Return to flip book view

STUDENT EDITION Grade 7 VOLUME 3 Mission 7 Angles Triangles and Prisms Mission 8 Probability and Sampling Mission 9 Putting it All Together NAME

2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum used under the CC BY 4 0 license Download the original for free at openupresources org Zearn is a registered trademark Printed in the U S A ISBN 979 8 88868 885 4

Table of Contents Mission 7 Lesson 1 Relationships of Angles 3 Lesson 2 Adjacent Angles 9 Lesson 3 Nonadjacent Angles 15 Lesson 4 Solving for Unknown Angles 21 Lesson 5 Using Equations to Solve for Unknown Angles 27 Lesson 6 Building Polygons Part 1 33 Lesson 7 Building Polygons Part 2 39 Lesson 8 Triangles with 3 Common Measures 45 Lesson 9 Drawing Triangles Part 1 51 Lesson 10 Drawing Triangles Part 2 57 Lesson 11 Slicing Solids 63 Lesson 12 Volume of Right Prisms 69 Lesson 13 Decomposing Bases for Area 75 Lesson 14 Surface Area of Right Prisms 81 Lesson 15 Distinguishing Volume andSurface Area 87 Lesson 16 Applying Volume and Surface Area 91 Lesson 17 Building Prisms 97 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 8 iv Lesson 1 Mystery Bags 103 Lesson 2 Chance Experiments 107 Lesson 3 What Are Probabilities 113 Lesson 4 Estimating Probabilities through Repeated Experiments 119 Lesson 5 More Estimating Probabilities 127 Lesson 6 Estimating Probabilities Using Simulation 133 Lesson 7 Simulating Multi Step Experiments 141 Lesson 8 Keeping Track of All Possible Outcomes 147 Lesson 9 Multi Step Experiments 155 Lesson 10 Designing Simulations 161 Lesson 11 Comparing Groups 167 Lesson 12 Larger Populations 173 Lesson 13 What Makes a Good Sample 179 Lesson 14 Sampling in a Fair Way 185 Lesson 15 Estimating Population Measures of Center 193 Lesson 16 Estimating Population Proportions 201 Lesson 17 More about Sampling Variability 209 Lesson 18 Comparing Populations Using Samples 215 Lesson 19 Comparing Populations with Friends 225 Lesson 20 Memory Test 229 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 9 Lesson 1 Planning Recipes 235 Lesson 2 Costs of Running a Restaurant 247 Lesson 3 More Costs of Running a Restaurant 251 Lesson 4 Restaurant Floor Plan 255 Lesson 5 How Crowded Is This Neighborhood 257 Lesson 6 Fermi Problems 263 Lesson 7 More Expressions and Equations 265 Lesson 8 Measurement Error Part 1 269 Lesson 9 Measurement Error Part 2 271 Lesson 10 Measuring Long Distances Over Uneven Terrain 273 Lesson 11 Building a Trundle Wheel 275 Lesson 12 Using a Trundle Wheel to Measure Distances 277 Lesson 13 Designing a 5K Course 279 Terminology 281 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

Grade 7 Mission 7 Angles Triangles and Prisms

2

ZEARN MATH STUDENT EDITION G7M7 LESSON 1 Lesson 1 Relationships of Angles Let s examine some special angles Warm Up 1 1 Answer the questions below Which angle is bigger a or b a 2 b Identify an obtuse angle in the diagram C D 60 50 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 3

G7M7 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Trace one copy of every different pattern block Each block contains either 1 or 2 angles with different degree measures Which blocks have only 1 unique angle Which have 2 2 If you trace three copies of the hexagon so that one vertex from each hexagon touches the same point as shown they fit together without any gaps or overlaps Use this to figure out the degree measure of the angle inside the hexagon pattern block 3 4 Use your pattern blocks to answer the following questions Figure out the degree measure of all of the other angles inside the pattern blocks that you traced in the first question Be prepared to 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 G7M7 LESSON 1 ACTIVITY 2 TASK 1 3 Use pattern blocks to determine the measure of each of these angles b c a ACTIVITY 2 TASK 2 43 If an angle has a measure of 180 then the two legs form a straight line An angle that forms a straight line is called a straight angle Find as many different combinations of pattern blocks as you can that make a straight angle 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 1 ZEARN MATH STUDENT EDITION Lesson Summary When two lines intersect and form four equal angles we call each one a right angle A right angle measures 90 You can think of a right angle as a quarter turn in one direction or the other An angle in which the two sides form a straight line is called a straight angle A straight angle measures 180 A straight angle can be made by putting right angles together You can think of a straight angle as a half turn so that you are facing in the opposite direction after you are done If you put two straight angles together you get an angle that is 360 You can think of this angle as turning all the way around so that you are facing the same direction as when you started the turn 90 90 90 90 180 360 When two angles share a side and a vertex and they don t overlap we call them adjacent angles TERMINOLOGY Adjacent angles Right angle Straight angle 6 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 1 Name Date GRADE 7 MISSION 7 LESSON 1 Exit Ticket Here are two different patterns made out of the same five identical isosceles triangles Without using a protractor determine the measures of angle x and angle y Explain or show your reasoning y x y y x y 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

8

ZEARN MATH STUDENT EDITION G7M7 LESSON 2 Lesson 2 Adjacent Angles Let s look at some special pairs of angles Warm Up Estimate the degree measure of each indicated angle 1 F C A D B I E H G T O N M R Q L S P K J W V Z U Concept Exploration ACTIVITY 1 2 Read the instructions below and complete the activity with a partner Your teacher will give you two small rectangular papers 1 On one of the papers draw a small half circle in the middle of one side 2 Cut a straight line starting from the center of the half circle all the way across the paper to make 2 separate pieces Your cut does not need to be perpendicular to the side of the paper 3 On each of these two pieces measure the angle that is marked by part of a circle Label the angle measure on the piece 4 What do you notice about these angle measures 5 Clare measured 70 degrees on one of her pieces Predict the angle measure of her other piece 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 2 ZEARN MATH STUDENT EDITION 6 On the other rectangular paper draw a small quarter circle in one of the corners 7 Repeat the previous steps to cut measure and label the two angles marked by part of a circle 8 What do you notice about these angle measures 9 Priya measured 53 degrees on one of her pieces Predict the angle measure of her other piece ACTIVITY 2 3 a BCA Use the protractor in the picture to find the measures of the angles below A D B c 10 180 170 160 0 10 20 150 30 14 40 0 b BCD C 10 0 20 170 180 30 160 0 40 0 15 14 100 90 80 110 80 90 100 70 60 0 110 0 7 12 120 5 0 0 13 0 6 13 0 0 5 Explain how to find the measure of angle ACD without repositioning the protractor 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 Use the protractor in the picture to find the measures of the angles below a LOK K L 10 0 20 170 180 30 160 0 40 0 15 14 100 90 80 110 80 90 100 70 60 110 120 70 120 5 0 60 3 1 0 13 0 0 5 b LOM c N 180 170 160 0 10 20 150 30 14 40 0 43 G7M7 LESSON 2 O M Explain how to find the measure of angle KOM without repositioning the protractor 53 Solve the problems below a Angle BAC is a right angle Find the measure of angle CAD C D A 64 B b Point O is on line RS Find the measure of angle SOP P 76 S O 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license R 11

G7M7 LESSON 2 ZEARN MATH STUDENT EDITION Lesson Summary If two angle measures add up to 90 then we say the angles are complementary Here are three examples of pairs of complementary angles 30 38 45 60 45 52 If two angle measures add up to 180 then we say the angles are supplementary Here are three examples of pairs of supplementary angles 55 125 152 28 TERMINOLOGY Complementary Supplementary 12 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 2 Name Date GRADE 7 MISSION 7 LESSON 2 Exit Ticket 1 Point F is on line CD Find the measure of angle CFE E 152 F C 2 D Angle SPR and angle RPQ are complementary Find the measure of angle RPQ Q 37 R P S 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

14

ZEARN MATH STUDENT EDITION G7M7 LESSON 3 Lesson 3 Nonadjacent Angles Let s look at angles that are not right next to one another Warm Up 1 Given a and b are numbers and a b 180 which statements also must be true a 180 b a 180 b 360 2a 2b a 90 and b 90 Concept Exploration ACTIVITY 1 2 Use any useful tools in the geometry toolkit to identify any pairs of angles in these figures that are complementary or supplementary 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 3 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Use a straightedge to draw two intersecting lines Use a protractor to measure all four angles whose vertex is located at the intersection Compare your drawing and measurements to the people in your group Make a conjecture about the relationships between angle measures at an intersection Lesson Summary When two lines cross they form two pairs of vertical angles Vertical angles are across the intersection point from each other Vertical angles always have equal measures We can see this because they are always supplementary with the same angle For example 150 150 30 30 This is always true b a b c a b 180 so a 180 b c b 180 so c 180 b That means a c 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 G7M7 LESSON 3 TERMINOLOGY Vertical angles 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

18

ZEARN MATH STUDENT EDITION G7M7 LESSON 3 Name Date GRADE 7 MISSION 7 LESSON 3 Exit Ticket A D 40 B C 62 90 90 125 140 50 28 55 F 40 E 1 Name two pairs of complementary angles in the diagram 2 Name two pairs of supplementary angles in the diagram 3 Draw another angle to make a pair of vertical angles Label your new angle with its measure 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

20

ZEARN MATH STUDENT EDITION G7M7 LESSON 4 Lesson 4 Solving for Unknown Angles Let s figure out some missing angles Warm Up 1 Below are some line segments Decide if each of these equations is true or false Be prepared to explain your reasoning A 1 CD BC BD 2 AB BD CD AD 3 AC AB AB 4 BD CD AC AB 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 21

G7M7 LESSON 4 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Read the instructions below and complete the activity with a partner If your teacher gives you the problem card 1 2 If your teacher gives you the data card Silently read your card and think about what 1 information you need to answer the question 2 Ask your partner for the specific information that you need 3 Explain to your partner how you are using the information to solve the problem 4 Solve the problem and explain your reasoning 3 to your partner 4 Silently read the information on your card Ask your partner What specific information do you need and wait for your partner to ask for information Only give information that is on your card Do not figure out anything for your partner Before telling your partner the information ask Why do you need that information After your partner solves the problem ask them to explain their reasoning and listen to their explanation Pause here so your teacher can review your work Ask your teacher for a new set of cards and repeat the activity trading roles with your partner 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 G7M7 LESSON 4 ACTIVITY 2 3 Match each figure to an equation that represents what is seen in the figure For each match explain how you know they are a match A B g g h C D g g h 180 2 g h 3 2h g 90 4 g h 48 180 5 g h 35 180 E g h 35 1 h Q h g h h 48 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 23

G7M7 LESSON 4 ZEARN MATH STUDENT EDITION Lesson Summary We can write equations that represent relationships between angles x 28 42 y z 64 The first pair of angles are supplementary so x 42 180 The second pair of angles are vertical angles so y 28 The third pair of angles are complementary so z 64 90 24 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 4 Name Date GRADE 7 MISSION 7 LESSON 4 Exit Ticket AD BE and CF are all diameters of the circle The measure of angle AOB is 40 degrees The measure of angle DOF is 120 degrees C B 40 A D O F E Find the measures of the angles 1 BOC 2 COD 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

26

ZEARN MATH STUDENT EDITION G7M7 LESSON 5 Lesson 5 Using Equations to Solve for Unknown Angles Let s figure out missing angles using equations Warm Up 1 Tyler thinks that this figure has enough information to figure out the values of a and b Do you agree Explain your reasoning 90 a b l Concept Exploration ACTIVITY 1 2 1 Elena and Diego each wrote equations to represent these diagrams For each diagram decide which equation you agree with and solve it You can assume that angles that look like right angles are indeed right angles Elena x 35 Diego x 35 180 35 x w 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 5 2 ZEARN MATH STUDENT EDITION Elena 35 w 41 180 Diego 35 w 180 w 35 3 41 Elena w 35 90 Diego 2w 35 90 w 35 w 4 Elena 2w 35 90 Diego w 35 90 w w 35 5 Elena w 148 180 Diego x 90 148 w x 148 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 G7M7 LESSON 5 ACTIVITY 2 3 Find the unknown angle measures Show your thinking Organize it so it can be followed by others 1 2 w 124 b 52 Q 3 Lines l and m are perpendicular 23 l 4 m 120 x 23 x l m 66 m 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 29

G7M7 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary To find an unknown angle measure sometimes it is helpful to write and solve an equation that represents the situation For example suppose we want to know the value of x in this diagram x x x 144 Using what we know about vertical angles we can write the equation 3x 90 144 to represent this situation Then we can solve the equation 3x 90 144 3x 90 90 144 90 3x 54 3x 13 54 13 x 18 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 G7M7 LESSON 5 Name Date GRADE 7 MISSION 7 LESSON 5 Exit Ticket Here are three intersecting lines 76 w w 1 Write an equation that represents a relationship between these angles 2 Describe in words the process you would use to find w 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

32

ZEARN MATH STUDENT EDITION G7M7 LESSON 6 Lesson 6 Building Polygons Part 1 Let s build shapes Warm Up 1 Decide whether each equation is true or false Be prepared to explain your reasoning 1 4 6 6 6 6 6 2 8 4 8 3 4 3 6 7 7 7 7 4 10 6 10 6 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 6 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Your teacher will give you some strips of different lengths and fasteners you can use to attach the corners as you build polygons Then answer the questions below 1 Use the pieces to build several polygons including at least one triangle and one quadrilateral 2 After you finish building several polygons select one triangle and one quadrilateral that you have made a Measure all the angles in the two shapes you selected b Using these measurements along with the side lengths as marked draw your triangle and quadrilateral as accurately as possible 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 G7M7 LESSON 6 ACTIVITY 2 3 Diego built a quadrilateral using side lengths of 4 in 5 in 6 in and 9 in Answer the questions below a Build such a shape b Is your shape an identical copy of Diego s shape Explain your reasoning 43 Jada built a triangle using side lengths of 4 in 5 in and 8 in Answer the questions below a Build such a shape b Is your shape an identical copy of Jada s shape 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 35

G7M7 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary Sometimes we are given a polygon and asked to find the lengths of the sides What options do you have if you need to build a polygon with some side lengths Sometimes we can make lots of different figures For example if you have side lengths 5 7 11 and 14 here are some of the many many quadrilaterals we can make with those side lengths 5 11 5 11 7 11 7 14 14 5 14 7 Sometimes it is not possible to make a figure with certain side lengths For example 18 1 1 1 try it We will continue to investigate the figures that can be made with given measures 36 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 6 Name Date GRADE 7 MISSION 7 LESSON 6 Exit Ticket When asked to draw a quadrilateral with all four sides measuring 5 cm Jada drew a square 5cm 5cm 5cm 5cm 1 Do you agree with Jada s answer Explain your reasoning 2 Is there a different shape Jada could have drawn that would answer the question 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 37

38

ZEARN MATH STUDENT EDITION G7M7 LESSON 7 Lesson 7 Building Polygons Part 2 Let s build more triangles Warm Up 1 At a park the slide is 5 meters east of the swings Lin is standing 3 meters away from the slide 1 How far away from the swings is Lin 2 Draw a diagram of the situation including where Lin could be 3 Is there anywhere else Lin could be Concept Exploration ACTIVITY 1 2 Your teacher will give you some strips of different lengths and fasteners you can use to attach the corners 1 Build as many different triangles as you can that have one side length of 5 inches and one of 4 inches Record the side lengths of each triangle you build 2 Are there any other lengths that could be used for the third side of the triangle but weren t in your set 3 Are there any lengths that were in your set but could not be used as the third side of the triangle 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 7 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 1 We ll explore a method for drawing a triangle that has three specific side lengths Your teacher will give you a piece of paper showing a 4 inch segment as well as some instructions for which strips to use and how to connect them Follow these instructions to mark the possible endpoints of one side a Put your 4 inch strip directly on top of the 4 inch segment on the piece of paper Hold it in place b For now ignore the 3 inch strip on the left side Rotate it so that it is out of the way c In the 3 inch strip on the right side put the tip of your pencil in the hole on the end that is not connected to anything Use the pencil to move the strip around its hinge drawing all the places where a 3 inch side could end d Remove the connected strips from your paper 40 2 What shape have you drawn while moving the 3 inch strip around Why Which tool in your geometry toolkit that can do something similar 3 Use your drawing to create two unique triangles each with a base of length 4 inches and a side of length 3 inches Use a different color to draw each triangle 4 Reposition the strips on the paper so that the 4 inch strip is on top of the 4 inch segment again In the 3 inch strip on the left side put the tip of your pencil in the hole on the end that is not connected to anything Use the pencil to move the strip around its hinge drawing all the places where another 3 inch side could end 5 Using a third color draw a point where the two marks intersect Using this third color draw a triangle with side lengths of 4 inches 3 inches and 3 inches 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M7 LESSON 7 Lesson Summary If we want to build a polygon with two given side lengths that share a vertex we can think of them as being connected by a hinge that can be opened or closed 3 3 3 3 3 4 All of the possible positions of the endpoint of the moving side form a circle 3 3 3 3 3 4 You may have noticed that sometimes it is not possible to build a polygon given a set of lengths For example if we have one really really long segment and a bunch of short segments we may not be able to connect them all up Here s what happens if you try to make a triangle with side lengths 21 4 and 2 The short sides don t seem like they can meet up because they are too far away from each other If we draw circles of radius 4 and 2 on the endpoints of the side of length 21 to represent positions for the shorter sides we can see that there are no places for the short sides that would allow them to meet up and form a triangle 4 2 21 4 2 21 In general the longest side length must be less than the sum of the other two side lengths If not we can t make a triangle If we can make a triangle with three given side lengths it turns out that the measures of the corresponding angles will always be the same For example if two triangles have side lengths 3 4 and 5 they will have the same corresponding angle measures 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

42

ZEARN MATH STUDENT EDITION Name G7M7 LESSON 7 Date GRADE 7 MISSION 7 LESSON 7 Exit Ticket Elena is trying to draw a triangle with side lengths 4 inches 3 inches and 5 inches She uses her ruler to draw a 4 inch line segment AB She uses her compass to draw a circle around point B with radius 3 inches A B She draws another circle around point A with radius 5 inches 1 What should Elena do next Explain and show how she can finish drawing the triangle Now Elena is trying to draw a triangle with side lengths 4 inches 3 inches and 8 inches She uses her ruler to draw a 4 inch line segment AB She uses her compass to draw a circle around point B with radius 3 inches She draws another circle around point A with radius 8 inches 2 Explain what Elena s drawing means A B 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 43

44

ZEARN MATH STUDENT EDITION G7M7 LESSON 8 Lesson 8 Triangles with 3 Common Measures Let s contrast triangles Warm Up 1 Examine each set of triangles What do you notice What is the same about the triangles in the set What is different Set 1 9 6 9 4 6 9 4 6 4 4 9 6 6 4 6 9 4 9 Set 2 41 56 83 41 83 56 83 41 56 56 83 41 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 8 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Examine this set of triangles and answer the questions 7 5 30 5 7 7 30 5 7 7 7 30 30 5 5 5 7 7 30 46 30 5 30 7 5 30 30 1 What is the same about the triangles in the set What is different 2 How many different triangles are there Explain or show your reasoning 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

ZEARN MATH STUDENT EDITION G7M7 LESSON 8 ACTIVITY 2 3 Examine this set of triangles and answer the questions 6 80 40 40 80 6 6 80 40 80 6 80 40 6 40 80 40 6 6 80 40 40 80 6 1 What is the same about the triangles in the set What is different 2 How many different triangles are there 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 47

G7M7 LESSON 8 ZEARN MATH STUDENT EDITION Lesson Summary Both of these quadrilaterals have a right angle and side lengths 4 and 5 5 4 4 5 However in one case the right angle is between the two given side lengths in the other it is not If we create two triangles with three equal measures but these measures are not next to each other in the same order that usually means the triangles are different Here is an example 32 5 6 32 5 6 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 G7M7 LESSON 8 Name Date GRADE 7 MISSION 7 LESSON 8 Exit Ticket Andre and Noah each drew a triangle with side lengths of 5 cm and 3 cm and an angle that measures 60 and then they showed each other their drawings Andre s triangle Noah s triangle 3 5 60 5 60 3 1 Did Andre and Noah draw different triangles Explain your reasoning 2 Explain what Andre and Noah would have to do to draw another triangle that is different from what either of them has already drawn 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

50

ZEARN MATH STUDENT EDITION G7M7 LESSON 9 Lesson 9 Drawing Triangles Part 1 Let s see how many different triangles we can draw with certain measurements Warm Up 1 Which one 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 51

G7M7 LESSON 9 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 52 Three students have each drawn a triangle For each description of a student s triangle 1 Draw a triangle with the given measurements 2 Measure and label the other side lengths and angle measures in your triangle 3 Decide whether the triangle you drew must be an identical copy of the triangle that the student drew Explain your reasoning Jada s triangle has one angle measuring 75 Andre s triangle has one angle measuring 75 and one angle measuring 45 Lin s triangle has one angle measuring 75 one angle measuring 45 and one side measuring 5 cm 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M7 LESSON 9 ACTIVITY 2 3 1 2 Answer the questions below about drawing triangles Draw as many different triangles as you can with each of these sets of measurements if possible If not possible explain why Two angles measure 60 and one side measures 4 cm Two angles measure 90 and one side measures 4 cm One angle measures 60 one angle measures 90 and one side measures 4 cm Which of these sets of measurements determine one unique triangle 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 53

G7M7 LESSON 9 ZEARN MATH STUDENT EDITION Lesson Summary Sometimes we are given two different angle measures and a side length and it is impossible to draw a triangle For example there is no triangle with side length 2 and angle measures 120 and 100 Sometimes we are given two different angle measures and a side length between them and we can draw a unique triangle For example if we draw a triangle with a side length of 4 between angles 90 and 60 there is only one way they can meet up and complete to a triangle Any triangle drawn with these three conditions will be identical to the one above with the same side lengths and same angle measures 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 Name G7M7 LESSON 9 Date GRADE 7 MISSION 7 LESSON 9 Exit Ticket When asked to draw a triangle with two 45 angles and a side length of 8 cm Diego drew this triangle 1 Do you agree with Diego s answer 2 Is there a different triangle Diego could have drawn that would answer the question 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 55

56

ZEARN MATH STUDENT EDITION G7M7 LESSON 10 Lesson 10 Drawing Triangles Part 2 Let s draw some more triangles Warm Up 1 Answer the questions below Use your geometry toolkit and compass if needed 1 Draw a 40 angle 2 Use a compass to make sure both sides of your angle have a length of 5 centimeters 3 If you connect the ends of the sides you drew to make a triangle is the third side longer or shorter than 5 centimeters How can you use a compass to explain your answer Concept Exploration ACTIVITY 1 2 1 Answer the questions below about drawing triangles Draw as many different triangles as you can with each of these sets of measurements a One angle measures 40 one side measures 4 cm and one side measures 5 cm 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 57

G7M7 LESSON 10 ZEARN MATH STUDENT EDITION b Two sides measure 6 cm and one angle measures 100 2 Did either of these sets of measurements determine one unique triangle How do you know ACTIVITY 2 3 1 Answer the questions below about drawing triangles Draw as many different triangles as you can with each of these sets of measurements a One angle measures 50 one measures 60 and one measures 70 b One angle measures 50 one measures 60 and one measures 100 2 58 Did either of these sets of measurements determine one unique triangle How do 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

ZEARN MATH STUDENT EDITION G7M7 LESSON 10 Lesson Summary A triangle has six measures three side lengths and three angle measures If we are given three measures then sometimes there is no triangle that can be made For example there is no triangle with side lengths 1 2 5 and there is no triangle with all three angles measuring 150 2 1 150 5 150 150 Sometimes only one triangle can be made By this we mean that any triangle we make will be the same having the same six measures For example if a triangle can be made with three given side lengths then the corresponding angles will have the same measures Another example is shown here an angle measuring 45 between two side lengths of 6 and 8 units With this information one unique triangle can be made 8 8 45 45 6 6 Sometimes two or more different triangles can be made with three given measures For example here are two different triangles that can be made with an angle measuring 45 and side lengths 6 and 8 Notice the angle is not between the given sides 6 6 8 45 8 45 Three pieces of information about a triangle s side lengths and angle measures may determine no triangles one unique triangle or more than one triangle It depends on the information 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

60

ZEARN MATH STUDENT EDITION Name G7M7 LESSON 10 Date GRADE 7 MISSION 7 LESSON 10 Exit Ticket Noah is trying to draw a triangle with a 30 angle and side lengths of 4 cm and 6 cm He uses his ruler to draw a 4 cm line segment He uses his protractor to draw a 30 angle on one end of the line segment 4 30 1 What should Noah do next Explain and show how he can finish drawing the triangle 2 Is there a different triangle Noah could draw that would answer the question 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 61

62

ZEARN MATH STUDENT EDITION G7M7 LESSON 11 Lesson 11 Slicing Solids Let s see what shapes you get when you slice a three dimensional object Warm Up 1 Describe each shape as precisely as you can 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Here is a rectangular prism and a pyramid with the same base and same height Use the images to answer the questions below 2 cm 2 cm 4 cm 4 cm 1 Think about slicing each solid parallel to its base halfway up What shape would each cross section be What is the same about the two cross sections What is different 2 Think about slicing each solid parallel to its base near the top What shape would each cross section be What is the same about the two cross sections What is different ACTIVITY 2 3 64 Your teacher will give you a set of cards Sort the images into groups that make sense to you Be prepared to 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 G7M7 LESSON 11 Lesson Summary When we slice a three dimensional object we expose new faces that are two dimensional The twodimensional face is a cross section Many different cross sections are possible when slicing the same three dimensional object Here are two lemons One is sliced horizontally and the other is sliced vertically producing different cross sections It takes practice imagining what the cross section of a three dimensional object will be for different slices It helps to experiment and see for yourself what happens TERMINOLOGY Cross section 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

66

ZEARN MATH STUDENT EDITION Name G7M7 LESSON 11 Date GRADE 7 MISSION 7 LESSON 11 Exit Ticket Here is a pyramid with a base that is a pentagon with all sides the same length 1 Describe the cross section that will result if the pyramid is sliced a horizontally parallel to the base b vertically through the top vertex perpendicular to the base 2 Describe another way you could slice the pyramid that would result in a different cross section 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

68

ZEARN MATH STUDENT EDITION G7M7 LESSON 12 Lesson 12 Volume of Right Prisms Let s look at volumes of prisms Warm Up 1 Rectangles A B and C represent bases of three prisms Answer the questions below 1 If each prism has the same height which one will have the greatest volume and which will have the least Explain your reasoning 2 If each prism has the same volume which one will have the tallest height and which will have the shortest 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 69

G7M7 LESSON 12 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 70 You will receive a paper with a copy of the shape below on it and some snap cubes Answer the questions below 1 Using the face of a snap cube as your area unit what is the area of the shape Explain or show your reasoning 2 Use snap cubes to build the shape from the paper Add another layer of cubes on top of the shape you have built Describe this three dimensional object 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 12 3 What is the volume of your object Explain your reasoning 4 Right now your object has a height of 2 What would the volume be a if it had a height of 5 b if it had a height of 8 5 ACTIVITY 2 3 You will receive a set of three dimensional figures Answer the questions below 1 For each figure determine whether the shape is a prism 2 For each prism a Find the area of the base of the prism b Find the height of the prism c Calculate the volume of the prism Is it a prism Area of prism base cm2 Height cm Volume cm3 Figure A Figure B Figure C Figure D Figure E Figure 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 71

G7M7 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary If we have a rectangular prism that is 3 units tall and has a base that is 4 units by 5 units we can think of this as 3 layers where each layer has 4 5 cubic units That means the volume of the original rectangular prism is 3 4 5 cubic units This works with any prism If we have a prism with height 3 cm that has a base of area 20 cm2 then the volume is 3 20 cm3 regardless of the shape of the base In general the volume of a prism with height h and area B is V B h For example these two prisms both have a volume of 100 cm3 5 cm 20 cm2 72 25 cm2 4 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 G7M7 LESSON 12 Name Date GRADE 7 MISSION 7 LESSON 12 Exit Ticket A box is shaped like an octagonal prism Here is what the base of the prism looks like For each question make sure to include the unit with your answer and explain or show your reasoning 41 in2 1 If the height of the box is 7 inches what is the volume of the box 2 If the volume of the box is 123 in3 what is the height of the 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 73

74

ZEARN MATH STUDENT EDITION G7M7 LESSON 13 Lesson 13 Decomposing Bases for Area Let s look at how some people use volume Warm Up 1 Answer the questions about the six solid figures shown below A B C D E F 1 Which of these solids are prisms Explain how you know 2 For each of the prisms what does the base look like a Shade one base in the picture b Draw a cross section of the prism parallel to the 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 75

G7M7 LESSON 13 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 A box of chocolates is a prism with a base in the shape of a heart and a height of 2 inches Below are the measurements of the base To calculate the volume of the box three different students have each drawn line segments showing how they plan on finding the area of the heart shaped base Answer the questions below 2 inches 4 inches 2 inches 1 inch 2 inches 5 inches 4 inches Lin s Plan 76 4 inches Jada s Plan Diego s Plan 1 For each student s plan describe the shapes the student must find the area of and the operations they must use to calculate the total area 2 Although all three methods could work one of them requires measurements that are not provided Which one is 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

ZEARN MATH STUDENT EDITION G7M7 LESSON 13 3 Between you and your partner decide which of you will use which of the remaining two methods 4 Using the quadrilaterals and triangles drawn in your selected plan find the area of the base 5 Trade with a partner and check each other s work If you disagree work to reach an agreement 6 Return their work Calculate the volume of the box of chocolates ACTIVITY 2 3 1 A house shaped prism is created by attaching a triangular prism on top of a rectangular prism Answer the questions about the prism below Draw the base of this prism and label its dimensions 5 5 11 7 8 2 What is the area of the base Explain or show your reasoning 3 What is the volume of the prism 6 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 13 ZEARN MATH STUDENT EDITION Lesson Summary To find the area of any polygon you can decompose it into rectangles and triangles There are always many ways to decompose a polygon Sometimes it is easier to enclose a polygon in a rectangle and subtract the area of the extra pieces To find the volume of a prism with a polygon for a base you find the area of the base B and multiply by the height h h B V Bh 78 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 13 Name Date GRADE 7 MISSION 7 LESSON 13 Exit Ticket Here is a prism with a pentagonal base The height is 8 cm 3 cm 5 cm 5 cm 2 cm 8 cm 7 cm What is the volume of the prism Show your thinking Organize it 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 79

80

ZEARN MATH STUDENT EDITION G7M7 LESSON 14 Lesson 14 Surface Area of Right Prisms Let s look at the surface area of prisms Warm Up Your teacher will show you a prism 1 What are some things you could measure about the object 2 What units would you use for these measurements 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 14 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 1 Answer the questions in your notes Here is a picture of your teacher s prism 2 in 2 in 2 in 2 in 2 in 2 in Three students are trying to calculate the surface area of this prism Noah says This is going to be a lot of work We have to find the areas of 14 different faces and add them up Elena says It s not so bad All 12 rectangles are identical copies so we can find the area for one of them multiply that by 12 and then add on the areas of the 2 bases Andre says Wait I see another way Imagine unfolding the prism into a net We can use 1 large rectangle instead of 12 smaller ones 11 in 82 1 Do you agree with any of them Explain your reasoning 2 How big is the 1 large rectangle Andre is talking about Explain or show your reasoning If you get stuck consider drawing a net for the prism 3 Will Noah s method always work for finding the surface area of any prism Elena s method Andre s method Be prepared to explain your reasoning 4 Which method do you prefer 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 G7M7 LESSON 14 ACTIVITY 2 2 1 2 Follow the directions below to calculate the surface area of the prism Between you and your partner choose who will use each of these two methods to find the surface area of the prism Adding the areas of all the faces Using the perimeter of the base Use your chosen method to calculate the surface area of the prism Show your thinking Organize it so it can be followed by others 5 cm 5 cm 3 cm 8 cm 2 cm 7 cm 3 Trade papers with your partner and check their work Discuss your thinking If you disagree work to reach an agreement 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 14 ZEARN MATH STUDENT EDITION Lesson Summary To find the surface area of a three dimensional figure whose faces are made up of polygons we can find the area of each face and add them up Sometimes there are ways to simplify our work For example all of the faces of a cube with side length are the same We can find the area of one face and multiply by 6 Since the area of one face of a cube is the surface area of a cube is We can use this technique to make it faster to find the surface area of any figure that has faces that are the same For prisms there is another way We can treat the prism as having three parts two identical bases and one long rectangle that has been taped along the edges of the bases The rectangle has the same height as the prism and its width is the perimeter of the base To find the surface area add the area of this rectangle to the areas of the two bases 84 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M7 LESSON 14 Name Date GRADE 7 MISSION 7 LESSON 14 Exit Ticket Find the surface area of this prism Show your reasoning Organize it so it can be followed by others 3 cm 3 cm 3 cm 9 cm 6 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 85

86

ZEARN MATH STUDENT EDITION G7M7 LESSON 15 Lesson 15 Distinguishing Volume and Surface Area Let s work with surface area and volume in context Warm Up 1 Answer the question below Mai s science teacher told her that when there is more ice touching the water in a glass the ice melts faster She wants to test this statement so she designs her science fair project to determine if crushed ice or ice cubes will melt faster in a drink She begins with two cups of warm water In one cup she puts a cube of ice In a second cup she puts crushed ice with the same volume as the cube What is your hypothesis Will the ice cube or crushed ice melt faster or will they melt at the same rate Explain your reasoning Concept Exploration ACTIVITY 1 2 The other day you calculated the volume of this heart shaped box of chocolates The depth of the box is 2 inches How much cardboard is needed to create the box 2 inches 4 inches 2 inches 1 inch 2 inches 5 inches 4 inches 4 inches 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 87

G7M7 LESSON 15 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Your teacher will give you cards with different figures and questions on them Follow the directions below 1 Sort the cards into two groups based on whether it would make more sense to think about the surface area or the volume of the figure when answering the question Pause here so your teacher can review your work 2 Your teacher will assign you a card to examine more closely What additional information would you need to be able to answer the question on your card 3 Estimate reasonable measurements for the figure on your card 4 Use your estimated measurements to calculate the answer to the question Lesson Summary Sometimes we need to find the volume of a prism and sometimes we need to find the surface area Here are some examples of quantities related to volume How much water a container can hold How much material it took to build a solid object Volume is measured in cubic units like in3 or m3 Here are some examples of quantities related to surface area How much fabric is needed to cover a surface How much of an object needs to be painted Surface area is measured in square units like in2 or m2 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 G7M7 LESSON 15 Name Date GRADE 7 MISSION 7 LESSON 15 Exit Ticket Shaunice built the birdhouse shown Shaunice will paint the outside of the birdhouse before drilling the hole How many square inches of paint will she need How many cubic inches of empty space will a bird have to nest inside this birdhouse 5 in 5 in 3 in 7 in 10 in 8 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 89

90

ZEARN MATH STUDENT EDITION G7M7 LESSON 16 Lesson 16 Applying Volume and Surface Area Let s explore things that are proportional to volume or surface area Warm Up 1 For each situation decide if it requires Noah to calculate surface area or volume Explain your reasoning 1 Noah is planning to paint the bird house he built He is unsure if he has enough paint 2 Noah is planning to use a box with a trapezoid base to hold modeling clay He is unsure if the clay will all fit in the 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 91

G7M7 LESSON 16 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 At a daycare Kiran sees children climbing on this foam play structure Kiran is thinking about building a structure like this for his younger cousins to play on 1 The entire structure is made out of soft foam so the children don t hurt themselves How much foam would Kiran need to build this play structure 2 The entire structure is covered with vinyl so it is easy to wipe clean How much vinyl would Kiran need to build this play structure 3 The foam costs 0 8 per in3 Here is a table that lists the costs for different amounts of vinyl Vinyl in2 Cost 75 0 45 125 0 75 What is the total cost for all the foam and vinyl needed to build this play structure 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 G7M7 LESSON 16 ACTIVITY 2 3 The daycare has two sandboxes that are both prisms with regular hexagons as their bases The smaller sandbox has a base area of 1 146 in2 and is filled 10 inches deep with sand 1 It took 14 bags of sand to fill the small sandbox to this depth What volume of sand comes in one bag Round to the nearest whole cubic inch 2 The daycare manager wants to add 3 more inches to the depth of the sand in the small sandbox How many bags of sand will they need to buy 3 The daycare manager also wants to add 3 more inches to the depth of the sand in the large sandbox The base of the large sandbox is a scaled copy of the base of the small sandbox with a scale factor of 1 5 How many bags of sand will they need to buy for the large sandbox 4 A lawn and garden store is selling 6 bags of sand for 19 50 How much will they spend to buy all the new sand for both sandboxes 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 16 ZEARN MATH STUDENT EDITION Lesson Summary Suppose we wanted to make a concrete bench like the one shown in this picture If we know that the finished bench has a volume of 10 ft3 and a surface area of 44 ft2 we can use this information to solve problems about the bench For example How much does the bench weigh How long does it take to wipe the whole bench clean How much will the materials cost to build the bench and to paint it To figure out how much the bench weighs we can use its volume 10 ft3 Concrete weighs about 150 pounds per cubic foot so this bench weighs about 1 500 pounds because 10 150 1 500 To figure out how long it takes to wipe the bench clean we can use its surface area 44 ft2 If it takes a person about 2 seconds per square foot to wipe a surface clean then it would take about 88 seconds to clean this bench because 44 2 88 It may take a little less than 88 seconds since the surfaces where the bench is touching the ground do not need to be wiped Would you use the volume or the surface area of the bench to calculate the cost of the concrete needed to build this bench And for the cost of the paint 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 G7M7 LESSON 16 Date GRADE 7 MISSION 7 LESSON 16 Exit Ticket Andre is preparing for the school play and needs to paint the cardboard castle backdrop that measures 14 14 feet by 6 feet 1 How much cardboard does he need to paint 2 If one bottle of paint covers an area of 40 square feet how many bottles of paint does Andre need for his backdrop 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

96

ZEARN MATH STUDENT EDITION G7M7 LESSON 17 Lesson 17 Building Prisms Let s build a triangular prism from scratch Warm Up 1 Here are some nets for various prisms Use them to answer these questions 1 What would each net look like when folded 2 What do you notice about the nets 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M7 LESSON 17 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 98 The base of a triangular prism has one side that is 7 cm long one side that is 5 5 cm long and one angle that measures 45 1 Draw as many different triangles as you can with these given measurements 2 Select one of the triangles you have drawn Measure and calculate to approximate its area 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

ZEARN MATH STUDENT EDITION G7M7 LESSON 17 ACTIVITY 2 3 Your teacher will give you an incomplete net Follow the instructions to complete the net and assemble the triangular prism Then answer the questions Complete the net and assemble the triangular prism 1 Draw an identical copy of the triangle you selected in the previous activity along the top of the rectangle with one vertex on point A 2 Draw another copy of your triangle flipped upside down along the bottom of the rectangle with one vertex on point C 3 Determine how long the rectangle needs to be to wrap all the way around your triangular bases Pause here so your teacher can review your work 4 Cut out and assemble your net After you finish assembling your triangular prism answer these questions Explain or show your reasoning 1 What is the volume of your prism 2 What is the surface area of your prism 3 Stand your prism up so it is sitting on its triangular base a If you were to cut your prism in half horizontally what shape would the cross section be b If you were to cut your prism in half vertically what shape would the cross section 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 99

G7M7 LESSON 17 ZEARN MATH STUDENT EDITION ACTIVITY 3 43 Compare your prism with your partner s prism then answer the questions 1 What is the same What is different 2 Find a way you can put your prism and your partner s prism together to make one new larger prism Describe your new prism 3 Draw the base of your new prism and label the lengths of the sides 4 As you answer these questions about your new prism look for ways you can use your calculations from the previous activity to help you Explain or show your reasoning a What is the area of its base b What is its height c What is its volume d What is its surface area 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

Grade 7 Mission 8 Probability and Sampling

102

ZEARN MATH STUDENT EDITION G7M8 LESSON 1 Lesson 1 Mystery Bags Let s make predictions based on what we know Warm Up 1 Andre and his dad have been fishing for 2 hours In that time they have caught 9 bluegills and 1 yellow perch The next time Andre gets a bite what kind of fish do you think it will be Explain your reasoning Concept Exploration ACTIVITY 1 2 1 Your teacher will give your group a bag of colored blocks Follow the instructions below to play the game in your group At the end of each round record each person s score in the table Follow these instructions to play one round of the game a Everyone in the group records the color written on the bag in the first column of the table b Without looking in the bag one person takes out one of the blocks and shows it to the group c If they get a block that is the same color as the bag they earn 1 point during round 1 2 points during round 2 3 points during round 3 d Next they put the block back into the bag shake the bag to mix up the blocks and pass the bag to the next person in the group e Repeat these steps until everyone in your group has had 4 turns 2 At the end of the round record each person s score in the table What color bag Person 1 s score Person 2 s score Person 3 s score Person 4 s score Round 1 Round 2 Round 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 103

G7M8 LESSON 1 ZEARN MATH STUDENT EDITION 3 Pause here so your teacher can give you a new bag of blocks for the next round 4 Repeat the previous steps to play rounds 2 and 3 of the game 5 After you finish playing all 3 rounds calculate the total score for each person in your group Lesson Summary One of the main ways that humans learn is by repeating experiments and observing the results Babies learn that dropping their cup makes it hit the floor with a loud noise by repeating this action over and over Scientists learn about nature by observing the results of repeated experiments again and again With enough data about the results of experiments we can begin to predict what may happen if the experiment is repeated in the future For example a baseball player who has gotten a hit 33 out of 100 times at bat might be expected to get a hit about 33 of his times at bat in the future as well In some cases we can predict the chances of things happening based on our knowledge of the situation For example a coin should land heads up about 50 of the time due to the symmetry of the coin In other cases there are too many unknowns to predict the chances of things happening For example the chances of rain tomorrow are based on similar weather conditions we have observed in the past In these situations we can experiment using past results to estimate chances 104 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 1 Name Date GRADE 7 MISSION 8 LESSON 1 Exit Ticket A large fish tank is filled with table tennis balls with numbers written on them Jada chooses 10 table tennis balls from the tank and writes down their numbers 1 3 5 1 3 2 4 1 5 3 A second tank is filled with golf balls with numbers written on them Jada chooses 10 golf balls from the tank and writes down their numbers 1 4 5 2 6 2 2 1 4 8 To win a prize Jada must get a ball with an even number Should she try to win the prize using the tank of table tennis balls or the tank of golf balls 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 105

106

ZEARN MATH STUDENT EDITION G7M8 LESSON 2 Lesson 2 Chance Experiments Let s investigate chance Warm Up 1 Which is more likely to happen 1 When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes you pull out a left shoe 2 When listening to a playlist which has 5 songs on it in shuffle mode the first song on the playlist plays first Concept Exploration ACTIVITY 1 2 1 Answer the questions about likelihood Label each event with one of these options impossible unlikely equally likely as not likely certain a You will win grand prize in a raffle if you purchased 2 out of the 100 tickets b You will wait less than 10 minutes before ordering at a fast food restaurant c You will get an even number when you roll a standard number cube d A four year old child is over 6 feet tall e No one in your class will be late to class next week f The next baby born at a hospital will be a boy g It will snow at our school on July 1 h The sun will set today before 11 00 p m i Spinning this spinner will result in black j Spinning this spinner will result in yellow 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 2 ZEARN MATH STUDENT EDITION 2 Discuss your answers to the previous question with your partner If you disagree work to reach an agreement 3 Invent another situation for each label for a total of 5 more events ACTIVITY 2 3 Your teacher will have 2 students play a short game 1 When the first person chose 3 numbers did they usually win 2 When the person chose 4 numbers did you expect them to win Why ACTIVITY 3 43 108 Your teacher will give you some cards that describe events 1 Order the events from least likely to most likely 2 After ordering the first set of cards pause here so your teacher can review your work Then your teacher will give you a second set of cards 3 Add the new set of cards to the first set so that all of the cards are ordered from least likely to most likely 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 2 Lesson Summary A chance experiment is something that happens where the outcome is unknown For example if we flip a coin we don t know if the result will be a head or a tail An outcome of a chance experiment is something that can happen when you do a chance experiment For example when you flip a coin one possible outcome is that you will get a head An event is a set of one or more outcomes We can describe events using these phrases Impossible Unlikely Equally likely as not Likely Certain For example if you flip a coin It is impossible that the coin will turn into a bottle of ketchup It is unlikely the coin will land on its edge It is equally likely as not that you will get a tail It is likely that you will get a head or a tail It is certain that the coin will land somewhere The probability of an event is a measure of the likelihood that an event will occur We will learn more about probabilities in the lessons to come TERMINOLOGY Chance experiment Event Outcome 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

110

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 2 Date GRADE 7 MISSION 8 LESSON 2 Exit Ticket Here are some scenarios According to market research a business has a 75 chance of making money in the first 3 years According to lab testing 65 of a certain kind of experimental light bulb will work after 3 years According to experts the likelihood of a car needing major repairs in the first 3 years is 0 7 1 Write the scenarios in order of likelihood from least to greatest after three years the business makes money the light bulb still works and the car needs major repairs 2 Name another chance experiment that has the same likelihood as one of the scenarios 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

112

ZEARN MATH STUDENT EDITION G7M8 LESSON 3 Lesson 3 What Are Probabilities Let s find out what s possible Warm Up 1 Which game would you choose to play Explain your reasoning Game 1 You flip a coin and win if it lands showing heads Game 2 You roll a standard number cube and win if it lands showing a number that is divisible by 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 113

G7M8 LESSON 3 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Answer the questions about sample space and outcomes For each situation list the sample space and tell how many outcomes there are a Han rolls a standard number cube once b Clare spins this spinner once c Kiran selects a letter at random from the word MATH d Mai selects a letter at random from the alphabet e Noah picks a card at random from a stack that has cards numbered 5 through 20 2 Next compare the likelihood of these outcomes Be prepared to explain your reasoning a Is Clare more likely to have the spinner stop on the black or gray section b Is Kiran or Mai more likely to get the letter T c 3 114 Is Han or Noah more likely to get a number that is greater than 5 Suppose you have a spinner that is evenly divided showing all the days of the week You also have a bag of papers that list the months of the year Are you more likely to spin the current day of the week or pull out the paper with the current month 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 3 ACTIVITY 2 3 Your teacher will give your group a bag of paper slips with something printed on them Repeat these steps until everyone in your group has had a turn Then answer the questions As a group guess what is printed on the papers in the bag and record your guess in the table Without looking in the bag one person takes out one of the papers and shows it to the group Everyone in the group records what is printed on the paper The person who took out the paper puts it back into the bag shakes the bag to mix up the papers and passes the bag to the next person in the group Guess the sample space What is printed on the paper Person 1 Person 2 Person 3 Person 4 1 How was guessing the sample space the fourth time different from the first 2 What could you do to get a better guess of the sample space 3 Look at all the papers in the bag Were any of your guesses correct 4 Are all of the possible outcomes equally likely Explain 5 Use the sample space to determine the probability that a fifth person would get the same outcome as person 1 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 115

G7M8 LESSON 3 ZEARN MATH STUDENT EDITION Lesson Summary The probability of an event is a measure of the likelihood that the event will occur Probabilities are expressed using numbers from 0 to 1 If the probability is 0 that means the event is impossible For example when you flip a coin the probability that it will turn into a bottle of ketchup is 0 The closer the probability of some event is to 0 the less likely it is If the probability is 1 that means the event is certain For example when you flip a coin the probability that it will land somewhere is 1 The closer the probability of some event is to 1 the more likely it is If we list all of the possible outcomes for a chance experiment we get the sample space for that experiment For example the sample space for rolling a standard number cube includes six outcomes 1 2 3 4 5 and 6 The probability that the number cube will land showing the number 4 is 16 In general if all outcomes in an experiment are equally likely and there are n possible outcomes then the probability of a single outcome is n1 Sometimes we have a set of possible outcomes and we want one of them to be selected at random That means that we want to select an outcome in a way that each of the outcomes is equally likely For example if two people both want to read the same book we could flip a coin to see who gets to read the book first TERMINOLOGY Probability Random Sample space 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 Name G7M8 LESSON 3 Date GRADE 7 MISSION 8 LESSON 3 Exit Ticket A mother decides to teach her son about a letter each day of the week She will choose a letter from the name of the day For example on Saturday she might teach about the letter S or the letter U but not the letter M 1 What letters are possible to teach using this method There are 15 2 What are 4 letters that can t be taught using this method 3 On TUESDAY the mother writes the word on a piece of paper and cuts it up so that each letter is on a separate piece of paper She mixes up the papers and picks one What is the probability that she will choose the piece of paper with the letter Y 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 117

118

ZEARN MATH STUDENT EDITION G7M8 LESSON 4 Lesson 4 Estimating Probabilities through Repeated Experiments Let s do some experimenting Warm Up 1 Locate and label these numbers on the number line a 0 5 b 0 75 c 0 33 d 0 67 0 1 e 0 25 2 Choose one of the numbers from the previous question Describe a game in which that number represents your theoretical probability of winning Concept Exploration ACTIVITY 1 2 Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube 1 List the outcomes in the sample space for rolling the number cube 2 What is the theoretical probability Mai will win the game 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 119

G7M8 LESSON 4 ZEARN MATH STUDENT EDITION 3 If Mai is given the option to flip a coin and win if it comes up heads is that a better option for her to win 4 With your group follow these instructions 10 times to create the graph One person rolls the number cube Everyone records the outcome Calculate the fraction of rolls that are a win for Mai so far Approximate the fraction with a decimal value rounded to the hundredths place Record both the fraction and the decimal in the last column of the table On the graph plot the number of rolls and the fraction that were wins Pass the number cube to the next person in the group Roll Outcome Total number of wins for Mai Fraction of games played that are wins 1 2 3 4 5 6 7 8 9 Fraction of games played that are wins 10 1 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of rolls 120 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 5 G7M8 LESSON 4 What appears to be happening with the points on the graph 6 a After 10 rolls what fraction of the total rolls were a win b How close is this fraction to the theoretical probability that Mai will win 7 Roll the number cube 10 more times Records your results in this table and on the graph from earlier Roll Outcome Total number of wins for Mai Fraction of games played that are wins 11 12 13 14 15 16 17 18 19 20 8 a After 20 rolls what fraction of the total rolls were a win b How close is this fraction to the theoretical probability that Mai will win 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 4 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 1 The theoretical probability of a coin landing heads up after a flip is 12 Use this to answer the questions below For each situation do you think the result is surprising or not Is it possible Be prepared to explain your reasoning a You flip the coin once and it lands heads up b You flip the coin twice and it lands heads up both times c 122 You flip the coin 100 times and it lands heads up all 100 times 4 If you flip the coin 100 times how many times would you expect the coin to land heads up Explain your reasoning 5 If you flip the coin 100 times what are some other results that would not be surprising 6 You ve flipped the coin 3 times and it has come up heads once The cumulative fraction of heads is currently 13 If you flip the coin one more time will it land heads up to make the cumulative fraction 24 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 4 Lesson Summary The expected theoretical probability for an event represents the proportion of the time we expect that event to occur in the long run For example the theoretical probability of a coin landing heads up after a flip is 12 which means that if we flip a coin many times we expect that it will land heads up about half of the time Even though the theoretical probability tells us what we should expect if we flip a coin many times that doesn t mean we are more likely to get heads if we just got three tails in a row The chances of getting heads are the same every time we flip the coin no matter what the outcome was for past flips 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

124

ZEARN MATH STUDENT EDITION G7M8 LESSON 4 Name Date GRADE 7 MISSION 8 LESSON 4 Exit Ticket A librarian is curious about the habits of the library s patrons He records the type of item that the first 10 patrons check out from the library Patron Item type 1 fiction book 2 non fiction book 3 fiction book 4 fiction book 5 audiobook 6 non fiction book 7 DVD 8 non fiction book 9 fiction book 10 DVD Based on the information from these patrons determine the expected theoretical probability that the next patron will check out a fiction book 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 125

126

ZEARN MATH STUDENT EDITION G7M8 LESSON 5 Lesson 5 More Estimating Probabilities Let s estimate some probabilities Warm Up 1 Answer the following questions 1 If the weather forecast calls for a 20 chance of light rain tomorrow would you say that it is likely to rain tomorrow 2 1 If the expected theoretical probability of a tornado today is 10 would you say that there will likely be a tornado today 3 If the expected theoretical probability of snow this week is 0 85 would you say that it is likely to snow this week Concept Exploration ACTIVITY 1 2 Your teacher will give you 4 spinners Make sure each person in your group uses a different spinner Then answer the questions 1 Spin your spinner 10 times and record your outcomes 2 Did you get all of the different possible outcomes in your 10 spins 3 What fraction of your 10 spins landed on 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 127

G7M8 LESSON 5 4 ZEARN MATH STUDENT EDITION Next share your outcomes with your group and record their outcomes a Outcomes for spinner A b Outcomes for spinner B c Outcomes for spinner C d Outcomes for spinner D 128 5 Do any of the spinners have the same sample space If so do they have the same theoretical probabilities for each number to result 6 For each spinner what is the theoretical probability that it lands on the number 3 Explain or show your reasoning 7 For each spinner what is the theoretical probability that it lands on something other than the number 3 Explain or show your reasoning 8 Noah put spinner D on top of his closed binder and spun it 10 times It never landed on the number 1 How might you explain why this happened 9 Han put spinner C on the floor and spun it 10 times It never landed on the number 3 so he says that the theoretical probability of getting a 3 is 0 How might you explain why this happened 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 5 ACTIVITY 2 3 Your teacher will give you a bag of blocks that are different colors Do not look into the bag or take out more than 1 block at a time Repeat these steps until everyone in your group has had 4 turns Take one block out of the bag and record whether or not it is green Put the block back into the bag and shake the bag to mix up the blocks Pass the bag to the next person in the group 1 What do you think is the probability of taking out a green block from this bag Explain or show your reasoning 2 How could you get a better estimate without opening the bag 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary Suppose a bag contains 5 blocks If we select a block at random from the bag then the expected theoretical probability of getting any one of the blocks is 51 Now suppose a bag contains 5 blocks Some of the blocks have a star and some have a moon If we select a block from the bag then we will either get a star block or a moon block The expected theoretical probability of getting a star block depends on how many there are in the bag In this example the expected theoretical probability of selecting a star block at random from the first bag is 15 because it contains only 1 star block The expected theoretical probability of getting a moon block is 45 The expected theoretical probability of selecting a star block at random from the second bag is 35 because it contains 3 star blocks The expected theoretical probability of getting a moon block from this bag is 52 This shows that two experiments can have the same sample space but different expected theoretical probabilities for each outcome 130 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 5 Date GRADE 7 MISSION 8 LESSON 5 Exit Ticket Jada Diego and Elena each use the same spinner that has four not necessarily equal sized sections marked A B C and D Jada says The probability of spinning B is 0 3 because I spun 10 times and it landed on B 3 times Diego says The probability of spinning B is 20 because I spun 5 times and it landed on B once Elena says The probability of spinning B is 27 because I spun 7 times and it landed on B twice 1 Based on their methods which probability estimate do you think is the most accurate Explain your reasoning 2 Andre measures the spinner and finds that the B section takes up 14 of the circle Explain why none of the methods match this probability exactly 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

132

ZEARN MATH STUDENT EDITION G7M8 LESSON 6 Lesson 6 Estimating Probabilities Using Simulation Let s simulate real world situations Warm Up 1 Which spinner doesn t belong Concept Exploration ACTIVITY 1 Diego must cross a busy intersection at a crosswalk on his way to school Some days he is able to cross immediately or wait only a short while Other days he must wait for more than 1 minute for the signal to indicate that he may cross the street We will simulate his luck at this intersection using different methods and estimate his probability of waiting more than 1 minute 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 6 2 ZEARN MATH STUDENT EDITION Your group will receive the supplies for one of the three different simulations Follow the instructions in your notes to simulate 15 days of Diego s walk The first 3 days have been done for you Then answer the questions that follow Simulate one day If your group gets a bag of papers reach into the bag and select one paper without looking inside If your group gets a spinner spin the spinner and see where it stops If your group gets two number cubes roll both cubes and add the numbers that land face up A sum of 2 8 means Diego has to wait Record in the table whether or not Diego had to wait more than 1 minute Calculate the total number of days and the cumulative fraction of days that Diego has had to wait so far On the graph plot the number of days and the fraction that Diego has had to wait Connect each point by a line If your group has the bag of papers put the paper back into the bag and shake the bag to mix up the papers Pass the supplies to the next person in the group Fraction of days Diego had to wait 1 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 2 4 6 8 10 12 14 16 18 20 22 24 Day 134 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 6 Day Does Diego have to wait more than 1 minute Total number of days Diego had to wait Fraction of days Deigo had to wait 1 No 0 0 1 0 00 2 Yes 1 1 2 0 50 3 Yes 2 2 3 0 67 4 5 6 7 8 9 10 11 12 13 14 15 1 Based on the data you have collected do you think the fraction of days Diego has to wait after the 15th day will be closer to 0 9 or 0 7 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 135

G7M8 LESSON 6 2 ZEARN MATH STUDENT EDITION Continue the simulation for 10 more days Record your results in this table and on the graph from earlier Day Does Diego have to wait more than 1 minute Total number of days Diego had to wait Fraction of days Deigo had to wait 16 17 18 19 20 21 22 23 24 25 136 3 What do you notice about the graph 4 Based on the graph estimate the probability that Diego will have to wait more than 1 minute to cross the crosswalk 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 6 ACTIVITY 2 3 For each situation below describe a chance experiment that would fairly represent it 1 Six people are going out to lunch together One of them will be selected at random to choose which restaurant to go to Who gets to choose 2 After a robot stands up it is equally likely to step forward with its left foot or its right foot Which foot will it use for its first step 3 In a computer game there are three tunnels Each time the level loads the computer randomly selects one of the tunnels to lead to the castle Which tunnel is it 4 Your school is taking 4 buses of students on a field trip Will you be assigned to the same bus that your math teacher is riding on 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary Sometimes it is easier to estimate a probability by doing a simulation A simulation is an experiment that approximates a situation in the real world Simulations are useful when it is hard or timeconsuming to gather enough information to estimate the probability of some event For example imagine Andre has to transfer from one bus to another on the way to his music lesson Most of the time he makes the transfer just fine but sometimes the first bus is late and he misses the second bus We could set up a simulation with slips of paper in a bag Each paper is marked with a time when the first bus arrives at the transfer point We select slips at random from the bag After many trials we calculate the fraction of the times that he missed the bus to estimate the probability that he will miss the bus on a given day 138 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 6 Date GRADE 7 MISSION 8 LESSON 6 Exit Ticket In a video game the chance of rain each day is always 30 At the beginning of each day in the video game the computer generates a random integer between 1 and 50 Explain how you could use this number to simulate the weather in the video game 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

140

ZEARN MATH STUDENT EDITION G7M8 LESSON 7 Lesson 7 Simulating Multi Step Experiments Let s simulate more complicated events Warm Up 1 What do you notice What do you wonder Concept Exploration ACTIVITY 1 2 Alpine Zoom is a ski business To make money over spring break they need it to snow at least 4 out of the 10 days The weather forecast says there is a 13 chance it will snow each day during the break 1 Describe a chance experiment that you could use to simulate whether it will snow on the first day of spring break 2 How could this chance experiment be used to determine whether Alpine Zoom will make money Pause here so your teacher can give you the supplies for a simulation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 7 3 ZEARN MATH STUDENT EDITION Simulate the weather for 10 days to see if Alpine Zoom will make money over spring break Record your results in the first row of the table Location Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Did they make money Simulation 1 Simulation 2 Simulation 3 Simulation 4 Simulation 5 142 4 Repeat the previous step 4 more times Record your results in the other rows of the table 5 Based on your group s simulations estimate the probability that Alpine Zoom will make money 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 7 ACTIVITY 2 3 Match each situation to a simulation Situations Simulations A In a small lake 25 of the fish are female You capture a fish record whether it is male or female and toss the fish back into the lake If you repeat this process 5 times what is the probability that at least 3 of the 5 fish are female 1 Toss a standard number cube 2 times and record the outcomes Repeat this process many times and find the proportion of the simulations in which a 1 or 2 appeared both times to estimate the probability 2 Make a spinner with four equal sections labeled 1 2 3 and 4 Spin the spinner 5 times and record the outcomes Repeat this process many times and find the proportion of the simulations in which a 4 appears 3 or more times to estimate the probability 3 Toss a fair coin 4 times and record the outcomes Repeat this process many times and find the proportion of the simulations in which exactly 3 heads appear to estimate the probability 4 Place 8 blue chips and 2 red chips in a bag Shake the bag select a chip record its color and then return the chip to the bag Repeat the process 4 more times to obtain a simulated outcome Then repeat this process many times and find the proportion of the simulations in which exactly 4 blues are selected to estimate the probability B Elena makes about 80 of her free throws Based on her past successes with free throws what is the probability that she will make exactly 4 out of 5 free throws in her next basketball game C On a game show a contestant must pick one of three doors In the first round the winning door has a vacation In the second round the winning door has a car What is the probability of winning a vacation and a car D Your choir is singing in 4 concerts You and one of your classmates both learned the solo Before each concert there is an equal chance the choir director will select you or the other student to sing the solo What is the probability that you will be selected to sing the solo in exactly 3 of the 4 concerts 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 7 ZEARN MATH STUDENT EDITION Lesson Summary The more complex a situation is the harder it can be to estimate the probability of a particular event happening Well designed simulations are a way to estimate a probability in a complex situation especially when it would be difficult or impossible to determine the probability from reasoning alone To design a good simulation we need to know enough information about the situation For example if we want to estimate the probability that it will rain every day for the next three days we could look up the weather forecast for the next three days Here is a table showing a weather forecast Probability of rain Today Tuesday Wednesday Thursday Friday 0 2 0 4 0 5 0 9 We can set up a simulation to estimate the probability of rain each day with three bags In the first bag we put 4 slips of paper that say rain and 6 that say no rain In the second bag we put 5 slips of paper that say rain and 5 that say no rain In the third bag we put 9 slips of paper that say rain and 1 that says no rain Then we can select one slip of paper from each bag and record whether or not there was rain on all three days If we repeat this experiment many times we can estimate the probability that there will be rain on all three days by dividing the number of times all three slips said rain by the total number of times we performed the simulation 144 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 7 Name Date GRADE 7 MISSION 8 LESSON 7 Exit Ticket The probability of a certain brand of battery going dead within 15 hours is 13 Noah has a toy that requires 4 of these batteries He wants to simulate the situation to estimate the probability that at least one battery will die before 15 hours are up 1 2 Noah will simulate the situation by putting marbles in a bag Drawing one marble from the bag will represent the outcome of one of the batteries in the toy after 15 hours Red marbles represent a battery that dies before 15 hours are up and green marbles represent a battery that lasts longer How many marbles of each color should he put in the bag Explain your reasoning Trial Result 1 GGRG 2 GRGR 3 GGGG 4 RGGG 5 GGGR After doing the simulation 5 times Noah has the following results What should he use as an estimate of the probability that at least one battery will die within 15 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 145

146

ZEARN MATH STUDENT EDITION G7M8 LESSON 8 Lesson 8 Keeping Track of All Possible Outcomes Let s explore sample spaces for experiments with multiple parts Warm Up 1 How many different meals are possible if each meal includes one main course one side dish and one drink Main courses Side dishes Drinks grilled chicken salad milk turkey sandwich applesauce juice pasta salad 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 147

G7M8 LESSON 8 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Consider the experiment Flip a coin and then roll a number cube Elena Kiran and Priya each use a different method for finding the sample space of this experiment Read about each method below and then answer the questions that follow Elena carefully writes a list of all the options Heads 1 Heads 2 Heads 3 Heads 4 Heads 5 Heads 6 Tails 1 Tails 2 Tails 3 Tails 4 Tails 5 Tails 6 Kiran makes a table 1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6 Priya draws a tree with branches in which each pathway represents a different outcome H 1 2 3 4 5 6 T 1 2 3 4 5 6 1 Compare the three methods What is the same about each method What is different Be prepared to explain why each method produces all the different outcomes without repeating any 2 Which method do you prefer for this situation Pause here so your teacher can review your work 148 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 8 Find the sample space for each of these experiments using any method Make sure you list every possible outcome without repeating any a Flip a dime then flip a nickel and then flip a penny Record whether each lands heads or tails up b Han s closet has a blue shirt a gray shirt a white shirt blue pants khaki pants and black pants He must select one shirt and one pair of pants to wear for the day c Spin a color and then spin a number d Spin the hour hand on an analog clock and then choose a m or p m 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 149

G7M8 LESSON 8 ZEARN MATH STUDENT EDITION ACTIVITY 2 43 A submarine sandwich shop makes sandwiches with one kind of bread one protein one choice of cheese and two vegetables as shown below Answer the questions Breads Italian white wheat Proteins Tuna ham turkey beans Cheese Provolone Swiss American none Vegetables Lettuce tomatoes peppers onions pickles Submarine sandwich and chips by jeffreyw via Wikimedia Commons Public Domain 150 1 How many different sandwiches are possible Explain your reasoning You do not need to write out the sample space 2 Andre knows he wants a sandwich that has ham lettuce and tomatoes on it He doesn t care about the type of bread or cheese How many of the different sandwiches would make Andre happy 3 If a sandwich is made by randomly choosing each of the options what is the probability it will be a sandwich that Andre would be happy with 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 8 Lesson Summary Sometimes we need a systematic way to count the number of outcomes that are possible in a given situation For example suppose there are 3 people A B and C who want to run for the president of a club and 4 different people 1 2 3 and 4 who want to run for vice president of the club We can use a tree a table or an ordered list to count how many different combinations are possible for a president to be paired with a vice president With a tree we can start with a branch for each of the people who want to be president Then for each possible president we add a branch for each possible vice president for a total of 3 4 12 possible pairs We can also start by counting vice presidents first and then adding a branch for each possible president for a total of 4 3 12 possible pairs AA 11 11 22 33 44 AA CC AA 22 11 33 44 AA 33 BB CC 11 22 33 44 CC BB CC 22 BB BB AA 44 BB CC A table can show the same result 1 2 3 4 A A 1 A 2 A 3 A 4 B B 1 B 2 B 3 B 4 C C 1 C 2 C 3 C 4 So does this ordered list A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

152

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 8 Date GRADE 7 MISSION 8 LESSON 8 Exit Ticket Andre is reviewing proportional relationships He wants to practice using a graph that goes through a point so that each coordinate is between 1 and 10 1 For the point how many outcomes are in the sample space 2 For how many outcomes are the x coordinate and the y coordinate the same 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 153

154

ZEARN MATH STUDENT EDITION G7M8 LESSON 9 Lesson 9 Multi Step Experiments Let s look at probabilities of experiments that have multiple steps Warm Up Is each equation true or false Explain your reasoning 8 8 8 8 8 3 10 10 10 10 10 5 10 6 4 6 3 6 4 6 5 Concept Exploration ACTIVITY 1 1 The other day you wrote the sample space for spinning each of these spinners once What is the probability of getting 1 Green and 3 2 Blue and any odd number 3 Any color other than red and any number other than 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 155

G7M8 LESSON 9 ZEARN MATH STUDENT EDITION ACTIVITY 2 1 2 Write the sample space for flipping a coin and rolling a number cube using the representation you are assigned 3 You looked at a list a table and a tree that showed the sample space for rolling a number cube and flipping a coin Answer the questions in your notes Your teacher will assign you one of these three structures to use to answer these questions Be prepared to explain your reasoning a What is the probability of getting tails and a 6 b What is the probability of getting heads and an odd number Pause here so your teacher can review your work 2 Suppose you roll two number cubes What is the probability of getting a Both cubes showing the same number b Exactly one cube showing an even number c At least one cube showing an even number d Two values that have a sum of 8 e Two values that have a sum of 13 3 156 Jada flips three quarters What is the probability that all three will land showing the same side 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 9 Lesson Summary Suppose we have two bags One contains 1 star block and 4 moon blocks The other contains 3 star blocks and 1 moon block If we select one block at random from each what is the probability that we will get two star blocks or two moon blocks To answer this question we can draw a tree diagram to see all of the possible outcomes star star star moon star moon star moon star star star moon star star moon moon star moon star star star star star moon moon There are 5 4 20 possible outcomes Of these 3 of them are both stars and 4 are both moons So the 7 probability of getting 2 star blocks or 2 moon blocks is 20 In general if all outcomes in an experiment are equally likely then the probability of an event is the fraction of outcomes in the sample space for which the event occurs 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

158

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 9 Date GRADE 7 MISSION 8 LESSON 9 Exit Ticket Lin plays a game that involves a standard number cube and a deck of ten cards numbered 1 through 10 If both the cube and card have the same number Lin gets another turn Otherwise the game continues with the next player What is the probability that Lin gets another turn 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

160

ZEARN MATH STUDENT EDITION G7M8 LESSON 10 Lesson 10 Designing Simulations Let s simulate some real life scenarios Warm Up 1 Find the value of each expression mentally 1 4 2 3 2 2 4 2 2 6 4 3 3 4 2 2 6 4 3 6 4 4 4 2 2 6 4 3 6 3 6 5 Concept Exploration ACTIVITY 1 2 A scientist is studying the genes that determine the color of a mouse s fur When two mice with brown fur breed there is a 25 chance that each baby will have white fur For the experiment to continue the scientist needs at least 2 out of 5 baby mice to have white fur To simulate this situation you can flip a coin twice for each baby mouse 1 If the coin lands heads up both times it represents a mouse with white fur Any other result represents a mouse with brown fur Have each person in the group simulate a litter of 5 offspring and record their results Next determine whether at least 2 of the offspring have white fur mouse 1 mouse 2 mouse 3 Mice by Kapa65 via Pixabay Public Domain mouse 4 mouse 5 Do at least 2 have white fur simulation 1 simulation 2 simulation 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 161

G7M8 LESSON 10 ZEARN MATH STUDENT EDITION 2 Based on the results from everyone in your group estimate the probability that the scientist s experiment will be able to continue 3 How could you improve your estimate ACTIVITY 2 3 162 Your teacher will give your group a paper describing a situation 1 Design a simulation that you could use to estimate the probability Show your thinking Organize it so it can be followed by others 2 Explain how you used the simulation to answer the questions posed in the situation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 10 Lesson Summary Many real world situations are difficult to repeat enough times to get an estimate for a probability If we can find probabilities for parts of the situation we may be able to simulate the situation using a process that is easier to repeat For example if we know that each egg of a fish in a science experiment has a 13 chance of having a mutation how many eggs do we need to collect to make sure we have 10 mutated eggs If getting these eggs is difficult or expensive it might be helpful to have an idea about how many eggs we need before trying to collect them We could simulate this situation by having a computer select random numbers between 1 and 100 If the number is between 1 and 13 it counts as a mutated egg Any other number would represent a normal egg This matches the 13 chance of each fish egg having a mutation We could continue asking the computer for random numbers until we get 10 numbers that are between 1 and 13 The number of times we asked the computer for a random number would give us an estimate of the number of fish eggs we would need to collect To improve the estimate this entire process should be repeated many times Because computers can perform simulations quickly we could simulate the situation 1 000 times or more 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

164

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 10 Date GRADE 7 MISSION 8 LESSON 10 Exit Ticket Elena is programming a video game She needs to simulate the power up that the player gets when they reach a certain level The computer can run a program to return a random integer between 1 and 100 Elena wants the best power up to be rewarded 15 of the time Explain how Elena could use the computer to simulate the player getting the best power up at least 2 out of 3 times 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

166

ZEARN MATH STUDENT EDITION G7M8 LESSON 11 Lesson 11 Comparing Groups Let s compare two groups Warm Up 1 What do you notice What do you wonder Women s gymnastics team 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 Height inches Men s volleyball team 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 Height inches Concept Exploration ACTIVITY 1 2 1 Answer the questions about the heights of different teams How much taller is the volleyball team than the gymnastics team Gymnastics team s heights in inches 56 59 60 62 62 63 63 63 64 64 68 69 Volleyball team s heights in inches 72 75 76 76 78 79 79 80 80 81 81 81 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 11 2 ZEARN MATH STUDENT EDITION Make dot plots to compare the heights of the tennis and badminton teams Tennis team s heights in inches 66 67 69 70 71 73 73 74 75 75 76 Badminton team s heights in inches 62 62 65 66 68 71 73 What do you notice about your dot plots 3 168 Elena says the members of the tennis team were taller than the badminton team Lin disagrees Do you agree with either of them 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 11 ACTIVITY 2 3 Compare the heights of these two families The heights in inches of Noah s family members 28 39 41 52 63 66 71 The heights in inches of Jada s family members 49 60 68 70 71 73 77 1 Calculate and compare the mean of each data set 2 Discuss your answers with your partner 3 Describe the variability and overlap in the data sets to show that the mean is not enough Lesson Summary Comparing two individuals is fairly straightforward The question Which dog is taller can be answered by measuring the heights of two dogs and comparing them directly Comparing two groups can be more challenging What does it mean for the basketball team to generally be taller than the soccer team To compare two groups we use the distribution of values for the two groups Most importantly a measure of center usually mean or median and its associated measure of variability usually mean absolute deviation or interquartile range can help determine the differences between groups For example if the average height of pugs in a dog show is 11 inches and the average height of the beagles in the dog show is 15 inches it seems that the beagles are generally taller On the other hand if the MAD is 3 inches it would not be unreasonable to find a beagle that is 11 inches tall or a pug that is 14 inches tall Therefore the heights of the two dog breeds may not be very different from one another TERMINOLOGY Interquartile range IQR Mean Mean absolute deviation MAD Median Mode 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

170

ZEARN MATH STUDENT EDITION G7M8 LESSON 11 Name Date GRADE 7 MISSION 8 LESSON 11 Exit Ticket Noah s parents are interested in moving to another part of town They look up all the prices of the homes for sale and record them in thousands of dollars Neighborhood 1 80 55 80 120 60 90 60 80 55 70 Neighborhood 2 110 120 160 110 100 110 140 150 120 120 Neighborhood 1 40 60 40 60 80 100 120 140 160 180 80 100 120 140 160 180 Neighborhood 2 Home prices thousand dollars Find the mean and MAD for each of the neighborhoods Then decide whether the two groups are very different or 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 171

172

ZEARN MATH STUDENT EDITION G7M8 LESSON 12 Lesson 12 Larger Populations Let s compare larger groups Warm Up 1 Consider the question In general do the students at this school have more letters in their first name or last name How many more letters 1 What are some ways you might get some data to answer the question 2 The other day we compared the heights of people on different teams and the lengths of songs on different albums What makes this question about first and last names harder to answer than those questions Concept Exploration ACTIVITY 1 2 Continue to consider the question from the warm up In general do the students at this school have more letters in their first name or last name How many more letters 1 How many letters are in your first name In your last name 2 Do the number of letters in your own first and last names give you enough information to make conclusions about students names in your entire school 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

G7M8 LESSON 12 3 ZEARN MATH STUDENT EDITION Your teacher will provide you with data from the class Record the mean number of letters as well as the mean absolute deviation for each data set a The first names of the students in your class b The last names of the students in your class 4 Which mean is larger By how much What does this difference tell you about the situation 5 Do the mean numbers of letters in the first and last names for everyone in your class give you enough information to make conclusions about students names in your entire school Explain your reasoning ACTIVITY 2 3 174 Consider the question Do people who are the only child have more pets 1 Earlier we used information about the people in your class to answer a question about the entire school Would surveying only the people in your class give you enough information to answer this new question Explain your reasoning 2 If you had to have an answer to this question by the end of class today how would you gather data to answer the question 3 If you could come back tomorrow with your answer to this question how would you gather data to answer the 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

ZEARN MATH STUDENT EDITION 4 G7M8 LESSON 12 If someone else in the class came back tomorrow with an answer that was different than yours what would that mean How would you determine which answer was better ACTIVITY 3 43 For each question identify the population and a possible sample 1 What is the mean number of pages for novels that were on the best seller list in the 1990s 2 What fraction of new cars sold between August 2010 and October 2016 were built in the United States 3 What is the median income for teachers in North America 4 What is the average lifespan of Tasmanian devils 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary A population is a set of people or things that we want to study Here are some examples of populations A sample is a subset of a population Here are some examples of samples from the listed populations All people in the world The leaders of each country All seventh graders at a school The seventh graders who are in band All apples grown in the U S The apples in the school cafeteria When we want to know more about a population but it is not feasible to collect data from everyone in the population we often collect data from a sample In the lessons that follow we will learn more about how to pick a sample that can help answer questions about the entire population TERMINOLOGY Population Sample 176 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 12 Date GRADE 7 MISSION 8 LESSON 12 Exit Ticket Lin wants to know how many games teenagers in the United States have on their phones 1 What is the population for Lin s question 2 Explain why collecting data for this population would be difficult 3 Give an example of a sample Lin could use to help answer her 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 177

178

ZEARN MATH STUDENT EDITION G7M8 LESSON 13 Lesson 13 What Makes a Good Sample Let s see what makes a good sample Warm Up 1 Find the value of each quotient mentally 34 000 10 340 100 34 10 3 4 100 Concept Exploration ACTIVITY 1 2 1 Your teacher will assign you to work with either means or medians Then answer the questions A young artist has sold 10 paintings Calculate the measure of center you were assigned for each of these samples a The first two paintings she sold were for 50 and 350 b At a gallery show she sold three paintings for 250 400 and 1 200 c Her oil paintings have sold for 410 400 and 375 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 13 2 ZEARN MATH STUDENT EDITION Here are the selling prices for all 10 of her paintings 50 200 250 275 280 350 375 400 410 1 200 Calculate the measure of center you were assigned for all of the selling prices 3 Compare your answers with your partner Were the measures of center for any of the samples close to the same measure of center for the population ACTIVITY 2 3 1 180 The price per pound of catfish at a fish market was recorded for 100 weeks Use these dot plots showing the population and three different samples from that population to answer the questions Here are dot plots showing the population and three different samples from that population 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

ZEARN MATH STUDENT EDITION 2 G7M8 LESSON 13 If the goal is to have the sample represent the population which of the samples would work best Which wouldn t work so well Explain your reasoning Lesson Summary A sample that is representative of a population has a distribution that closely resembles the distribution of the population in shape center and spread For example consider the distribution of plant heights in cm for a population of plants shown in this dot plot The mean for this population is 4 9 cm and the MAD is 2 6 cm A representative sample of this population should have a larger peak on the left and a smaller one on the right like this one The mean for this sample is 4 9 cm and the MAD is 2 3 cm Here is the distribution for another sample from the same population This sample has a mean of 5 7 cm and a MAD of 1 5 cm These are both very different from the population and the distribution has a very different shape so it is not a representative sample TERMINOLOGY Representative 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

182

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 13 Date GRADE 7 MISSION 8 LESSON 13 Exit Ticket Andre is designing a website that will display reviews of school lunches Each item on the menu is rated from 0 to 5 stars The main display can only show 6 reviews so Andre needs to decide how to choose which reviews to show at the top This is a dot plot of all 40 reviews for the lasagna This is a plot of the stars shown on the first page of results 1 If each rating also has a sentence or two explaining the rating what are some good reasons to keep this sample displayed first What are some good reasons to change the sample that is displayed first 2 Is the sample representative of the population 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

184

ZEARN MATH STUDENT EDITION G7M8 LESSON 14 Lesson 14 Sampling in a Fair Way Let s explore ways to get representative samples Warm Up 1 A survey was taken at a movie theater to estimate the average age of moviegoers The dot plot below shows the ages of the first 20 people surveyed Use this dot plot to answer the questions 3 4 5 6 7 8 9 10 11 12 Age years 1 What questions do you have about the data from the survey 2 What assumptions would you make based on these results 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 14 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Take turns with your partner reading each option aloud For each situation discuss these questions Would the different methods for selecting a sample lead to different conclusions about the population What are the benefits of each method What might each method overlook Which of the methods listed would be the most likely to produce samples that are representative of the population being studied Can you think of a better way to select a sample for this situation Lin is running in an election to be president of the seventh grade She wants to predict her chances of winning She has the following ideas for surveying a sample of the students who will be voting a Ask everyone on her basketball team who they are voting for b Ask every third girl waiting in the lunch line who they are voting for c 2 Ask the first 15 students to arrive at school one morning who they are voting for A nutritionist wants to collect data on how much caffeine the average American drinks per day She has the following ideas for how she could obtain a sample a Ask the first 20 adults who arrive at a grocery store after 10 00 a m about the average amount of caffeine they consume each day b Every 30 minutes ask the first adult who comes into a coffee shop about the average amount of caffeine they consume each day 186 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 14 ACTIVITY 2 3 1 Your teacher will have some students draw straws from a bag Record the data then answer the questions As each straw is taken out and measured record its length in inches in the table Straw 1 Straw 2 Straw 3 Straw 4 Straw 5 Sample 1 Sample 2 2 Estimate the mean length of all the straws in the bag based on a the mean of the first sample b the mean of the second sample 3 Were your two estimates the same Did the mean length of all the straws in the bag change in between selecting the two samples Explain your reasoning 4 The actual mean length of all of the straws in the bag is about 2 37 inches How do your estimates compare to this mean length 5 If you repeated the same process again but you selected a larger sample such as 10 or 20 straws instead of just 5 would your estimate be more accurate 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 187

G7M8 LESSON 14 ZEARN MATH STUDENT EDITION ACTIVITY 3 43 188 There were a total of 35 straws in the bag Suppose we put the straws in order from shortest to longest and then assigned each straw a number from 1 to 35 For each of these methods decide whether it would be fair way to select a sample of 5 straws Explain your reasoning 1 Select the straws numbered 1 through 5 2 Write the numbers 1 through 35 on pieces of paper that are all the same size Put the papers into a bag Without looking select five papers from the bag Use the straws with those numbers for your sample 3 Using the same bag as the previous question select one paper from the bag Use the number on that paper to select the first straw for your sample Then use the next 4 numbers in order to complete your sample For example if you select number 17 then you also use straws 18 19 20 and 21 for your sample 4 Create a spinner with 35 sections that are all the same size and number them 1 through 35 Spin the spinner 5 times and use the straws with those numbers for your sample 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 14 Lesson Summary A sample is selected at random from a population if it has an equal chance of being selected as every other sample of the same size For example if there are 25 students in a class then we can write each of the students names on a slip of paper and select 5 papers from a bag to get a sample of 5 students selected at random from the class Other methods of selecting a sample from a population are likely to be biased This means that it is less likely that the sample will be representative of the population as a whole For example if we select the first 5 students who walk in the door that will not give us a random sample because students who typically come late are not likely to be selected A sample that is selected at random may not always be a representative sample but it is more likely to be representative than using other methods It is not always possible to select a sample at random For example if we want to know the average length of wild salmon it is not possible to identify each one individually select a few at random from the list and then capture and measure those exact fish When a sample cannot be selected at random it is important to try to reduce bias as much as possible when selecting the sample 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

190

ZEARN MATH STUDENT EDITION Name G7M8 LESSON 14 Date GRADE 7 MISSION 8 LESSON 14 Exit Ticket A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm She wants to test the plants at the farm but it will ruin the crop if she tests all of them 1 If the farm has 5 000 spinach plants describe a method that would produce a random sample of 10 plants 2 Why would a random sample be useful in this situation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

192

ZEARN MATH STUDENT EDITION G7M8 LESSON 15 Lesson 15 Estimating Population Measures of Center Let s use samples to estimate measures of center for the population Warm Up Would you use the median or mean to describe the center of each data set Explain your reasoning 1 Heights of 50 basketball players Ages of 30 people at a family dinner party 12 20 10 15 8 6 10 4 5 0 2 66 68 70 72 74 76 78 80 0 Height in Inches 5 10 15 20 25 30 35 40 45 50 55 Age in years Backpack weights of sixth grade students How many books students read over summer break 0 2 4 6 8 10 12 14 16 Number of books 0 2 4 6 8 10 12 14 16 Backpack weight in kilograms 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 15 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 194 Here are the ages in years of a random sample of 10 viewers for 3 different television shows The shows are titled Science Experiments YOU Can Do Learning to Read and Trivia the Game Show Sample 1 6 6 5 4 8 5 7 8 6 6 Sample 2 15 14 12 13 12 10 12 11 10 8 Sample 3 43 60 50 36 58 50 73 59 69 51 1 Calculate the mean for one of the samples Make sure each person in your group works with a different sample Record the answers for all three samples 2 Which show do you think each sample represents 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 G7M8 LESSON 15 ACTIVITY 2 3 Here are three more samples of viewer ages collected for the same 3 television shows Sample 4 57 71 5 54 52 13 59 65 10 71 Sample 5 15 5 4 5 4 3 25 2 8 3 Sample 6 6 11 9 56 1 3 11 10 11 2 1 Calculate the mean for one of these samples Record all three answers 2 Which show do you think each of these samples represents Explain your reasoning 3 For each show estimate the mean age for all the show s viewers 4 Calculate the mean absolute deviation for one of the shows samples Make sure each person in your group works with a different sample Record all three answers in the table Learning to Read Science Experiments YOU Can Do Trivia the Game Show Which sample number MAD 5 What do the different values for the MAD tell you about each group 6 An advertiser has a commercial that appeals to 15 to 16 year olds Based on these samples are any of these shows a good fit for this commercial 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 195

G7M8 LESSON 15 ZEARN MATH STUDENT EDITION ACTIVITY 3 43 A movie rating website has many people rate a new movie on a scale of 0 to 100 Here is a dot plot showing a random sample of 20 of these reviews 0 10 20 30 40 50 60 70 80 90 100 Movie rating 196 1 Would the mean or median be a better measure for the center of this data Explain your reasoning 2 Use the sample to estimate the measure of center that you chose for all the reviews 3 For this sample the mean absolute deviation is 19 6 and the interquartile range is 15 Which of these values is associated with the measure of center that you chose 4 Movies must have an average rating of 75 or more from all the reviews on the website to be considered for an award Do you think this movie will be considered for the award Use the measure of center and measure of variability that you chose to justify 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 15 Lesson Summary Some populations have greater variability than others For example we would expect greater variability in the weights of dogs at a dog park than at a beagle meetup Dog park Beagle meetup Mean weight 12 8 kg Mean weight 10 1 kg MAD 2 3 kg MAD 0 8 kg The lower MAD indicates there is less variability in the weights of the beagles We would expect that the mean weight from a sample that is randomly selected from a group of beagles will provide a more accurate estimate of the mean weight of all the beagles than a sample of the same size from the dogs at the dog park In general a sample of a similar size from a population with less variability is more likely to have a mean that is close to the population 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 197

198

ZEARN MATH STUDENT EDITION G7M8 LESSON 15 Name Date GRADE 7 MISSION 8 LESSON 15 Exit Ticket Each dot plot represents a sample of 100 data points Sample 1 15 20 25 30 35 40 45 50 55 60 55 60 65 70 75 Movie rating Sample 2 15 20 25 30 35 40 45 50 65 70 75 Movie rating 1 Estimate the population means using these samples 2 Based on the dot plots which estimate is more likely to be accurate 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 199

200

ZEARN MATH STUDENT EDITION G7M8 LESSON 16 Lesson 16 Estimating Population Proportions Let s estimate population proportions using samples Warm Up 1 1 A teacher asked all the students in one class how many minutes it takes them to get to school Here is a table of their responses 20 10 15 8 5 15 10 5 20 5 15 10 3 10 18 5 25 5 5 12 10 30 5 10 What fraction of the students in this class say a It takes them 5 minutes to get to school b It takes them more than 10 minutes to get to school 2 If the whole school has 720 students can you use this data to estimate how many of them would say that it takes them more than 10 minutes to get to school Be prepared to 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 201

G7M8 LESSON 16 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 The track coach at a high school needs a student whose reaction time is less than 0 4 seconds to help out at track meets All the twelfth graders in the school measured their reaction times You will receive a bag of papers that list their results 1 Work with your partner to select a random sample of 20 reaction times and record them in the table 2 What proportion of your sample is less than 0 4 seconds 3 Estimate the proportion of all twelfth graders at this school who have a reaction time of less than 0 4 seconds Explain your reasoning 4 There are 120 twelfth graders at this school Estimate how many of them have a reaction time of less than 0 4 seconds 5 Suppose another group in your class comes up with a different estimate than yours for the previous question a What is another estimate that would be reasonable b What is an estimate you would consider unreasonable 202 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 16 ACTIVITY 2 3 Here are the results of a survey of 20 people who read The Adventures of Super Sam regarding what special ability they think the new hero should have Response What new ability Response What new ability 1 Fly 11 Freeze 2 Freeze 12 Freeze 3 Freeze 13 Fly 4 Fly 14 Invisibility 5 Fly 15 Freeze 6 Freeze 16 Fly 7 Fly 17 Freeze 8 Super strength 18 Fly 9 Freeze 19 Super strength 10 Fly 20 Freeze 1 What proportion of this sample want the new hero to have the ability to fly 2 If there are 2 024 dedicated readers of The Adventures of Super Sam estimate the number of readers who want the new hero to fly 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 16 43 ZEARN MATH STUDENT EDITION Two other comic books did a similar survey of their readers The results are below In a survey of people who read Beyond Human 42 out of 60 people want a new hero to be able to fly In a survey of people who read Mysterious Planets 14 out of 40 people want a new hero to be able to fly 1 Do you think the proportion of all readers who want a new hero that can fly are nearly the same for the three different comic books Explain your reasoning Flame 002 by Will Eisner pencils and Lou Fine inks uploaded by Roygbiv666 Public Domain Super Heroes via Wikimedia Commons Public Domain 2 204 If you were in charge of these three comics would you give the ability to fly to any of the new heroes Explain your reasoning using the proportions you calculated 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 16 Lesson Summary Sometimes a data set consists of information that fits into specific categories For example we could survey students about whether they have a pet cat or dog The categories for these data would be neither dog only cat only both Suppose we surveyed 10 students Here is a table showing possible results Option Number of Responses Neither dog nor cat 2 Dog only 4 Cat only 1 Both dog and cat 3 In this sample 3 of the students said they have both a dog and a cat We can say that the proportion 3 or 0 3 If this sample is representative of all 720 of these students who have both a dog and a cat is 10 3 of 720 or about 216 students at the school have students at the school we can predict that about 10 both a dog and a cat In general a proportion is a number from 0 to 1 that represents the fraction of the data that belongs to a given category TERMINOLOGY Proportion 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

206

ZEARN MATH STUDENT EDITION G7M8 LESSON 16 Name Date GRADE 7 MISSION 8 LESSON 16 Exit Ticket 1 A chemical engineer is trying to increase the amount of the useful product in a reaction She performs the reaction with her new equipment 10 times and gets the following amounts of the useful product Amount of Useful Product in Grams 47 1 48 2 48 3 47 5 48 5 48 1 47 2 48 2 48 4 48 3 What proportion of the reactions were above the 48 grams threshold 2 Other chemists typically get 65 of their reactions to produce more than 48 grams Should the engineer say that she was able to increase the useful product when compared to the other chemists 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

208

ZEARN MATH STUDENT EDITION G7M8 LESSON 17 Lesson 17 More about Sampling Variability Let s compare samples from the same population Warm Up 1 The other day you worked with the reaction times of twelfth graders to see if they were fast enough to help out at the track meet Look back at the sample you collected 1 Calculate the mean reaction time for your sample 2 Did you and your partner get the same sample mean Explain why or why not Concept Exploration ACTIVITY 1 2 Your teacher will display a blank dot plot Use the dot plot to solve the problems below 1 Plot your sample mean from the previous activity on your teacher s dot plot 2 What do you notice about the distribution of the sample means from the class a Where is the center b Is there a lot of variability c 3 Is it approximately symmetric The population mean is 0 442 seconds How does this value compare to the sample means from 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 209

G7M8 LESSON 17 The dot plot below shows the reaction times of the population Use this dot plot to solve the problems below 3 0 ZEARN MATH STUDENT EDITION 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 1 05 1 1 1 15 1 2 1 25 Reaction time seconds 1 What do you notice about the distribution of the population a Where is the center b Is there a lot of variability c Is it approximately symmetric 2 Compare the two displayed dot plots 3 Based on the distribution of sample means from the class do you think the mean of a random sample of 20 items is likely to be a within 0 01 seconds of the actual population mean b within 0 1 seconds of the actual population mean Explain or show your reasoning 210 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 17 ACTIVITY 2 43 The other day you worked with 2 different samples of viewers from each of 3 different television shows Each sample included 10 viewers Here are the mean ages for 100 different samples of viewers from each show 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 Sample means for Trivia the Game Show 9 9 5 10 10 5 11 11 5 12 12 5 13 13 5 14 6 8 7 Sample means for Science Experiments YOU Can Do 5 5 2 5 4 5 6 5 8 6 6 2 6 4 6 6 Sample means for Learning to Read 1 For each show use the dot plot to estimate the population mean a Trivia the Game Show b Science Experiments YOU Can Do c Learning to Read 2 For each show are most of the sample means within 1 year of your estimated population mean 3 Suppose you take a new random sample of 10 viewers for each of the 3 shows Which show do you expect to have the new sample mean closest to the population mean 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 211

G7M8 LESSON 17 ZEARN MATH STUDENT EDITION Lesson Summary This dot plot shows the weights in grams of 18 cookies The triangle indicates the mean weight which is 11 6 grams 8 9 10 11 12 13 14 15 16 Cookie weights grams This dot plot shows the means of 20 samples of 5 cookies selected at random Again the triangle shows the mean for the population of cookies Notice that most of the sample means are fairly close to the mean of the entire population 8 9 10 11 12 13 14 15 16 Means of samples of size 5 This dot plot shows the means of 20 samples of 10 cookies selected at random Notice that the means for these samples are even closer to the mean for the entire population 8 9 10 11 12 13 14 15 16 Means of samples of size 10 In general as the sample size gets bigger the mean of a sample is more likely to be closer to the mean of the population 212 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 17 Name Date GRADE 7 MISSION 8 LESSON 17 Exit Ticket Jada collects data about the number of letters people get in the mail each week The population distribution is shown in the dot plot 14 16 18 20 22 24 26 28 30 32 34 36 Which of the following dot plots are likely to represent the means from samples of size 10 from this population Explain your reasoning Dot Plot 1 14 16 18 20 22 24 26 28 30 32 34 36 14 16 18 20 22 24 26 28 30 32 34 36 Dot Plot 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 213

214

ZEARN MATH STUDENT EDITION G7M8 LESSON 18 Lesson 18 Comparing Populations Using Samples Let s compare different populations using samples Warm Up 1 Without calculating tell whether each pair of data sets have the same mean and whether they have the same mean absolute deviation Set A 1 3 3 5 6 8 10 14 Set B 21 23 23 25 26 28 30 34 Set X 1 2 3 4 5 Set Y 1 2 3 4 5 Set P 47 53 58 62 Set Q 37 43 68 72 6 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 18 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Consider the question Do tenth grade students backpacks generally weigh more than seventh grade students backpacks Here are dot plots showing the weights of backpacks for a random sample of students from these two grades Grade 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Grade 10 Backpack weight pounds 216 1 Did any seventh grade backpacks in this sample weigh more than a tenth grade backpack 2 The mean weight of this sample of seventh grade backpacks is 6 3 pounds Do you think the mean weight of backpacks for all seventh grade students is exactly 6 3 pounds 3 The mean weight of this sample of tenth grade backpacks is 14 8 pounds Do you think there is a meaningful difference between the weight of all seventh grade and tenth grade students backpacks 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 18 ACTIVITY 2 3 Here are 10 more random samples of seventh grade students backpack weights Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Sample number Mean weight pounds 1 5 8 2 9 2 3 5 5 4 7 3 5 7 2 6 6 6 7 5 2 8 5 2 9 6 3 10 6 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 18 ZEARN MATH STUDENT EDITION 1 a Which sample has the highest mean weight b Which sample has the lowest mean weight c What is the difference between these two sample means 2 All of the samples have a mean absolute deviation of about 2 8 pounds Express the difference between these two sample means as a multiple of the MAD 3 Are these samples very different Explain or show your reasoning Remember our sample of tenth grade students backpacks had a mean weight of 14 8 pounds The MAD for this sample is 2 7 pounds Your teacher will assign you one of the samples of seventh grade students backpacks to use 4 a What is the difference between the sample means for the tenth grade students backpacks and the seventh grade students backpacks b Express the difference between these two sample means as a multiple of the larger of the MADs 5 218 Do you think there is a meaningful difference between the weights of all seventh grade and tenthgrade students backpacks 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 18 ACTIVITY 3 43 When anthropologists find steel artifacts they can test the amount of carbon in the steel to learn about the people that made the artifacts Here are some box plots showing the percentage of carbon in samples of steel that were found in two different regions Region 1 Region 2 0 32 0 36 0 40 0 44 0 48 0 52 0 56 0 60 0 64 0 68 0 72 0 76 Percentage of carbon in steel 1 Was there any steel found in region 1 that had a more carbon than some of the steel found in region 2 b less carbon than some of the steel found in region 2 2 Do you think there is a meaningful difference between all the steel artifacts found in regions 1 and 2 3 Which sample has a distribution that is not approximately symmetric Sample median IQR Region 1 0 64 0 05 Region 2 0 47 0 03 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 219

G7M8 LESSON 18 220 ZEARN MATH STUDENT EDITION 4 What is the difference between the sample medians for these two regions 5 Express the difference between these two sample medians as a multiple of the larger interquartile range 6 The anthropologists who conducted the study concluded that there was a meaningful difference between the steel from these regions Do you agree 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 18 Lesson Summary Sometimes we want to compare two different populations For example is there a meaningful difference between the weights of pugs and beagles Here are histograms showing the weights for a sample of dogs from each of these breeds 8 7 6 5 4 3 2 1 0 6 6 5 7 7 5 8 8 5 9 9 5 Pug weights kg 10 10 5 11 Beagle weights kg The black triangles show the mean weight of each sample 6 9 kg for the pugs and 10 1 kg for the beagles The black lines show the weights that are within 1 MAD of the mean We can think of these as typical weights for the breed These typical weights do not overlap In fact the distance between the means is 10 1 6 9 or 3 2 kg over 6 times the larger MAD So we can say there is a meaningful difference between the weights of pugs and beagles Is there a meaningful difference between the weights of male pugs and female pugs Here are box plots showing the weights for a sample of male and female pugs Male pug weights kg Female pug weights kg 4 4 5 5 5 5 6 6 5 7 7 5 8 8 5 We can see that the medians are different but the weights between the first and third quartiles overlap Based on these samples we would say there is not a meaningful difference between the weights of male pugs and female pugs In general if the measures of center for two samples are at least two measures of variability apart we say the difference in the measures of center is meaningful Visually this means the range of typical values does not overlap If they are closer then we don t consider the difference to be meaningful 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

222

ZEARN MATH STUDENT EDITION G7M8 LESSON 18 Name Date GRADE 7 MISSION 8 LESSON 18 Exit Ticket Noah is interested in comparing the number of movies watched by students and teachers over the winter break He takes a random sample of 10 students and 10 teachers and makes a dot plot of their responses Students 0 1 2 3 4 5 6 7 8 6 7 8 Movies watched over break Teachers 0 1 2 3 4 5 Movies watched over break Noah then computes the measures of center and variability for each group Students Mean 5 7 movies MAD 0 76 movies Teachers Mean 2 7 movies MAD 0 9 movies 1 Is Noah s choice of mean and MAD appropriate for the data he has Explain your reasoning 2 Should Noah conclude that there is a meaningful difference in the mean number of movies watched over winter break between the two groups 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 223

224

ZEARN MATH STUDENT EDITION G7M8 LESSON 19 Lesson 19 Comparing Populations with Friends Let s ask important questions to compare groups Warm Up 1 Dot plots histograms and box plots are different ways to represent a data set graphically Which of those displays would be the easiest to use to find each feature of the data 1 the mean 2 the median 3 the mean absolute deviation 4 the interquartile range 5 the symmetry Concept Exploration ACTIVITY 1 2 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 If your teacher gives you the data card 1 1 Silently read the information on your card 2 Ask your partner What specific information do you need Wait for your partner to ask for information Only give information that is on your card Do not figure out anything for your partner 3 Before telling your partner the information ask Why do you need that information 4 After your partner solves the problem ask them to explain their reasoning and listen to their explanation Silently read your card and think about what information you need to answer the question 2 Ask your partner for the specific information that you need 3 Explain to your partner how you are using the information to solve the problem 4 Solve the problem and explain your reasoning to your partner Pause here so your teacher can review your work Ask your teacher for a new set of cards and repeat the activity trading roles with 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 225

G7M8 LESSON 19 ZEARN MATH STUDENT EDITION Lesson Summary When using samples to compare two populations there are a lot of factors to consider Are the samples representative of their populations If the sample is biased then it may not have the same center and variability as the population Which characteristic of the populations makes sense to compare the mean the median or a proportion How variable is the data If the data is very spread out it can be more difficult to make conclusions with certainty Knowing the correct questions to ask when trying to compare groups is important to correctly interpret the results 226 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M8 LESSON 19 Name Date GRADE 7 MISSION 8 LESSON 19 Exit Ticket Use the box plot to answer the questions 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 1 What measure of center is shown in the box plot What measure of variability What are the values for each of these characteristics 2 Draw another box plot with the same measure of variability that is meaningfully different from the one shown 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

228

ZEARN MATH STUDENT EDITION G7M8 LESSON 20 Lesson 20 Memory Test Let s put it all together Warm Up 1 Your teacher will give you a paper that lists a data set with 100 numbers in it Explain whether each method of obtaining a sample of size 20 would produce a random sample Option 1 A spinner has 10 equal sections on it Spin once to get the row number and again to get the column number for each member of your sample Repeat this 20 times Option 2 Since the data looks random already use the first two rows Option 3 Cut up the data and put them into a bag Shake the bag to mix up the papers and take out 20 values Option 4 Close your eyes and point to one of the numbers to use as your first value in your sample Then keep moving one square from where your finger is to get a path of 20 values for your sample 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M8 LESSON 20 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Continue working with the data set your teacher gave you for the Warm Up The data marked with a star all came from students at Springfield Middle School 1 When you select the first value for your random sample what is the probability that it will be a value that came from a student at Springfield Middle School 2 What proportion of your entire sample would you expect to be from Springfield Middle School 3 If you take a random sample of size 10 how many scores would you expect to be from Springfield Middle School 4 Select a random sample of size 10 5 Did your random sample have the expected number of scores from Springfield Middle School ACTIVITY 2 3 230 Work with your partner to solve problem 1 Then solve problems 2 and 3 on your own 1 Decide which measure of center makes the most sense to use based on the distribution of your sample Discuss your thinking with your partner If you disagree work to reach an agreement 2 Estimate this measure of center for your population based on your sample 3 Calculate the measure of variability for your sample that goes with the measure of center that 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

ZEARN MATH STUDENT EDITION G7M8 LESSON 20 ACTIVITY 3 43 Using only the values you computed in Activities 1 and 2 compare your sample to your partner s Is it reasonable to conclude that the measures of center for each of your populations are meaningfully different 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 231

232

Grade 7 Mission 9 Putting it All Together

234

ZEARN MATH STUDENT EDITION G7M9 LESSON 1 Lesson 1 Planning Recipes Let s choose some recipes for a restaurant Warm Up 1 Imagine you could open a restaurant 1 Select a recipe for a main dish you would like to serve at your restaurant 2 Record the amount of each ingredient from your recipe in the first two columns of the table You may not need to use every row Image by Pexels via Pixaby Public Domain Ingredient 3 Amount Amount per serving Calories per serving How many servings does this recipe make Determine the amount of each ingredient in one serving and record it in the third column of 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 235

G7M9 LESSON 1 4 ZEARN MATH STUDENT EDITION Restaurants are asked to label how many calories are in each meal on their menu a Use the information to calculate the amount of calories from each ingredient in your meal and record it in the last column of the table b Next find the total calories in one serving of your meal 5 236 If a person wants to eat 2 000 calories per day what percentage of their daily calorie intake would one serving of your meal be Grains Mass g Calories Fat g Sodium g Biscuits refrigerated dough 1 58 178 6 14 567 Bread crumbs 1 oz 28 35 112 1 5 208 Cornmeal 1 c 157 581 2 75 11 Egg noodles 1 c 38 146 1 69 8 Hamburger or hot dog buns 1 44 123 1 72 217 Oats 1 c 81 307 5 28 5 Pasta 1 c 91 338 1 37 5 Pie crust refrigerated 1 229 1019 58 3 937 Pita bread 1 oz 28 35 8 0 34 152 Quinoa 1 c 170 626 10 32 8 Ramen noodles 1 pkg 81 356 14 25 1503 Rice flour 1 c 158 578 2 24 0 Rice brown 1 c 185 679 5 92 9 Rice white 1 c 185 675 1 22 9 Saltine crackers 5 14 9 62 1 29 140 Taco shells 1 12 9 61 2 81 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 G7M9 LESSON 1 Grains Mass g Calories Fat g Sodium g Tortillas 1 49 146 3 71 364 Wheat bread 1 slice 29 79 1 31 137 Wheat flour 1 c 125 455 1 22 2 White bread 1 slice 29 77 0 97 142 Vegetables Mass g Calories Fat g Sodium g Asparagus 1 c 134 27 0 16 3 Avocados 1 c 150 240 22 10 Bell peppers 1 c 149 46 0 45 6 Broccoli 1 c 91 31 0 34 30 Carrots 1 c 128 52 0 31 88 Cauliflower 1 c 107 27 0 3 32 Celery 1 c 101 16 0 17 81 Chives 1 tbsp 3 1 0 02 0 Corn 1 c 145 125 1 96 22 Cucumber 1 c 133 16 0 21 3 Green beans 1 c 100 31 0 22 6 Lettuce 1 c 47 8 0 14 7 Mushrooms 1 c 70 15 0 24 4 Onions 1 c 160 64 0 16 6 Peas frozen 1 c 134 103 0 54 145 Potatoes 12 c 75 59 0 11 14 Spinach 1 c 30 7 0 12 24 Squash 1 c 113 18 0 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 237

G7M9 LESSON 1 238 ZEARN MATH STUDENT EDITION Vegetables Mass g Calories Fat g Sodium g Sweet potatoes 1 c 133 114 0 07 73 Tomatoes 1 c 149 27 0 3 7 Fruit Mass g Calories Fat g Sodium g Apple juice 1 c 248 114 0 32 10 Apples 1 c 110 53 0 14 0 Bananas 1 c 225 200 0 74 2 Blueberries 1 c 148 84 0 49 1 Cantaloupe 1 c 177 60 0 34 28 Cherries 1 c 138 87 0 28 0 Cranberries dried 14 c 40 123 0 44 2 Grapes 1 c 151 104 0 24 3 Lemon juice 1 c 244 54 0 59 2 Mandarin oranges 1 c 252 154 0 25 15 Mangoes 1 c 165 99 0 63 2 Orange juice 1 c 249 122 0 3 5 Oranges 1 c 180 85 0 22 0 Peaches 1 c 154 60 0 38 0 Pears 1 c 140 80 0 2 1 Pineapple canned 1 c 181 109 0 2 2 Pomegranate juice 1 c 1249 134 0 72 22 Raisins 1 c 165 493 0 76 18 Raspberries 1 c 123 64 0 8 1 Strawberries 1 c 152 49 0 46 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 G7M9 LESSON 1 Meat Mass g Calories Fat g Sodium g Bacon 1 slice 26 106 10 21 122 Chicken thigh 1 193 427 32 06 156 Chicken light meat 3 oz 85 100 1 45 60 Cob 3 oz 85 61 0 17 93 Crab 3 oz 85 73 0 82 251 Ground beef 4 oz 113 375 33 9 75 Ground turkey 4 oz 113 172 9 44 80 Halibut 3 oz 85 77 1 13 58 Ham 1 oz 28 35 38 1 53 319 Hot dogs 1 51 141 12 33 498 Lobster 1 150 116 1 12 634 Pepperoni 3 oz 85 428 39 34 1345 Pork sausage 1 25 72 6 2 185 Pork tenderloin 3 oz 85 102 3 44 Salmon 1 fillet 108 373 12 34 55 Shrimp 3 oz 85 72 0 43 101 Tofu 12 c 126 98 5 25 15 Trout 1 fillet 79 111 4 88 40 Tuna canned 1 oz 28 35 24 0 27 70 Turkey 3 oz 85 92 2 12 105 Nuts Beans and Seeds Mass g Calories Fat g Sodium g Almonds 1 c 143 828 71 4 1 Black beans 1 c 240 218 0 7 331 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 1 240 ZEARN MATH STUDENT EDITION Nuts Beans and Seeds Mass g Calories Fat g Sodium g Cashews 1 oz 28 35 157 12 43 3 Chickpeas 1 c 240 211 4 68 667 Coconut 1 c 80 283 26 8 16 Fava beans 1 c 256 182 0 56 1160 Flaxseed 1 tbsp 10 3 55 4 34 3 White beans 1 c 262 299 1 02 969 Kidney beans 1 c 256 215 1 54 758 Lentils 1 c 192 676 2 04 12 Lima beans 1 c 164 216 0 72 85 Macadamia nuts 1 c 134 962 101 53 7 Peanut butter 2 tbsp 32 191 16 22 136 Peanuts 1 oz 28 35 166 14 08 116 Pecans 1 c 109 753 78 45 0 Pinto beans 1 c 240 197 1 34 643 Pistachios 1 c 123 689 55 74 1 Pumpkin seeds 1 c 129 721 63 27 9 Sesame seeds 1 c 144 825 71 52 16 Sunflower seeds 1 c 46 269 23 67 4 Dairy Mass g Calories Fat g Sodium g Almond milk 1 c 262 39 2 88 186 Blue cheese 1 oz 28 35 100 8 15 325 Butter 1 pat 5 36 4 06 1 Cheddar cheese 1 c 132 533 43 97 862 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 1 Dairy Mass g Calories Fat g Sodium g Coconut milk 1 c 226 445 48 21 29 Cream cheese 1 tbsp 14 5 51 4 99 46 Egg white 1 33 17 0 06 55 Egg yolk 1 17 55 4 51 8 Eggs 1 50 72 4 76 71 Evaporated milk 1 c 252 270 5 04 252 Whipping cream 1 c 120 408 43 3 32 Margarine 1 tbsp 14 2 101 11 38 4 Milk skim 1 c 245 83 0 2 103 Milk whole 1 c 244 149 7 93 105 Mozzarella cheese 1 c 132 389 26 11 879 Parmesan cheese 1 c 100 420 27 84 1804 Sour cream 1 tbsp 12 16 1 27 10 Soy milk 1 c 243 80 3 91 90 Swiss cheese 1 c 132 519 40 91 247 Yogurt 6 oz 170 107 2 64 119 Sauces and Other Liquids Mass g Calories Fat g Sodium g Barbecue sauce 1 tbsp 17 29 0 11 175 Chicken broth 1 c 249 15 0 52 924 Cream of chicken soup 12 c 126 113 7 27 885 Gravy 1 c 233 1 5 5 1305 Honey 1 c 339 25 0 14 Italian dressing 1 tbsp 14 7 35 3 1 146 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 1 242 ZEARN MATH STUDENT EDITION Sauces and Other Liquids Mass g Calories Fat g Sodium g Jams and jellies 1 tbsp 20 56 0 01 6 Ketchup 1 tbsp 17 17 0 02 154 Mayonnaise 1 tbsp 15 103 11 67 73 Mustard 1 tsp 5 3 0 17 55 Pasta sauce 12 c 132 66 2 13 577 Ranch dressing 1 tbsp 15 64 6 68 135 Salsa 2 tbsp 36 10 0 06 256 Soy sauce 1 tbsp 16 8 0 09 879 Vanilla extract 1 tsp 4 2 12 0 0 Vegetable broth 1 c 221 11 0 15 654 Vegetable oil 1 tbsp 14 124 14 0 Vinegar 1 tbsp 15 3 0 0 Water 1 fl oz 29 6 0 0 1 Worcestershire sauce 1 tbsp 17 13 0 167 Spices and Other Powders Mass g Calories Fat g Sodium g Baking powder 1 tsp 4 6 2 0 488 Baking soda 1 tsp 4 6 0 0 1259 Black pepper 1 tsp 2 3 6 0 07 0 Chicken bouillon 1 cube 4 8 10 0 23 1152 Chili powder 1 tsp 2 7 8 0 39 77 Cinnamon 1 tsp 2 6 6 0 03 0 Cocoa powder 1 c 86 196 11 78 18 Cornstarch 1 c 128 488 0 06 12 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 1 Spices and Other Powders Mass g Calories Fat g Sodium g Cumin 1 tsp 2 1 8 0 47 4 Garlic 1 clove 3 4 0 01 0 5 Garlic powder 1 tsp 3 1 10 0 02 2 Onion powder 1 tsp 2 4 8 0 02 2 Onion soup mix 1 tbsp 7 5 22 0 03 602 Oregano 1 tsp 1 3 0 04 0 Paprika 1 tsp 2 3 6 0 3 2 Parsley 1 tsp 0 5 1 0 03 2 Powdered sugar 1 c 120 467 0 2 Salt 1 tsp 6 0 0 2325 Sugar 1 tsp 2 8 11 0 0 Taco seasoning 2 tsp 5 7 18 0 411 ENRICHMENT The labels on packaged foods tell how much of different nutrients they contain Here is what some different food labels say about their sodium content cheese crackers 351 mg 14 daily value apple chips 15 mg

G7M9 LESSON 1 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 Calculate the calories fat and sodium content of one serving of a recipe For a meal to be considered 1 low calorie it must have 120 calories or less per 100 grams of food low fat it must have 3 grams of fat or less per 100 grams of food low sodium it must have 140 milligrams of sodium or less per 100 grams of food Does the meal you chose in the previous activity meet the requirements to be considered a low calorie b low fat c low sodium Be prepared to explain your reasoning 244 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 2 G7M9 LESSON 1 Select or invent another recipe you would like to serve at your restaurant that does meet the requirements to be considered either low calorie low fat or low sodium Show that your recipe meets that requirement Organize your thinking so it can be followed by others Ingredient Amount per serving Calories per serving Fat per serving Sodium per serving Grams 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

246

ZEARN MATH STUDENT EDITION G7M9 LESSON 2 Lesson 2 Costs of Running a Restaurant Let s explore how much the food will cost Warm Up 1 1 Your teacher will give you access to a spreadsheet program Use it to solve the problems below Type each formula into the cells of a spreadsheet program and press enter Record what the cell displays Make sure to type each formula exactly as it is written here 1 A B C D 40 32 1 5 3 6 14 7 0 5 6 2 a Predict what will happen if you type the formula A1 C1 into cell C2 of your spreadsheet b Type in the formula and press enter to check your prediction 3 a Predict what will happen next if you delete the formula in cell A1 and replace it with the number 100 b Replace the formula with the number and press enter to check your prediction 4 a Predict what will happen if you copy cell C2 and paste it into cell D2 of your spreadsheet b Copy and paste the formula to check your prediction 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 2 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 Set up a spreadsheet with these column labels in the first row Then solve the problems below 1 A B C D ingredient unit in recipe amount in recipe amount per serving 2 a Type the information about the ingredients in your recipe into the first 3 columns of the spreadsheet b Type a formula into cell D2 to automatically calculate the amount per serving for your first ingredient c 3 Copy cell D2 and paste it into the cells beneath it to calculate the amount per serving for the rest of your ingredients Pause here so your teacher can review your work Add these column labels to your spreadsheet Then solve the problems below E F G H purchase price purchase amount purchase unit cost per purchase unit a Research the cost of each ingredient in your meal and record the information in columns E F and G b Type a formula into cell H2 to automatically calculate the cost per purchase unit for your first ingredient c 248 Copy cell H2 and paste it into the cells beneath it to calculate the cost per purchase unit for the rest of your 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

ZEARN MATH STUDENT EDITION 43 G7M9 LESSON 2 Add these column labels to your spreadsheet Then solve the problems below I J K conversion from purchase units to recipe units cost per recipe unit cost per serving a Complete column I with how many of your recipe unit are in 1 of your purchase unit for each ingredient For example if your recipe unit was cups and your purchase unit was gallons then your conversion would be 16 because there are 16 cups in 1 gallon b Type a formula into cell J2 to calculate the cost per recipe unit for your first ingredient c Type a formula into cell K2 to calculate the cost per serving for your first ingredient d Compare formulas with your partner Discuss your thinking If you disagree work to reach an agreement e Copy cells J2 and K2 and paste them into the cells beneath them to calculate the cost per recipe unit and cost per serving for the rest of your ingredients Type a formula into the first empty cell below your last ingredient in column K to calculate the total cost per serving for all of the ingredients in your recipe Record the answer here 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 249

250

ZEARN MATH STUDENT EDITION G7M9 LESSON 3 Lesson 3 More Costs of Running a Restaurant Let s explore how much it costs to run a restaurant Warm Up 1 1 Solve the problems below Restaurants have many more expenses than just the cost of the food a Make a list of other items you would have to spend money on if you were running a restaurant b Identify which expenses on your list depend on the number of meals ordered and which are independent of the number of meals ordered c Identify which of the expenses that are independent of the number of meals ordered only have to be paid once and which are ongoing d Estimate the monthly cost for each of the ongoing expenses on your list Next calculate the total of these monthly expenses 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 3 2 ZEARN MATH STUDENT EDITION Tell whether each restaurant is making a profit or losing money if they have to pay the amount you predicted in ongoing expenses per month Organize your thinking so it can be followed by others a Restaurant A sells 6 000 meals in one month at an average price of 17 per meal and an average cost of 4 60 per meal b Restaurant B sells 8 500 meals in one month at an average price of 8 per meal and an average cost of 2 20 per meal c Restaurant C sells 4 800 meals in one month at an average price of 29 per meal and an average cost of 6 90 per meal 3 a Predict how many meals your restaurant would sell in one month b How much money would you need to charge for each meal to be able to cover all the ongoing costs of running a restaurant 4 252 What percentage of the cost of the ingredients is the markup on your meal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 3 Content Exploration ACTIVITY 1 2 A sample of full service restaurants and a sample of fast food restaurants were surveyed about the average number of customers they serve per day 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Full Service Restaurants 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Fast Food Restaurants 1 How does the average number of customers served per day at a full service restaurant generally compare to the number served at a fast food restaurant Explain your reasoning 2 About how many customers do you think your restaurant will serve per day 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 253

G7M9 LESSON 3 3 ZEARN MATH STUDENT EDITION Here are prices for plates and forks Plates Forks Disposable 165 paper plates for 12 50 3600 plastic forks for 10 Reusable 12 ceramic plates for 28 80 24 metal forks for 30 a Using your predicted number of customers per day from the previous question write an equation for the total cost d of using disposable plates and forks for every customer for n days b Is d proportional to n Explain your reasoning c Use your equation to predict the cost of using disposable plates and forks for 1 year Explain any assumptions you make with this calculation 4 a How much would it cost to buy enough reusable plates and forks for your predicted number of customers per day b If it costs 10 75 a day to wash the reusable plates and forks write an expression that represents the total cost r of buying and washing reusable plates and forks after n days c Is r proportional to n Explain your reasoning d How many days can you use the reusable plates and forks for the same cost that you calculated for using disposable plates and forks for 1 year 254 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 4 Lesson 4 Restaurant Floor Plan Let s design the floor plan for a restaurant Warm Up 1 1 Solve the problems below Restaurant owners say it is good for each customer to have about 300 in2 of space at their table How many customers would you seat at each table A B C 1 ft 2 It is good to have about 15 ft2 of floor space per customer in the dining area a How many customers would you like to be able to seat at one time b What size and shape dining area would be large enough to fit that many customers c 3 Select an appropriate scale and create a scale drawing of the outline of your dining area Using the same scale what size would each of the tables from the first question appear on your scale drawing 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 255

G7M9 LESSON 4 ZEARN MATH STUDENT EDITION 4 To ensure fast service it is good for all of the tables to be within 60 ft of the place where the servers bring the food out of the kitchen Decide where the food pickup area will be and draw it on your scale drawing Next show the limit of how far away tables can be positioned from this place 5 It is good to have at least 1 12 ft between each table and at least 3 12 ft between the sides of tables where the customers will be sitting On your scale drawing show one way you could arrange tables in your dining area ENRICHMENT The dining area usually takes up about 60 of the overall space of a restaurant because there also needs to be room for the kitchen storage areas office and bathrooms Given the size of your dining area how much more space would you need for these other areas Content Exploration ACTIVITY 1 2 Some restaurants have very large refrigerators or freezers that are like small rooms The energy to keep these rooms cold can be expensive A standard walk in refrigerator rectangular 10 feet wide 10 feet long and 7 feet tall will cost about 150 per month to keep cold A standard walk in freezer rectangular 8 feet wide 10 feet long and 7 feet tall will cost about 372 per month to keep cold Here is a scale drawing of a walk in refrigerator and freezer About how much would it cost to keep them both cold Show your reasoning 14 ft 9 ft Refrigerator 9 ft Freezer 7 5 ft 7 5 ft 4 ft 256 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 5 Lesson 5 How Crowded Is This Neighborhood Let s see how proportional relationships apply to where people live Warm Up 1 1 The figure shows four squares Each square encloses an array of dots Squares A and B have side lengths of 2 inches Squares C and D have side lengths of 1 inch Complete the table with information about each square Square Area of the square in square inches Number of dots Number of dots per square inch A B C D 2 Compare each square to the others What is the same and what is 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 257

G7M9 LESSON 5 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 258 The figure shows two arrays each enclosed by a square that is 2 inches wide 1 Let a be the area of the square and d be the number of dots enclosed by the square For each square plot a point that represents its values of a and d 2 Draw lines from 0 0 to each point For each line write an equation that represents the proportional relationship 3 What is the constant of proportionality for each relationship What do the constants of proportionality tell us about the dots and squares 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 5 ACTIVITY 2 3 Here are pictures of two different neighborhoods This image depicts an area that is 0 3 kilometers long and 0 2 kilometers wide Maps of neighborhoods by United States Census Bureau via American Fact Finder Public Domain This image depicts an area that is 0 4 kilometers long and 0 2 kilometers wide Maps of neighborhoods by United States Census Bureau via American Fact Finder Public Domain For each neighborhood find the number of houses per square kilometer 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 5 ZEARN MATH STUDENT EDITION ACTIVITY 3 43 260 New York City has a population of 8 406 thousand people and covers an area of 1 214 square kilometers Los Angeles has a population of 3 884 thousand people and covers an area of 1 302 square kilometers 1 The points labeled A and B each correspond to one of the two cities Which is which Label them on the graph 2 Write an equation for the line that passes through 0 0 and A What is the constant of proportionality 3 Write an equation for the line that passes through 0 0 and B What is the constant of proportionality 4 What do the constants of proportionality tell you about the crowdedness of these two cities 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 5 ENRICHMENT 1 Predict where these types of regions would be shown on the graph a a suburban region where houses are far apart with big yards b a neighborhood in an urban area with many high rise apartment buildings c 2 a rural state with lots of open land and not many people Next use this data to check your predictions Place Description Population Area km2 Chalco A suburb of Omaha Nebraska 10 994 7 5 Anoka County A county in Minnesota near Minneapolis St Paul 339 534 1 155 Guttenberg A city in New Jersey 11 176 0 49 New York A state 19 746 227 141 300 Rhode Island A state 1 055 173 3 140 Alaska A state 736 732 1 717 856 Tok A community in Alaska 1 258 342 7 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 261

262

ZEARN MATH STUDENT EDITION G7M9 LESSON 6 Lesson 6 Fermi Problems Let s estimate some quantities Warm Up 1 What is your exact age at this moment Content Exploration ACTIVITY 1 2 How many times has your heart beaten in your lifetime 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 6 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 264 Estimate the number of strands of hair 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 7 Lesson 7 More Expressions and Equations Let s solve harder problems by writing equivalent expressions Warm Up 1 Student tickets for the school play cost 2 less than adult tickets 1 If a represents the price of one adult ticket write an expression for the price of a student ticket 2 Write an expression that represents the amount of money they collected each night a The first night the school sold 60 adult tickets and 94 student tickets b The second night the school sold 83 adult tickets and 127 student tickets 3 Write an expression that represents the total amount of money collected from ticket sales on both nights 4 Over these two nights they collected a total of 1 651 in ticket sales a Write an equation that represents this situation b What was the cost of each type of ticket 5 Is your solution reasonable 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 265

G7M9 LESSON 7 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 The souvenir stand sells hats postcards and magnets They have twice as many postcards as hats and 100 more magnets than post cards 1 Let h represent the total number of hats Write an expression in terms of h for the total number of items they have to sell 2 The owner of the stand pays 8 for each hat 0 10 for each post card and 0 50 for each magnet Write an expression for the total cost of the items 3 The souvenir stand sells the hats for 11 75 each the postcards for 0 25 each and the magnets for 3 50 each Write an expression for the total amount of money they would take in if they sold all the items 4 Profits are calculated by subtracting costs from income Write an expression for the profits of the souvenir stand if they sell all the items they have Use properties to write an equivalent expression with fewer terms 5 The souvenir stand sells all these items and makes a total profit of 953 25 a Write an equation that represents this situation b How many of each item does the souvenir stand sell Explain or show your reasoning 266 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 7 ACTIVITY 2 3 Basic crochet stitches are called single double and triple Jada measures her average stitch size and sees that a double crochet stitch is not really twice as long it uses 12 inch less than twice as much yarn as a single crochet stitch Jada s triple crochet stitch uses 1 inch less than three times as much yarn as a single crochet stitch 1 Write an expression that represents the amount of yarn Jada needs to crochet a scarf that includes 800 single crochet stitches 400 double crochet stitches and 200 triple crochet stitches 2 Write an equivalent expression with as few terms as possible 3 If Jada uses 5540 inches of yarn for the entire scarf what length of yarn does she use for a single crochet stitch 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

268

ZEARN MATH STUDENT EDITION G7M9 LESSON 8 Lesson 8 Measurement Error Part 1 Let s check how accurate our measurements are Warm Up Use the image to solve the problems below 1 1 2 3 4 5 6 7 8 9 10 11 12 13 1 Estimate the length of each pencil 2 How accurate are your estimates 3 For each estimate what is the largest possible percent error 14 15 16 17 18 19 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 8 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 270 A wood floor is made by laying multiple boards end to end Each board is measured with a maximum percent error of 5 What is the maximum percent error for the total length of the floor 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M9 LESSON 9 Lesson 9 Measurement Error Part 2 Warm Up 1 Imagine that you measure the length and width of a rectangle and you know the measurements are accurate within 5 of the actual measurements If you use your measurements to find the area what is the maximum percent error for the area of the rectangle Content Exploration ACTIVITY 1 2 1 Answer the questions about measurement error of rectangular prisms below The length width and height of a rectangular prism were measured to be 10 cm 12 cm and 25 cm Assuming that these measurements are accurate to the nearest cm what is the largest percent error possible for a each of the dimensions b the volume of the prism 2 If the length width and height of a right rectangular prism have a maximum percent error of 1 what is the largest percent error possible for the volume of the prism 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

272

ZEARN MATH STUDENT EDITION G7M9 LESSON 10 Lesson 10 Measuring Long Distances Over Uneven Terrain Let s measure long distances over uneven terrain Warm Up 1 How do people measure distances in different situations What tools do they use Come up with at least three different methods and situations where those methods are used Content Exploration ACTIVITY 1 2 The school is considering holding a 5K fundraising walk on the school grounds Your class is supposed to design the course for the walk 1 What will you need to do to design the course for the walk 2 Come up with a method to measure the course Pause here so your teacher can review your plan 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 10 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 274 Let s see how close different measuring methods are to each other Your teacher will show you a path to measure 1 Use your method to measure the length of the path at least two times 2 Decide what distance you will report to the class 3 Compare your results with those of two other groups Express the differences between the measurements in terms of percentages 4 Discuss the advantages and disadvantages of each group s method 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M9 LESSON 11 Lesson 11 Building a Trundle Wheel Let s build a trundle wheel Warm Up 1 A tool that surveyors use to measure distances is called a trundle wheel 1 How does a trundle wheel measure distance 2 Why is this method of measuring distances better than the methods we used in the previous lesson 3 How could we construct a simple trundle wheel What materials would we need 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 11 ZEARN MATH STUDENT EDITION Content Exploration ACTIVITY 1 2 276 Your teacher will give you some supplies Construct a trundle wheel and use it to measure the length of the classroom Record the following information 1 The diameter of your trundle wheel 2 The number of clicks across the classroom 3 The length of the classroom Be prepared to 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 G7M9 LESSON 12 Lesson 12 Using a Trundle Wheel to Measure Distances Let s use our trundle wheels Content Exploration ACTIVITY 1 1 1 Earlier you made trundle wheels so that you could measure long distances Your teacher will show you a path to measure Measure the path with your trundle wheel three times and calculate the distance Record your results in the table Trial number Number of clicks Computation Distance 1 2 3 2 Decide what distance you will report to the class Be prepared to explain your reasoning 3 Compare this distance with the distance you measured the other day for this same path 4 Compare your results with the results of two other groups Express the differences between the measurements in terms of percentages 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

278

ZEARN MATH STUDENT EDITION G7M9 LESSON 13 Lesson 13 Designing a 5K Course Let s map out the 5K course Warm Up 1 Your teacher will give you a map of the school grounds 1 On the map draw in the path you measured earlier with your trundle wheel and label its length 2 Invent another route for a walking course and draw it on your map Estimate the length of the course you drew 3 How many laps around your course must someone complete to walk 5 km Content Exploration ACTIVITY 1 2 Solve the problems below using your trundle wheel 1 Measure your proposed race course with your trundle wheel at least two times Decide what distance you will report to the class 2 Revise your course if needed 3 Create a visual display that includes a A map of your final course b The starting and ending locations c The number of laps needed to walk 5 km d Any other information you think would be helpful to the race organizers 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M9 LESSON 13 ZEARN MATH STUDENT EDITION ENRICHMENT The map your teacher gave you didn t include a scale Create one 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 G7V3 Terminology Example A negative number is a number that is less than zero On a horizontal number line negative numbers are usually shown to the left of 0 C Adjacent angles Adjacent angles share a side and a vertex In this diagram angle ABC is adjacent to angle DBC A B D Chance experiment A chance experiment is something you can do over and over again and you don t know what will happen each time For example each time you spin the spinner it could land on black gray or white Complementary Complementary angles have measures that add up to 90 degrees For example a 15 angle and a 75 angle are complementary 75 75 15 15 Cross section A cross section is the new face you see when you slice through a three dimensional figure For example if you slice a rectangular pyramid parallel to the base you get a smaller rectangle as the cross section 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7V3 ZEARN MATH STUDENT EDITION Event An event is a set of one or more outcomes in a chance experiment For example if we roll a number cube there are six possible outcomes Examples of events are rolling a number less than 3 rolling an even number or rolling a 5 Interquartile range The interquartile range is one way to measure how spread out a data set is We sometimes call this the IQR To find the interquartile range we subtract the first quartile from the third quartile 22 29 30 31 Q1 32 43 44 Q2 45 50 50 59 Q3 For example the IQR of this data set is 20 because 50 30 20 Mean The mean is one way to measure the center of a data set We can think of it as a balance point For example for the data set 7 9 12 13 14 the mean is 11 To find the mean add up all the numbers in the data set Then divide by how many numbers there are 7 9 12 13 14 55 and 55 5 11 Mean absolute deviation MAD The mean absolute deviation is one way to measure how spread out a data set is Sometimes we call this the MAD For example for the data set 7 9 12 13 14 the MAD is 2 4 This tells us that these travel times are typically 2 4 minutes away from the mean which is 11 282 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7V3 To find the MAD add up the distance between each data point and the mean Then divide by how many numbers there are 4 2 1 2 3 12 and 12 5 2 4 Median The median is one way to measure the center of a data set It is the middle number when the data set is listed in order For the data set 7 9 12 13 14 the median is 12 For the data set 3 5 6 8 11 12 there are two numbers in the middle The median is the average of these two numbers 6 8 14 and 14 2 7 Mode The mode is a measure of center that identifies the value that occurs most frequently in a data set The mode is easily identifiable in most visual displays of numerical data including line plots dot plots and stem plots as a peak in the data For the data set 2 2 3 5 8 9 9 9 the mode is 9 For the data set 1 1 3 6 7 7 7 10 11 15 17 17 17 there are two numbers that occur most often 7 and 17 This data set would be considered bimodal or having two modes and a visual display would show two peaks Outcome An outcome of a chance experiment is one of the things that can happen when you do the experiment For example the possible outcomes of tossing a coin are heads and tails Population A population is a set of people or things that we want to study For example if we want to study the heights of people on different sports teams the population would be all the people on the teams Right angle A right angle is half of a straight angle It measures 90 degrees right angle Random Outcomes of a chance experiment are random if they are all equally likely to happen 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7V3 ZEARN MATH STUDENT EDITION Representative A sample is representative of a population if its distribution resembles the population s distribution in center shape and spread For example this dot plot represents a population 1 6 1 8 2 2 2 2 4 2 6 Dollars per pound of catfish 2 8 1 6 1 8 2 2 2 2 4 2 6 Dollars per pound of catfish 2 8 This dot plot shows a sample that is representative of the population Sample A sample is part of a population For example a population could be all the seventh grade students at one school One sample of that population is all the seventh grade students who are in band Sample Space The sample space is the list of every possible outcome for a chance experiment For example the sample space for tossing two coins is heads heads tails heads heads tails tails tails Straight angle A straight angle is an angle that forms a straight line It measures 180 degrees straight angle Supplementary Supplementary angles have measures that add up to 180 degrees For example a 15 angle and a 165 angle are supplementary 165 165 15 284 15 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7V3 Vertical angles Vertical angles are opposite angles that share the same vertex They are formed by a pair of intersecting lines Their angle measures are equal C A E For example angles AEC and DEB are vertical angles If angle AEC measures 120 then angle DEB must also measure 120 Angles AED and BEC are another pair of vertical angles D B 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 285

286

287

288

289

290

zearn org NAME Grade 7 Student Edition Vol 1 Mission 1 Scale Drawings Mission 2 Introducing Proportional Relationships Mission 3 Measuring Circles Mission 4 Proportional Relationships and Percentages Mission 5 Rational Number Arithmetic Mission 6 Expressions Equations and Inequalities Student Edition Vol 2 Vol 3 Mission 7 Angles Triangles and Prisms Mission 8 Probability and Sampling Mission 9 Putting It All Together G7 Vol 3 Zearnmath_SE_Grade7_Vol3 indd 1 Grade 7 Volume 3 MISSIONS 1 2 3 4 5 6 7 8 9 12 16 22 1 19 PM