe how two copies of it can be composed into a parallelogram 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 8 Lesson 8 Area of Triangles Let s use what we know about parallelograms to find the area of triangles Warm Up 1 Answer the following questions about these figures Here is Triangle M M Han made a copy of Triangle M and composed three different parallelograms using the original M and the copy as shown here M M M 1 For each parallelogram Han composed identify a base and a corresponding height and write the measurements on the drawing 2 Find the area of each parallelogram Han composed Show your 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 45

G6M1 LESSON 8 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Find the areas of at least two of the triangles below Show your reasoning A B C D Lesson Summary We can reason about the area of a triangle by using what we know about parallelograms Here are three general ways to do this 46 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 8 Make a copy of the triangle and join the original and the copy along an edge to create a parallelogram Because the two triangles have the same area one copy of the triangle has half the area of that parallelogram A B 2 units 8 units C D 6 units 4 units The area of Parallelogram B is 16 square units because the base is 8 units and the height 2 units The area of Triangle A is half of that which is 8 square units The area of Parallelogram D is 24 square units because the base is 4 units and the height 6 units The area of Triangle C is half of that which is 12 square units Decompose the triangle into smaller pieces and compose them into a parallelogram In the new parallelogram b 6 h 2 and 6 2 12 so its area is 12 square units Because the original triangle and the parallelogram are composed of the same parts the area of the original triangle is also 12 square units Draw a rectangle around the triangle Sometimes the triangle has half of the area of the rectangle The large rectangle can be decomposed into smaller rectangles The one on the left has area 4 3 or 12 square units the one on the right has area 2 3 or 6 square units The large triangle is also decomposed into two right triangles Each of the right triangles is half of a smaller rectangle so their areas are 6 square units and 3 square units The large triangle has area 9 square 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 47

G6M1 LESSON 8 ZEARN MATH STUDENT EDITION Sometimes the triangle is half of what is left of the rectangle after removing two copies of the smaller right triangles The right triangles being removed can be composed into a small rectangle with area 2 3 square units What is left is a parallelogram with area 5 3 2 3 which equals 15 6 or 9 square units Notice that we can compose the same parallelogram with two copies of the original triangle The original triangle is half of the parallelogram so its area is 12 9 or 4 5 square units 48 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 8 Name Date GRADE 6 MISSION 1 LESSON 8 Exit Ticket Elena Lin and Noah all found the area of Triangle Q to be 14 square units but reasoned about it differently as shown in the diagrams Explain at least one student s way of thinking and why his or her answer is correct Q Q Elena Lin Q Noah 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 9 Lesson 9 Formula for the Area of a Triangle Let s write and use a formula to find the area of a triangle Warm Up 1 Study the examples and non examples of bases and heights in a triangle Then answer the questions These dashed segments represent heights of the triangle base base base These dashed segments do not represent heights of the triangle base base base Select all the statements that are true about bases and heights in a triangle a Any side of a triangle can be a base b There is only one possible height c A height is always one of the sides of a triangle d A height that corresponds to a base must be drawn at an acute angle to the base e A height that corresponds to a base must be drawn at a right angle to the base f Once we choose a base there is only one segment that represents the corresponding height g A segment representing a height must go through a vertex 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

G6M1 LESSON 9 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Use the triangles to complete the table For each triangle label a side that can be used as the base and a segment showing its corresponding height Record the measurements for the base and height in the table and find the area of the triangle The side length of each square on the grid is 1 unit In the last row write an expression for the area of any triangle using b and h A B D C Triangle Base units Height units b h Area square units A B C D Any triangle 52 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 9 ACTIVITY 2 3 For each triangle circle a base measurement that you can use to find the area of the triangle Then find the area of any three triangles Show your reasoning A C B 3 cm 4 cm 7 cm 4 cm 6 cm 5 cm 3 5 cm E D 10 cm 8 73 cm 5 cm 3 5 cm 8 cm 6 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 53

G6M1 LESSON 9 ZEARN MATH STUDENT EDITION Lesson Summary We can choose any of the three sides of a triangle to call the base The term base refers to both the side and its length the measurement The corresponding height is the length of a perpendicular segment from the base to the vertex opposite of it The opposite vertex is the vertex that is not an endpoint of the base Here are three pairs of bases and heights for the same triangle The dashed segments in the diagrams represent heights base base base A segment showing a height must be drawn at a right angle to the base but it can be drawn in more than one place It does not have to go through the opposite vertex as long as it connects the base and a line that is parallel to the base and goes through the opposite vertex as shown here base The base height pairs in a triangle are closely related to those in a parallelogram Recall that two copies of a triangle can be composed into one or more parallelograms Each parallelogram shares at least one base with the triangle base base For any base that they share the corresponding height is also shared as shown by the dashed segments We can use the base height measurements and our knowledge of parallelograms to find the area of any triangle 54 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 9 The formula for the area of a parallelogram with base b and height h is b h A triangle takes up half of the area of a parallelogram with the same base and height We can therefore express the area A of a triangle as A A 1 2 b h b 12 h 3 h 4 h 6 b 3 b 5 c B 1 2 5 6 15 The area of Triangle B is 4 5 square units because 12 3 3 4 5 The area of Triangle C is 24 square units because 12 12 4 24 The area of Triangle A is 15 square units because In each case one side of the triangle is the base but neither of the other sides is the height This is because the angle between them is not a right angle In right triangles however the two sides that are perpendicular can be a base and a height The area of this triangle is 18 square units whether we use 4 units or 9 units for the base b 4 h 9 TERMINOLOGY Opposite Vertex 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 9 Name Date GRADE 6 MISSION 1 LESSON 9 Exit Ticket For each triangle identify a base and a corresponding height Use them to find the area Show your reasoning B A 5 cm 5 cm 7 2 in 4 cm 4 8 cm 6 in 2 5 in 6 cm 3 in 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 10 Lesson 10 Bases and Heights of Triangles Let s use different base height pairs to find the area of a triangle Warm Up 1 On the grid draw a triangle with an area of 12 square units Try to draw a non right triangle Be prepared to explain how you know the area of your triangle is 12 square units Concept Exploration ACTIVITY 1 2 Here are three copies of the same triangle The triangle is rotated so that the side chosen as the base is at the bottom and is horizontal Draw a height that corresponds to each base Use an index card to help you Side a as the base Side b as the base Side c as the base b c a c a b a b c Pause for your teacher s instructions before moving to the next question 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

G6M1 LESSON 10 3 ZEARN MATH STUDENT EDITION Draw a line segment to show the height for the chosen base in each triangle A B base base C D base base E F base base 60 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 10 Lesson Summary A height of a triangle is a perpendicular segment between the side chosen as the base and the opposite vertex We can use tools with right angles to help us draw height segments An index card or any stiff paper with a right angle is a handy tool for drawing a line that is perpendicular to another line 1 Choose a side of a triangle as the base Identify its opposite vertex 2 Line up one edge of the index card with that base 3 Slide the card along the base until a perpendicular edge of the card meets the opposite vertex 4 Use the card edge to draw a line from the vertex to the base That segment represents the height opposite vertex opposite vertex base base opposite vertex base opposite vertex base Sometimes we may need to extend the line of the base to identify the height such as when finding the height of an obtuse triangle or whenever the opposite vertex is not directly over the base In these cases the height segment is typically drawn outside of the triangle opposite vertex opposite vertex base base opposite vertex opposite vertex base base Even though any side of a triangle can be a base some base height pairs can be more easily determined than others so it helps to choose strategically For example when dealing with a right triangle it often makes sense to use the two sides that make the right angle as the base and the height because one side is already perpendicular to the other 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

G6M1 LESSON 10 ZEARN MATH STUDENT EDITION If a triangle is on a grid and has a horizontal or a vertical side you can use that side as a base and use the grid to find the height as in these examples b h h b 62 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 10 Name Date GRADE 6 MISSION 1 LESSON 10 Exit Ticket 1 For each triangle below draw a height segment that corresponds to the given base and label it h Use an index card if needed A B base 2 base Which triangle has the greatest area The least area Explain your reasoning A B C 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 63

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ZEARN MATH STUDENT EDITION G6M1 LESSON 11 Lesson 11 Polygons Let s investigate polygons and their areas Warm Up 1 Which one doesn t belong S T U V 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

G6M1 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Here are five polygons Here are five figures that are not polygons 2 66 Circle the figures that are polygons Use the examples to help A B C F G H D E I J 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

ZEARN MATH STUDENT EDITION 3 G6M1 LESSON 11 What do the figures you circled have in common What characteristics helped you decide whether a figure was a polygon ACTIVITY 2 43 Find the area of two quadrilaterals of your choice Show your reasoning A B D E C F 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

G6M1 LESSON 11 ZEARN MATH STUDENT EDITION ACTIVITY 3 53 1 In each of the diagrams below find the area of the shaded region Explain or show your reasoning Note Each grid square is 1 square unit 2 13 cm 9 cm 5 cm 20 cm 68 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 11 3 16 cm 11 cm 10 cm 4 cm ACTIVITY 3 63 Jessalyn designed a new school flag shown below that she ll make with two different fabric colors purple and orange How much of each color of fabric will she need to construct her flag 2 ft 3 ft 3 4 ft 5 ft 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

G6M1 LESSON 11 ZEARN MATH STUDENT EDITION Lesson Summary A polygon is a two dimensional figure composed of straight line segments Each end of a line segment connects to one other line segment The point where two segments connect is a vertex The plural of vertex is vertices The segments are called the edges or sides of the polygon The sides never cross each other There are always an equal number of vertices and sides Here is a polygon with 5 sides The vertices are labeled A B C D and E B A polygon encloses a region To find the area of a polygon is to find the area of the region inside it We can find the area of a polygon by decomposing the region inside it into triangles and rectangles A C E D The first two diagrams show the polygon decomposed into triangles and rectangles the sum of their areas is the area of the polygon The last diagram shows the polygon enclosed with a rectangle subtracting the areas of the triangles from the area of the rectangle gives us the area of the polygon TERMINOLOGY Edge Polygon Quadrilateral Vertex vertices 70 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 11 Date GRADE 6 MISSION 1 LESSON 11 Exit Ticket 1 Here are two five pointed stars A student said Both figures A and B are polygons They are both composed of line segments and are two dimensional Neither have curves Do you agree with the statement Explain your reasoning A 2 B Here is a five sided polygon Describe or show the strategy you would use to find its area Mark up and label the diagram to show your reasoning so that it can be followed by others It is not necessary to actually calculate the area 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 12 Lesson 12 What Is Surface Area Let s cover the surfaces of some three dimensional objects Warm Up 1 Estimate an answer How many sticky notes would it take to cover the box excluding the bottom 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

G6M1 LESSON 12 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Earlier you learned about a box being covered with sticky notes Answer the questions below about the box 1 How could you find the actual number of sticky notes it will take to cover the box excluding the bottom What information would you need to know 2 Use the information you have to find the number of sticky notes to cover the box Show your reasoning ACTIVITY 2 3 74 Here is a sketch of a rectangular prism built from 12 cubes It has six faces but you can only see three of them in the sketch It has a surface area of 32 square units You have 12 snap cubes from your teacher Use all of your snap cubes to build a different rectangular prism with different edge lengths than shown in the prism here 1 How many faces does your figure have 2 What is the surface area of your figure in square 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

ZEARN MATH STUDENT EDITION 3 G6M1 LESSON 12 Draw your figure on isometric dot paper Color each face a different color 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

G6M1 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary The surface area of a figure in square units is the number of unit squares it takes to cover the entire surface without gaps or overlaps If a three dimensional figure has flat sides the sides are called faces The surface area is the total of the areas of the faces For example a rectangular prism has six faces The surface area of the prism is the total of the areas of the six rectangular faces So the surface area of a rectangular prism that has edge lengths 2 cm 3 cm and 4 cm has a surface area of 2 3 2 3 2 4 2 4 3 4 3 4 or 52 square centimeters TERMINOLOGY Face Surface area 76 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 12 Date GRADE 6 MISSION 1 LESSON 12 Exit Ticket A rectangular prism is 3 units high 2 units wide and 5 units long What is its surface area in square units Explain or show your 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 77

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ZEARN MATH STUDENT EDITION G6M1 LESSON 13 Lesson 13 Polyhedra Let s investigate polyhedra Warm Up 1 Study the examples and non examples of polyhedra Use them to answer the questions below Here are pictures that represent polyhedra Here are pictures that do not represent polyhedra 1 Your teacher will give you some figures or objects Sort them into polyhedra and non polyhedra 2 What features helped you distinguish the polyhedra from the other figures 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

G6M1 LESSON 13 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Use the images of prisms and pyramids to answer the questions below Here are some polyhedra called prisms Here are some polyhedra called pyramids a Look at the prisms What are their characteristics or features b Look at the pyramids What are their characteristics or features 2 80 Which of the following nets can be folded into Pyramid P Select all that apply 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

ZEARN MATH STUDENT EDITION 3 G6M1 LESSON 13 Your teacher will give your group a set of polygons and assign a polyhedron a Decide which polygons are needed to compose your assigned polyhedron List the polygons and how many of each are needed b Arrange the cut outs into a net that if taped and folded can be assembled into the polyhedron Sketch the net If possible find more than one way to arrange the polygons show a different net for the same polyhedron Lesson Summary A polyhedron is a three dimensional figure composed of faces Each face is a filled in polygon and meets only one other face along a complete edge The ends of the edges meet at points that are called vertices edge edge face face face face vertex vertex edge vertex vertex edge A polyhedron always encloses a three dimensional region The plural of polyhedron is polyhedra Here are some drawings of polyhedra 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

G6M1 LESSON 13 ZEARN MATH STUDENT EDITION A prism is a type of polyhedron with two identical faces that are parallel to each other and that are called bases The bases are connected by a set of rectangles or sometimes parallelograms A prism is named for the shape of its bases For example if the base is a pentagon then it is called a pentagonal prism triangular triangular pentagonal rectangular triangular pentagonal pentagonalrectangular rectangular prism prism prism prism prism prism prism prism prism A pyramid is a type of polyhedron that has one special face called the base All of the other faces are triangles that all meet at a single vertex A pyramid is named for the shape of its base For example if the base is a pentagon then it is called a pentagonal pyramid rectangular hexagonal heptagonal decagonal rectangular hexagonal heptagonal decagonal rectangular hexagonal heptagonal decagonal rectangular hexagonal heptagonal decagonal pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid pyramid A net is a two dimensional representation of a polyhedron It is composed of polygons that form the faces of a polyhedron A cube has 6 square faces so its net is composed of six squares as shown here A net can be cut out and folded to make a model of the polyhedron In a cube every face shares its edges with 4 other squares In a net of a cube not all edges of the squares are joined with another edge When the net is folded however each of these open edges will join another edge It takes practice to visualize the final polyhedron by just looking at a net TERMINOLOGY 82 Base of a prism or pyramid Prism Face Pyramid Net Vertex Vertices Polyhedron Polyhedra Edge 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 13 Date GRADE 6 MISSION 1 LESSON 13 Exit Ticket 1 Write your best definition or description of a polyhedron If possible use the terms you learned in this lesson 2 Which of these five polyhedra are prisms Which are pyramids 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 14 Lesson 14 Nets and Surface Area Let s use nets to find the surface area of polyhedra Warm Up 1 Match each net with its corresponding polyhedron and name the polyhedron Be prepared to explain how you know the net and polyhedron go together A 1 B 2 C 3 D 4 E 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 85

G6M1 LESSON 14 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 You will be given the nets of three polyhedra Use the nets to answer the questions in your notes A 1 C Name the polyhedron that each net would form when assembled 86 B A B 2 Cut out your nets and use them to create three dimensional shapes 3 Find the surface area of each polyhedron Explain your reasoning clearly C 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 14 Lesson Summary A net of a pyramid has one polygon that is the base The rest of the polygons are triangles A pentagonal pyramid and its net are shown here base A net of a prism has two copies of the polygon that is the base The rest of the polygons are rectangles A pentagonal prism and its net are shown here base base In a rectangular prism there are three pairs of parallel and identical rectangles Any pair of these identical rectangles can be the bases base base base base base 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

G6M1 LESSON 14 ZEARN MATH STUDENT EDITION Because a net shows all the faces of a polyhedron we can use it to find its surface area For instance the net of a rectangular prism shows three pairs of rectangles 4 units by 2 units 3 units by 2 units and 4 units by 3 units 6 square units 8 square units 12 square units The surface area of the rectangular prism is 52 square units because 8 8 6 6 12 12 52 88 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 14 Date GRADE 6 MISSION 1 LESSON 14 Exit Ticket 1 What kind of polyhedron can be assembled from this net 2 Find the surface area in square units of the polyhedron Show your 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 89

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ZEARN MATH STUDENT EDITION G6M1 LESSON 15 Lesson 15 More Nets More Surface Area Let s draw nets and find the surface area of polyhedra Warm Up 1 Kiran is wrapping this box of sports cards as a present for a friend What do you notice What do you wonder 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

G6M1 LESSON 15 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 You will be given a drawing of a polyhedron Follow the directions to draw its net and calculate its surface area 1 What polyhedron do you have 2 Study your polyhedron Then draw its net on graph paper Use the side length of a grid square as the unit 3 Label each polygon on the net with a name or number 4 Find the surface area of your polyhedron Show your thinking in an organized manner so that it can be followed by others 92 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 15 ACTIVITY 2 3 1 Solve the following problems Show your reasoning Jamica has a 12 inch by 12 inch sheet of paper and needs to create the net of the polyhedron below Is the sheet of paper large enough 5 in 6 in 3 in 4 in 2 Sophie has a box she uses to store personal items and she wants to decorate the outside of the box by wrapping it in decorative paper The box is 12 in wide 6 in deep and 4 in tall and she has a single sheet of decorative paper that is 22 in by 22 in Does she have enough paper to wrap her box 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

G6M1 LESSON 15 ZEARN MATH STUDENT EDITION Lesson Summary The surface area of a polyhedron is the sum of the areas of all of the faces Because a net shows us all faces of a polyhedron at once it can help us find the surface area We can find the areas of all polygons in the net and add them 5 5 6 6 5 5 5 5 5 6 6 6 5 6 6 6 5 5 6 6 6 6 5 5 A square pyramid has a square and four triangles for its faces Its surface area is the sum of the areas of the square base and the four triangular faces 6 6 4 12 5 6 96 The surface area of this square pyramid is 96 square units 94 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 15 Date GRADE 6 MISSION 1 LESSON 15 Exit Ticket 1 In this net the two triangles are right triangles All quadrilaterals are rectangles What is its surface area in square units Show your reasoning 2 If the net is assembled which of the following polyhedra would it make 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 16 Lesson 16 Distinguishing Between Surface Area and Volume Let s contrast surface area and volume Warm Up 1 For each quantity choose one or more appropriate units of measurement For the last two quantities think of a quantity that could be appropriately measured with the given units Quantities Units 1 Perimeter of a parking lot millimeters mm 2 Volume of a semi truck feet ft 3 Surface area of a refrigerator meters m 4 Length of an eyelash square inches sq in 5 Area of a state square feet sq ft 6 Volume of an ocean square miles sq mi 7 miles cubic kilometers cu km 8 cubic meters cubic yards cu yd 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

G6M1 LESSON 16 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Your teacher will give you 16 cubes Build two different shapes using 8 cubes for each For each shape 98 Give a name or a label e g Mae s First Shape or Eric s Steps Determine the volume Determine the surface area Record the name volume and surface area on a sticky note 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 16 ACTIVITY 2 3 Three rectangular prisms each have a height of 1 cm Prism A has a base that is 1 cm by 11 cm Prism B has a base that is 2 cm by 7 cm Prism C has a base that is 3 cm by 5 cm 1 Find the surface area and volume of each prism Use the dot paper to draw the prisms if needed 2 Analyze the volumes and surface areas of the prisms What do you notice Write 1 2 observations about them 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

G6M1 LESSON 16 ZEARN MATH STUDENT EDITION Lesson Summary Length is a one dimensional attribute of a geometric figure We measure lengths using units like millimeters centimeters meters kilometers inches feet yards and miles Area is a two dimensional attribute We measure area in square units For example a square that is 1 centimeter on each side has an area of 1 square centimeter Volume is a three dimensional attribute We measure volume in cubic units For example a cube that is 1 kilometer on each side has a volume of 1 cubic kilometer Surface area and volume are different attributes of three dimensional figures Surface area is a two dimensional measure while volume is a three dimensional measure Two figures can have the same volume but different surface areas For example A rectangular prism with side lengths of 1 cm 2 cm and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm A rectangular prism with side lengths of 1 cm 1 cm and 4 cm has the same volume but a surface area of 18 sq cm Similarly two figures can have the same surface area but different volumes 100 A rectangular prism with side lengths of 1 cm 1 cm and 5 cm has a surface area of 22 sq cm and a volume of 5 cu cm A rectangular prism with side lengths of 1 cm 2 cm and 3 cm has the same surface area but a volume of 6 cu 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 16 Date GRADE 6 MISSION 1 LESSON 16 Exit Ticket Choose two figures that have the same surface area but different volumes Show your 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 101

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ZEARN MATH STUDENT EDITION G6M1 LESSON 17 Lesson 17 Squares and Cubes Let s investigate perfect squares and perfect cubes Warm Up 1 Answer the questions about squares 1 The number 9 is a perfect square Find four numbers that are perfect squares and two numbers that are not perfect squares 2 A square has side length 7 km What is its area 3 The area of a square is 64 sq cm What is its side length Concept Exploration ACTIVITY 1 2 Answer the questions about cubes 1 The number 27 is a perfect cube Find four other numbers that are perfect cubes and two numbers that are not perfect cubes 2 A cube has an edge length of 4 cm What is its volume 3 A cube has an edge length of 10 cm What is its volume 4 A cube has an edge length of s cm What is its volume 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

G6M1 LESSON 17 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 104 Answer the questions about exponents Make sure to include correct units of measure as part of each answer 1 A square has side length of 10 cm Use an exponent to express its area 2 The area of a square is 72 sq in What is its side length 3 The area of a square is 81 m2 Use an exponent to express this area 4 A cube has edge length 5 in Use an exponent to express its volume 5 The volume of a cube is 63 cm3 What is its edge length 6 A cube has edge length s units Use an exponent to write an expression for its volume 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 17 Lesson Summary When we multiply two of the same numbers together such as 5 5 we say we are squaring the number We can write it like this 52 Because 5 5 25 we write 52 25 and we say 5 squared is 25 When we multiply three of the same numbers together such as 4 4 4 we say we are cubing the number We can write it like this 43 Because 4 4 4 64 we write 43 64 and we say 4 cubed is 64 We also use this notation for square and cubic units A square with side length 5 inches has area 25 in2 A cube with edge length 4 cm has volume 64 cm3 To read 25 in2 we say 25 square inches just like before The area of a square with side length 7 kilometers is 72 km2 The volume of a cube with edge length 2 millimeters is 23 mm3 In general the area of a square with side length s is s2 and the volume of a cube with edge length s is s3 TERMINOLOGY Cubed Exponent Squared 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

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ZEARN MATH STUDENT EDITION Name G6M1 LESSON 17 Date GRADE 6 MISSION 1 LESSON 17 Exit Ticket 1 Which is larger 52 or 33 2 A cube has an edge length of 21 cm Use an exponent to express its volume 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 18 Lesson 18 Surface Area of a Cube Let s write a formula to find the surface area of a cube Warm Up 1 Select the greater expression of each pair without calculating the value of each expression Be prepared to explain your choices a 10 3 or 10 b 13 or 12 12 c 97 97 97 97 97 97 or 5 97 Concept Exploration ACTIVITY 1 2 Answer the following questions about a cube with edge length 5 inches a Draw a net for this cube and label its sides with measurements b What is the shape of each face 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

G6M1 LESSON 18 c ZEARN MATH STUDENT EDITION What is the area of each face d What is the surface area of this cube e What is the volume of this cube 3 Answer the following questions about a cube with edge length 17 units a Draw a net for this cube and label its sides with measurements b Explain why the area of each face of this cube is 17 square units c Write an expression for the surface area in square units d Write an expression for the volume in cubic units 110 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

ZEARN MATH STUDENT EDITION G6M1 LESSON 18 ACTIVITY 2 43 Answer the following questions about a cube with edge length s 1 Draw a net for this cube 2 Write an expression for the area of each face Label each face with its area 3 Write an expression for the surface area 4 Write an expression for the volume 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

G6M1 LESSON 18 ZEARN MATH STUDENT EDITION Lesson Summary The volume of a cube with edge length s is s S S S A cube has 6 faces that are identical squares The surface area of a cube with edge length s is 6 s S S S S S S 112 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

ZEARN MATH STUDENT EDITION Name G6M1 LESSON 18 Date GRADE 6 MISSION 1 LESSON 18 Exit Ticket 1 A cube has edge length 11 inches Write an expression for its volume and an expression for its surface area 2 A cube has a volume of 7 cubic centimeters What is its surface area 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

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ZEARN MATH STUDENT EDITION G6M1 LESSON 19 Lesson 19 Designing a Tent Let s design some tents Concept Exploration ACTIVITY 1 1 Use the information below to help you design some tents Have you ever been camping You might know that sleeping bags are all about the same size but tents come in a variety of shapes and sizes Your task is to design a tent to accommodate up to four people and estimate the amount of fabric needed to make your tent Your design and estimate must be based on the information given and have mathematical justification First look at these examples of tents the average specifications of a camping tent and standard sleeping bag measurements Talk to a partner about Similarities and differences among the tents Information that will be important in your designing process The pros and cons of the various designs Tent Styles 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

G6M1 LESSON 19 ZEARN MATH STUDENT EDITION Tent Height Specifications Height Description Height of Tent Notes Sitting Height 3 feet Campers are able to sit lie or crawl inside tent Kneeling Height 4 feet Campers are able to kneel inside tent Found mainly in 3 4 person tents Stooping Height 5 feet Campers are able to move around on their feet inside tent but most campers will not be able to stand upright Standing Height 6 feet Most adult campers are able to stand upright inside tent Roaming Height 7 feet Adult campers are able to stand upright and walk around inside tent Sleeping Bag Measurements Standard 34 74 How many people can sleep in your tent What is the height of your tent 116 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

ZEARN MATH STUDENT EDITION Sketch the bottom panel of your tent and the locations where sleeping bags will go G6M1 LESSON 19 Sketch the overall design of your tent What decisions are important when choosing a tent design What decisions are important when choosing a tent design Use the remaining space to show any work sketches of side panels calculations etc needed to estimate the amount of fabric that will be necessary to make your tent 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

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Grade 6 Mission 2 Introducing Ratios

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ZEARN MATH STUDENT EDITION G6M2 LESSON 1 Lesson 1 Introducing Ratios and Ratio Language Let s describe two quantities at the same time Warm Up 1 Use this diagram to answer the questions below 1 If you sorted this set by color how many groups would you have 2 If you sorted this set by area how many groups would you have 3 Think of a third way you could sort these figures What categories would you use How many groups would you have 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

G6M2 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Think of a way to sort your teacher s collection into two or three categories 2 1 Record your categories in the top row of the table and the amounts in the second row Category Name Category Amount 2 Write at least two sentences that describe ratios in the collection Remember there are many ways to write a ratio The ratio of one category to another category is to The ratio of one category to another category is There are of one category for every of another category ACTIVITY 2 3 1 Sort your collection into three categories You can experiment with different ways of arranging these categories Count the items in each category and record the information in the table Category Name Category Amount 2 3 122 Write at least two sentences that describe ratios in the collection Remember there are many ways to write a ratio The ratio of one category to another category is to The ratio of one category to another category is There are of one category for every of another category Make a visual display of your items that clearly shows one of your statements Be prepared to share your display with the class 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 1 Lesson Summary A ratio is an association between two or more quantities There are many ways to describe a situation in terms of ratios For example look at this collection Here are some correct ways to describe the collection The ratio of squares to circles is 6 3 The ratio of circles to squares is 3 to 6 Notice that the shapes can be arranged in equal groups which allow us to describe the shapes using other numbers There are 2 squares for every 1 circle There is 1 circle for every 2 squares TERMINOLOGY Ratio 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

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ZEARN MATH STUDENT EDITION Name G6M2 LESSON 1 Date GRADE 6 MISSION 2 LESSON 1 Exit Ticket Here is a collection of dogs mice and cats Write two sentences that describe a ratio of types of animals in this collection 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 2 Lesson 2 Representing Ratios with Diagrams Let s use diagrams to represent ratios Warm Up 1 Find the value of each expression mentally 1 24 4 2 1 24 4 3 24 14 4 5 4 Concept Exploration ACTIVITY 1 2 Elena mixed 2 cups of white paint with 6 tablespoons of blue paint Here is a diagram that represents this situation white paint cups Discuss the statements that follow and circle all those that correctly describe blue paint tablespoons this situation Make sure that both you and your partner agree with each circled answer a The ratio of cups of white paint to tablespoons of blue paint is 2 6 b For every cup of white paint there are 2 tablespoons of blue paint c There is 1 cup of white paint for every 3 tablespoons of blue paint d There are 3 tablespoons of blue paint for every cup of white paint e For each tablespoon of blue paint there are 3 cups of white paint f For every 6 tablespoons of blue paint there are 2 cups of white paint g The ratio of tablespoons of blue paint to cups of white paint is 6 to 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 127

G6M2 LESSON 2 3 ZEARN MATH STUDENT EDITION Jada mixed 8 cups of flour with 2 pints of water to make paste for an art project a Draw a diagram that represents the situation b Write at least two sentences describing the ratio of flour and water ACTIVITY 2 43 Your teacher will give you cards describing different recipes for spaghetti sauce In the diagrams 1 a circle represents a cup of tomato sauce a square represents a tablespoon of oil a triangle represents a teaspoon of oregano Take turns with your partner to match a sentence with a diagram a For each match that you find explain to your partner how you know it s a match b For each match that your partner finds listen carefully to their explanation If you disagree discuss your thinking and work to reach an agreement 3 After you and your partner have agreed on all of the matches check your answers with the answer key If there are any errors discuss why and revise your matches 4 There were two diagrams that each matched with two different sentences Which were they 5 128 Diagram matched with both sentences and Diagram matched with both sentences and Select one of the other diagrams and invent another sentence that could describe the ratio shown in the diagram 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 2 Lesson Summary Ratios can be represented using diagrams The diagrams do not need to include realistic details For example a recipe for lemonade says Mix 2 scoops of lemonade powder with 6 cups of water Instead of this We can draw something like this This diagram shows that the ratio of cups of water to scoops of lemonade powder is 6 to 2 We can also see that for every scoop of lemonade powder there are 3 cups of water 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 2 Name Date GRADE 6 MISSION 2 LESSON 2 Exit Ticket There are 3 cats in a room and no other creatures Each cat has 2 ears 4 paws and 1 tail 1 Draw a diagram that shows an association between numbers of ears paws and tails in the room 2 Complete each statement a The ratio of to to b There are paws for every tail c paws for every ear There are is 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 3 Lesson 3 Recipes Let s explore how ratios affect the way a recipe tastes Warm Up 1 This flower is made up of hexagons trapezoids and triangles 1 Write sentences to describe the ratios of the shapes that make up this pattern 2 How many of each shape would be in two copies of this flower pattern 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

G6M2 LESSON 3 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Here are diagrams representing three mixtures of powdered drink mix and water A B Key 1 teaspoon drink mix C 1 cup water 1 How would the taste of Mixture A compare to the taste of Mixture B 2 Use the diagrams to complete each statement a Mixture B uses cups of water and teaspoons of drink mix The ratio of cups of water to teaspoons of drink mix in Mixture B is b Mixture C uses cups of water and teaspoons of drink mix The ratio of cups of water to teaspoons of drink mix in Mixture C is 3 134 How would the taste of Mixture B compare to the taste of Mixture C 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 3 ACTIVITY 2 3 A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla 1 Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies 2 How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla Indicate the additional batches by adding more ingredients to your diagram 3 How much flour and vanilla would you need for 5 batches of cookies 4 Whether the ratio of cups of flour to teaspoons of vanilla is 5 2 10 4 or 15 6 the recipes would make cookies that taste the same We call these equivalent ratios a Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios b How many batches can you make using this new ratio of ingredients 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

G6M2 LESSON 3 ZEARN MATH STUDENT EDITION Lesson Summary A recipe for fizzy juice says Mix 5 cups of cranberry juice with two cups of soda water To double this recipe we would use 10 cups of cranberry juice with 4 cups of soda water To triple this recipe we would use 15 cups of cranberry juice with 6 cups of soda water This diagram shows a single batch of the recipe a double batch and a triple batch We say that the ratios 5 2 10 4 and 15 6 are equivalent Even though the amounts of each ingredient within a single double or triple batch are not the same they would make fizzy juice that tastes the same 136 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 3 Date GRADE 6 MISSION 2 LESSON 3 Exit Ticket Usually when Elena makes bird food she mixes 9 cups of seeds with 6 tablespoons of maple syrup However today she is short on ingredients Think of a recipe that would yield a smaller batch of bird food but still taste the same Explain or show your 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 137

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ZEARN MATH STUDENT EDITION G6M2 LESSON 4 Lesson 4 Color Mixtures Let s see what color mixing has to do with ratios Warm Up 1 Find the value of each product mentally 1 6 15 2 12 15 3 6 45 4 13 45 Concept Exploration ACTIVITY 1 2 1 Your teacher mixed milliliters of blue water and milliliters of yellow water in the ratio 5 15 Use this mixture to help with the recipes below Doubling the original recipe a Draw a diagram to represent the amount of each color that you will combine to double your teacher s recipe 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

G6M2 LESSON 4 ZEARN MATH STUDENT EDITION b Use a marker to label an empty cup with the ratio of blue water to yellow water in this double batch c Predict whether these amounts of blue and yellow will make the same shade of green as your teacher s mixture Next check your prediction by measuring those amounts and mixing them in the cup d Is the ratio in your mixture equivalent to the ratio in your teacher s mixture Explain your reasoning 2 Tripling the original recipe a Draw a diagram to represent triple your teacher s recipe b Label an empty cup with the ratio of blue water to yellow water c Predict whether these amounts will make the same shade of green Next check your prediction by mixing those amounts d Is the ratio in your new mixture equivalent to the ratio in your teacher s mixture Explain your reasoning 140 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

ZEARN MATH STUDENT EDITION 3 G6M2 LESSON 4 Next invent your own recipe for a bluer shade of green water a Draw a diagram to represent the amount of each color you will combine b Label the final empty cup with the ratio of blue water to yellow water in this recipe c Test your recipe by mixing a batch in the cup Does the mixture yield a bluer shade of green d Is the ratio you used in this recipe equivalent to the ratio in your teacher s mixture Explain your 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 141

G6M2 LESSON 4 ZEARN MATH STUDENT EDITION Lesson Summary When mixing colors doubling or tripling the amount of each color will create the same shade of the mixed color In fact you can always multiply the amount of each color by the same number to create a different amount of the same mixed color For example a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint To make two batches of dark orange paint we can mix 8 ml of red paint with 4 ml of yellow paint To make three batches of dark orange paint we can mix 12 ml of red paint with 6 ml of yellow paint Here is a diagram that represents 1 2 and 3 batches of this recipe red paint ml yellow paint ml 1 batch orange 2 batches orange 3 batches orange We say that the ratios 4 2 8 4 and 12 6 are equivalent because they describe the same color mixture in different numbers of batches and they make the same shade of orange 142 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 4 Date GRADE 6 MISSION 2 LESSON 4 Exit Ticket A recipe for orange water says Mix 3 teaspoons yellow water with 1 teaspoon red water For this recipe we might say The ratio of teaspoons of yellow water to teaspoons of red water is 3 1 1 Write a ratio for 2 batches of this recipe 2 Write a ratio for 4 batches of this recipe 3 Explain why we can say that any two of these three ratios are equivalent 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 5 Lesson 5 Defining Equivalent Ratios Let s investigate equivalent ratios some more Warm Up How many dots are in Dot Pattern 1 Explain how you saw them 1 How many dots are in Dot Pattern 2 Explain how you saw them 2 Concept Exploration ACTIVITY 1 Use the ingredients from a tuna casserole recipe to answer the questions 3 Ingredients 3 cups cooked elbow shaped pasta 6 ounce can tuna drained 10 ounce can cream of chicken soup 1 cup shredded cheddar cheese 1 1 2 cups French fried onions Instructions Combine the pasta tuna soup and half of the cheese Transfer into a 9 inch by 13 inch baking dish Put the remaining cheese on top Bake 30 minutes at 350 degrees During the last 5 minutes add the French fried onions Let sit for 10 minutes before serving 1 What is the ratio of the ounces of soup to the cups of shredded cheese to the cups of pasta in one batch of casserole 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

G6M2 LESSON 5 2 ZEARN MATH STUDENT EDITION How much of each of these 3 ingredients would be needed to make a twice the amount of casserole b half the amount of casserole c five times the amount of casserole d one fifth the amount of casserole 3 What is the ratio of cups of pasta to ounces of tuna in one batch of casserole 4 How many batches of casserole would you make if you used the following amounts of ingredients a 9 cups of pasta and 18 ounces of tuna b 36 ounces of tuna and 18 cups of pasta c 1 cup of pasta and 2 ounces of tuna ACTIVITY 2 43 146 The ratios 5 3 and 10 6 are equivalent ratios 1 Is the ratio 15 12 equivalent to these Explain your reasoning 2 Is the ratio 30 18 equivalent to these Explain your reasoning 3 Give two more examples of ratios that are equivalent to 5 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

ZEARN MATH STUDENT EDITION 4 How do you know when ratios are equivalent and when they are not equivalent 5 Write a definition of equivalent ratios G6M2 LESSON 5 Pause here so your teacher can review your work and assign you a ratio to use for your visual display 53 Create a visual display that includes the title Equivalent Ratios your best definition of equivalent ratios the ratio your teacher assigned to you at least two examples of ratios that are equivalent to your assigned ratio an explanation of how you know these examples are equivalent at least one example of a ratio that is not equivalent to your assigned ratio an explanation of how you know this example is not equivalent Be prepared to share your display with the class 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

G6M2 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary All ratios that are equivalent to a b can be made by multiplying both a and b by the same number 9 6 For example the ratio 18 12 is equivalent to 9 6 because both 9 and 6 are multiplied by the same number 2 2 18 12 9 6 3 2 is also equivalent to 9 6 because both 9 and 6 are multiplied by the same number 13 1 3 2 Nope 18 15 TERMINOLOGY Equivalent ratios 148 1 3 3 2 9 6 Is 18 15 equivalent to 9 6 No because 18 is 9 2 but 15 is not 6 2 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 5 Date GRADE 6 MISSION 2 LESSON 5 Exit Ticket 1 Write another ratio that is equivalent to the ratio 4 6 2 How do you know that your new ratio is equivalent to 4 6 Explain or show your 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 149

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ZEARN MATH STUDENT EDITION G6M2 LESSON 6 Lesson 6 Introducing Double Number Line Diagrams Let s use number lines to represent equivalent ratios Warm Up 1 Find the value of each product mentally Then write your answer in your notes 1 4 5 4 2 4 5 8 3 1 10 65 4 2 10 65 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

G6M2 LESSON 6 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 The other day we made drink mixtures by mixing 4 teaspoons of powdered drink mix for every cup of water Below are two ways to represent multiple batches of this recipe Drink mix teaspoons Water cups 0 4 8 12 16 0 1 2 3 4 Drink mix teaspoons Water cups 152 1 How can we tell that 4 1 and 12 3 are equivalent ratios 2 How are these representations the same How are these representations different 3 How many teaspoons of drink mix should be used with 3 cups of water 4 How many cups of water should be used with 16 teaspoons of drink mix 5 What numbers should go in the empty boxes on the double number line diagram What do these numbers mean 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 6 ACTIVITY 2 3 Here is a diagram showing Elena s recipe for light blue paint White paint cups Blue paint tablespoons 1 Complete the double number line diagram to show the amounts of white paint and blue paint in different sized batches of light blue paint 0 0 2 Compare your double number line diagram with your partner Discuss your thinking If needed revise your diagram 3 How many cups of white paint should Elena mix with 12 tablespoons of blue paint How many batches would this make 4 How many tablespoons of blue paint should Elena mix with 6 cups of white paint How many batches would this make 5 Use your double number line diagram to find another amount of white paint and blue paint that would make the same shade of light blue paint 6 How do you know that these mixtures would make the same shade of light blue paint 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

G6M2 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary You can use a double number line diagram to find many equivalent ratios For example a recipe for fizzy juice says Mix 5 cups of cranberry juice with 2 cups of soda water The ratio of cranberry juice to soda water is 5 2 Multiplying both ingredients by the same number creates equivalent ratios 0 5 10 15 20 25 0 2 4 6 8 10 Cranberry juice cups Soda water cups This double number line shows that the ratio 20 8 is equivalent to 5 2 If you mix 20 cups of cranberry juice with 8 cups of soda water it makes 4 times as much fizzy juice that tastes the same as the original recipe TERMINOLOGY Double Number Line Diagram 154 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 6 Date GRADE 6 MISSION 2 LESSON 6 Exit Ticket A recipe for one batch of cookies uses 5 cups of flour and 2 teaspoons of vanilla 1 Complete the double number line diagram to show the amount of flour and vanilla needed for 1 2 3 4 and 5 batches of cookies 0 0 2 If you use 20 cups of flour how many teaspoons of vanilla should you use 3 If you use 6 teaspoons of vanilla how many cups of flour 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 155

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ZEARN MATH STUDENT EDITION G6M2 LESSON 7 Lesson 7 Creating Double Number Line Diagrams Let s draw double number line diagrams like a pro Warm Up 1 1 Answer the questions about the number line Locate and label the following numbers on the number line 1 2 1 4 1 3 4 1 5 0 2 1 75 2 Based on where you placed the numbers locate and label four more fractions or decimals on the number line Concept Exploration ACTIVITY 1 2 We made green water by mixing 5 ml of blue water with 15 ml of yellow water Use the double number line to answer the questions below 0 5 10 0 15 30 Blue water ml Yellow water ml 1 On the number line for blue water label the four tick marks shown 2 On the number line for yellow water draw and label tick marks to show the amount of yellow water needed for each amount of blue water 3 How much yellow water should be used for 1 ml of blue water Circle where you can see this on the double number line 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

G6M2 LESSON 7 ZEARN MATH STUDENT EDITION 4 How much yellow water should be used for 11 ml of blue water 5 How much yellow water should be used for 8 ml of blue water 6 Why is it useful to know how much yellow water should be used with 1 ml of blue water ACTIVITY 2 3 1 A recipe for art paste says For every 2 pints of water mix in 8 cups of flour Answer the questions about this recipe below Follow the instructions to draw a double number line diagram representing the recipe for art paste a Use a ruler to draw two parallel lines b Label the first line pints of water Label the second line cups of flour c Draw at least 6 equally spaced tick marks that line up on both lines d Along the water line label the tick marks with the amount of water in 0 1 2 3 4 and 5 batches of art paste e Along the flour line label the tick marks with the amount of flour in 0 1 2 3 4 and 5 batches of art paste 2 Compare your double number line diagram with your partner s Discuss your thinking If needed revise your diagram 3 Next use your double number line to answer these questions a How much flour should be used with 10 pints of water b How much water should be used with 24 cups of flour c 158 How much flour per pint of water does this recipe 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 7 Lesson Summary Here are some guidelines to keep in mind when drawing a double number line diagram The two parallel lines should have labels that describe what the numbers represent The tick marks and numbers should be spaced at equal intervals Numbers that line up vertically make equivalent ratios For example the ratio of the number of eggs to cups of milk in a recipe is 4 1 Here is a double number line that represents the situation 0 4 8 12 16 20 0 1 2 3 4 5 Number of eggs Cups of milk We can also say that this recipe uses 4 eggs per cup of milk because the word per means for each TERMINOLOGY Per 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

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ZEARN MATH STUDENT EDITION Name G6M2 LESSON 7 Date GRADE 6 MISSION 2 LESSON 7 Exit Ticket Each of these cats has 2 ears 4 paws and 1 tail 1 Draw a double number line diagram that represents a ratio in the situation 2 Write a sentence that describes this situation and that uses the word per 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 8 Lesson 8 How Much for One Let s use ratios to describe how much things cost Warm Up 1 Find the quotient mentally 246 12 Concept Exploration ACTIVITY 1 2 1 Answer each question and show your reasoning If you get stuck consider drawing a double number line diagram Eight avocados cost 4 a How much do 16 avocados cost b How much do 20 avocados cost c 2 How much do 9 avocados cost Twelve large bottles of water cost 9 a How many bottles can you buy for 3 b What is the cost per bottle of water c 3 How much would 7 bottles of water cost A 10 pound sack of flour costs 8 a How much does 40 pounds of flour cost b What is the cost per pound of flour 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

G6M2 LESSON 8 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 1 Answer the following questions about unit rates Four bags of chips cost 6 a What is the cost per bag b At this rate how much will 7 bags of chips cost 2 At a used book sale 5 books cost 15 a What is the cost per book b At this rate how many books can you buy for 21 3 Neon bracelets cost 1 for 4 a What is the cost per bracelet b At this rate how much will 11 neon bracelets cost Pause here so you teacher can review your work 4 164 Your teacher will assign you one of the problems Create a visual display that shows your solution to the problem Be prepared to share your solution with the group 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 8 Lesson Summary The unit price is the price of 1 thing for example the price of 1 ticket 1 slice of pizza or 1 kilogram of peaches If 4 movie tickets cost 28 then the unit price would be the cost per ticket We can create a double number line to find the unit price 0 7 14 21 28 35 0 1 2 3 4 5 Cost in dollars Number of tickets This double number line shows that the cost for 1 ticket is 7 We can also find the unit price by dividing 28 4 7 or by multiplying 28 14 7 TERMINOLOGY Unit price 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 8 Name Date GRADE 6 MISSION 2 LESSON 8 Exit Ticket Here is a double number line showing that it costs 3 to buy 2 bags of rice 0 3 0 2 Cost dollars Rice number of bags 1 At this rate how many bags of rice can you buy with 12 2 Find the cost per bag 3 How much do 20 bags of rice cost 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

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ZEARN MATH STUDENT EDITION G6M2 LESSON 9 Lesson 9 Constant Speed Let s use ratios to work with how fast things move Warm Up 1 Find the quotient mentally 1 30 10 2 34 10 3 3 4 10 4 34 100 Concept Exploration ACTIVITY 1 2 Your teacher will set up a straight path with a 1 meter warm up zone and a 10 meter measuring zone Follow the following instructions to collect the data 1 a The person with the stopwatch the timer stands at the finish line The person being timed the mover stands at the warm up line b On the first round the mover starts moving at a slow steady speed along the path When the mover reaches the start line they say Start and the timer starts the stopwatch c The mover keeps moving steadily along the path When they reach the finish line the timer stops the stopwatch and records the time rounded to the nearest second in the table 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

G6M2 LESSON 9 ZEARN MATH STUDENT EDITION d On the second round the mover follows the same instructions but this time moving at a quick steady speed The timer records the time the same way e Repeat these steps until each person in the group has gone twice once at a slow steady speed and once at a quick steady speed Your slow moving time seconds 2 Your fast moving time seconds After you finish collecting the data use the double number line diagrams to answer the questions Use the times your partner collected while you were moving Moving slowly 0 10 Distance traveled meters Elapsed time seconds 0 Moving quickly 0 10 Distance traveled meters Elapsed time seconds 0 a Estimate the distance in meters you traveled in 1 second when moving slowly b Estimate the distance in meters you traveled in 1 second when moving quickly c 170 Trade diagrams with someone who is not your partner How is the diagram representing someone moving slowly different from the diagram representing someone moving quickly 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 9 ACTIVITY 2 3 Lin and Diego both ran for 10 seconds each at their own constant speed Lin ran 40 meters and Diego ran 55 meters 1 Who was moving faster Explain your reasoning 2 How far did each person move in 1 second If you get stuck consider drawing double number line diagrams to represent the situations 3 Use your data from the previous activity to find how far you could travel in 10 seconds at your quicker speed 4 Han ran 100 meters in 20 seconds at a constant speed Is this speed faster slower or the same as Lin s Diego s Yours 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

G6M2 LESSON 9 ZEARN MATH STUDENT EDITION Lesson Summary Suppose a train traveled 100 meters in 5 seconds at a constant speed To find its speed in meters per second we can create a double number line 0 20 40 60 80 100 0 1 2 3 4 5 Distance traveled meters Elapsed time seconds The double number line shows that the train s speed was 20 meters per second We can also find the speed by dividing 100 5 20 Once we know the speed in meters per second many questions about the situation become simpler to answer because we can multiply the amount of time an object travels by the speed to get the distance For example at this rate how far would the train go in 30 seconds Since 20 30 600 the train would go 600 meters in 30 seconds TERMINOLOGY Meters per second 172 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 9 Name Date GRADE 6 MISSION 2 LESSON 9 Exit Ticket Two trains are traveling at constant speeds on different tracks Train A 0 12 5 0 1 100 Distance traveled meters Elapsed time seconds Train B 0 100 0 4 Distance traveled meters Elapsed time seconds Which train is traveling faster Explain your 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 173

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ZEARN MATH STUDENT EDITION G6M2 LESSON 10 Lesson 10 Comparing Situations by Examining Ratios Let s use ratios to compare situations Warm Up 1 Mai and Jada each ran on a treadmill The treadmill display shows the distance in miles each person ran and the amount of time it took them in minutes and seconds Here is Mai s treadmill display Here is Jada s treadmill display 1 What is the same about their workouts What is different about their workouts 2 If each person ran at a constant speed the entire time who was running faster Explain your reasoning Concept Exploration ACTIVITY 1 2 Diego paid 47 for 3 tickets to a concert Andre paid 141 for 9 tickets to a concert Did they pay at the same rate Explain your 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 175

G6M2 LESSON 10 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 176 Lin and Noah each have their own recipe for making fruit punch Lin mixes 3 liters of orange juice with 4 liters of strawberry juice Noah mixes 4 liters of orange juice with 5 liters of strawberry juice How do the two mixtures compare in taste Explain your 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 10 Lesson Summary Sometimes we want to know whether two situations are described by the same rate To do that we can write an equivalent ratio for one or both situations so that one part of their ratios has the same value Then we can compare the other part of the ratios For example do these two paint mixtures make the same shade of orange Kiran mixes 9 teaspoons of red paint with 15 teaspoons of yellow paint Tyler mixes 7 teaspoons of red paint with 10 teaspoons of yellow paint 0 3 6 9 12 0 5 10 15 20 red paint teaspoons yellow paint teaspoons Here is a double number line that represents Kiran s paint mixture The ratio 9 15 is equivalent to the ratios 3 5 and 6 10 For 10 teaspoons of yellow paint Kiran would mix in 6 teaspoons of red paint This is less red paint than Tyler mixes with 10 teaspoons of yellow paint The ratios 6 10 and 7 10 are not equivalent so these two paint mixtures would not be the same shade of orange When we talk about two things happening at the same rate we mean that the ratios of the quantities in the two situations are equivalent There is also something specific about the situation that is the same If two ladybugs are moving at the same rate then they are traveling at the same constant speed If two bags of apples are selling for the same rate then they have the same unit price If we mix two kinds of juice at the same rate then the mixtures have the same taste If we mix two colors of paint at the same rate then the mixtures have the same shade TERMINOLOGY Same rate 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 177

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ZEARN MATH STUDENT EDITION Name G6M2 LESSON 10 Date GRADE 6 MISSION 2 LESSON 10 Exit Ticket Andre ran 2 kilometers in 15 minutes and Jada ran 3 kilometers in 20 minutes Both ran at a constant speed Did they run at the same speed Explain your 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 179

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ZEARN MATH STUDENT EDITION G6M2 LESSON 11 Lesson 11 Representing Ratios with Tables Let s use tables to represent equivalent ratios Warm Up 1 1 Look for a pattern in the figures How many total tiles will be in a the 4th figure b the 5th figure c 2 the 10th figure How do you see it growing 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 181

G6M2 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Noah s recipe for one batch of fruit punch uses 4 liters of orange juice and 5 liters of strawberry juice Use the double number line to show how many liters of each ingredient to use for different sized batches of fruit punch Orange juice liters Strawberry juice liters 182 2 If someone mixes 36 liters of orange juice and 45 liters of strawberry juice how many batches would they make 3 If someone uses 400 liters of orange juice how much strawberry juice would they need 4 If someone uses 455 liters of strawberry juice how much orange juice would they need 5 Explain the trouble with using a double number line diagram to answer the last two questions 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 11 ACTIVITY 2 3 1 A recipe for trail mix says Mix 7 ounces of almonds with 5 ounces of raisins Here is a table that has been started to show how many ounces of almonds and raisins would be in different sized batches of this trail mix Complete the table so that ratios represented by each row are equivalent Almonds oz Raisins oz 7 5 28 10 3 5 250 56 2 What methods did you use to fill in the table 3 How do you know that each row shows a ratio that is equivalent to 7 5 Explain your 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 183

G6M2 LESSON 11 ZEARN MATH STUDENT EDITION Lesson Summary A table is a way to organize information Each horizontal set of entries is called a row and each vertical set of entries is called a column The table shown has 2 columns and 5 rows A table can be used to represent a collection of equivalent rations Here is a double number line diagram and a table that both represent the situation The price is 2 for every 3 mangoes 0 2 4 6 8 10 0 3 6 9 12 15 price in dollars number of mangos column column Price in dollars Number of mangoes row 2 3 row 4 6 row 6 9 row 8 12 row 10 15 TERMINOLOGY Table 184 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 11 Name Date GRADE 6 MISSION 2 LESSON 11 Exit Ticket In previous lessons we worked with a diagram and a double number line that represent this cookie recipe Here is a table that represents the same situation Flour cups Vanilla tablespoons 5 2 15 6 1 2 1 2 1 Write a sentence that describes a ratio shown in the table 2 What does the second row of numbers represent 3 Complete the last row for a different batch size that hasn t been used so far in the table Explain or show your 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 185

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ZEARN MATH STUDENT EDITION G6M2 LESSON 12 Lesson 12 Navigating a Table of Equivalent Ratios Let s use a table of equivalent ratios like a pro Warm Up 1 Find the product mentally 1 1 21 3 2 1 21 6 3 5 6 18 4 1 5 6 4 Concept Exploration ACTIVITY 1 2 Use the table to help you solve these problems Explain or show your reasoning 1 Noah bought 4 tacos and paid 6 At this rate how many tacos could he buy for 15 2 Jada s family bought 50 tacos for a party and paid 72 Were Jada s tacos the same price as Noah s tacos Number of tacos Price in dollars 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 187

G6M2 LESSON 12 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Lin is paid 90 for 5 hours of work She used the following table to calculate how much she would be paid at this rate for 8 hours of work 15 8 188 Amount earned Time worked hours 90 5 18 1 144 8 15 8 1 What is the meaning of the 18 that appears in the table 2 Why was the number 3 Explain how Lin used this table to solve the problem 4 At this rate how much would Lin be paid for 3 hours of work For 2 1 hours of work 1 5 used as a multiplier 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 12 Lesson Summary Finding a row containing a 1 is often a good way to work with tables of equivalent ratios For example the price for 4 lbs of granola is 5 At that rate what would be the price for 62 lbs of granola Here are tables showing two different approaches to solving this problem Both of these approaches are correct However one approach is more efficient Less efficient 2 2 2 2 2 lbs Granola lbs Price 4 5 8 10 16 20 32 40 64 80 62 77 50 Granola lbs Price 4 5 1 1 25 62 77 50 2 2 2 2 2 50 More efficient 14 62 14 62 Notice how the more efficient approach starts by finding the price for 1 lb of granola Remember that dividing by a whole number is the same as multiplying by a unit fraction In this example we can divide by 4 or multiply by 14 to find the unit price 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 189

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ZEARN MATH STUDENT EDITION G6M2 LESSON 12 Name Date GRADE 6 MISSION 2 LESSON 12 Exit Ticket A shop sells bagels for 5 per dozen You can use the table to answer the questions Explain your reasoning Number of bagels Price in dollars 12 5 1 At this rate how much would 6 bagels cost 2 How many bagels can you buy for 50 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 191

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ZEARN MATH STUDENT EDITION G6M2 LESSON 13 Lesson 13 Tables and Double Number Line Diagrams Let s contrast double number lines and tables Warm Up 1 Find the quotients mentally then locate and label the quotients on the number line 150 2 150 4 150 8 0 150 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 193

G6M2 LESSON 13 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 The other day we saw that Han can run 100 meters in 20 seconds Han wonders how long it would take him to run 3 000 meters at this rate He made a table of equivalent ratios Do you agree that this table represents the situation Explain your reasoning 20 100 10 50 1 5 3 000 194 2 Complete the last row with the missing number 3 What question about the situation does this number answer 4 What could Han do to improve his table 5 Priya can bike 150 meters in 20 seconds At this rate how long would it take her to bike 3 000 meters 6 Priya s neighbor has a dirt bike that can go 360 meters in 15 seconds At this rate how long would it take them to ride 3 000 meters 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 13 ACTIVITY 2 3 The International Space Station orbits around the Earth at a constant speed You and your partner will each be given a double number line or a table that represents this situation 1 Complete the parts of your representation that you can figure out for sure 2 Share information with your partner and use the information that your partner shares to complete your representation 3 What is the speed of the International Space Station 4 Place the two completed representations side by side Discuss with your partner some ways in which they are the same and some ways in which they are different 5 Record at least one way that they are the same and one way they are different 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 195

G6M2 LESSON 13 ZEARN MATH STUDENT EDITION Lesson Summary On a double number line diagram we put labels in front of each line to tell what the numbers represent On a table we put labels at the top of each column to tell what the numbers represent Here are two different ways we can represent the situation A snail is moving at a constant speed down a sidewalk traveling 6 centimeters per minute 3 0 6 12 18 0 1 2 3 Distance traveled cm Elapsed time min 3 3 Distance Traveled cm Elapsed time min 12 2 6 1 60 10 18 3 3 Both double number lines and tables can help us use multiplication to make equivalent ratios but there is an important difference between the two representations On a double number line the numbers on each line are listed in order With a table you can write the ratios in any order For this reason sometimes a table is easier to use to solve a problem For example what if we wanted to know how far the snail travels in 10 minutes Notice that 60 centimeters in 10 minutes is shown on the table but there is not enough room for this information on the double number line 196 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 13 Date GRADE 6 MISSION 2 LESSON 13 Exit Ticket In a sprint to the finish a professional cyclist travels 380 meters in 20 seconds At that rate how far does the cyclist travel in 3 seconds 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 197

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ZEARN MATH STUDENT EDITION G6M2 LESSON 14 Lesson 14 Solving Equivalent Ratio Problems Let s practice getting information from our partner Warm Up 1 What information would you need to solve the problem below A red car and a blue car enter the highway at the same time and travel at a constant speed How far apart are they after 4 hours Concept Exploration ACTIVITY 1 2 You will be given either a problem card or a data card Do not show or read your card to your partner If your teacher gives you the problem card If your teacher gives you the data card 1 1 Read your card silently 2 Ask your partner What specific information do you need and wait for them to ask for information If your partner asks for information that is not on the card do not do the calculations for them Tell them you don t have that information 3 Have them explain Why do you need that information before telling them the information 4 After your partner solves the problem ask them to explain their reasoning even if you understand what they have done Read your card silently and think about what you need to know to be able to answer the questions 2 Ask your partner for the specific information that you need 3 Explain how you are using the information to solve the problem 4 Solve the problem and show your reasoning to your partner Both you and your partner should record a solution to each 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 199

G6M2 LESSON 14 ZEARN MATH STUDENT EDITION Lesson Summary To solve problems about something happening at the same rate we often need Two pieces of information that allow us to write a ratio that describes the situation A third piece of information that gives us one number of an equivalent ratio Solving the problem often involves finding the other number in the equivalent ratio Suppose we are making a large batch of fizzy juice and the recipe says Mix 5 cups of cranberry juice with 2 cups of soda water We know that the ratio of cranberry juice to soda water is 5 20 and that we need 2 5 cups of cranberry juice per cup of soda water We still need to know something about the size of the large batch If we use 16 cups of soda water what number goes with 16 to make a ratio that is equivalent to 5 2 To make this large batch taste the same as the original recipe we would need to use 40 cups of cranberry juice 200 Cranberry juice cups Soda water cups 5 2 2 5 1 40 16 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

ZEARN MATH STUDENT EDITION Name G6M2 LESSON 14 Date GRADE 6 MISSION 2 LESSON 14 Exit Ticket Jada wants to know how fast the water comes out of her faucet What information would she need to know to be able to determine that 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 201

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ZEARN MATH STUDENT EDITION G6M2 LESSON 15 Lesson 15 Part Part Whole Ratios Let s look at situations where you can add the quantities in a ratio together Warm Up Determine if each problem is true or false 1 1 5 45 45 5 1 5 20 1 4 24 1 6 1 6 42 42 1 486 12 480 12 6 12 Concept Exploration ACTIVITY 1 2 1 A recipe for maroon paint says to mix 5 ml of red paint with 3 ml of blue paint Answer the following questions about this recipe Use snap cubes to represent the amounts of red and blue paint in the recipe Then draw a sketch of your snap cube representation of the maroon paint a What amount does each cube represent b How many milliliters of maroon paint will there 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 203

G6M2 LESSON 15 ZEARN MATH STUDENT EDITION 2 a Suppose each cube represents 2 ml How much of each color paint is there Red ml Blue ml Maroon ml b Suppose each cube represents 5 ml How much of each color paint is there Red ml Blue ml Maroon ml 3 a Suppose you need 80 ml of maroon paint How much red and blue paint would you mix Be prepared to explain your reasoning Red ml Blue ml Maroon 80 ml b If the original recipe is for one batch of maroon paint how many batches are in 80 ml of maroon paint ACTIVITY 2 3 204 Solve each of the following problems and show your thinking If you get stuck consider drawing a tape diagram to represent the situation 1 The ratio of students wearing sneakers to those wearing boots is 5 to 6 If there are 33 students in the class and all of them are wearing either sneakers or boots how many of them are wearing sneakers 2 A recipe for chicken marinade says Mix 3 parts oil with 2 parts soy sauce and 1 part orange juice If you need 42 cups of marinade in all how much of each ingredient should you use 3 Elena makes fruit punch by mixing 4 parts cranberry juice to 3 parts apple juice to 2 parts grape juice If one batch of fruit punch includes 30 cups of apple juice how large is this batch of fruit punch 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 15 Lesson Summary A tape diagram is another way to represent a ratio All the parts of the diagram that are the same size have the same value For example this tape diagram represents the ratio of ducks to swans in a pond which is 4 5 The first tape represents the number of ducks It has 4 parts The second tape represents the number of swans It has 5 parts There are 9 parts in all because 4 5 9 Suppose we know there are 18 of these birds in the pond and we want to know how many are ducks The 9 equal parts on the diagram need to represent 18 birds in all This means that each part of the tape diagram represents 2 birds because 18 9 2 There are 4 parts of the tape representing ducks and 4 2 8 so there are 8 ducks in the pond Ducks Swans Ducks 2 2 2 2 18 Swans 2 2 2 2 2 TERMINOLOGY Tape diagram 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 205

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ZEARN MATH STUDENT EDITION Name G6M2 LESSON 15 Date GRADE 6 MISSION 2 LESSON 15 Exit Ticket The first floor of a house consists of a kitchen playroom and dining room The areas of the kitchen playroom and dining room are in the ratio 4 3 2 The combined area of these three rooms is 189 square feet What is the area of each room 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 207

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ZEARN MATH STUDENT EDITION G6M2 LESSON 16 Lesson 16 Solving More Ratio Problems Let s compare all our strategies for solving ratio problems Warm Up 1 Describe a situation with two quantities that this tape diagram could represent 3 3 3 3 3 3 3 3 3 3 Concept Exploration ACTIVITY 1 TASK 1 2 1 A teacher is planning a class trip to the aquarium The aquarium requires 2 chaperones for every 15 students The teacher plans accordingly and orders a total of 85 tickets How many tickets are for chaperones and how many are for students Solve this problem in one of three ways a Use a triple number line Kids 0 15 0 2 0 17 Chaperones Total 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 209

G6M2 LESSON 16 ZEARN MATH STUDENT EDITION b Use a table Fill rows as needed c Kids Chaperones Total 15 2 17 Use a tape diagram Kids 85 Chaperones 2 210 After your small group discusses all three strategies which do you prefer for this problem and why 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 16 Lesson Summary When solving a problem involving equivalent ratios it is often helpful to use a diagram Any diagram is fine as long as it correctly shows the mathematics and you can explain it Let s compare three different ways to solve the same problem The ratio of adults to kids in a school is 2 7 If there is a total of 180 people how many of them are adults Tape diagrams are especially useful for this type of problem because both parts of the ratio have the same units number of people and we can see the total number of parts Number of adults Number of kids Number of adults This tape diagram has 9 equal parts and they need to represent Number of kids 180 people total That means each part represents 180 9 or 20 people 20 20 20 20 180 20 20 20 20 20 Two parts of the tape diagram represent adults There are 40 adults in the school because 2 20 40 20 Double or triple number lines are useful when we want to see how far apart the numbers are from one another They are harder to use with very big or very small numbers but they could support our reasoning Adults 0 2 4 0 7 14 0 9 18 Kids Total 180 Tables are especially useful when the problem has very large or very small numbers We ask ourselves 9 times what is 180 The answer is 20 Next we multiply 2 by 20 to get the total number of adults in the school Another reason to make diagrams is to communicate our thinking to others Here are some good habits when making diagrams 20 Adults Kids Total 2 7 9 180 Label each part of the diagram with what it represents Label important amounts Make sure you read what the question is asking and answer it Make sure you make the answer easy to find Include units in your answer For example write 4 cups instead of just 4 Double check that your ratio language is correct and matches your diagram 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 211

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ZEARN MATH STUDENT EDITION Name G6M2 LESSON 16 Date GRADE 6 MISSION 2 LESSON 16 Exit Ticket You are having a pizza making party You will need 6 ounces of dough and 4 ounces of sauce for each person at the party including yourself the host Once you have a total count of guests you buy exactly the needed amount of all the ingredients The dough and sauce that you buy weigh 130 ounces all together 1 How many ounces of dough did you buy 2 How many ounces of sauce did you buy 3 How many guests are coming to the party 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 213

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ZEARN MATH STUDENT EDITION G6M2 LESSON 17 Lesson 17 A Fermi Problem Let s solve a Fermi problem Warm Up 1 Andre likes a hot cocoa recipe with 1 cup of milk and 3 tablespoons of cocoa He poured 1 cup of milk but accidentally added 5 tablespoons of cocoa 1 How can you fix Andre s mistake and make his hot cocoa taste like the recipe 2 Explain how you know your adjustment will make Andre s hot cocoa taste the same as the one in the recipe 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 215

G6M2 LESSON 17 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 216 Answer the problems about the Fermi question your class chose in your notes 1 Record the Fermi question that your class will explore together 2 Make an estimate of the answer If making an estimate is too hard consider writing down a number that would definitely be too low and another number that would definitely be too high 3 What are some smaller sub questions we would need to figure out to reasonably answer our bigger question 4 Think about how the smaller questions above should be organized to answer the big question Label each smaller question with a number to show the order in which they should be answered If you notice a gap in the set of sub questions i e there is an unlisted question that would need to be answered before the next one could be tackled write another question to fill the gap 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

ZEARN MATH STUDENT EDITION G6M2 LESSON 17 ACTIVITY 2 3 Answer the problems about your own Fermi questions in your notes 1 Brainstorm at least five Fermi problems that you want to research and solve If you get stuck consider starting with How much would it cost to or How long would it take to 2 Pause here so your teacher can review your questions and approve one of them 3 Use the graphic organizer to break your problem down into sub questions Subquestion Subquestion Answer Answer Fermi problem Subquestion Subquestion Answer Answer 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 217

G6M2 LESSON 17 218 ZEARN MATH STUDENT EDITION 4 Find the information you need to get closer to answering your question Measure make estimates and perform any necessary calculations If you get stuck consider using tables or double number line diagrams 5 Create a visual display that includes your Fermi problem and your solution Organize your thinking so it can be followed by others 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

Grade 6 Mission 3 Unit Rates And Percentages

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ZEARN MATH STUDENT EDITION G6M3 LESSON 1 Lesson 1 Using Unit Rate to Solve Problems Reason about rate per 1 to solve problems Warm Up 1 Use the picture to estimate the height of Hyperion the tallest known tree Hyperion Statue of Liberty Human adult Concept Exploration ACTIVITY 1 2 A window washing crew can finish 15 windows in 18 minutes If this crew was assigned to wash all the windows on the outside of the Burj Khalifa how long will the crew be washing at this rate 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 221

G6M3 LESSON 1 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 In 2011 a professional climber scaled the outside of the Burj Khalifa making it all the way to 828 meters the highest point on which a person can stand in 6 hours Assuming they climbed at the same rate the whole way 222 1 How far did they climb in the first 2 hours 2 How far did they climb in 5 hours 3 How far did they climb in the final 15 minutes 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 1 Lesson Summary There are many real world situations in which something keeps happening at the same rate For example a bus stop that is serviced by 4 buses per hour a washing machine that takes 45 minutes per load of laundry a school cafeteria that serves 15 students per minute In situations like these we can use equivalent ratios to predict how long it will take for something to happen some number of times or how many times it will happen in a particular length of time How long will it take the school cafeteria to serve 600 students Number of students Time in minutes 15 1 60 4 600 40 The table shows that it will take the cafeteria 40 minutes to serve 600 students How many students can the cafeteria serve in 1 hour 0 300 600 900 0 20 40 60 Number of students Time in minutes The double number line shows that the cafeteria can serve 900 students in 1 hour 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 223

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 1 Date GRADE 6 MISSION 3 LESSON 1 Exit Ticket The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds How far does the elevator travel in 11 seconds Explain your 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 225

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ZEARN MATH STUDENT EDITION G6M3 LESSON 2 Lesson 2 Anchoring Units of Measurement Let s see how big different things are Warm Up 1 Estimate the volume of the tiny salt shaker Lesson ACTIVITY 1 2 Your teacher will assign you one of the following lengths 1 centimeter 1 foot 1 inch 1 meter or 1 yard Estimate and cut a piece of string as close to your assigned length as you can without using a measurement tool ACTIVITY 2 3 1 Your teacher will give you some cards with the names of different units of measurement and other cards with pictures of objects Sort the units of measurement into groups based on the attribute they measure Pause here so your teacher can review your groups 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 227

G6M3 LESSON 2 ZEARN MATH STUDENT EDITION 2 Match each picture card that has L in the top right corner with the closest unit to the length of the object 3 Match each picture card that has V in the top right corner with the closest unit to the volume of the object 4 Match each picture card that has WM in the top right corner with the closest unit to the weight or mass of the object Lesson Summary We can use everyday objects to estimate standard units of measurement For units of length 1 millimeter is about the thickness of a dime 1 centimeter is about the width of a pinky finger 1 inch is about the length from the tip of your thumb to the first knuckle 1 foot is the length of a football 1 yard is about the length of a baseball bat 1 meter is about the length of a baseball bat and ball 1 kilometer is about the distance someone walks in ten minutes 1 mile is about the distance someone runs in ten minutes For units of volume 228 1 milliliter is about the volume of a raindrop For units of weight and mass 1 gram is about the mass of a raisin 1 cup is about the volume of a school milk carton 1 ounce is about the weight of a slice of bread 1 quart is about the volume of a large sports drink bottle 1 pound is about the weight of a loaf of bread 1 liter is about the volume of a reusable water bottle 1 kilogram is about the mass of a textbook 1 ton is about the weight of a small car 1 gallon is about the volume of a large milk jug 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

ZEARN MATH STUDENT EDITION Name G6M3 LESSON 2 Date GRADE 6 MISSION 3 LESSON 2 Exit Ticket Lin and Elena have discovered they have so much in common 1 They each walk 500 units to school Who walks 500 feet and who walks 500 yards Explain your reasoning School Lin s house Elena s house 2 They each have a fish tank holding 20 units of water Whose tank holds 20 gallons and whose holds 20 cups Explain your reasoning Elena s Fish Tank 3 Lin s Fish Tank They each have a brother who weighs 40 units Whose brother weighs 40 pounds and whose weighs 40 kilograms Explain your reasoning Elena s Brother Lin s Brother 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 229

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ZEARN MATH STUDENT EDITION G6M3 LESSON 3 Lesson 3 Measuring with Different Sized Units Let s measure things Warm Up 1 Does it take more black rods or gray rods lined up end to end to measure the width of a piece of printer paper Concept Exploration ACTIVITY 1 2 You will work with different units of measure at 5 different stations Station 1 Each large cube is 1 cubic inch Count how many cubic inches completely pack the box without gaps Each small cube is 1 cubic centimeter Each rod is composed of 10 cubic centimeters Count how many cubic centimeters completely fill the box Cubic inches Cubic centimeters Meters Feet Volume of the box Station 2 Your teacher showed you a length Use the meter stick to measure the length to the nearest meter Use a ruler to measure the length to the nearest foot Length of 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 231

G6M3 LESSON 3 ZEARN MATH STUDENT EDITION Station 3 Count how many times you can fill the quart bottle from the gallon jug Count how many times you can fill the liter bottle from the gallon jug Quarts Liters 1 gallon of water Station 4 Select 2 3 different objects to measure on the scale Record the weights in ounces pounds grams and kilograms Ounces Pounds Grams Kilograms Object 1 Object 2 Object 3 Station 5 Count how many level teaspoons of salt fill the graduated cylinder to 20 milliliters 40 milliliters and 50 milliliters Pour the salt back into the original container Milliliters 232 Small amount of salt 20 Medium amount of salt 40 Large amount of salt 50 Teaspoons 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

ZEARN MATH STUDENT EDITION 3 G6M3 LESSON 3 After you finish all five stations answer these questions with your group 1 a Which is larger a cubic inch or a cubic centimeter b Did more cubic inches or cubic centimeters fit in the cardboard box Why 2 Did it take more feet or meters to measure the indicated length Why 3 Which is larger a quart or a liter Explain your reasoning 4 Use the data from Station 4 to put the units of weight and mass in order from smallest to largest Explain your reasoning 5 a About how many teaspoons of salt would it take to fill the graduated cylinder to 100 milliliters b If you poured 15 teaspoons of salt into an empty graduated cylinder about how many milliliters would it fill c How many milliliters per teaspoon are there d How many teaspoons per milliliter are there 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 233

G6M3 LESSON 3 ZEARN MATH STUDENT EDITION Lesson Summary The size of the unit we use to measure something affects the measurement If we measure the same quantity with different units it will take more of the smaller unit and fewer of the larger unit to express the measurement For example a room that measures 4 yards in length will measure 12 feet There are 3 feet in a yard so one foot is 234 1 3 of a yard It takes 3 times as many feet to measure the same length as it does with yards It takes 1 3 as many yards to measure the same length as it does with 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 3 Name Date GRADE 6 MISSION 3 LESSON 3 Exit Ticket 1 Lin has a pet German Shepherd that weighs 38 when measured in one unit and 84 when measured in a different unit Which measurement is in pounds and which is in kilograms 38 2 170 Behind Lin s house there is a kiddie pool that holds 180 or 680 units of water depending on which unit you are using to measure Which measurement is in gallons and which is in liters 180 4 84 Elena has a pet parakeet that weighs 6 when measured in one unit and 170 when measured in a different unit Which measurement is in ounces and which is in grams 6 3 680 Behind Elena s house there is a portable storage container that holds 29 or 1 024 units depending on which unit you are using to measure Which measurement is in cubic feet and which is in cubic meters 29 1 024 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 235

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ZEARN MATH STUDENT EDITION G6M3 LESSON 4 Lesson 4 Converting Units Let s convert measurements to different units Warm Up 1 Find the values mentally 1 1 of 32 4 2 3 of 32 4 3 3 of 32 8 4 3 of 64 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 237

G6M3 LESSON 4 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Elena and her mom are on a road trip outside the United States Elena sees this road sign Elena s mom is driving 75 miles per hour when she gets pulled over for speeding The police officer explains that 8 kilometers is approximately 5 miles a How many kilometers are in 1 mile b How many miles are in 1 kilometer 3 238 MAXIMUM 80 If the speed limit is 80 kilometers per hour and Elena s mom was driving 75 miles per hour was she speeding By how much 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 4 ACTIVITY 2 43 1 A veterinarian uses weights in kilograms to figure out what dosages of medicines to prescribe for animals For every 10 kilograms there are 22 pounds Calculate each animal s weight in kilograms Explain or show your reasoning If you get stuck consider drawing a double number line or table a Fido the Labrador weighs 88 pounds b Spot the Beagle weighs 33 pounds c 2 Bella the Chihuahua weighs 5 1 2 pounds A certain medication says it can only be given to animals over 25 kilograms How much is this in pounds 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 239

G6M3 LESSON 4 ZEARN MATH STUDENT EDITION Lesson Summary When we measure something in two different units the measurements form an equivalent ratio We can reason with these equivalent ratios to convert measurements from one unit to another Suppose you cut off 20 inches of hair Your Canadian friend asks how many centimeters of hair that was Since 100 inches equal 254 centimeters we can use equivalent ratios to find out how many centimeters equal 20 inches Using a double number line 0 20 40 60 80 100 0 50 8 101 6 152 4 203 2 254 length in length cm Using a table Length in Length cm 100 254 1 2 54 20 50 8 One quick way to solve the problem is to start by finding out how many centimeters are in 1 inch We can then multiply 2 54 and 20 to find that 20 inches equals 50 8 centimeters 240 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

ZEARN MATH STUDENT EDITION Name G6M3 LESSON 4 Date GRADE 6 MISSION 3 LESSON 4 Exit Ticket A large bucket holds 5 gallons of water which is about the same as 19 liters of water A small bucket holds 2 gallons of water About how many liters does it hold 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 241

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ZEARN MATH STUDENT EDITION G6M3 LESSON 5 Lesson 5 Comparing Speeds and Prices Let s compare some speeds and some prices Warm Up 1 Is the value of each expression closer to 12 1 or 112 1 20 18 2 9 20 3 7 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 243

G6M3 LESSON 5 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 1 2 Some students did treadmill workouts each one running at a constant speed Answer the questions about their workouts Explain or show your reasoning Tyler ran 4 200 meters in 30 minutes Kiran ran 6 300 meters in Mai ran 6 3 kilometers in 45 minutes 1 2 hour What is the same about the workouts done by a Tyler and Kiran b Kiran and Mai c 244 Mai and Tyler 2 At what rate did each of them run 3 How far did Mai run in her first 30 minutes on the treadmill 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 5 ACTIVITY 2 3 Four different stores posted ads about special sales on 15 oz cans of baked beans BAKED BEANS BAKED BEANS BAKED BEANS BAKED BEANS 8 for 6 10 for 10 2 for 3 80 each 1 Which store is offering the best deal Explain your reasoning 2 The last store listed is also selling 28 oz cans of baked beans for 1 40 each How does that price compare to the other prices 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 245

G6M3 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary Distance meters Time minutes 3 000 20 1 500 10 150 1 Distance meters Time minutes 2 550 17 150 1 Diego ran 3 kilometers in 20 minutes Andre ran 2 550 meters in 17 minutes Who ran faster Since neither their distances nor their times are the same we have two possible strategies Find the time each person took to travel the same distance The person who traveled that distance in less time is faster Find the distance each person traveled in the same time The person who traveled a longer distance in the same amount of time is faster It is often helpful to compare distances traveled in 1 unit of time 1 minute for example which means finding the speed such as meters per minute Let s compare Diego and Andre s speeds in meters per minute Both Diego and Andre ran 150 meters per minute so they ran at the same speed Finding ratios that tell us how much of quantity per 1 unit of quantity is an efficient way to compare rates in different situations Here are some familiar examples 246 Car speeds in miles per hour Fruit and vegetable prices in dollars per pound 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 5 Name Date GRADE 6 MISSION 3 LESSON 5 Exit Ticket Bottles of sparkling water usually cost 1 69 each This week they are on sale for 4 for 5 SPARKLING WATER 4 for 5 Regular 1 69 each You bought one last week and one this week Did you pay more or less for the bottle this week How much more or less 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 247

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ZEARN MATH STUDENT EDITION G6M3 LESSON 6 Lesson 6 Interpreting Rates Let s explore unit rates Warm Up 1 1 Think of two things you have heard described in terms of something per something Share your ideas with your group and listen to everyone else s idea Make a group list of all unique ideas Be prepared to share these with the class Concept Exploration ACTIVITY 1 2 1 Priya Han Lin and Diego are all on a camping trip with their families The first morning Priya and Han make oatmeal for the group The instructions for a large batch say Bring 15 cups of water to a boil and then add 6 cups of oats Priya says The ratio of the cups of oats to the cups of water is 6 15 That s 0 4 cups of oats per cup of water Han says The ratio of the cups of water to the cups of oats is 15 6 That s 2 5 cups of water per cup of oats Who is correct Explain your reasoning If you get stuck consider using the table Water cups Oats cups 15 6 1 1 2 The next weekend after the camping trip Lin and Diego each decide to cook a large batch of oatmeal to have breakfasts ready for the whole week a Lin decides to cook 5 cups of oats How many cups of water should she boil 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 249

G6M3 LESSON 6 ZEARN MATH STUDENT EDITION b Diego boils 10 cups of water How many cups of oats should he add into the water 3 Did you use Priya s rate 0 4 cups of oats per cup of water or Han s rate 2 5 cups of water per cup of oats to help you answer each of the previous two questions Why ACTIVITY 2 3 1 For each situation find the unit rates A cheesecake recipe says Mix 12 oz of cream cheese with 15 oz of sugar a How many ounces of cream cheese are there for every ounce of sugar b How many ounces of sugar is that for every ounce of cream cheese 2 Mai s family drinks a total of 10 gallons of milk every 6 weeks a How many gallons of milk does the family drink per week b How many weeks does it take the family to consume 1 gallon of milk 3 Tyler paid 16 for 4 raffle tickets a What is the price per ticket b How many tickets is that per dollar 250 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

ZEARN MATH STUDENT EDITION 4 G6M3 LESSON 6 For each problem decide which unit rate from the previous situations you prefer to use Next solve the problem and show your thinking a If Lin wants to make extra cheesecake filling how much cream cheese will she need to mix with 35 ounces of sugar b How many weeks will it take Mai s family to finish 3 gallons of milk c How much would all 1 000 raffle tickets cost Lesson Summary Suppose a farm lets us pick 2 pounds of blueberries for 5 dollars We can say 2 5 We get pound of blueberries per dollar The blueberries cost 5 2 dollars per pound Blueberries pounds Price dollars 2 5 1 5 2 2 5 1 The cost per pound and the number of pounds per dollar are the two unit rates for this situation A unit rate tells us how much of one quantity for 1 of the other quantity Each of these numbers is useful in the right situation If we want to find out how much 8 pounds of blueberries will cost it helps to know how much 1 pound of blueberries will cost 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 251

G6M3 LESSON 6 ZEARN MATH STUDENT EDITION Blueberries pounds Price dollars 1 5 2 8 8 2 5 If we want to find out how many pounds we can buy for 10 dollars it helps to know how many pounds we can buy for 1 dollar Blueberries pounds Price dollars 2 5 1 10 2 5 10 Which unit rate is most useful depends on what question we want to answer so be ready to find either one TERMINOLOGY Unit Rate 252 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 6 Name Date GRADE 6 MISSION 3 LESSON 6 Exit Ticket Two pounds of grapes cost 6 1 Complete the table showing the price of different amounts of grapes at this rate Grapes pounds Price dollars 2 6 1 1 2 Explain the meaning of each of the numbers you found 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 253

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ZEARN MATH STUDENT EDITION G6M3 LESSON 7 Lesson 7 Equivalent Ratios Have the Same Unit Rates Let s revisit equivalent ratios Warm Up 1 Which one doesn t belong Be prepared to explain your reasoning a 5 miles in 15 minutes b 3 minutes per mile c 20 miles per hour d 2 kilometers per hour Concept Exploration ACTIVITY 1 2 1 Two burritos cost 14 00 Answer the following questions using the table below Complete the table to show the cost for 4 5 and 10 burritos at that rate Next find the cost for a single burrito in each case 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 255

G6M3 LESSON 7 ZEARN MATH STUDENT EDITION Number of burritos Cost in dollars 2 14 00 Unit price dollars per burrito 4 5 10 b 2 What do you notice about the values in this table 3 256 Noah bought b burritos and paid c dollars Lin bought twice as many burritos as Noah and paid twice the cost he did Number of burritos Cost in dollars Unit price dollars per burrito Noah b c c b Lin 2 b 2 c 1 How much did Lin pay per burrito 2 Explain why if you can buy b burritos for c dollars or buy 2 b burritos for 2 c dollars the cost per item is the same in either case 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 7 ACTIVITY 2 43 Complete the table Then explain the strategy you used to do so Time in hours 53 Speed bracelets per hour 2 6 5 6 7 6 66 6 100 6 Here is a partially filled table from an earlier activity Use the same strategy you used for the bracelet problem to complete this table Number of burritos 63 Number of bracelets Cost in dollars Unit price dollars per burrito 14 00 7 00 28 00 7 00 5 7 00 10 7 00 Next compare your results with those in the first table in the previous activity Do they match Explain why or why not 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 257

G6M3 LESSON 7 ZEARN MATH STUDENT EDITION Lesson Summary The table shows different amounts of apples selling at the same rate which means all of the ratios in the table are equivalent In each case we can find the unit price in dollars per pound by dividing the price by the number of pounds Apples pounds Price dollars Unit price dollars per pound 4 10 10 4 2 50 8 20 20 8 2 50 20 50 50 20 2 50 The unit price is always the same Whether we buy 4 pounds of apples for 10 dollars or 8 pounds of apples for 20 dollars the apples cost 2 50 dollars per pound We can also find the number of pounds of apples we can buy per dollar by dividing the number of pounds by the price Apples pounds Price dollars Pounds per dollar 4 10 4 10 0 4 8 20 8 20 0 4 20 50 20 50 0 4 The number of pounds we can buy for a dollar is the same as well Whether we buy 4 pounds of apples for 10 dollars or 8 pounds of apples for 20 dollars we are getting 0 4 pounds per dollar This is true in all contexts when two ratios are equivalent the two unit rates will always be equal 258 Quantity x Quantity y Unit rate 1 Unit rate 2 a b a b b a s a s b s a s b a b s b s a b a 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 7 Name Date GRADE 6 MISSION 3 LESSON 7 Exit Ticket A cheetah can run at its top speed for about 25 seconds Complete the table to represent a cheetah running at a constant speed Explain or show your reasoning Time seconds Distance meters 4 120 Speed meters per second 25 270 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 259

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ZEARN MATH STUDENT EDITION G6M3 LESSON 8 Lesson 8 More about Constant Speed Let s investigate constant speed some more Warm Up 1 While training for a race Andre s dad ran 12 miles in 75 minutes on a treadmill If he runs at that rate 1 How long would it take him to run 8 miles 2 How far could he run in 30 minutes Concept Exploration ACTIVITY 1 2 Kiran and Clare live 24 miles away from each other along a rail trail One Saturday the two friends started walking toward each other along the trail at 8 00 a m with a plan to have a picnic when they meet Kiran walks at a speed of 3 miles per hour while Clare walks 3 4 miles per hour 1 After one hour how far apart will they be 2 Make a table showing how far apart the two friends are after 0 hours 1 hour 2 hours and 3 hours 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 261

G6M3 LESSON 8 262 ZEARN MATH STUDENT EDITION 3 At what time will the two friends meet and have their picnic 4 Kiran says If I walk 3 miles per hour toward you and you walk 3 4 miles per hour toward me it s the same as if you stay put and I jog 6 4 miles per hour What do you think Kiran means by this Is he correct 5 Several months later they both set out at 8 00 a m again this time with Kiran jogging and Clare still walking at 3 4 miles per hour This time they meet at 10 30 a m How fast was Kiran jogging 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 8 Lesson Summary When two objects are each moving at a constant speed and their distance to time ratios are equivalent we say that they are moving at the same speed If their time distance ratios are not equivalent they are not moving at the same speed We describe speed in units of distance per unit of time like miles per hour or meters per second A snail that crawls 5 centimeters in 2 minutes is traveling at a rate of 2 5 centimeters per minute A toddler that walks 9 feet in 6 seconds is traveling at a rate of 1 5 feet per second A cyclist who bikes 20 kilometers in 2 hours is traveling at a rate of 10 kilometers per hour We can also use pace to describe distance and time We measure pace in units such as hours per mile or seconds per meter A snail that crawls 5 centimeters in 2 minutes has a pace of 0 4 minutes per centimeter A toddler walking 9 feet in 6 seconds has a pace of A cyclist who bikes 20 kilometers in 2 hours has a pace of 0 1 hours per kilometer 2 3 seconds per foot Speed and pace are reciprocals Both can be used to compare whether one object is moving faster or slower than another object An object with the higher speed is faster than one with a lower speed because the former travels a greater distance in the same amount of time An object with the greater pace is slower than one with a smaller pace because the former takes more time to travel the same distance Because speed is a rate per 1 unit of time for ratios that relate distance and time we can multiply the amount of time traveled by the speed to find the distance traveled Time minutes Distance centimeters 2 5 1 2 5 4 4 2 5 TERMINOLOGY Pace Speed 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 263

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 8 Date GRADE 6 MISSION 3 LESSON 8 Exit Ticket A penguin walks 10 feet in 6 seconds At this speed 1 How far does the penguin walk in 45 seconds 2 How long does it take the penguin to walk 45 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 265

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ZEARN MATH STUDENT EDITION G6M3 LESSON 9 Lesson 9 Solving Rate Problems Let s use unit rates like a pro Warm Up 1 How much is shaded in each one Concept Exploration ACTIVITY 1 2 Your teacher will give you a set of cards showing different offers 1 Find card A and work with your partner to decide whether the offer on card A is a good deal Explain or show your reasoning 2 Next split cards B E so you and your partner each have two a Decide individually if your two cards are good deals Explain your reasoning b For each of your cards explain to your partner if you think it is a good deal and why Listen to your partner s explanations for their cards If you disagree 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 267

G6M3 LESSON 9 c 3 ZEARN MATH STUDENT EDITION Revise any decisions about your cards based on the feedback from your partner When you and your partner are in agreement about cards B E place all the cards you think are a good deal in one stack and all the cards you think are a bad deal in another stack Be prepared to explain your reasoning ACTIVITY 2 3 Wild animals from around the world wanted to hold an athletic competition but no one would let them on an airplane They decided to just measure how far each animal could sprint in one minute and send the results to you to decide the winner Animal Sprint distance Cougar 1 408 yards Antelope 1 mile Hare 49 632 inches Kangaroo 1 073 meters Ostrich 1 15 kilometers Coyote 3 773 feet You look up the following information about converting units of length 1 inch 2 54 centimeters 268 1 Which animal sprinted the farthest 2 What are the place rankings for all of the animals 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 9 Lesson Summary Sometimes we can find and use more than one unit rate to solve a problem Suppose a grocery store is having a sale on shredded cheese A small bag that holds 8 ounces is sold for 2 A large bag that holds 2 kilograms is sold for 16 How do you know which is a better deal Here are two different ways to solve this problem Compare dollars per kilogram The large bag costs 8 per kilogram because 16 2 8 The small bag holds 1 2 pound of cheese because there are 16 ounces in 1 pound and 8 16 1 2 1 2 The small bag costs 4 per pound because 2 4 This is about 8 80 per kilogram because there are about 2 2 pounds in 1 kilogram and 4 00 2 2 8 80 The large bag is a better deal because it costs less money for the same amount of cheese Compare ounces per dollar With the small bag we get 4 ounces per dollar because 8 2 4 The large bag holds 2 000 grams of cheese There are 1 000 grams in 1 kilogram and 2 1 000 2 000 This means 125 grams per dollar because 2 000 16 125 There are about 28 35 grams in 1 ounce and 125 28 35 4 4 so this is about 4 4 ounces per dollar The large bag is a better deal because you get more cheese for the same amount of money Another way to solve the problem would be to compare the unit prices of each bag in dollars per ounce Try 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 269

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 9 Date GRADE 6 MISSION 3 LESSON 9 Exit Ticket A restaurant sells 10 tacos for 8 49 or 6 of the same kind of taco for 5 40 Which is the better deal Explain how you know 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 271

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ZEARN MATH STUDENT EDITION G6M3 LESSON 10 Lesson 10 What Are Percentages Let s learn about percentages Warm Up Find each answer mentally 1 1 A sticker costs 25 cents How many dollars is that 2 A pen costs 1 50 dollars How many cents is that 3 How many cents are in one dollar 4 How many dollars are in one cent Lesson ACTIVITY 1 2 1 Answer the questions about coins and percentages Complete the table to show the values of these U S coins Coin Penny Nickel Dime Quarter Half Dollar Dollar Value cents The value of a quarter is 25 of the value of a dollar because there are 25 cents for every 100 cents 1 Quarter 1 Dollar 25 100 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 273

G6M3 LESSON 10 2 ZEARN MATH STUDENT EDITION Write the name of the coin that matches each expression a 25 of a dollar d 100 of a dollar b 5 of a dollar e 10 of a dollar c f 1 of a dollar 50 of a dollar 3 The value of 6 dimes is what percent of the value of a dollar 4 The value of 6 quarters is what percent of the value of a dollar ACTIVITY 2 3 A 1 coin is worth 100 of the value of a dollar The double number line below shows this Use the double number line to answer the questions about coins and percentages 0 1 Value of coins dollars 0 274 25 50 75 100 125 150 1 The coins in Jada s pocket are worth 75 of a dollar How much are they worth in dollars 2 The coins in Diego s pocket are worth 150 of a dollar How much are they worth in dollars 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

ZEARN MATH STUDENT EDITION 3 G6M3 LESSON 10 Elena has 3 quarters and 5 dimes What percentage of a dollar does she have Lesson Summary A percentage is a rate per 100 We can find percentages of 10 using a double number line where 10 and 100 are aligned as shown here 0 2 50 5 00 7 50 10 00 12 50 15 00 0 25 50 75 100 125 150 Money dollars Looking at the double number line we can see that 5 00 is 50 of 10 00 and that 12 50 is 125 of 10 00 TERMINOLOGY Percent Percentage 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 275

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 10 Date GRADE 6 MISSION 3 LESSON 10 Exit Ticket 1 Fill in the blank The value of 8 dimes is of the value of a dollar 2 Name a combination of coins that is 130 of the value of a dollar 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 277

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ZEARN MATH STUDENT EDITION G6M3 LESSON 11 Lesson 11 Percentages and Double Number Lines Let s use double number lines to represent percentages Warm Up 1 Each of three friends Lin Jada and Andre had the goal of raising 40 How much money did each person raise Be prepared to explain your reasoning 1 Lin raised 100 of her goal 2 Jada raised 50 of her goal 3 Andre raised 150 of his goal Concept Exploration ACTIVITY 1 2 Elena biked 8 miles on Saturday Use the double number line to answer the questions Be prepared to explain your reasoning 0 Distance miles 0 25 50 75 100 125 1 What is 100 of her Saturday distance 2 On Sunday she biked 75 of her Saturday distance How far was that 3 On Monday she biked 125 of her Saturday distance How far was that 150 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 279

G6M3 LESSON 11 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Jada has a new puppy that weighs 9 pounds The vet says that the puppy is now at about 20 of its adult weight What will be the adult weight of the puppy 0 9 0 20 Weight pounds 43 Andre also has a puppy that weighs 9 pounds The vet says that this puppy is now at about 30 of its adult weight What will be the adult weight of Andre s puppy 0 9 0 30 Weight pounds 53 What is the same about Jada and Andre s puppies What is different Lesson Summary We can use a double number line to solve problems about percentages For example what is 30 of 50 pounds We can draw a double number line like this 0 50 0 30 100 Weight pounds We divide the distance between 0 and 100 and the distance between 0 and 50 pounds into ten equal parts We label the tick marks on the top line by counting by 5s 50 10 5 and on the bottom line counting by 10 100 10 10 We can then see that 30 of 50 pounds is 15 pounds We can also use a table to solve this problem 280 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 11 Weight pounds Percentage 50 100 5 10 15 30 1 10 3 1 10 3 Suppose we know that 140 of an amount is 28 What is 100 of that amount Let s use a double number line to find out 0 28 100 140 Money dollars 0 We divide the distance between 0 and 140 and that between 0 and 28 into fourteen equal intervals We label the tick marks on the top line by counting by 2s and on the bottom line counting by 10 We would then see that 100 is 20 Or we can use a table as shown 1 14 10 Money dollars Percentage 28 140 2 10 20 100 1 14 10 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 281

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 11 Date GRADE 6 MISSION 3 LESSON 11 Exit Ticket A large bottle of juice contains 500 milliliters of juice A medium bottle contains 70 as much juice as the large bottle How many milliliters of juice are in the medium bottle 0 Juice ml 0 100 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 283

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ZEARN MATH STUDENT EDITION G6M3 LESSON 12 Lesson 12 Percentages and Tape Diagrams Let s use tape diagrams to understand percentages Warm Up 1 What do you notice What do you wonder 80 Concept Exploration ACTIVITY 1 2 Jada has a new puppy that weighs 9 pounds It is now at about 20 of its adult weight Here is a diagram that Jada drew about the weight of her puppy 9 9 9 9 9 20 a The adult weight of the puppy will be 45 pounds How can you see that in the diagram b What fraction of its adult weight is the puppy now How can you see that in the diagram 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 285

G6M3 LESSON 12 3 ZEARN MATH STUDENT EDITION Jada s friend has a dog that weighs 90 pounds Here is a diagram Jada drew that represents the weight of her friend s dog and the weight of her puppy 9 9 9 9 9 9 9 9 9 9 9 a How many times greater is the dog s weight than the puppy s b Compare the weight of the puppy and the dog using fractions c Compare the weight of the puppy and the dog using percentages ACTIVITY 2 43 Noah has 5 Answer the questions about Noah and his friends 1 a Elena has 40 as much as Noah How much does Elena have b Compare Elena s and Noah s money using fractions Draw a diagram to illustrate 2 a Diego has 150 as much as Noah How much does Diego have b Compare Diego s and Noah s money using fractions Draw a diagram to illustrate 286 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 12 Lesson Summary Tape diagrams can help us make sense of percentages Consider two problems that we solved earlier using double number lines and tables What is 30 of 50 pounds and What is 100 of a number if 140 of it is 28 Here is a tape diagram that shows that 30 of 50 pounds is 15 pounds 5 5 5 5 5 5 5 5 5 5 10 100 This diagram shows that if 140 of some number is 28 then that number must be 20 4 4 4 4 4 4 4 20 100 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 287

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 12 Date GRADE 6 MISSION 3 LESSON 12 Exit Ticket Complete the statement with a situation and a unit of your choice Then answer the question and draw a diagram A small holds 75 as much as a large 1 If the small unit holds 36 units how much does the large unit hold 2 Draw a diagram to illustrate your answer 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 289

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ZEARN MATH STUDENT EDITION G6M3 LESSON 13 Lesson 13 Benchmark Percentages Let s contrast percentages and fractions Warm Up 1 What percentage of each diagram is shaded Concept Exploration ACTIVITY 1 2 Answer the questions below 1 a How much is 50 of 10 liters of milk 10 b How far is 50 of a 2 000 kilometer trip 2 000 How long is 50 of a 24 hour day d How can you find 50 of any number 50 c 2 a How far is 10 of a 2 000 kilometer trip b How much is 10 of 10 liters of milk c How long is 10 of a 24 hour day d How can you find 10 of any number 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 291

G6M3 LESSON 13 ZEARN MATH STUDENT EDITION 3 a How long is 75 of a 24 hour day b How far is 75 of a 2 000 kilometer trip c How much is 75 of 10 liters of milk d How can you find 75 of any number ACTIVITY 2 3 1 Explain how you can calculate each value mentally 9 is 50 of what number 50 9 292 2 9 is 25 of what number 3 9 is 10 of what number 4 9 is 75 of what number 5 9 is 150 of what number 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 13 Lesson Summary Certain percentages are easy to think about in terms of fractions 1 4 0 0 x 25 1 4 1 2 1 2 3 4 x 50 x 75 x 100 25 of a number is always 50 of a number is always 41 kilometers 75 of a number is always 10 of a number is always 7 We can also find multiples of 10 using tenths For example 70 of a number is always 10 of 7 that number so 70 of 30 days is 10 30 or 21 days 0 1 10 x 3 4 1 10 of that number For example 25 of 40 liters is 1 4 40 or 10 liters of that number For example 50 of 82 kilometers is of that number For example 75 of 1 pound is 3 4 1 2 82 or pound of that number For example 10 of 95 meters is 9 5 meters 7 10 x x 0 10 20 30 40 50 60 70 80 90 100 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 293

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 13 Date GRADE 6 MISSION 3 LESSON 13 Exit Ticket Answer each question and explain your reasoning 1 How long is 50 of 60 minutes 2 How long is 10 of 60 minutes 3 How long is 75 of 60 minutes 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 295

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ZEARN MATH STUDENT EDITION G6M3 LESSON 14 Lesson 14 Solving Percentage Problems Let s solve more percentage problems Warm Up 1 Find the products mentally 6 0 8 2 4 5 0 6 4 Concept Exploration ACTIVITY 1 2 Han and Clare go shopping and they each have a coupon Answer each question and show your reasoning 1 Han buys an item with a normal price of 15 and uses a 10 off coupon How much does he save by using the coupon 2 Clare buys an item with a normal price of 24 but saves 6 by using a coupon For what percentage off is this coupon ACTIVITY 2 3 Your teacher will give you either a problem card or a data card Do not show or read your card to your partner If your teacher gives you the problem card 1 Read your card silently and think about what you need to know to be able to answer the questions 2 Ask your partner for the specific information that you need 3 Explain how you are using the information to solve the problem 4 Solve the problem and show your reasoning to your 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 297

G6M3 LESSON 14 ZEARN MATH STUDENT EDITION If your teacher gives you the data card 1 Read your card silently 2 Ask your partner What specific information do you need and wait for them to ask for information If your partner asks you for information that is not on the card do not do the calculations for them Tell them you don t have that information 3 Have them explain Why do you need that information before telling them the information 4 After your partner solves the problem ask them to explain their reasoning even if you understand what they have done Both partners should record a solution to the problem Lesson Summary A pot can hold 36 liters of water What percentage of the pot is filled when it contains 9 liters of water Here are two different ways to solve this problem Using a double number line 0 9 18 27 36 0 25 50 75 100 Volume liters We can divide the distance between 0 and 36 into four equal intervals so 9 is of 36 or 9 is 25 of 36 Using a table 14 298 Volume liters Percentage 36 100 9 25 14 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

ZEARN MATH STUDENT EDITION Name G6M3 LESSON 14 Date GRADE 6 MISSION 3 LESSON 14 Exit Ticket It takes Jada 20 minutes to walk to school It takes Andre 80 as long to walk to school How long does it take Andre to walk to school 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 299

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ZEARN MATH STUDENT EDITION G6M3 LESSON 15 Lesson 15 Finding This Percent of That Let s solve percentage problems like a pro Warm Up 1 Find the value of each expression mentally 0 23 100 50 100 1 145 100 7 100 Concept Exploration ACTIVITY 1 2 A school held several evening activities last month a music concert a basketball game a drama play and literacy night The music concert was attended by 250 people How many people came to each of the other activities 1 Attendance at a basketball game was 30 of attendance at the concert 2 Attendance at the drama play was 140 of attendance at the concert 3 Attendance at literacy night was 44 of attendance at the concert 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 301

G6M3 LESSON 15 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 During a sale every item in a store is 80 of its regular price 1 If the regular price of a T shirt is 10 what is its sale price 2 The regular prices of five items are shown here Find the sale price of each item Item 1 Item 2 Item 3 Item 4 Item 5 1 4 10 55 120 Regular price Sale price 3 You found 80 of many values Was there a process you repeated over and over to find the sale prices If so describe it 100 80 x 4 302 Select all the expressions that could be used to find 80 of x Be prepared to explain your reasoning 8 100 x 8 10 x 8 5 x 80 x 0 8 x 80 100 x 4 10 x 4 5 x 8 x 0 08 x 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 15 Lesson Summary To find 49 of a number we can multiply the number by 49 or 0 49 100 49 100 0 49x x To find 135 of a number we can multiply the number by To find 6 of a number we can multiply the number by 0 6 100 49 100 x x 135 or 1 35 100 6 or 0 06 100 x 135 100 x 0 0 06 x 0 49 x x 1 35 x 0 6 49 100 135 In general to find P of x we can multiply P 100 x 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 303

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ZEARN MATH STUDENT EDITION G6M3 LESSON 15 Name Date GRADE 6 MISSION 3 LESSON 15 Exit Ticket Order these three values from least to greatest Explain or show your reasoning 65 of 80 82 of 50 170 of 30 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 305

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ZEARN MATH STUDENT EDITION G6M3 LESSON 16 Lesson 16 Finding the Percentage Let s find percentages in general Warm Up 1 Is each statement true or false Be prepared to explain your reasoning 1 25 of 512 is equal to 14 500 2 90 of 133 is equal to 0 9 133 3 30 of 44 is equal to 3 of 440 4 The percentage 21 is of 28 is equal to the percentage 30 is of 40 Concept Exploration ACTIVITY 1 2 A school held a jump roping contest Diego jumped rope for 20 minutes 1 Jada jumped rope for 15 minutes What percentage of Diego s time is that 2 Lin jumped rope for 24 minutes What percentage of Diego s time is that 3 Noah jumped rope for 9 minutes What percentage of Diego s time is that 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 307

G6M3 LESSON 16 4 5 ZEARN MATH STUDENT EDITION Record your answers in this table Write the quotients in the last column as decimals Time minutes Percentage Time 20 Diego 20 100 Jada 15 15 20 Lin 24 24 20 Noah 9 9 20 20 20 1 What do you notice about the numbers in the last two columns of the table ACTIVITY 2 3 308 A restaurant has a sign by the front door that says Maximum occupancy 75 people Answer each question and explain or show your reasoning 1 What percentage of its capacity is 9 people 2 What percentage of its capacity is 51 people 3 What percentage of its capacity is 84 people 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 16 Lesson Summary What percentage of 90 kg is 36 kg One way to solve this problem is to first find what percentage 1 kg is of 90 and then multiply by 36 Mass kg Percentage 90 100 1 90 36 1 1 90 100 36 36 90 100 1 90 36 1 From the table we can see that 1 kg is 90 100 so 36 kg is 36 90 100 or 40 of 90 We can confirm this on a double number line 0 9 18 27 36 45 54 63 72 81 90 0 10 20 30 40 50 60 70 80 90 100 In general to find what percentage a number C is of another number B is to calculate find do that by multiplying BC 100 C B of 100 We can Suppose a school club has raised 88 for a project but needs a total of 160 What percentage of its 88 88 goal has the club raised To find what percentage 88 is of 160 we find 160 of 100 or 160 100 which 11 equals 20 100 or 55 The club raised 55 of its goal 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 309

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ZEARN MATH STUDENT EDITION Name G6M3 LESSON 16 Date GRADE 6 MISSION 3 LESSON 16 Exit Ticket A jet plane can carry up to 200 000 liters of fuel It used 130 000 liters of fuel during a flight What percentage of the fuel capacity did it use on this flight 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 311

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ZEARN MATH STUDENT EDITION G6M3 LESSON 17 Lesson 17 Painting a Room Let s see what it takes to paint a room Warm Up 1 What are some tools that are helpful when painting a room Lesson ACTIVITY 1 2 Here is the floor plan of a bedroom If you paint all the walls in the room how many square feet do you need to cover Imagine you are planning to repaint all the walls in this room including inside the closet The east wall is 3 yards long The south wall is 10 feet long but has a window 5 feet by 3 feet that does not need to be painted The west wall is 3 yards long but has a door 7 feet tall and 3 feet wide that does not need to be painted The north wall includes a closet 6 5 feet wide with floor to ceiling mirrored doors that do not need to be painted There is however a smaller wall between the west wall and the closet that does need to be painted on all sides The wall is 0 5 feet wide and extends 2 feet into the room 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 313

G6M3 LESSON 17 The ceiling in this room is 8 feet high All of the corners are right angles 3 43 53 314 ZEARN MATH STUDENT EDITION An advertisement about the paint that you want to use reads Just 2 quarts covers 175 square feet If you need to apply two coats of paint on all the walls how much paint do you need to buy Paint can only be purchased in 1 quart 1 gallon and 5 gallon containers How much will all supplies for the project cost if the cans of paint cost 10 90 for a quart 34 90 for a gallon and 165 00 for 5 gallons You have a coupon for 20 off all quart sized paint cans How does that affect the cost of the projects 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

ZEARN MATH STUDENT EDITION G6M3 LESSON 17 ACTIVITY 2 63 1 After buying the supplies you start painting the east wall It takes you 96 minutes to put two coats of paint on that wall not including a lunch break between the two coats Your friend stops by to see how you are doing and comments that you are 25 finished with the painting Are they correct 73 Your friend offers to help you with the rest of the painting It takes the two of you 150 more minutes of painting time to finish the entire room How much time did your friend save you 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 315

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ZEARN MATH STUDENT EDITION G6V1 Terminology Area Area is the number of square units that covers a two dimensional region without any gaps or overlaps For example the area of region A is 8 square units The area of the shaded region of B is 12 square unit A B Base of a parallelogram or triangle We can choose any side of a parallelogram or triangle to be the shape s base Sometimes we use the word base to refer to the length of this side Base Base Base Base of a prism or pyramid base The word base can also refer to a face of a polyhedron A prism has two identical bases that are parallel A pyramid has one base A prism or pyramid is named for the shape of its base base base pentagonal prism hexagonal pyramid Compose Compose means put together We use the word compose to describe putting more than one figure together to make a new shape Cubed We use the word cubed to mean to the third power This is because a cube with side length s has a volume of s s s or s3 Decompose Decompose means take apart We use the word decompose to describe taking a figure apart to make more than one new shape 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 317

G6V1 ZEARN MATH STUDENT EDITION Double Number Line Diagram 0 3 6 9 12 0 5 10 15 20 Red paint teaspoons A double number line diagram uses a pair of parallel number lines to represent equivalent ratios The locations of the tick marks match on both number lines The tick marks labeled 0 line up but the other numbers are usually different Yellow paint teaspoons B Edge C Each straight side of a polygon is called an edge For example the edges of this polygon are segments AB BC CD DE and EA A E D Equivalent ratios Two ratios are equivalent if you can multiply each of the numbers in the first ratio by the same factor to get the numbers in the second ratio For example 8 6 is equivalent to 4 3 because 8 12 4 and 6 12 3 A recipe for lemonade says to use 8 cups of water and 6 lemons If we use 4 cups of water and 3 lemons it will make half as much lemonade Both recipes taste the same because 8 6 and 4 3 are equivalent ratios Cups of water Number of lemons 8 6 4 3 Exponent In expressions like 53 and 82 the 3 and the 2 are called exponents They tell you how many factors to multiply For example 53 5 5 5 and 82 8 8 Face Each flat side of a polyhedron is called a face For example a cube has 6 faces and they are all squares Height of a parallelogram or triangle The height is the shortest distance from the base of the shape to the opposite side for a parallelogram or opposite vertex for a triangle Height 2 Height 1 Base 2 Base 1 We can show the height in more than one place but it will always be perpendicular to the chosen base 318 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

ZEARN MATH STUDENT EDITION G6V1 Meters per second Meters per second is a unit for measuring speed It tells how many meters an object goes in one second For example a person walking 3 meters per second is going faster than another person walking 2 meters per second Net A net is a two dimensional representation of a polyhedron It can be cut out and folded to make a model of the polyhedron Here is a net for a cube Opposite Vertex B For each side of a triangle there is one vertex that is not on that side This is the opposite vertex C For example point A is the opposite vertex to side BC A Pace Pace is one way to describe how fast something is moving Pace tells how much time it takes the object to travel a certain distance For example Diego walks at a pace of 10 minutes per mile Elena walks at a pace of 11 minutes per mile Elena walks slower than Diego because it takes her more time to travel the same distance Parallelogram A parallelogram is a four sided polygon with two pairs of parallel sides Here are two examples of parallelograms 45 135 27 2 45 135 152 8 152 8 27 2 Per The word per means for each For example if the price is 5 per ticket that means you will pay 5 for each ticket Buying 4 tickets would cost 20 because 4 5 20 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 319

G6V1 ZEARN MATH STUDENT EDITION Percent The word percent means for each 100 The symbol for percent is For example a quarter is worth 25 cents and a dollar is worth 100 cents We can say that a quarter is worth 25 of a dollar 1 Quarter 25 1 Dollar 100 Percentage A percentage is a rate per 100 For example a fish tank can hold 36 liters Right now there is 27 liters of water in the tank The percentage of the tank that is full is 75 0 9 18 27 36 0 25 50 75 100 Volume liters B Polygon A polygon is a closed two dimensional shape with straight sides that do not cross each other Figure ABCDE is an example of a polygon A C E D Polyhedron Polyhedra A polyhedron is a three dimensional figure with faces that are polygonal regions filled in polygons Each face meets one and only one other face along a complete edge The points where edges meet are called vertices The plural of polyhedron is polyhedra A polyhedron always encloses a three dimensional region Here are some drawings of polyhedra 320 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

ZEARN MATH STUDENT EDITION G6V1 Prism A prism is a type of polyhedron with two parallel faces that are identical copies of each other called bases connected by rectangles A prism is named for the shape of its bases for example if its base is a pentagon then it is called a pentagonal prism triangular prism pentagonal prism rectangular prism Here are some drawings of some prisms Pyramid A pyramid is a type of polyhedron that has one base All the other faces are triangles and they all meet at a single vertex Here are some drawings of pyramids rectangular pyramid hexagonal pyramid heptagonal pyramid Quadrilateral A quadrilateral is a type of polygon that has 4 sides A rectangle is an example of a quadrilateral A pentagon is not a quadrilateral because it has 5 sides Ratio A ratio is an association between two or more quantities For example the ratio 3 2 could describe a recipe that uses 3 cups of flour for every 2 eggs or a boat that moves 3 meters every 2 seconds One way to represent the ratio 3 2 is with a diagram that has 3 blue squares for every 2 green squares Region A region is the space inside of a shape Some examples of two dimensional regions are inside a circle or inside a polygon Some examples of three dimensional regions are the inside of a cube or the inside of a sphere Same rate We use the words same rate to describe two situations that have equivalent ratios For example a sink is filling with water at a rate of 2 gallons per minute If a tub is also filling with water at a rate of 2 gallons per minute then the sink and the tub are filling at the same rate 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 321

G6V1 ZEARN MATH STUDENT EDITION Speed Speed is one way to describe how fast something is moving Speed tells how much distance the object travels in a certain amount of time For example Tyler walks at a speed of 4 miles per hour Priya walks at a speed of 5 miles per hour Priya walks faster than Tyler because she travels more distance in the same amount of time Squared We use the word squared to mean to the second power This is because a square with side length s has an area of s s or s2 Surface area The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron without any gaps or overlaps For example if the faces of a cube each have an area of 9 cm2 then the surface area of the cube is 6 9 or 54 cm2 Table A table organizes information into horizontal rows and vertical columns The first row or column usually tells what the numbers represent For example here is a table showing the tail lengths of three different pets This table has four rows and two columns 322 Pet Tail length inches Dog 22 Cat 12 Gerbil 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

ZEARN MATH STUDENT EDITION G6V1 Tape diagram A tape diagram is a group of rectangles put together to represent a relationship between quantities 10 10 10 10 10 10 10 10 For example this tape diagram shows a ratio of 30 gallons of yellow paint to 50 gallons of blue paint If each rectangle were labeled 5 instead of 10 then the same picture could represent the equivalent ratio of 15 gallons of yellow paint to 25 gallons of blue paint Unit price The unit price is the cost for one item or for one unit of measure For example if 10 feet of chain link fencing costs 150 then the unit price is 150 10 or 15 per foot Unit Rate A unit rate is a rate per 1 For example 12 people share 2 pies equally One unit rate is 6 people per pie because 12 2 6 The other unit rate is 16 of a pie per person because 2 12 16 Vertex vertices B A vertex is a point where two or more edges meet When we have more than one vertex we call them vertices The vertices in this polygon are labeled A B C D and E A C E 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 323

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zearn org NAME Grade 6 Student Edition Vol 1 Mission 1 Area and Surface Area Mission 2 Introducing Ratios Vol 2 Mission 4 Dividing Fractions Mission 5 Arithmetic in Base Ten Mission 6 Expressions and Equations Student Edition Mission 3 Unit Rates and Percentages Vol 3 Mission 7 Rational Numbers Mission 8 Data Sets and Distributions Mission 9 Putting It All Together G6 Vol 1 Grade 6 Volume 1 MISSIONS 1 2 3 4 5 6 7 8 9