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STUDENT EDITION Grade 7 VOLUME 2 Mission 4 Proportional Relationships and Percentages Mission 5 Rational Number Arithmetic Mission 6 Expressions Equations and Inequalities 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 886 1

Table of Contents Mission 4 Lesson 1 Relative Areas of Scaled Copies 3 Lesson 2 Ratios and Rates With Fractions 9 Lesson 3 Revisiting Proportional Relationships 15 Lesson 4 Half as Much Again 21 Lesson 5 Say It with Decimals 27 Lesson 6 Increasing and Decreasing 33 Lesson 7 One Hundred Percent 39 Lesson 8 Percent Increase and Decrease with Equations 45 Lesson 9 More and Less than 1 51 Lesson 10 Tax and Tip 57 Lesson 11 Percentage Contexts 63 Lesson 12 Find the Percentage 69 Lesson 13 Measurement Error 75 Lesson 14 Percent Error 81 Lesson 15 Error Intervals 87 Lesson 16 Posing Percentage Problems 91 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 5 Lesson 1 Interpreting Negative Numbers 97 Lesson 2 Changing Temperatures 105 Lesson 3 Changing Elevation 113 Lesson 4 Money and Debts 121 Lesson 5 Representing Subtraction 127 Lesson 6 Subtracting Rational Numbers 135 Lesson 7 Adding and Subtracting to Solve Problems 141 Lesson 8 Position Speed and Direction 147 Lesson 10 Multiply 153 Lesson 11 Dividing Rational Numbers 157 Lesson 12 Negative Rates 163 Lesson 13 Expressions with Rational Numbers 169 Lesson 14 Solving Problems with Rational Numbers 175 Lesson 15 Solving Equations With Rational Numbers 181 Lesson 16 Representing Contexts with Equations 187 Lesson 17 The Stock Market 193 Mission 6 iv Lesson 1 Relationships between Quantities 199 Lesson 2 Reasoning about Contexts with Tape Diagrams Part 1 205 Lesson 3 Reasoning about Contexts with Tape Diagrams Part 2 211 Lesson 4 Reasoning about Equations and Tape Diagrams Part 1 217 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

Lesson 5 Reasoning about Equations and Tape Diagrams Part 2 223 Lesson 6 Distinguishing between Two Types of Situations 229 Lesson 7 Reasoning about Solving Equations Part 1 235 Lesson 8 Reasoning about Solving Equations Part 2 241 Lesson 9 Dealing with Negative Numbers 247 Lesson 10 Different Options for Solving One Equation 253 Lesson 11 Using Tape Diagrams and Equations to Solve Problems 259 Lesson 12 Solving Problems about Percent Increase or Decrease 267 Lesson 13 Reintroducing Inequalities 273 Lesson 14 Finding Solutions to Inequalities in Context 279 Lesson 15 Efficiently Solving Inequalities 287 Lesson 16 Inequalities in Context 295 Lesson 17 Modeling with Inequalities 301 Lesson 18 Subtraction in Equivalent Expressions 307 Lesson 19 Expanding and Factoring 313 Lesson 20 Combining Like Terms Part 1 319 Lesson 21 Combining Like Terms Part 2 325 Lesson 22 Combining Like Terms Part 3 331 Terminology 337 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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Grade 7 Mission 4 Proportional Relationships and Percentages

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ZEARN MATH STUDENT EDITION G7M4 LESSON 1 Lesson 1 Relative Areas of Scaled Copies Let s explore the U S flag Warm Up 1 Use the diagram to answer the questions I L A H D B J G E K C F 1 Which of the geometric objects are scaled versions of each other 2 Pick two of the objects that are scaled copies and find the scale factor 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 3

G7M4 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Read the information about the United States flag then answer the questions One standard size for the United States flag is 19 feet by 10 feet On a flag of this size the union the blue rectangle in the top left corner is 7 58 feet by 5 38 feet There are many places that display flags of different sizes Many classrooms display a U S flag Flags are often displayed on stamps There was a flag on the space shuttle Astronauts on the Apollo missions had a flag on a shoulder patch 1 Choose one of the four options and determine an appropriate size for this flag that maintains the same ratio of side lengths as the standard 19 ft by 10 ft flag Find the size of the union 2 Share your answer with another group that used a different option What do your dimensions have in common ACTIVITY 2 3 4 On a U S flag that is 19 feet by 10 feet the union is 7 58 feet by 5 38 feet For each question below first estimate the answer and then compute the actual percentage 1 What percentage of the flag is taken up by the union 2 What percentage of the flag is red Be prepared to share 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 G7M4 LESSON 1 Lesson Summary Imagine you have a painting that is 15 feet wide and 5 feet high To sketch a scaled copy of the painting the ratio of the width and height of a scaled copy must be equivalent to 15 5 What is the height of a scaled copy that is 2 feet across We know that the height is h 13 2 or 23 1 3 the width so Width Height 15 5 2 h Sometimes ratios include fractions and decimals We will be working with these kinds of ratios in the next few lessons 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 5

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 1 Date GRADE 7 MISSION 4 LESSON 1 Exit Ticket The side lengths of the below flag are in the ratio 2 3 If a flag is 12 feet long what is its height 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 7

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ZEARN MATH STUDENT EDITION G7M4 LESSON 2 Lesson 2 Ratios and Rates With Fractions Let s calculate some rates with fractions Warm Up Find each quotient mentally 1 1 5 2 2 3 1 2 4 2 1 3 1 3 1 2 1 3 1 3 Concept Exploration ACTIVITY 1 2 A train is traveling at a constant speed and goes 7 5 kilometers in 6 minutes At that rate 1 How far does the train go in 1 minute 2 How far does the train go in 100 minutes Freight train photo by hpgruesen via Pixabay Public Domain 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 9

G7M4 LESSON 2 ZEARN MATH STUDENT EDITION ACTIVITY 2 10 3 Lin ran 2 34 miles in 25 of an hour Noah ran 8 23 miles in notice What do you wonder 4 3 43 Pick one of the questions that was displayed but don t tell anyone which question you picked of an hour What do you 1 Find the answer to the question you picked 2 When you and your partner are both done share the answer you got do not share the question and ask your partner to guess which question you answered If your partner can t guess explain the process you used to answer the question 3 Switch with your partner and take a turn guessing the question that your partner answered 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 2 Lesson Summary There are 12 inches in a foot so we can say that for every 1 foot there are 12 inches or the ratio of feet to inches is 1 12 We can find the unit rates by dividing the numbers in the ratio 1 1 12 12 12 1 12 1 so there is 12 foot per inch so there are 12 inches per foot The numbers in a ratio can be fractions and we calculate the unit rates the same way by dividing the numbers in the ratio For example if someone runs 34 mile in 11 2 minutes the ratio of minutes to miles is 11 3 2 4 11 2 3 4 22 3 so the person s pace is 22 3 minutes per mile 3 4 3 11 2 22 so the person s 3 speed is 22 miles per 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 11

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ZEARN MATH STUDENT EDITION G7M4 LESSON 2 Name Date GRADE 7 MISSION 4 LESSON 2 Exit Ticket Clare mixes 2 Han mixes 1 2 3 1 2 1 3 cups of water with cups of water with 1 4 cup of orange juice concentrate cup of orange juice concentrate Whose orange juice mixture tastes stronger 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 13

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ZEARN MATH STUDENT EDITION G7M4 LESSON 3 Lesson 3 Revisiting Proportional Relationships Let s use constants of proportionality to solve more problems Warm Up 1 A recipe calls for 12 cup sugar and 1 cup flour Complete the table to show how much sugar and flour to use in different numbers of batches of the recipe Sugar cups Flour cups 1 2 1 3 4 1 3 4 2 1 2 1 Concept Exploration ACTIVITY 1 2 Two students are solving the same problem At a hardware store they can cut a length of rope off of a big roll so you can buy any length you like The cost for 6 feet of rope is 7 50 How much would you pay for 50 feet of rope if the price per foot remained constant a Kiran knows he can solve the problem this way What would be Kiran s answer 1 6 50 Length of rope feet Price of rope dollars 6 7 50 1 1 25 50 1 6 50 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 15

G7M4 LESSON 3 ZEARN MATH STUDENT EDITION b Kiran wants to know if there is a more efficient way of solving the problem Priya says she can solve the problem with only 2 rows in the table What do you think Priya s method is Length of rope feet Price of rope dollars 6 7 50 50 3 Tyler swims at a constant speed 5 meters every 4 seconds a Find how long it takes Tyler to swim 114 meters Distance meters Time seconds 5 4 114 b Write an equation to represent the proportional relationship 43 A factory produces 3 bottles of sparkling water for every 8 bottles of plain water a Find how many bottles of sparkling water the company produces when it produces 600 bottles of plain water Number of bottles of sparkling water 16 Number of bottles of plain 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

ZEARN MATH STUDENT EDITION G7M4 LESSON 3 b Write an equation to represent the proportional relationship 53 A certain shade of light blue paint is made by mixing 1 12 quarts of blue paint with 5 quarts of white paint a Find how much white paint you need to mix with 4 quarts of blue paint b Write an equation to represent the proportional relationship Lesson Summary If we identify two quantities in a problem and one is proportional to the other then we can calculate the constant of proportionality and use it to answer other questions about the situation For example Andre runs at a constant speed 5 meters every 2 seconds How long does it take him to run 91 meters at this rate In this problem there are two quantities time in seconds and distance in meters Since Andre is running at a constant speed time is proportional to distance We can make a table with distance and time as column headers and fill in the given information Distance meters Time seconds 5 2 91 To find the value in the right column we multiply the value in the left column by This means that it takes Andre 25 seconds to run one meter 2 5 because 2 5 5 2 At this rate it would take Andre 25 91 182 5 or 36 4 seconds to run 91 meters In general if t is the time it takes to run d meters at that pace then t 25 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 17

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 3 Date GRADE 7 MISSION 4 LESSON 3 Exit Ticket It costs 3 45 to buy 34 lb of chopped walnuts How much would it cost to purchase 7 5 lbs of walnuts 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 19

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ZEARN MATH STUDENT EDITION G7M4 LESSON 4 Lesson 4 Half as Much Again Let s use fractions to describe increases and decreases Warm Up 1 What do you notice What do you wonder 1 1 Concept Exploration ACTIVITY 1 2 Complete the table to show the total distance walked in each case 1 a Jada s pet turtle walked 10 feet and then half that length again Initial distance b Jada s baby brother walked 3 yards and then half that length again 10 c 3 Jada s hamster walked 4 5 feet and then half that length again d Jada s robot walked 1 mile and then half that length again e A person walked x meters and then half that length again Total distance 4 5 1 x 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 21

G7M4 LESSON 4 ZEARN MATH STUDENT EDITION 2 Explain how you computed the total distance in each case 3 Two students each wrote an equation to represent the relationship between the initial distance walked x and the total distance walked y 1 2 Mai wrote y x Kiran wrote y 3 2 x x Do you agree with either of them Explain your reasoning ACTIVITY 2 3 Match each situation with a diagram A diagram may not have a match 1 A B x x y C y D x y y a Han ate x ounces of blueberries Mai ate b Mai biked x miles Han biked c 22 x 2 3 1 3 less than that more than that Han bought x pounds of apples Mai bought 2 3 of that 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 2 G7M4 LESSON 4 For each diagram write an equation that represents the relationship between x and y a Diagram A b Diagram B c Diagram C d Diagram D 3 Write a story for one of the diagrams that doesn t have a match Lesson Summary Using the distributive property provides a shortcut for calculating the final amount in situations that involve adding or subtracting a fraction of the original amount For example one day Clare runs 4 miles The next day she plans to run that same distance plus half as much again How far does she plan to run the next day 1 2 Tomorrow she will run 4 miles plus of 4 miles We can use the distributive property to find this in one step 1 4 12 4 1 12 4 Clare plans to run 1 1 2 4 or 6 miles 1 2 4 4 1 12 4 This works when we decrease by a fraction too If Tyler spent dollars on a new shirt and Noah spent less than Tyler then Noah spent 23 x dollars since x 13 x 23 x 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 1 3 23

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ZEARN MATH STUDENT EDITION G7M4 LESSON 4 Name Date GRADE 7 MISSION 4 LESSON 4 Exit Ticket 1 Tyler ate x fruit snacks and Han ate snacks Han ate 2 Mai skated x miles and Clare skated skated 3 4 3 5 less than that Write an expression for the number of fruit farther than that Write an expression for the distance Clare 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 25

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ZEARN MATH STUDENT EDITION G7M4 LESSON 5 Lesson 5 Say It with Decimals Let s use decimals to describe increases and decreases Warm Up A calculator gives the following decimal representations for some unit fractions What do you notice What do you wonder 1 1 2 0 5 1 7 0 142857143 1 3 0 3333333 1 8 0 125 1 4 0 25 1 9 0 1111111 1 5 0 2 1 10 0 1 1 6 0 1666667 1 11 0 0909091 Concept Exploration ACTIVITY 1 Use long division to express each fraction as a decimal 2 1 Use long division to express each fraction as a decimal 9 25 11 30 4 11 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 5 ZEARN MATH STUDENT EDITION 2 What is similar about your answers to the previous question What is different 3 Use the decimal representations to decide which of these fractions has the greatest value Explain your reasoning ACTIVITY 2 3 1 Match each diagram with a description and an equation Diagrams A Descriptions x y B x y 2 28 Equations An increase by 1 4 y 1 6x An increase by 1 3 y 1 3x An increase by 2 3 y 0 75x A decrease by 1 5 y 0 4x A decrease by 1 4 y 1 25x Draw a diagram for one of the unmatched equations 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 5 Lesson Summary Long division gives us a way of finding decimal representations for fractions For example to find a decimal representation for So 9 8 9 8 we can divide 9 by 8 1 125 Sometimes it is easier to work with the decimal representation of a number and sometimes it is easier to work with its fraction representation It is important to be able to work with both For example consider the following pair of problems 6 5 1 125 8 9 000 8 10 8 20 16 40 40 0 Priya earned x dollars doing chores and Kiran earned How much did Kiran earn Priya earned x dollars doing chores and Kiran earned 1 2 times as much as Priya How much did Kiran earn Since 6 5 as much as Priya 1 2 these are both exactly the same problem and the answer is 6 5 x or 1 2x When we work with percentages in later lessons the decimal representation will come in especially handy TERMINOLOGY Repeating decimal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 5 Date GRADE 7 MISSION 4 LESSON 5 Exit Ticket Kiran read for x minutes and Andre read for 58 more than that Write an equation that relates the number of minutes Kiran read with y the number of minutes that Andre read Use decimals in your equation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 31

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ZEARN MATH STUDENT EDITION G7M4 LESSON 6 Lesson 6 Increasing and Decreasing Let s use percentages to describe increases and decreases Warm Up 1 The table shows the scores from 3 different sports teams from their last 2 games Sports team Total points in game 1 Total points in game 2 Football team 22 30 Basketball team 100 108 Baseball team 4 12 1 What do you notice about the teams scores What do you wonder 2 Which team improved the most Explain your reasoning Concept Exploration ACTIVITY 1 2 1 Answer the following questions about percent changes cereal box says that now it contains 20 more Originally it came with 18 5 ounces of cereal How A much cereal does the box come with now 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 6 2 ZEARN MATH STUDENT EDITION The price of a shirt is 18 50 but you have a coupon that lowers the price by 20 What is the price of the shirt after using the coupon ACTIVITY 2 3 Match each situation to a diagram Be prepared to explain your reasoning 1 Compared with last year s strawberry harvest this year s strawberry harvest is a 25 increase 2 This year s blueberry harvest is 75 of last year s 3 Compared with last year this year s peach harvest decreased 25 4 This year s plum harvest is 125 of last year s plum harvest A B 100 last year last year this year this year 25 34 100 25 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 6 Draw a diagram to represent the following situations 1 The number of ducks living at the pond increased by 40 2 The number of mosquitoes decreased by 80 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary Imagine that it takes Andre 34 more than the time it takes Jada to get to school Then we know that Andre s time is 1 34 or 1 75 times Jada s time We can also describe this in terms of percentages 100 Jada s time Andre s time 175 We say that Andre s time is 75 more than Jada s time We can also see that Andre s time is 175 of Jada s time In general the terms percent increase and percent decrease describe an increase or decrease in a quantity as a percentage of the starting amount For example if there were 500 grams of cereal in the original package then 20 more means that 20 of 500 grams has been added to the initial amount 500 0 2 500 600 so there are 600 grams of cereal in the new package We can see that the new amount is 120 of the initial amount because 500 0 2 500 1 0 2 500 100 20 120 TERMINOLOGY Percentage decrease Percentage increase 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 Name G7M4 LESSON 6 Date GRADE 7 MISSION 4 LESSON 6 Exit Ticket The number of fish in a lake decreased by 25 between last year and this year Last year there were 60 fish in the lake What is the population this year If you get stuck consider drawing a diagram 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 37

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ZEARN MATH STUDENT EDITION G7M4 LESSON 7 Lesson 7 One Hundred Percent Let s solve more problems about percent increase and percent decrease Warm Up 1 What do you notice What do you wonder 0 5 10 15 20 25 30 35 0 50 100 150 200 250 300 350 cups of chocolate milk Concept Exploration ACTIVITY 1 2 1 For each problem complete the double number line diagram to show the percentages that correspond to the original amount and to the new amount The gas tank in dad s car holds 12 gallons The gas tank in mom s truck holds 50 more than that How much gas does the truck s tank hold 0 gas gallons 0 2 50 100 150 At a movie theater the size of popcorn bags decreased 20 If the old bags held 15 cups of popcorn how much do the new bags hold 0 popcorn cups 0 20 40 60 80 100 120 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 39

G7M4 LESSON 7 3 ZEARN MATH STUDENT EDITION A school had 1 200 students last year and only 1 080 students this year What was the percentage decrease in the number of students 0 120 240 360 480 600 720 840 960 1080 1200 number of people 0 4 One week gas was 1 25 per gallon The next week gas was 1 50 per gallon By what percentage did the price increase 0 0 25 0 5 0 75 1 1 25 1 5 1 75 2 price of gas dollars 0 5 After a 25 discount the price of a T shirt was 12 What was the price before the discount 0 price of shirt dollars 0 6 25 50 75 100 125 Compared to last year the population of Boom Town has increased 25 The population is now 6 600 What was the population last year 0 number of people 0 40 25 50 75 100 125 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 7 ACTIVITY 2 3 Two students are working on the same problem Determine if you agree with either student Priya and Clare are working on the same problem A juice box has 20 more juice in its new packaging The original packaging held 12 fluid ounces How much juice does the new packaging hold Here is how Priya set up her double number line 0 12 14 4 80 100 120 140 12 15 80 100 120 140 juice fluid ounces 0 20 40 60 Here is how Clare set up her double number line 0 juice fluid ounces 0 20 40 60 Do you agree with either of them 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 41

G7M4 LESSON 7 ZEARN MATH STUDENT EDITION Lesson Summary We can use a double number line diagram to show information about percent increase and percent decrease 0 100 200 300 400 500 600 700 0 20 40 60 80 100 120 140 cereal grams The initial amount of cereal is 500 grams which is lined up with 100 in the diagram We can find a 20 increase to 500 by adding 20 of 500 500 0 2 500 1 20 500 600 In the diagram we can see that 600 corresponds to 120 If the initial amount of 500 grams is decreased by 40 we can find how much cereal there is by subtracting 40 of the 500 grams 500 0 4 500 0 6 500 300 So a 40 decrease is the same as 60 of the initial amount In the diagram we can see that 300 is lined up with 60 To solve percentage problems we need to be clear about what corresponds to 100 For example suppose there are 20 students in a class and we know this is an increase of 25 from last year In this case the number of students in the class last year corresponds to 100 So the initial amount 100 is unknown and the final amount 125 is 20 students 0 4 8 12 16 20 24 28 0 25 50 75 100 125 150 175 number of students Looking at the double number line if 20 students is a 25 increase from the previous year then there were 16 students in the class last year 42 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M4 LESSON 7 Date GRADE 7 MISSION 4 LESSON 7 Exit Ticket A company claims that their new bottle holds 25 more laundry soap If their original container held 53 fluid ounces of soap how much does the new container hold 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 43

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ZEARN MATH STUDENT EDITION G7M4 LESSON 8 Lesson 8 Percent Increase and Decrease with Equations Let s use equations to represent increases and decreases Warm Up 1 How do you get from one number to the next using multiplication or division 1 From 100 to 106 2 From 100 to 90 3 From 90 to 100 4 From 106 to 100 Concept Exploration ACTIVITY 1 2 Money in a particular savings account increases by about 6 after a year How much money will be in the account after one year if the initial amount is 100 50 200 125 x dollars If you get stuck consider using diagrams or a table to organize your work 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 8 3 ZEARN MATH STUDENT EDITION The value of a new car decreases by about 15 in the first year How much will a car be worth after one year if its initial value was 1 000 5 000 5 020 x dollars If you get stuck consider using diagrams or a table to organize your work ACTIVITY 2 43 46 Match an equation to each of these situations Be prepared to share your reasoning 1 The water level in a reservoir is now 52 meters If this was a 23 increase what was the initial depth 2 The snow is now 52 inches deep If this was a 77 decrease what was the initial depth 0 23x 52 1 23x 52 0 77x 52 1 77x 52 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M4 LESSON 8 Lesson Summary We can use equations to express percent increase and percent decrease For example if y is 15 more than x x 0 15x 1 15x we can represent this using any of these equations y x 0 15x y 1 0 15 x y 1 15x So if someone makes an investment of x dollars and its value increases by 15 to 1 250 then we can write and solve the equation 1 15x 1 250 to find the value of the initial investment Here is another example if a is 7 less than b b 0 93b 0 07b we can represent this using any of these equations a b 0 07b a 1 0 07 b a 0 93b So if the amount of water in a tank decreased 7 from its starting value of b to its ending value of 348 gallons then you can write 0 93b 348 Often an equation is the most efficient way to solve a problem involving percent increase or percent decrease 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 8 Date GRADE 7 MISSION 4 LESSON 8 Exit Ticket Tyler s mom purchased a savings bond for Tyler The value of the savings bond increases by 4 each year One year after it was purchased the value of the savings bond was 156 Find the value of the bond when Tyler s mom purchased it 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 49

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ZEARN MATH STUDENT EDITION G7M4 LESSON 9 Lesson 9 More and Less than 1 Let s explore percentages smaller than 1 Warm Up 1 Determine the percentage mentally 1 10 is what percentage of 50 2 5 is what percentage of 50 3 1 is what percentage of 50 4 17 is what percentage of 50 Concept Exploration ACTIVITY 1 2 During one waiter s shift he delivered 13 appetizers 17 entr es and 10 desserts 1 What percentage of the dishes were desserts 2 What percentage of the dishes were appetizers 3 What percentage of the dishes were entr es 4 What do your percentages add up to 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 9 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 1 Answer the questions about percentages Find each percentage of 60 What do you notice about your answers a 30 of 60 b 3 of 60 c 0 3 of 60 d 0 03 of 60 2 20 of 5 000 is 1 000 and 21 of 5 000 is 1 050 Find each percentage of 5 000 and be prepared to explain your reasoning If you get stuck consider using the double number line diagram a 1 of 5 000 b 0 1 of 5 000 c 20 1 of 5 000 d 20 4 of 5 000 52 0 1000 1050 0 20 21 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 9 15 of 80 is 12 and 16 of 80 is 12 8 Find each percentage of 80 and be prepared to explain your reasoning a 15 1 of 80 b 15 7 of 80 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 9 ZEARN MATH STUDENT EDITION Lesson Summary A percentage such as 30 is a rate per 100 To find 30 of a quantity we multiply it by 30 100 or 0 3 The same method works for percentages that are not whole numbers like 7 8 or 2 5 To find 2 5 of a quantity we multiply it by 2 5 100 or 0 025 In the square 2 5 of the area is shaded For example to calculate 2 5 interest on a bank balance of 80 we multiply 0 025 80 2 so the interest is 2 We can sometimes find percentages like 2 5 mentally by using convenient whole number percents For example 25 of 80 is one fourth of 80 which is 20 Since 2 5 is one tenth of 25 we know that 2 5 of 80 is one tenth of 20 which is 2 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 G7M4 LESSON 9 Date GRADE 7 MISSION 4 LESSON 9 Exit Ticket Find each percentage of 75 Explain your reasoning 1 What is 10 of 75 2 What is 1 of 75 3 What is 0 1 of 75 4 What is 0 5 of 75 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 55

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ZEARN MATH STUDENT EDITION G7M4 LESSON 10 Lesson 10 Tax and Tip Let s learn about sales tax and tips Warm Up 1 You are on vacation and want to buy a pair of sunglasses for 10 or less You find a pair with a price tag of 10 The cashier says the total cost will be 10 45 What do you notice What do you wonder 10 45 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 57

G7M4 LESSON 10 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Different cities have different sales tax rates Here are the sales tax charges on the same items in two different cities Complete the tables City 1 Item Price dollars Sales tax dollars Total cost dollars Paper towels 8 00 0 48 8 48 Lamp 25 00 1 50 Pack of gum 1 00 Laundry soap 12 00 x City 2 Item Price dollars Sales tax dollars Total cost dollars Paper towels 8 00 0 64 8 64 Lamp 25 00 2 00 Pack of gum 1 00 Laundry soap 12 00 x 58 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 10 ACTIVITY 2 3 Jada has a meal in a restaurant She adds up the prices listed on the menu for everything they ordered and gets a subtotal of 42 00 Date Sep 12th Time 6 55 PM Server 27 c 43 a When the check comes it says they also need to pay 3 99 in sales tax What percentage of the subtotal is the sales tax Bread Stix Chicken Parm Chef Salad Lemon Soda Tea 9 50 15 50 12 00 2 00 3 00 Subtotal Sales Tax Total 42 00 3 99 45 99 b After tax the total is 45 99 What percentage of the subtotal is the total They actually pay 52 99 The additional 7 is a tip for the server What percentage of the subtotal is the tip The tax rate at this restaurant is 9 5 Date Sep 12th Time 6 04 PM Server 27 Date Sep 12th Time 7 12 PM Server 27 Bread Stix Ravioli Bites Cheesecake 9 50 10 50 4 95 Garden Salad Broccoli Bites Subtotal Sales Tax Total 24 95 Subtotal Sales Tax Total 1 61 a Another person s subtotal is 24 95 How much will their sales tax be b Some other person s sales tax is 1 61 How much was their subtotal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 10 ZEARN MATH STUDENT EDITION Lesson Summary Many places have sales tax A sales tax is an amount of money that a government agency collects on the sale of certain items For example a state might charge a tax on all cars purchased in the state Often the tax rate is given as a percentage of the cost For example a state s tax rate on car sales might be 2 which means that for every car sold in that state the buyer has to pay a tax that is 2 of the sales price of the car Fractional percentages often arise when a state or city charges a sales tax on a purchase For example the sales tax in Arizona is 7 5 This means that when someone buys something they have to add 0 075 times the amount on the price tag to determine the total cost of the item For example if the price tag on a T shirt in Arizona says 11 50 then the sales tax is 0 075 11 5 0 8625 which rounds to 86 cents The customer pays 11 50 0 86 or 12 36 for the shirt The total cost to the customer is the item price plus the sales tax We can think of this as a percent increase For example in Arizona the total cost to a customer is 107 5 of the price listed on the tag A tip is an amount of money that a person gives someone who provides a service It is customary in many restaurants to give a tip to the server that is between 10 and 20 of the cost of the meal If a person plans to leave a 15 tip on a meal then the total cost will be 115 of the cost of the meal 60 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M4 LESSON 10 Date GRADE 7 MISSION 4 LESSON 10 Exit Ticket At a dinner the meal costs 22 and a sales tax of 1 87 was added to the bill 1 How much would the sales tax be on a 66 meal 2 What is the tax rate for meals in this city 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M4 SLESSON 11 Lesson 11 Percentage Contexts Let s learn about more situations that involve percentages Warm Up 1 Which of these expressions represent a 15 tip on a 20 meal Which represent the total bill 15 20 20 0 15 20 1 15 20 15 100 20 Concept Exploration ACTIVITY 1 2 1 A car dealership pays a wholesale price of 12 000 to purchase a vehicle The car dealership wants to make a 32 profit a By how much will they mark up the price of the vehicle b After the markup what is the retail price of the vehicle 3 During a special sales event the dealership offers a 10 discount off of the retail price After the discount how much will a customer pay for this vehicle 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 11 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 64 Answer these questions about commission 1 For each gym membership sold the gym keeps 42 and the employee who sold it gets 8 What is the commission the employee earned as a percentage of the total cost of the gym membership 2 If an employee sells a family pass for 135 what is the amount of the commission they get to keep 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 11 Lesson Summary There are many everyday situations where a percentage of an amount of money is added to or subtracted from that amount in order to be paid to some other person or organization Goes to How it works Sales Tax the government added to the price of the item Gratuity tip the server added to the cost of the meal Interest the lender or account holder added to the balance of the loan credit card or bank account Markup the seller added to the price of an item so the seller can make a profit Markdown discount the customer subtracted from the price of an item to encourage the customer to buy it Commission the salesperson subtracted from the payment that is collected For example If a restaurant bill is 34 and the customer pays 40 they left 6 dollars as a tip for the server That is 18 of 34 so they left an 18 tip From the customer s perspective we can think of this as an 18 increase of the restaurant bill If a realtor helps a family sell their home for 200 000 and earns a 3 commission then the realtor makes 6 000 because 0 03 200 000 6 000 and the family gets 194 000 because 200 000 6 000 194 000 From the family s perspective we can think of this as a 3 decrease on the sale price of the home 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 11 Date GRADE 7 MISSION 4 LESSON 11 Exit Ticket The bike store marks up the wholesale cost of all of the bikes they sell by 30 1 Andre wants to buy a bike that has a price tag of 125 What was the wholesale cost of this bike 2 If the bike is discounted by 20 how much will Andre pay before tax 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M4 LESSON 12 Lesson 12 Find the Percentage Let s find unknown percentages Warm Up 1 Identify the percentages of the costs below a What percentage of the car price is the tax car price tax b What percentage of the food cost is the tip food cost c tip What percentage of the shirt cost is the discount shirt cost discount 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 12 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Answer these questions below a A salesperson sold a car for 18 250 and their commission is 693 50 What percentage of the sale price is their commission b The bill for a meal was 33 75 The customer left 40 00 What percentage of the bill was the tip c 70 The original price of a bicycle was 375 Now it is on sale for 295 What percentage of the original price was the markdown 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 12 ACTIVITY 2 3 Your teacher will give you either a problem card or a data card Do not show or read your card to your partner If your teacher gives you the problem card 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 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 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 3 Solve the problem and explain your reasoning to your partner 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 4 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 71

G7M4 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary To find a 30 increase over 50 we can find 130 of 50 1 3 50 65 To find a 30 decrease from 50 we can find 70 of 50 0 7 50 35 If we know the initial amount and the final amount we can also find the percent increase or percent decrease For example a plant was 12 inches tall and grew to be 15 inches tall What percent increase is this Here are two ways to solve this problem The plant grew 3 inches because 15 12 3 We can divide this growth by the original height 3 12 0 25 So the height of the plant increased by 25 The plant s new height is 125 of the original height because 15 12 1 25 This means the height increased by 25 because 125 100 25 A rope was 2 4 meters long Someone cut it down to 1 9 meters What percent decrease is this Here are two ways to solve the problem The rope is now 2 4 1 9 or 0 5 meters shorter We can divide this decrease by the original length 0 5 2 4 0 2083 So the length of the rope decreased by approximately 20 8 72 The rope s new length is about 79 2 of the original length because 1 9 2 4 0 7916 The length decreased by approximately 20 8 because 100 79 2 20 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M4 LESSON 12 Date GRADE 7 MISSION 4 LESSON 12 Exit Ticket With a coupon you can get a pair of shoes that normally costs 84 for only 72 What percentage was the discount 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M4 LESSON 13 Lesson 13 Measurement Error Let s use percentages to describe how accurately we can measure Warm Up 1 Your teacher will give you two rulers and three line segments labeled A B and C 1 Use the centimeter ruler to measure each line segment to the nearest centimeter Record these lengths in the first column of the table 2 Use the millimeter ruler to measure each line segment to the nearest tenth of a centimeter Record these lengths in the second column of the table Line Segment Length cm as measured with the first ruler Length cm as measured with the second ruler A B C Concept Exploration ACTIVITY 1 2 A soccer field is 120 yards long Han measures the length of the field using a 30 foot long tape measure and gets a measurement of 358 feet 10 inches 1 What is the amount of the error 2 Express the error as a percentage of the actual length of the field 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 13 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Your teacher will tell you which three items to measure Keep using the paper rulers from the earlier activity 1 Between you and your partner decide who will use which ruler 2 Measure the three items assigned by your teacher and record your measurements in the first column of the appropriate table Using the cm ruler Item Measured length cm Actual length cm Difference Percentage Measured length mm Actual length mm Difference Percentage Using the mm ruler Item 76 3 After you finish measuring the items share your data with your partner Next ask your teacher for the actual lengths 4 Calculate the difference between your measurements and the actual lengths in both tables 5 For each difference what percentage of the actual length is this amount Record your answers in the last column of the tables 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 13 Lesson Summary When we are measuring a length using a ruler or measuring tape we can get a measurement that is different from the actual length This could be because we positioned the ruler incorrectly or it could be because the ruler is not very precise There is always at least a small difference between the actual length and a measured length even if it is a microscopic difference Here are two rulers with different markings 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 The second ruler is marked in millimeters so it is easier to get a measurement to the nearest tenth of a centimeter with this ruler than with the first For example a line that is actually 6 2 cm long might be measured to be 6 cm long by the first ruler because we measure to the nearest centimeter The measurement error is the positive difference between the measurement and the actual value Measurement error is often expressed as a percentage of the actual value We always use a positive number to express measurement error and when appropriate use words to describe whether the measurement is greater than or less than the actual value For example if we get 6 cm when we measure a line that is actually 6 2 cm long then the measurement error is 0 2 cm or about 3 2 because 0 2 6 2 0 032 TERMINOLOGY Measurement error 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 77

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 13 Date GRADE 7 MISSION 4 LESSON 13 Exit Ticket Clare estimates that her brother is 4 feet tall When they get measured at the doctor s office her brother s height is 4 feet 2 inches 1 Should Clare s or the doctor s measurement be considered the actual height Explain your reasoning 2 What was the error expressed in inches 3 What was the error expressed as a percentage of the actual height 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M4 LESSON 14 Lesson 14 Percent Error Let s use percentages to describe other situations that involve error Warm Up 1 Estimate 1 25 of 15 8 2 9 of 38 3 1 2 of 127 4 0 53 of 6 5 0 06 of 202 Concept Exploration ACTIVITY 1 2 Instructions to care for a plant say to water it with 34 cup of water every day The plant has been getting 25 too much water How much water has the plant been getting 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 14 ZEARN MATH STUDENT EDITION 3 The pressure on a bicycle tire is 63 psi This is 5 higher than what the manual says is the correct pressure What is the correct pressure 43 The crowd at a sporting event is estimated to be 2 500 people The exact attendance is 2 486 people What is the percent error ACTIVITY 2 53 82 A metal measuring tape expands when the temperature goes above 50 F For every degree Fahrenheit above 50 its length increases by 0 00064 1 The temperature is 100 degrees Fahrenheit How much longer is a 30 foot measuring tape than its correct length 2 What is the percent error 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M4 LESSON 14 Lesson Summary Percent error can be used to describe any situation where there is a correct value and an incorrect value and we want to describe the relative difference between them For example if a milk carton is supposed to contain 16 fluid ounces and it only contains 15 fluid ounces the measurement error is 1 oz and the percent error is 6 25 because 1 16 0 0625 We can also use percent error when talking about estimates For example a teacher estimates there are about 600 students at their school If there are actually 625 students then the percent error for this estimate was 4 because 625 600 25 and 25 625 0 04 TERMINOLOGY Percent error 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 83

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ZEARN MATH STUDENT EDITION Name G7M4 LESSON 14 Date GRADE 7 MISSION 4 LESSON 14 Exit Ticket To be labeled as a jumbo egg the egg is supposed to weigh 2 5 oz Priya buys a carton of jumbo eggs and measures one of the eggs as 2 4 oz What is the percent error 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M4 LESSON 15 Lesson 15 Error Intervals Let s solve more problems about percent error Warm Up 1 An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1 What is a possible reading on the scale if you put 500 kilograms of iron ore on it Concept Exploration ACTIVITY 1 2 A saw mill cuts boards that are 16ft long After they are cut the boards are inspected and rejected if the length has a percent error of 1 5 or more a List some board lengths that should be accepted b List some board lengths that should be rejected 3 The saw mill also cuts boards that are 10 12 and 14 feet long An inspector rejects a board that was 2 3 inches too long What was the intended length of the board 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M4 LESSON 15 ZEARN MATH STUDENT EDITION ACTIVITY 2 43 You will receive either a problem card or a data card Do not read or show your card to your partner Carefully read the directions for the type of card that you were given and then discuss with 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 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 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 3 Solve the problem and explain your reasoning to your partner 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 4 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 Lesson Summary Percent error is often used to express a range of possible values For example if a box of cereal is guaranteed to have 750 grams of cereal with a margin of error of less than 5 what are possible values for the actual number of grams of cereal in the box The error could be as large as 0 05 750 37 5 and could be either above or below the correct amount 750 37 5 37 5 5 5 Therefore the box can have anywhere between 712 5 and 787 5 grams of cereal in it but it should not have 700 grams or 800 grams because both of those are more than 37 5 grams away from 750 grams 88 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M4 LESSON 15 Date GRADE 7 MISSION 4 LESSON 15 Exit Ticket A fisherman weighs an ahi tuna a very large fish on a scale and gets a reading of 135 pounds The reading on the scale may have an error of up to 5 What are two possible values for the actual weight of the fish 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 89

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ZEARN MATH STUDENT EDITION G7M4 LESSON 16 Lesson 16 Posing Percentage Problems Let s explore how percentages are used in the news Warm Up 1 You will receive a variety of news clippings that include percentages Follow the directions below 1 Sort the clippings into two piles those that are about increases and those that are about decreases 2 Were there any clippings that you had trouble deciding which pile they should go in Concept Exploration ACTIVITY 1 2 1 In the Warm Up you sorted news clippings into two piles Use the piles of clippings to answer the questions below For each pile choose one example Draw a diagram that shows how percentages are being used to describe the situation a Increase Example b Decrease Example 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 91

G7M4 LESSON 16 2 ZEARN MATH STUDENT EDITION For each example write two questions that you can answer with the given information Next find the answers Explain or show your reasoning ACTIVITY 2 3 Choose an example from the previous activities that you find the most interesting Create a visual display that includes a title that describes the situation the news clipping your diagram of the situation the two questions you asked about the situation the answers to each of your questions an explanation of how you calculated each answer Pause here so your teacher can review your work 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 43 53 G7M4 LESSON 16 Examine each display Write one comment and one question for the group Next read the comments and questions your classmates wrote for your group Revise your display using the feedback from your classmates Lesson Summary Statements about percentage increase or decrease need to specify what the whole is to be mathematically meaningful Sometimes advertisements media etc leave the whole ambiguous in order to make somewhat misleading claims We should be careful to think critically about what mathematical claim is being made For example if a disinfectant claims to kill 99 of all bacteria does it mean that It kills 99 of the number of bacteria on a surface Or is it 99 of the types of bacteria commonly found inside the house Or 99 of the total mass or volume of bacteria Does it even matter if the remaining 1 are the most harmful bacteria Resolving questions of this type is an important step in making informed decisions 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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Grade 7 Mission 5 Rational Number Arithmetic

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ZEARN MATH STUDENT EDITION G7M5 LESSON 1 Lesson 1 Interpreting Negative Numbers Let s review what we know about signed numbers Warm Up 1 30 C Here is a weather thermometer Three of the numbers have been left off 1 What numbers go in the boxes 2 What temperature does the thermometer show 20 C 15 C 5 C 0 C 10 C 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 97

G7M5 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Here are some weather thermometers measuring different temperatures C 98 C C C 10 10 10 10 5 5 5 5 0 0 0 0 5 5 5 5 1 What temperature is shown on each thermometer 2 Which thermometer shows the highest temperature 3 Which thermometer shows the lowest temperature 4 Suppose the temperature outside is 4 C Is that colder or warmer than the coldest temperature shown 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 G7M5 LESSON 1 ACTIVITY 2 3 Here is a picture of some sea animals The number line on the left shows the vertical position of each animal above or below sea level in meters Vertical position meters 10 5 0 5 10 1 How far above or below sea level is each animal Measure to their eye level 2 A mobula ray is 3 meters above the surface of the ocean How does its distance from the surface of the ocean compare to the vertical distance from the eyes of a The jumping dolphin b The flying seagull c The octopus 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 1 3 ZEARN MATH STUDENT EDITION An albatross is 5 meters above the surface of the ocean How does its distance from the surface compare to the vertical distance from the eyes of a The jumping dolphin b The flying seagull c 4 The octopus A clownfish is 2 meters below the surface of the ocean How does its distance from the surface compare to the vertical distance from the eyes of a The jumping dolphin b The flying seagull c 5 100 The octopus The vertical distance of a new dolphin from the dolphin in the picture is 3 meters What is its distance from the surface of the ocean 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 1 Lesson Summary We can use positive and negative numbers to represent temperature and elevation When numbers represent temperatures positive numbers indicate temperatures that are warmer than zero and negative numbers indicate temperatures that are colder than zero This thermometer shows a temperature of 1 degree Celsius which we write 1 C 5 0 5 10 C When numbers represent elevations positive numbers indicate positions above sea level and negative numbers indicate positions below sea level We can see the order of signed numbers on a number line 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 A number is always less than numbers to its right So 7 3 We use absolute value to describe how far a number is from 0 The numbers 15 and 15 are both 15 units from 0 so 15 15 and 15 15 We call 15 and 15 opposites They are on opposite sides of 0 on the number line but the same distance from 0 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 101

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ZEARN MATH STUDENT EDITION G7M5 LESSON 1 Name Date GRADE 7 MISSION 5 LESSON 1 Exit Ticket Here is a set of signed numbers 7 3 1 2 1 0 8 0 8 10 2 1 Order the numbers from least to greatest 2 If these numbers represent temperatures in degrees Celsius which is the coldest 3 If these numbers represent elevations in meters which is the farthest away from sea level 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M5 LESSON 2 Lesson 2 Changing Temperatures Let s add signed numbers Warm Up 1 Which pair of arrows doesn t belong 1 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 2 3 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 105

G7M5 LESSON 2 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Complete the table and draw a number line diagram for each situation Start C Change C Final C Addition equation a 40 10 degrees warmer 50 40 10 50 b 40 5 degrees colder c 40 30 degrees colder d 40 40 degrees colder e 40 50 degrees colder a 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 b c d e 106 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 2 Complete the table and draw a number line diagram for each situation Start C Change C a 20 30 degrees warmer b 20 35 degrees warmer c 20 15 degrees warmer d 20 15 degrees colder Addition equation Final C a 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30 35 40 45 50 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 107

G7M5 LESSON 2 ZEARN MATH STUDENT EDITION ACTIVITY 2 43 One winter day the temperature in Houston is 8 degrees Celsius Find the temperatures in these other cities Explain or show your reasoning 1 In Orlando it is 10 warmer than it is in Houston 2 In Salt Lake City it is 8 colder than it is in Houston 3 In Minneapolis it is 20 colder than it is in Houston 4 In Fairbanks it is 10 colder than it is in Minneapolis 5 Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks Lesson Summary If it is 42 outside and the temperature increases by 7 then we can add the initial temperature and the change in temperature to find the final temperature 42 7 49 If the temperature decreases by 7 we can either subtract 42 7 to find the final temperature or we can think of the change as 7 Again we can add to find the final temperature 42 7 35 108 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 2 In general we can represent a change in temperature with a positive number if it increases and a negative number if it decreases Then we can find the final temperature by adding the initial temperature and the change If it is 3 and the temperature decreases by 7 then we can add to find the final temperature 3 7 4 We can represent signed numbers with arrows on a number line We can represent positive numbers with arrows that start at 0 and point to the right For example this arrow represents 10 because it is 10 units long and it points to the right 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 We can represent negative numbers with arrows that start at 0 and point to the left For example this arrow represents 4 because it is 4 units long and it points to the left 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 9 10 To represent addition we put the arrows tip to tail So this diagram represents 3 5 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 5 6 6 7 8 And this represents 3 5 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 7 8 9 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 109

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ZEARN MATH STUDENT EDITION Name G7M5 LESSON 2 Date GRADE 7 MISSION 5 LESSON 2 Exit Ticket 1 Write a story about temperatures that this expression could represent 27 11 2 Draw a number line diagram and write an expression to represent this situation On Tuesday at lunchtime it was 29 C By sunset the temperature had dropped to 16 C 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 111

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ZEARN MATH STUDENT EDITION G7M5 LESSON 3 Lesson 3 Changing Elevation Let s solve problems about adding signed numbers Warm Up 1 1 Answer these questions about opposites Draw arrows on a number line to represent these situations a The temperature was 5 degrees Then the temperature rose 5 degrees b A climber was 30 feet above sea level Then she descended 30 feet 2 What s the opposite a Running 150 feet east b Jumping down 10 steps c Pouring 8 gallons into a fish tank 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 3 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 A mountaineer is climbing on a cliff She is 400 feet above the ground If she climbs up this will be a positive change If she climbs down this will be a negative change a Complete the table starting elevation feet change feet A 400 300 up B 400 150 down C 400 400 down D 400 final elevation feet 50 b Write an addition equation and draw a number line diagram for B Include the starting elevation change and final elevation in your diagram 114 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 3 A spelunker is down in a cave next to the cliff If she climbs down deeper into the cave this will be a negative change If she climbs up whether inside the cave or out of the cave and up the cliff this will be a positive change a Complete the table starting elevation feet change feet A 200 150 down B 200 100 up C 200 200 up D 200 250 up E 200 final elevation feet 500 b Write an addition equation and draw a number line diagram for C and D Include the starting elevation change and final elevation in your diagram 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 115

G7M5 LESSON 3 c ZEARN MATH STUDENT EDITION What does the expression 75 100 tell us about the spelunker What does the value of the expression tell us ACTIVITY 2 43 1 35 30 5 2 0 15 0 85 12 5 3 116 Find the sums 1 2 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 G7M5 LESSON 3 Lesson Summary The opposite of a number is the same distance from 0 but on the other side of 0 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 The opposite of 9 is 9 When we add opposites we always get 0 This diagram shows that 9 9 0 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 When we add two numbers with the same sign the arrows that represent them point in the same direction When we put the arrows tip to tail we see the sum has the same sign 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 To find the sum we add the magnitudes and give it the correct sign For example 5 4 5 4 On the other hand when we add two numbers with different signs we subtract their magnitudes because the arrows point in the opposite direction and give it the sign of the number with the larger magnitude For example 5 12 12 5 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 117

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ZEARN MATH STUDENT EDITION Name G7M5 LESSON 3 Date GRADE 7 MISSION 5 LESSON 3 Exit Ticket Find each sum 1 56 56 2 240 370 3 5 7 4 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 119

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ZEARN MATH STUDENT EDITION G7M5 LESSON 4 Lesson 4 Money and Debts Let s apply what we know about signed numbers to money Warm Up 1 Priya wants to buy three tickets for a concert She has earned 135 and each ticket costs 50 She borrows the rest of the money she needs from a bank and buys the tickets 1 How can you represent the amount of money that Priya has after buying the tickets 2 How much more money will Priya need to earn to pay back the money she borrowed from the bank 3 How much money will she have after she pays back the money she borrowed from the bank Concept Exploration ACTIVITY 1 2 At the beginning of the month Kiran had 24 in his school cafeteria account Use a variable to represent the unknown quantity in each transaction below and write an equation to represent it Then represent each transaction on a number line What is the unknown quantity in each case 1 In the first week he spent 16 on lunches How much was in his account then 2 Then he deposited some more money and his account balance was 28 How much did he deposit 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 4 ZEARN MATH STUDENT EDITION 3 Then he spent 34 on lunches the next week How much was in his account then 4 Then he deposited enough money to pay off his debt to the cafeteria How much did he deposit 5 Explain why it makes sense to use a negative number to represent Kiran s account balance when he owes money ACTIVITY 2 3 Answer the questions about the bank statement below Responsible Bank 210 2nd Street Anytown MH 06930 Checking Account Statement Page 1 of 1 Andre Person 1729 Euclid Ave Anytown MH 06930 Date Description 2017 10 03 2017 10 05 Previous Balance Check Number 256 ATM Deposit Cash Wire Transfer Point of Sale Grocery Store Funds Transfer from Savings Check Number 257 Online Payment Phone Services 2017 10 06 2017 10 10 2017 10 17 2017 10 25 2017 10 28 2017 10 29 122 Withdrawals Statement Period Account No 2017 10 01 to 2017 11 01 1120635978 Deposits 28 50 45 00 37 91 16 43 50 00 42 00 72 50 Balance 39 87 11 37 56 37 18 46 2 03 52 03 10 03 62 47 1 If we put withdrawals and deposits in the same column how can they be represented 2 Andre withdraws 40 to buy a music player What is his new balance 3 If Andre deposits 100 in this account will he still be in debt 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 G7M5 LESSON 4 Lesson Summary Banks use positive numbers to represent money that gets put into an account and negative numbers to represent money that gets taken out of an account When you put money into an account it is called a deposit When you take money out of an account it is called a withdrawal People also use negative numbers to represent debt If you take out more money from your account than you put in then you owe the bank money and your account balance will be a negative number to represent that debt For example if you have 200 in your bank account and then you write a check for 300 you will owe the bank 100 and your account balance will be 100 Starting balance Deposits and withdrawals New balance 0 50 0 50 50 150 50 150 200 300 200 300 100 In general you can find a new account balance by adding the value of the deposit or withdrawal to it You can also tell quickly how much money is needed to repay a debt using the fact that to get to zero from a negative value you need to add its opposite TERMINOLOGY Deposit Withdrawal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 123

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ZEARN MATH STUDENT EDITION Name G7M5 LESSON 4 Date GRADE 7 MISSION 5 LESSON 4 Exit Ticket 1 Clare has 150 in her bank account She buys a bike for 200 What is Clare s account balance now 2 If Clare earns 75 the next week from delivering newspapers and deposits it in her account what will her account balance be then 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 125

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ZEARN MATH STUDENT EDITION G7M5 LESSON 5 Lesson 5 Representing Subtraction Let s subtract signed numbers Warm Up 1 For the equations in the second and third columns write two more equations using the same numbers that express the same relationship in a different way If you get stuck consider looking at the examples in the first column 2 3 5 11 x 7 9 1 8 3 2 5 5 3 2 5 2 3 Concept Exploration ACTIVITY 1 2 1 Below is an unfinished number line diagram that represents a sum of 8 Answer the questions about the number line Here is an unfinished number line diagram that represents a sum of 8 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 a How long should the other arrow be b For an equation that goes with this diagram Mai writes 3 8 Tyler writes 8 3 Do you agree with either of them c What is the unknown number 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 127

G7M5 LESSON 5 3 ZEARN MATH STUDENT EDITION Answer the questions about the 2 unfinished diagrams that represent sums below 1 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 a What equation would Mai write if she used the same reasoning as before b What equation would Tyler write if he used the same reasoning as before c How long should the other arrow be d What number would complete each equation Be prepared to explain your reasoning 2 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 a What equation would Mai write if she used the same reasoning as before b What equation would Tyler write if he used the same reasoning as before c How long should the other arrow be d What number would complete each equation Be prepared to explain your reasoning 128 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 5 Draw a number line diagram for 8 3 What is the unknown number How do you know 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 ACTIVITY 2 53 1 Answer the questions about the expressions Match each diagram to one of these expressions 3 7 3 7 3 7 3 7 a 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 b c d 2 Which expressions in the first question have the same value What do you notice 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 5 63 ZEARN MATH STUDENT EDITION Complete each of the tables What do you notice Expression 130 Value Expression 8 8 5 5 8 8 5 5 8 5 5 9 8 5 5 9 8 12 5 2 8 12 5 2 Value 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 5 Lesson Summary The equation 7 5 is equivalent to 5 7 The diagram illustrates the second equation 10 9 8 7 6 5 4 3 2 1 0 5 1 2 3 4 5 6 7 8 9 10 5 6 7 8 9 10 Notice that the value of 7 5 is 2 5 7 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 We can solve the equation 5 7 by adding 5 to both sides This shows that 7 5 7 5 Likewise 3 5 is equivalent to 5 3 5 3 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 Notice that the value of 3 5 is 2 5 3 10 9 8 7 6 5 4 3 2 1 0 1 We can solve the equation 5 3 by adding 5 to both sides This shows that 3 5 3 5 In general a b a b If a b x then x b a We can add b to both sides of this second equation to get that x 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 131

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ZEARN MATH STUDENT EDITION Name G7M5 LESSON 5 Date GRADE 7 MISSION 5 LESSON 5 Exit Ticket 1 Which other expression has the same value as 14 8 Explain your reasoning a 14 8 b 14 8 c 14 8 d 14 8 2 Which other expression has the same value as 14 8 Explain your reasoning a 14 8 b 14 8 c 14 8 d 14 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 133

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ZEARN MATH STUDENT EDITION G7M5 LESSON 6 Lesson 6 Subtracting Rational Numbers Let s bring addition and subtraction together Warm Up 1 1 Answer the questions about the equations Solve each equation mentally a 247 c 458 b c 43 87 58 92 c 2 15 8 c 51 8 Rewrite each addition equation as a subtraction equation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 6 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 136 A mountaineer is changing elevations Write an expression that represents the difference between the final elevation and beginning elevation Then write the value of the change The first one is done for you Beginning elevation feet Final elevation feet Difference between final and beginning Change 400 900 900 400 500 400 50 400 120 200 610 200 50 200 500 200 0 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 6 ACTIVITY 2 3 1 Answer the questions about the subtraction expressions in the table Find the value of each subtraction expression A B 3 2 2 3 5 9 9 5 11 2 2 11 6 3 3 6 1 2 3 6 3 6 1 2 2 1 2 3 1 2 3 1 2 2 1 2 2 What do you notice about the expressions in Column A compared to Column B 3 What do you notice about their values 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary When we talk about the difference of two numbers we mean subtract them Usually we subtract them in the order they are named For example the difference of 8 and 6 is 8 6 The difference of two numbers tells you how far apart they are on the number line 8 and 6 are 14 units apart because 8 6 14 14 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 8 9 10 Notice that if you subtract them in the opposite order you get the opposite number 14 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 In general the distance between two numbers a and b on the number line is a b Note that the distance between two numbers is always positive no matter the order But the difference can be positive or negative depending on the order 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 G7M5 LESSON 6 Date GRADE 7 MISSION 5 LESSON 6 Exit Ticket Select all of the choices that are equal to 5 12 1 7 2 7 3 The difference between 5 and 12 4 The difference between 12 and 5 5 5 12 6 5 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 139

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ZEARN MATH STUDENT EDITION G7M5 LESSON 7 Lesson 7 Adding and Subtracting to Solve Problems Let s apply what we know about signed numbers to different situations Warm Up 1 Answer the following questions without computing 1 Is the solution to 2 7 x 3 5 positive or negative 2 Which of the following are solutions to 2 7 x 3 5 3 5 2 7 3 5 2 7 3 5 2 7 3 5 2 7 Concept Exploration ACTIVITY 1 2 Answer the questions about a store s inventory of cell phones A store tracks the number of cell phones it has in stock and how many phones it sells The table shows the inventory for one phone model at the beginning of each day last week The inventory changes when they sell phones or get shipments of phones into the store Inventory Change Monday 18 2 Tuesday 16 5 Wednesday 11 7 Thursday 4 6 Friday 2 20 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 141

G7M5 LESSON 7 ZEARN MATH STUDENT EDITION 1 What do you think it means when the change is positive Negative 2 What do you think it means when the inventory is positive Negative 3 Based on the information in the table what do you think the inventory will be at on Saturday morning Explain your reasoning 4 What is the difference between the greatest inventory and the least inventory ACTIVITY 2 3 Han s family got a solar panel Each month they get a credit to their account for the electricity that is generated by the solar panel The credit they receive varies based on how sunny it is In January they used 83 56 worth of electricity and generated 6 75 worth of electricity Here is their electricity bill from January Current charges 83 56 Solar Credit 6 75 Amount due 76 81 1 142 In July they were traveling away from home and only used 19 24 worth of electricity Their solar panel generated 22 75 worth of electricity What was their amount due in July 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 3 G7M5 LESSON 7 The table shows the value of the electricity they used and the value of the electricity they generated each week for a month What amount is due for this month Used Generated Week 1 13 45 6 33 Week 2 21 78 8 94 Week 3 18 12 7 70 Week 4 24 05 5 36 What is the difference between the value of the electricity generated in week 1 and week 2 Between week 2 and week 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 143

G7M5 LESSON 7 ZEARN MATH STUDENT EDITION Lesson Summary Sometimes we use positive and negative numbers to represent quantities in context Here are some contexts we have studied that can be represented with positive and negative numbers temperature elevation inventory an account balance electricity flowing in and flowing out In these situations using positive and negative numbers and operations on positive and negative numbers helps us understand and analyze them To solve problems in these situations we just have to understand what it means when the quantity is positive when it is negative and what it means to add and subtract them When two points in the coordinate plane lie on a horizontal line you can find the distance between them by subtracting their x coordinates y When two points in the coordinate plane lie on a vertical line you can find the distance between them by subtracting their y coordinates Remember the distance between two numbers is independent of the order but the difference depends on the order 4 5 3 2 1 5 4 3 2 2 4 2 5 5 4 2 4 5 2 3 2 2 3 4 144 3 5 5 1 1 3 2 3 2 1 2 3 4 5 x 2 3 4 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 G7M5 LESSON 7 Name Date GRADE 7 MISSION 5 LESSON 7 Exit Ticket Here is some record keeping from a coffee shop about their paper cups Cups are delivered 2 000 at a time Day Change Monday 2000 Tuesday 125 Wednesday 127 Thursday 1719 Friday 356 Saturday 782 Sunday 0 1 Explain what a positive and negative number means in this situation 2 How many paper cups are left at the end of the week 3 How many cups do you think were used on Thursday 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 145

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ZEARN MATH STUDENT EDITION G7M5 LESSON 8 Lesson 8 Position Speed and Direction Let s use signed numbers to represent movement Warm Up 1 Solve the problems involving distance rate and time a An airplane moves at a constant speed of 120 miles per hour for 3 hours How far does it go b A train moves at constant speed and travels 6 miles in 4 minutes What is its speed in miles per minute c A car moves at a constant speed of 50 miles per hour How long does it take the car to go 200 miles 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 147

G7M5 LESSON 8 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Use the number line and table to answer the questions a After each move record your location in the table Then write an expression to represent the ending position that uses the starting position the speed and the time The first row is done for you Direction Speed units per second Time seconds Ending position units Expression 0 right 5 3 15 0 5 3 0 left 4 6 0 right 2 8 0 right 6 2 0 left 1 1 5 Starting position b How can you see the direction of movement in the expression c 148 Using a starting position p a speed s and a time t write two expressions for an ending position One expression should show the result of moving right and one expression should show the result of moving left 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 8 ACTIVITY 2 3 A traffic safety engineer set up a camera along a highway and recorded the speed and direction of cars and trucks that passed by the camera Positions to the east of the camera are positive and to the west are negative Vehicles that are traveling towards the east have a positive velocity and vehicles that are traveling towards the west have a negative velocity a Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period Then write an equation Velocity meters per second Time after passing the camera seconds Ending position meters Equation describing position 25 10 250 25 10 250 20 30 32 40 35 20 28 0 b If a car is traveling east when it passes the camera will its position be positive or negative 60 seconds after it passes the camera If we multiply two positive numbers is the result positive or negative c If a car is traveling west when it passes the camera will its position be positive or negative 60 seconds after it passes the camera If we multiply a positive and a negative number is the result positive or negative 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 8 ZEARN MATH STUDENT EDITION Lesson Summary We can use signed numbers to represent the position of an object along a line We pick a point to be the reference point and call it zero Positions to the right of zero are positive Positions to the left of zero are negative 4 units to the left of zero 10 9 8 7 6 5 4 3 reference point 2 1 0 1 7 units to the right of zero 2 3 4 5 6 7 8 9 10 When we combine speed with direction indicated by the sign of the number it is called velocity For example if you are moving 5 meters per second to the right then your velocity is 5 meters per second If you are moving 5 meters per second to the left then your velocity is 5 meters per second If you start at zero and move 5 meters per second for 10 seconds you will be 5 10 50 meters to the right of zero In other words 5 10 50 If you start at zero and move 5 meters per second for 10 seconds you will be 5 10 50 meters to the left of zero In other words 5 10 50 In general a negative number times a positive number is a negative number 150 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M5 LESSON 8 Date GRADE 7 MISSION 5 LESSON 8 Exit Ticket Four runners start at the same point Lin Elena Diego Andre For each runner write a multiplication equation that describes their journey Lin runs for 25 seconds at 8 2 meters per second What is her finish point Elena runs for 28 seconds and finishes at 250 meters What is her velocity Diego runs for 32 seconds at 8 1 meters per second What is his finish point Andre runs for 35 seconds and finishes at 285 meters What is his velocity 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M5 LESSON 10 Lesson 10 Multiply Let s get more practice multiplying signed numbers Warm Up Which expression doesn t belong 1 7 9x 7 9 10 7 9 x 79 Concept Explorations ACTIVITY 1 Match expressions that are equal to each other 2 1 8 a 1 12 g 64 b 1 3 5 h 1 2 6 m 1 15 n 1 12 i 1 4 32 o 2 6 1 j 3 5 p 2 4 1 2 e 16 k 1 3 4 q 2 4 f l r c 1 3 5 d 2 16 1 3 4 3 5 1 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 153

G7M5 LESSON 10 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Evaluate the expressions in one of the columns Your partner will work on the other column Check in with your partner after you finish each row Your answers in each row should be the same If your answers aren t the same work together to find the error Column A Column B 790 10 7 9 10 6 7 7 0 1 60 2 1 2 8 4 1 2 2 5 3 25 2 5 13 4 10 3 2 7 3 5 1 6 29 2 Lesson Summary A positive times a positive is always positive For example 3 5 7 8 A negative times a negative is also positive For example 3 5 7 8 21 40 21 40 A negative times a positive or a positive times a negative is always negative For example 3 7 3 7 21 5 8 5 8 40 A negative times a negative times a negative is also negative For example 3 4 5 60 154 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M5 LESSON 10 Date GRADE 7 MISSION 5 LESSON 10 Exit Ticket Noah was doing some homework and answered the following questions 1 2 7 2 5 6 75 2 3 5 5 3 4 5 7 3 5 15 28 3 3 Do you agree with his answers If you disagree 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 155

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ZEARN MATH STUDENT EDITION G7M5 LESSON 11 Lesson 11 Dividing Rational Numbers Let s divide signed numbers Warm Up 1 Consider the equation 27x 35 Without computing answer the following questions 1 Is the solution to this equation positive or negative 2 Are either of these two numbers solutions to the equation 35 27 35 27 Concept Exploration ACTIVITY 1 2 Find the missing values in the equations below a 3 4 b 3 12 c 3 12 d 4 12 e 4 12 3 Rewrite the unknown factor problems as division problems 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 11 43 ZEARN MATH STUDENT EDITION Complete the sentences Be prepared to explain your reasoning a The sign of a positive number divided by a positive number is always b The sign of a positive number divided by a negative number is always c The sign of a negative number divided by a positive number is always d The sign of a negative number divided by a negative number is always 53 Han and Clare walk towards each other at a constant rate meet up and then continue past each other in opposite directions We will call the position where they meet up 0 feet and the time when they meet up 0 seconds Han s velocity is 4 feet per second Clare s velocity is 5 feet per second a Where is each person 10 seconds before they meet up b When is each person at the position 10 feet from the meeting place 158 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 11 ACTIVITY 2 63 A water well drilling rig has dug to a height of 60 feet after one full day of continuous use Answer the questions 1 Assuming the rig drilled at a constant rate what was the height of the drill after 15 hours 2 If the rig has been running constantly and is currently at a height of 147 5 feet for how long has the rig been running 3 Use the coordinate grid to show the drill s progress time in hours 0 10 20 30 40 50 60 70 80 90 100 50 100 height in feet 150 4 200 250 At this rate how many hours will it take until the drill reaches 250 feet 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 159

G7M5 LESSON 11 ZEARN MATH STUDENT EDITION Lesson Summary Any division problem is actually a multiplication problem 6 2 3 because 2 3 6 6 2 3 because 2 3 6 6 2 3 because 2 3 6 6 2 3 because 2 3 6 Because we know how to multiply signed numbers that means we know how to divide them 160 The sign of a positive number divided by a negative number is always negative The sign of a negative number divided by a positive number is always negative The sign of a negative number divided by a negative number is always positive 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 11 Date GRADE 7 MISSION 5 LESSON 11 Exit Ticket Match each expression with its value 1 15 12 0 8 2 12 15 0 8 3 12 15 1 25 4 15 12 1 25 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 161

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ZEARN MATH STUDENT EDITION G7M5 LESSON 12 Lesson 12 Negative Rates Let s apply what we know about signed numbers Warm Up 1 Solve 1 If you eat 5 grapes per minute for 8 minutes how many grapes will you eat 2 If you hear 9 new songs per day for 3 days how many new songs will you hear 3 If you run 15 laps per practice how many practices will it take you to run 30 laps Concept Exploration ACTIVITY 1 2 1 A large aquarium should contain 10 000 liters of water when it is filled correctly A different aquarium should contain 15 000 liters of water when filled correctly A large aquarium should contain 10 000 liters of water when it is filled correctly It will overflow if it gets up to 12 000 liters The fish will get sick if it gets down to 4 000 liters The aquarium has an automatic system to help keep the correct water level If the water level is too low a faucet fills it If the water level is too high a drain opens One day the system stops working correctly The faucet starts to fill the aquarium at a rate of 30 liters per minute and the drain opens at the same time draining the water at a rate of 20 liters per minute a Is the water level rising or falling How do you know b How long will it take until the tank starts overflowing or the fish get sick 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 12 3 ZEARN MATH STUDENT EDITION A different aquarium should contain 15 000 liters of water when filled correctly It will overflow if it gets to 17 600 liters One day there is an accident and the tank cracks in 4 places Water flows out of each crack at a rate of 12 liter per hour An emergency pump can re fill the tank at a rate of 2 liters per minute How many minutes must the pump run to replace the water lost each hour ACTIVITY 2 3 1 Answer the questions about the submarine ride and hot air balloon ride Be prepared to explain your reasoning Challenger Deep is the deepest known point in the ocean at 35 814 feet below sea level In 1960 Jacques Piccard and Don Walsh rode down in the Trieste and became the first people to visit the Challenger Deep a If sea level is represented by 0 feet explain how you can represent the depth of a submarine descending from sea level to the bottom of Challenger Deep b Trieste s descent was a change in depth of 3 feet per second We can use the relationship y 3x to model this where y is the depth in feet and x is the time in seconds Using this model how much time would the Trieste take to reach the bottom c 164 It took the Trieste 3 hours to ascend back to sea level This can be modeled by a different relationship y kx What is the value of k 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

ZEARN MATH STUDENT EDITION 4 G7M5 LESSON 12 The design of the Trieste was based on the design of a hot air balloon built by Auguste Piccard Jacques s father In 1932 Auguste rode in his hot air balloon up to a record breaking height a Auguste s ascent took 7 hours and went up 51 683 feet Write a relationship y kx to represent his ascent from his starting location b Auguste s descent took 3 hours and went down 52 940 feet Write another relationship to represent his descent c Did Auguste Piccard end up at a greater or lesser altitude than his starting point How much higher or lower 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary We saw earlier that we can represent speed with direction using signed numbers Speed with direction is called velocity Positive velocities always represent movement in the opposite direction from negative velocities We can do this with vertical movement moving up can be represented with positive numbers and moving down with negative numbers The magnitude tells you how fast and the sign tells you which direction We could actually do it the other way around if we wanted to but usually we make up positive and down negative 166 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 12 Date GRADE 7 MISSION 5 LESSON 12 Exit Ticket 1 A submarine is descending to examine the seafloor 2 100 feet below the surface It takes the submarine 2 hours to make this descent Write an equation to represent the relationship between the submarine s elevation and time 2 Another submarine s descent can be represented as y 240x where y is the elevation and x is time in hours How long will it take this submarine to make the descent 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 167

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ZEARN MATH STUDENT EDITION G7M5 LESSON 13 Lesson 13 Expressions with Rational Numbers Let s develop our signed number sense Warm Up 1 Decide if each statement is true or false Be prepared to explain your reasoning 1 38 76 15 6 is negative 2 10 000 99 999 0 3 34 43 0 4 30 80 50 50 30 80 Concept Exploration ACTIVITY 1 2 You will receive a set of cards Group them into pairs of expressions that have the same value 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 13 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 For each set of values a and b evaluate the given expressions and record your answers in the table Then answer the questions that follow a b 1 2 6 1 2 6 6 1 When a 1 2 When a 1 2 a b a b has the smallest value is the closest to zero and b 6 which expression has the smallest value is the closest to zero When a 6 and b 12 which expression has the largest value 170 a b and b 6 which expression has the largest value 3 4b 1 2 has the largest value 2 a has the smallest value is the closest to zero 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 13 Lesson Summary We can represent sums differences products and quotients of rational numbers and combinations of these with numerical and algebraic expressions Sums 1 2 9 8 5 x Differences 1 2 9 8 5 x Products Quotients 12 9 12 9 8 5x 8 5 x We can write the product of two numbers in different ways By putting a little dot between the factors like this 8 5 x By putting the factors next to each other without any symbol between them at all like this 8 5x We can write the quotient of two numbers in different ways as well By writing the division symbol between the numbers like this 8 5 x By writing a fraction bar between the numbers like this 8 5 x 8 5 When we have an algebraic expression like x and are given a value for the variable we can find the value of the expression For example if x is 2 then the value of the expression is 4 25 because 8 5 2 4 25 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION Name G7M5 LESSON 13 Date GRADE 7 MISSION 5 LESSON 13 Exit Ticket In each equation select an operation to make the equation true 3 4 1 24 18 2 24 3 12 15 3 4 12 15 27 5 18 3 4 3 4 32 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 173

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ZEARN MATH STUDENT EDITION G7M5 LESSON 14 Lesson 14 Solving Problems with Rational Numbers Let s use all four operations with signed numbers to solve problems Warm Up 1 Which equation doesn t belong 1 x 50 2 60t 30 x 90 100 0 01 0 001x Concept Exploration ACTIVITY 1 2 1 A tank of water is being drained Due to a problem the sensor does not start working until some time into the draining process The sensor starts its recording at time zero when there are 770 liters in the tank Given that the drain empties the tank at a constant rate of 14 liters per minute complete the table Time after sensor starts minutes Change in water liters Expression Water in the tank liters 0 0 770 0 14 770 1 14 770 1 14 756 5 70 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 175

G7M5 LESSON 14 2 ZEARN MATH STUDENT EDITION Later someone wants to use the data to find out how long the tank had been draining before the sensor started Complete this table Time after sensor starts minutes Change in water liters Expression Water in the tank liters 1 14 770 1 14 756 0 0 770 0 14 770 1 14 770 1 14 784 2 28 3 4 5 3 176 If the sensor started working 15 minutes into the tank draining how much was in the tank to begin 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 G7M5 LESSON 14 ACTIVITY 2 3 A utility company charges 0 12 per kilowatt hour for energy a customer uses They give a credit of 0 025 for every kilowatt hour of electricity a customer with a solar panel generates that they don t use themselves A customer has a charge of 82 04 and a credit of 4 10 on this month s bill 1 What is the amount due this month 2 How many kilowatt hours did they use 3 How many kilowatt hours did they generate that they didn t use themselves 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 14 ZEARN MATH STUDENT EDITION Lesson Summary We can apply the rules for arithmetic with rational numbers to solve problems In general a b a b If a b x then x b a We can add b to both sides of this second equation to get that x a b Remember the distance between two numbers is independent of the order but the difference depends on the order And when multiplying or dividing 178 The sign of a positive number multiplied or divided by a negative number is always negative The sign of a negative number multiplied or divided by a positive number is always negative The sign of a negative number multiplied or divided by a negative number is always positive 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 14 Date GRADE 7 MISSION 5 LESSON 14 Exit Ticket Lin s sister has a checking account If the account balance ever falls below zero the bank charges her a fee of 5 95 per day Today the balance in Lin s sister s account is 2 67 1 If she does not make any deposits or withdrawals what will be the balance in her account after 2 days 2 In 14 days Lin s sister will be paid 430 and will deposit it into her checking account If there are no other transactions besides this deposit and the daily fee will Lin continue to be charged 5 95 each day after this deposit is made 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 179

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ZEARN MATH STUDENT EDITION G7M5 LESSON 15 Lesson 15 Solving Equations With Rational Numbers Let s solve equations that include negative values Warm Up The variables a through h all represent different numbers Mentally find numbers that make each equation true 1 3 5 5 3 a 7 b 1 c d 1 6 6 e 11 f 0 g h 0 Concept Exploration ACTIVITY 1 Match each equation to its solution Be prepared to explain your reasoning 2 1 1 2 x 5 a x 4 5 1 2 2 2x 9 b x 3 12 x c 4 2x 7 d x 4 5 5 x 2 6 5 e x 2 6 2 x 1 4 1 2 f x 10 1 2 x 3 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 181

G7M5 LESSON 15 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 1 The Hiking Club is on a trip to hike up a mountain Answer the following questions about the Hiking Club The members increased their elevation 290 feet during their hike this morning Now they are at an elevation of 450 feet a Explain how to find their elevation before the hike b Han says the equation e 290 450 describes the situation What does the variable represent c Han says that he can rewrite his equation as e 450 290 to solve for e Compare Han s strategy to your strategy for finding the beginning elevation 2 The temperature fell 4 degrees in the last hour Now it is 21 degrees Write and solve an equation to find the temperature it was 1 hour ago 3 There are 3 times as many students participating in the hiking trip this year than last year There are 42 students on the trip this year a Explain how to find the number of students that came on the hiking trip last year b Mai says the equation 3s 42 describes the situation What does the variable represent c 182 Mai says that she can rewrite her equation as s 13 42 to solve for s Compare Mai s strategy to your strategy for finding the number of students on last year s trip 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 15 The cost of the hiking trip this year is 23 of the cost of last year s trip This year s trip cost 32 Write and solve an equation to find the cost of last year s trip ACTIVITY 3 43 Your teacher will give you a set of cards with numbers on them 1 Match numbers with their additive inverses 2 Next match numbers with their multiplicative inverses 3 What do you notice about the numbers and their inverses 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 15 ZEARN MATH STUDENT EDITION Lesson Summary To solve the equation x 8 5 we can add the opposite of 8 or 8 to each side x 8 5 x 8 8 5 8 x 13 Because adding the opposite of a number is the same as subtracting that number we can also think of it as subtracting 8 from each side We can use the same approach for this equation 12 t 12 2 9 2 9 t 29 11 7 9 2 9 t To solve the equation 8x 5 we can multiply each side by the reciprocal of 8 or 1 8 8x 5 1 8 8x 1 8 x 5 8 5 Because multiplying by the reciprocal of a number is the same as dividing by that number we can also think of it as dividing by 8 We can use the same approach for this equation 12 29 t 92 12 92 29 t 54 t 184 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M5 LESSON 15 Date GRADE 7 MISSION 5 LESSON 15 Exit Ticket The Hiking Club is taking another trip The hike leader s watch shows that they gained 296 feet in altitude from their starting position Their altitude is now 285 feet but there is no record of their starting altitude Write and solve an equation to represent this situation and find their starting altitude 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 185

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ZEARN MATH STUDENT EDITION G7M5 LESSON 16 Lesson 16 Representing Contexts with Equations Let s write equations that represent situations Warm Up 1 Is the solution positive or negative 8 7 1 4 a 8 7b 1 4 8 7 c 1 4 8 7 d 1 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 187

G7M5 LESSON 16 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Use the bank of equations to answer the following about each situation For each situation Find two equations that could represent the situation from the bank of equations Some equations will not be used Explain what the variable v represents in the situation Determine the value of the variable that makes the equation true and explain your reasoning Bank of equations 3v 9 v 16 6 v 4 12 v 16 6 6 v 16 188 4 1 3 v v 1 3 6 v 9 3 v 1 3 9 v 12 4 4 3 v 4 3 v 3v 6 v 1 3 6 v 4v 12 1 Between 6 a m and noon the temperature rose 12 degrees Fahrenheit to 4 degrees Fahrenheit 2 At midnight the temperature was 6 degrees By 4 a m the temperature had fallen to 16 degrees 3 The temperature is 0 degrees at midnight and dropping 3 degrees per hour The temperature is 6 degrees at a certain time 4 The temperature is 0 degrees at midnight and dropping 3 degrees per hour The temperature is 9 degrees at a certain time 5 The temperature at 9 p m is one third the temperature at midnight 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 16 ACTIVITY 2 3 Your teacher will assign your group one of the situations below Create a visual display about your situation that includes the following An equation that represents your situation What your variable and each term in the equation represent How the operations in the equation represent the relationships in the story How you use inverses to solve for the unknown quantity The solution to your equation 1 As a 7 14 inch candle burns down its height decreases take for the candle to burn completely 3 4 2 On Monday 19 of the enrolled students in a school were absent There were 4 512 students present How many students are enrolled at the school 3 A hiker begins at sea level and descends 25 feet every minute How long will it take to get to an elevation of 750 feet 4 Jada practices the violin for the same amount of time every day On Tuesday she practices for 35 minutes How much does Jada practice in a week 5 The temperature has been dropping 2 12 degrees every hour and the current temperature is 15 F How many hours ago was the temperature 0 F 6 The population of a school increased by 12 and now the population is 476 What was the population before the increase 7 During a 5 off sale Diego pays 74 10 for a new hockey stick What was the original price 8 A store buys sweaters for 8 and sells them for 26 How many sweaters does the store need to sell to make a profit of 990 inch each hour How many hours does 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 189

G7M5 LESSON 16 ZEARN MATH STUDENT EDITION Lesson Summary We can use variables and equations involving signed numbers to represent a story or answer questions about a situation For example if the temperature is 3 C and then falls to 17 C we can let represent the temperature change and write the equation 3 x 17 We can solve the equation by adding 3 to each side Since 17 3 14 the change is 14 C Here is another example if a starfish is descending by 3 2 feet every hour then we can solve 32 h 6 to find out how many hours h it takes the starfish to go down 6 feet We can solve this equation by multiplying each side by 23 Since starfish 4 hours to descend 6 feet 190 2 3 6 4 we know it will take the 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 16 Date GRADE 7 MISSION 5 LESSON 16 Exit Ticket A balloon is floating above a lake and a sunken canoe is below the surface of the lake The balloon s vertical position is 12 meters and the canoe s is 4 8 meters The equation 12 d 4 8 represents this situation 1 What does the variable d represent 2 What value of d makes the equation true 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 191

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ZEARN MATH STUDENT EDITION G7M5 LESSON 17 Lesson 17 The Stock Market Let s learn about the Stock Market Warm Up 1 Answer these percentage questions 1 Lin deposited 300 in a savings account that has a 2 interest rate per year How much is in her account after 1 year After 2 years 2 Diego wants to sell his bicycle It cost 150 when he bought it but has depreciated by 15 How much should he sell it for 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 17 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Here is some information from the stock market in September 2016 Complete the table Company Value on day 1 dollars Value on day 2 dollars Change in value dollars Change in value as a percentage of day 1 value Mobile Tech Company 107 95 111 77 3 82 3 54 114 03 2 43 2 18 Electrical Appliance Company Oil Corporation 26 14 25 14 Department Store Company 7 38 7 17 Jewelry Company 194 70 30 2 Which company s change in dollars had the largest magnitude 3 Which company s change in percentage had the largest magnitude 3 83 2 27 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M5 LESSON 17 ACTIVITY 2 3 1 2 3 A person who wants to make money by investing in the stock market usually buys a portfolio or a collection of different stocks That way if one of the stocks decreases in value they won t lose all of their money at once Here is an example of someone s stock portfolio Complete the table to show the total value of each investment Name Price dollars Number of shares Technology Company 107 75 98 Airline Company 133 54 27 Film Company 95 95 135 Sports Clothing Company 58 96 100 Total value dollars Here is the same portfolio the next year Complete the table to show the new total value of each investment Company Old price dollars Price change New price dollars Number of shares Technology Company 107 75 2 43 98 Airline Company 133 54 7 67 27 Film Company 95 95 Sports Clothing Company 58 96 87 58 5 56 Total value dollars 135 100 Did the entire portfolio increase or decrease in value over the year 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M5 LESSON 17 ZEARN MATH STUDENT EDITION ACTIVITY 3 196 43 Your teacher will give you a list of stocks Select a combination of stocks with a total value close to but no more than 100 53 Your teacher will give you a new list Using the new list how did the total value of your selected stocks change 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 6 Expressions Equations and Inequalities

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ZEARN MATH STUDENT EDITION G7M6 LESSON 1 Lesson 1 Relationships between Quantities Let s try to solve some new kinds of problems Warm Up 1 A movie theater sells popcorn in bags of different sizes The table shows the volume of popcorn and the price of the bag Complete one column of the table with prices where popcorn is priced at a constant rate That is the amount of popcorn is proportional to the price of the bag Then complete the other column with realistic example prices where the amount of popcorn and price of the bag are not in proportion Volume of Popcorn ounces Price of Bag Proportional Price of Bag not Proportional 10 6 6 20 35 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 199

G7M6 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 200 A state park charges an entrance fee based on the number of people in a vehicle A car containing 2 people is charged 14 a car containing 4 people is charged 20 and a van containing 8 people is charged 32 1 How much do you think a bus containing 30 people would be charged 2 If a bus is charged 122 how many people do you think it contains 3 What rule do you think the state park uses to decide the entrance fee for a vehicle 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 1 Lesson Summary In much of our previous work that involved relationships between two quantities we were often able to describe amounts as being so much more than another or so many times as much as another We wrote equations like x 3 8 and 4x 20 and solved for unknown amounts Number of pies Total cost in dollars 1 13 2 23 3 33 5 53 In this mission we will see situations where relationships between amounts involve more operations For example a pizza store might charge the amounts shown in the table for delivering pies We can see that each additional pie adds 10 to the total cost and that each total includes a 3 additional cost maybe representing a delivery fee In this situation 8 pies will cost 8 10 3 and a total cost of 63 means 6 pies were ordered In this mission we will see many situations like this one and will learn how to use diagrams and equations to answer questions about unknown amounts 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 201

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ZEARN MATH STUDENT EDITION G7M6 LESSON 1 Name Date GRADE 7 MISSION 6 LESSON 1 Exit Ticket A movie theater sells popcorn in bags of different sizes The table shows the volume of popcorn and the price of the bag Volume of Popcorn ounces Price of Bag 10 6 20 8 35 11 48 13 6 If the theater wanted to offer a 60 ounce bag of popcorn what would be a good price 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 203

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ZEARN MATH STUDENT EDITION G7M6 LESSON 2 Lesson 2 Reasoning about Contexts with Tape Diagrams Part 1 Let s use tape diagrams to make sense of different kinds of stories Warm Up 1 Answer the questions about the following tape diagrams C a b a b a b a b x y Z x x x 1 What do you notice What do you wonder 2 What are some possible values for a b and c in the first diagram For x y and z in the second diagram How did you decide on those values 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 2 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Here are three stories with a diagram that represents it With your group decide who will go first That person explains why the diagram represents the story Work together to find any unknown amounts in the story Then switch roles for the second diagram and switch again for the third Mai made 50 flyers for five volunteers in her club to hang up around school She gave 5 flyers to the first volunteer 18 flyers to the second volunteer and divided the remaining flyers equally among the three remaining volunteers 5 18 x x x 50 2 To thank her five volunteers Mai gave each of them the same number of stickers Then she gave them each two more stickers Altogether she gave them a total of 30 stickers y 2 y 2 y 2 y 2 y 2 30 3 Mai distributed another group of flyers equally among the five volunteers Then she remembered that she needed some flyers to give to teachers so she took 2 flyers from each volunteer Then the volunteers had a total of 40 flyers to hang up w 2 w 2 w 2 w 2 w 2 40 206 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 2 ACTIVITY 2 3 Here are three more stories Draw a tape diagram to represent each story Then describe how you would find any unknown amounts in the stories 1 Noah and his sister are making gift bags for a birthday party Noah puts 3 pencil erasers in each bag His sister puts x stickers in each bag After filling 4 bags they have used a total of 44 items 2 Noah s family also wants to blow up a total of 60 balloons for the party Yesterday they blew up 24 balloons Today they want to split the remaining balloons equally between four family members 3 Noah s family bought some fruit bars to put in the gift bags They bought one box each of four flavors apple strawberry blueberry and peach The boxes all had the same number of bars Noah wanted to taste the flavors and ate one bar from each box There were 28 bars left for the gift bags 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 2 ZEARN MATH STUDENT EDITION Lesson Summary Tape diagrams are useful for representing how quantities are related and can help us answer questions about a situation Suppose a school receives 46 copies of a popular book The library takes 26 copies and the remainder are split evenly among 4 teachers How many books does each teacher receive This situation involves 4 equal parts and one other part We can represent the situation with a rectangle labeled 26 books given to the library along with 4 equal sized parts books split among 4 teachers We label the total 46 to show how many the rectangle represents in all We use a letter to show the unknown amount which represents the number of books each teacher receives Using the same letter x means that the 46 same number is represented four times Some situations have parts that are all equal but each part has been increased from an original amount 26 x x x x A company manufactures a special type of sensor and packs them in boxes of 4 for shipment Then a new design increases the weight of each sensor by 9 grams The new package of 4 sensors weighs 76 grams How much did each sensor weigh originally We can describe this situation with a rectangle representing a total of 76 split into 4 equal parts Each part shows that the new weight x 9 is 9 more than the original weight x 208 76 x 9 x 9 x 9 x 9 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 2 Name Date GRADE 7 MISSION 6 LESSON 2 Exit Ticket Here is a story Lin bought 4 bags of apples Each bag had the same number of apples After eating 1 apple from each bag she had 28 apples left A B 28 x 1 x 1 x 1 C x 1 x 1 28 1 x 1 x x 1 x x x x 1 28 1 Which diagram best represents the story Explain why the diagram represents it 2 What part of the story does x represent 3 Describe how you would find the unknown amount in the story 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M6 LESSON 3 Lesson 3 Reasoning about Contexts with Tape Diagrams Part 2 Let s see how equations can describe tape diagrams Warm Up 1 Select all the expressions that are equivalent to 7 2 3n Explain how you know each expression you select is equivalent 1 9 10n 2 14 3n 3 14 21n 4 2 3n 7 5 7 2 3n 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 3 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Answer the questions about the tape diagrams 2 B A 5 x C x x 5 x D x x x 19 x 5 x 2 19 212 x E x 5 2 x 19 19 1 2 x 2 x 2 x 2 x 2 19 Match each equation to one of the tape diagrams Be prepared to explain how the equation matches the diagram 2x 5 19 x 5 2 19 2 5x 19 19 x 2 5 2 x 5 19 19 2 x 5 5 x 2 19 19 2 5x 19 5 2x Sort the equations into categories of your choosing Explain the criteria for each category 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 3 ACTIVITY 2 3 Use the equations below to answer the questions 114 3x 18 114 3 y 18 1 Draw a tape diagram to match each equation 2 Use any method to find values for x and y that make the equations true 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 3 ZEARN MATH STUDENT EDITION Lesson Summary We have seen how tape diagrams represent relationships between quantities Because of the meaning and properties of addition and multiplication more than one equation can often be used to represent a single tape diagram Let s take a look at two tape diagrams 46 x 26 x x x We can describe this diagram with several different equations Here are some of them 26 4x 46 because the parts add up to the whole 4x 26 46 because addition is commutative 46 4x 26 because if two quantities are equal it doesn t matter how we arrange them around the equal sign 4x 46 26 because one part the part made up of 4 x s is the difference between the whole and the other part 76 x 9 x 9 x 9 x 9 For this diagram 214 4 x 9 76 because multiplication means having multiple groups of the same size x 9 4 76 because multiplication is commutative 76 4 x 9 because division tells us the size of each equal part 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 3 Name Date GRADE 7 MISSION 6 LESSON 3 Exit Ticket 1 Circle the equation that the diagram does not match 2 Then draw a diagram that matches the equation you circled 30 6 6 3x 30 3 x 6 30 3x 30 6 30 3x 6 x x x 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 215

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ZEARN MATH STUDENT EDITION G7M6 LESSON 4 Lesson 4 Reasoning about Equations and Tape Diagrams Part 1 Let s see how tape diagrams can help us answer questions about unknown amounts in stories Warm Up 1 Find a solution to each equation without writing anything down x 1 5 2 x 1 10 3 x 1 15 500 100 x 1 Concept Exploration ACTIVITY 1 2 Draw a tape diagram to represent each situation For some of the situations you need to decide what to represent with a variable 1 Diego has 7 packs of markers Each pack has x markers in it After Lin gives him 9 more markers he has a total of 30 markers 2 Elena is cutting a 30 foot piece of ribbon for a craft project She cuts off 7 feet and then cuts the remaining piece into 9 equal lengths of x feet each 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 4 ZEARN MATH STUDENT EDITION 3 A construction manager weighs a bundle of 9 identical bricks and a 7 pound concrete block The bundle weighs 30 pounds 4 A skating rink charges a group rate of 9 plus a fee to rent each pair of skates A family rents 7 pairs of skates and pays a total of 30 5 Andre bakes 9 pans of brownies He donates 7 pans to the school bake sale and keeps the rest to divide equally among his class of 30 students ACTIVITY 2 3 218 Each situation in the previous activity is represented by one of the equations Use the equations to answer the questions 7x 9 30 30 9x 7 30x 7 9 1 Match each situation to an equation 2 Find the solution to each equation Use your diagrams to help you reason 3 What does each solution tell you about its 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 G7M6 LESSON 4 Lesson Summary Many situations can be represented by equations Writing an equation to represent a situation can help us express how quantities in the situation are related to each other and can help us reason about unknown quantities whose value we want to know Here are three situations 1 An architect is drafting plans for a new supermarket There will be a space 144 inches long for rows of nested shopping carts The first cart is 34 inches long and each nested cart adds another 10 inches The architect wants to know how many shopping carts will fit in each row 2 A bakery buys a large bag of sugar that has 34 cups They use 10 cups to make some cookies Then they use the rest of the bag to make 144 giant muffins Their customers want to know how much sugar is in each muffin 3 Kiran is trying to save 144 to buy a new guitar He has 34 and is going to save 10 a week from money he earns mowing lawns He wants to know how many weeks it will take him to have enough money to buy the guitar We see the same three numbers in the situations 10 34 and 144 How could we represent each situation with an equation In the first situation there is one shopping cart with length 34 and then an unknown number of carts with length 10 Similarly Kiran has 34 dollars saved and then will save 10 each week for an unknown number of weeks Both situations have one part of 34 and then equal parts of size 10 that all add together to 144 Their equation is 34 10x 144 Since it takes 11 groups of 10 to get from 34 to 144 the value of x in these two situations is 144 34 10 or 11 There will be 11 shopping carts in each row and it will take Kiran 11 weeks to raise the money for the guitar In the bakery situation there is one part of 10 and then 144 equal parts of unknown size that all add together to 34 The equation is 10 144x 34 Since 24 is needed to get from 10 to 34 the value of x is 34 10 144 or 16 There is 16 cup of sugar in each giant muffin 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M6 LESSON 4 Name Date GRADE 7 MISSION 6 LESSON 4 Exit Ticket Here is a diagram and its corresponding equation Find the solution to the equation and explain your reasoning 23 x x x x 17 4x 17 23 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M6 LESSON 5 Lesson 5 Reasoning about Equations and Tape Diagrams Part 2 Let s use tape diagrams to help answer questions about situations where the equation has parentheses Warm Up 1 Solve each equation mentally x 1 5 2 x 1 10 3 x 1 15 500 100 x 1 Concept Exploration ACTIVITY 1 2 Draw a tape diagram to represent each situation For some of the situations you need to decide what to represent with a variable 1 Each of 5 gift bags contains x pencils Tyler adds 3 more pencils to each bag Altogether the gift bags contain 20 pencils 2 Noah drew an equilateral triangle with sides of length 5 inches He wants to increase the length of each side by x inches so the triangle is still equilateral and has a perimeter of 20 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 223

G7M6 LESSON 5 ZEARN MATH STUDENT EDITION 3 An art class charges each student 3 to attend plus a fee for supplies Today 20 was collected for the 5 students attending the class 4 Elena ran 20 miles this week which was three times as far as Clare ran this week Clare ran 5 more miles this week than she did last week ACTIVITY 2 3 224 Each situation in the previous activity is represented by one of the equations Use the equations to answer the questions x 3 5 20 3 x 5 20 1 Match each situation to an equation 2 Find the solution to each equation Use your diagrams to help you reason 3 What does each solution tell you about its 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 G7M6 LESSON 5 Lesson Summary Equations with parentheses can represent a variety of situations 1 Lin volunteers at a hospital and is preparing toy baskets for children who are patients She adds 2 items to each basket after which the supervisor s list shows that 140 toys have been packed into a group of 10 baskets Lin wants to know how many toys were in each basket before she added the items 2 A large store has the same number of workers on each of 2 teams to handle different shifts They decide to add 10 workers to each team bringing the total number of workers to 140 An executive at the company that runs this chain of stores wants to know how many employees were in each team before the increase Each basket in the first story has an unknown number of toys x that is increased by 2 Then ten groups of x 2 give a total of 140 toys An equation representing this situation is 10 x 2 140 Since 10 times a number is 140 that number is 14 which is the total number of items in each basket Before Lin added the 2 items there were 14 2 or 12 toys in each basket The executive in the second story knows that the size of each team of employees has been increased by 10 There are now 2 teams of y 10 each An equation representing this situation is 2 y 10 140 Since 2 times an amount is 140 that amount is 70 which is the new size of each team The value of y is 70 10 or 60 There were 60 employees on each team before the increase 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 225

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ZEARN MATH STUDENT EDITION G7M6 LESSON 5 Name Date GRADE 7 MISSION 6 LESSON 5 Exit Ticket Here is a diagram and its corresponding equation Find the solution to the equation and explain your reasoning 38 x 7 x 7 x 7 x 7 4 x 7 38 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M6 LESSON 6 Lesson 6 Distinguishing between Two Types of Situations Let s think about equations with and without parentheses and the kinds of situations they describe Warm Up Which equation doesn t belong 1 4 x 3 9 4 3x 9 4 x 12 9 9 12 4x Concept Exploration ACTIVITY 1 2 Your teacher will give you a set of cards that show equations Sort the cards into 2 categories of your choosing Be prepared to explain the meaning of your categories Then sort the cards into 2 categories in a different way Be prepared to explain the meaning of your new categories 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 6 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Use the tape diagrams to answer the questions B A x x x 12 y 12 90 y 12 y 12 90 Story 1 Lin had 90 flyers to hang up around the school She gave 12 flyers to each of three volunteers Then she took the remaining flyers and divided them up equally between the three volunteers Story 2 Lin had 90 flyers to hang up around the school After giving the same number of flyers to each of three volunteers she had 12 left to hang up by herself 230 1 Which diagram goes with which story Be prepared to explain your reasoning 2 In each diagram what part of the story does the variable represent 3 Write an equation corresponding to each story If you get stuck use the diagram 4 Find the value of the variable in the story 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 6 Lesson Summary In this mission we encounter two main types of situations that can be represented with an equation Here is an example of each type 1 After adding 8 students to each of 6 same sized teams there were 72 students altogether 2 After adding an 8 pound box of tennis rackets to a crate with 6 identical boxes of ping pong paddles the crate weighed 72 pounds The first situation has all equal parts since additions are made to each team An equation that represents this situation is 6 x 8 72 where x represents the original number of students on each team Eight students were added to each group there are 6 groups and there are a total of 72 students In the second situation there are 6 equal parts added to one other part An equation that represents this situation is 6x 8 72 where x represents the weight of a box of ping pong paddles There are 6 boxes of ping pong paddles there is an additional box that weighs 8 pounds and the crate weighs 72 pounds altogether In the first situation there were 6 equal groups and 8 students added to each group 6 x 8 72 In the second situation there were 6 equal groups but 8 more pounds in addition to that 6x 8 72 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 6 Date GRADE 7 MISSION 6 LESSON 6 Exit Ticket Write an equation for each story Then find the number of problems originally assigned by each teacher You may consider drawing a diagram to represent the story 1 Five students came for after school tutoring Lin s teacher assigned each of them the same number of problems to complete Then he assigned each student 2 more problems 30 problems were assigned in all 2 Five students came for after school tutoring Priya s teacher assigned each of them the same number of problems to complete Then she assigned 2 more problems to one of the students 27 problems were assigned in all 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 233

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ZEARN MATH STUDENT EDITION G7M6 LESSON 7 Lesson 7 Reasoning about Solving Equations Part 1 Let s see how a balanced hanger is like an equation and how moving its weights is like solving the equation Warm Up 1 In the two diagrams all the triangles weigh the same and all the squares weigh the same For each diagram come up with 1 One thing that must be true 2 One thing that could be true 3 One thing that cannot possibly be true 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 7 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 On each balanced hanger figures with the same letter have the same weight 2 1 Match each hanger to an equation Complete the equation by writing x y z or w in the empty box 2 Find the solution to each equation Use the hanger to explain what the solution means A B w 1 C D z 1 x 1 1 y x 1 1 y 1 1 1 1 1 1 1 1 w z 1 1 w 1 1 x 1 1 1 1 1 1 1 1 1 1 1 1 2 236 3 5 3 2 3 6 2 3 7 3 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

ZEARN MATH STUDENT EDITION G7M6 LESSON 7 ACTIVITY 2 3 Here are some balanced hangers where each piece is labeled with its weight For each diagram 1 Write an equation 2 Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram 3 Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation A B w 7 C D z y w y w 10 6 8 31 w z w 2 2 17 2 w 1 w 3 2 Lesson Summary In this lesson we worked with two ways to show that two amounts are equal a balanced hanger and an equation We can use a balanced hanger to think about steps to finding an unknown amount in an associated equation The hanger shows a total weight of 7 units on one side that is balanced with 3 equal unknown weights and a 1 unit weight on the other An equation that represents the relationship is 7 3x 1 1 x 1 x 1 x 1 7 3x 1 1 1 1 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 237

G7M6 LESSON 7 ZEARN MATH STUDENT EDITION We can remove a weight of 1 unit from each side and the hanger will stay balanced This is the same as subtracting 1 from each side of the equation 1 x 1 x 1 x 1 7 1 3x 1 1 1 1 1 1 An equation for the new balanced hanger is 6 3x 1 x 1 x 1 x 6 3x 1 1 1 So the hanger will balance with side 13 6 13 3x 1 3 of the weight on each 1 x 6 3x 1 1 1 1 x x 1 The two sides of the hanger balance with these weights two 1 unit weights on one side and one weight of unknown size on the other so the unknown weight is equivalent to 2 1 x 2 x 1 Here is a concise way to write the steps above 7 3x 1 238 6 3x after subtracting 1 from each side 2 x after multiplying each side by 1 3 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M6 LESSON 7 Name Date GRADE 7 MISSION 6 LESSON 7 Exit Ticket Solve the equation You may consider using a diagram to help you 5x 1 4 61 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 239

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ZEARN MATH STUDENT EDITION G7M6 LESSON 8 Lesson 8 Reasoning about Solving Equations Part 2 Let s use hangers to understand two different ways of solving equations with parentheses Warm Up 1 Select all the expressions equivalent to 2 x 3 1 2 x 3 4 2 x 3 2 x 3 2 5 2 x 3 3 2 x 2 3 6 x 2 3 Concept Exploration ACTIVITY 1 2 1 Use the hanger diagram and equations below to solve the following problems Explain why either of these equations could represent this hanger 14 2 x 3 or 14 2x 6 x 3 14 x 3 2 Find the weight of one circle 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 241

G7M6 LESSON 8 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Here are some balanced hangers Each piece is labeled with its weight x 5 16 y z 200 1 1 x y 5 200 16 3000 20 8 z 1 1 y z 200 1 1 w 2 3 20 3 w 2 3 z 1 1 For each diagram 1 242 Assign one of these equations to each hanger 2 x 5 16 3 y 200 3 000 20 8 4 z 1 1 20 3 2 w 2 3 2 Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram 3 Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 8 Lesson Summary The balanced hanger shows 3 equal unknown weights and 3 2 unit weights on the left and an 18 unit weight on the right There are 3 unknown weights plus 6 units of weight on the left We could represent this balanced hanger with an equation and solve the equation the same way we did before x 2 x 2 3x 6 18 3x 12 x 4 18 x 2 x Since there are 3 groups of x 2 on the left we could represent this hanger with a different equation 3 x 2 18 2 x 2 18 3 x 2 18 18 3 x 2 18 x 2 The two sides of the hanger balance with these weights 3 groups of x 2 on one side and 18 or 3 groups of 6 on the other side x 2 x 2 x 2 The two sides of the hanger will balance with each side 13 3 x 2 13 18 1 3 of the weight on x 2 6 x 2 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 243

G7M6 LESSON 8 ZEARN MATH STUDENT EDITION We can remove 2 units of weight from each side and the hanger will stay balanced This is the same as subtracting 2 from each side of the equation x 4 2 An equation for the new balanced hanger is x 4 This gives the solution to the original equation 2 x 4 x 2 4 2 x 4 Here is a concise way to write the steps above 3 x 2 18 x 2 6 after multiplying each side by 13 x 4 after subtracting 2 from each side 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 G7M6 LESSON 8 Name Date GRADE 7 MISSION 6 LESSON 8 Exit Ticket Solve the equation 3 x 4 5 36 You may consider using the diagram to help you x 4 5 x 4 5 36 x 4 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 245

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ZEARN MATH STUDENT EDITION G7M6 LESSON 9 Lesson 9 Dealing with Negative Numbers Let s show that doing the same to each side works for negative numbers too Warm Up 1 Which equation doesn t belong 15 5 3 4 2 6 2 5 3 3 4 12 Concept Exploration ACTIVITY 1 2 Solve each equation Be prepared to explain your reasoning 1 x 6 4 2 x 4 6 3 2 x 1 200 4 2x 3 23 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 9 ZEARN MATH STUDENT EDITION ACTIVITY 2 Here are some equations that all have the same solution Explain how you know that each equation has the same solution as the previous equation 3 x x 3 9 900 900 900 43 248 6 9 x 3 100 x 3 x 3 100 100x 300 Keep your work secret from your partner Start with the equation 5 x Follow the directions below 1 Do the same thing to each side at least three times to create an equation that has the same solution as the starting equation Write the equation you ended up with on a slip of paper and trade equations with your partner 2 See if you can figure out what steps they used to transform 5 x into their equation When you think you know check with them to see if you are right 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 9 Lesson Summary When we want to find a solution to an equation sometimes we just think about what value in place of the variable would make the equation true Sometimes we perform the same operation on each side for example subtract the same amount from each side The balanced hangers helped us to understand that doing the same to each side of an equation keeps the equation true Since negative numbers are just numbers then doing the same thing to each side of an equation works for negative numbers as well Here are some examples of equations that have negative numbers and steps you could take to solve them Example 1 2 2 x 5 6 2 x 5 12 6 x 5 3 x 5 5 3 5 x 2 multiply each side by 1 2 add 5 to each side Example 2x 5 6 2x 5 5 6 5 2x 11 2x 2 11 2 x 11 2 subtract 5 from each side divide each side by 2 Doing the same thing to each side maintains equality even if it is not helpful to solving for the unknown amount For example we could take the equation 3x 7 8 and add to each side 3x 7 8 3x 7 2 8 2 3x 5 10 add 2 to each side If 3x 7 8 is true then 3x 5 10 is also true but we are no closer to a solution than we were before adding 2 We can use moves that maintain equality to make new equations that all have the same solution Helpful combinations of moves will eventually lead to an equation like x 5 which gives the solution to the original equation and every equation we wrote in the process of solving 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 249

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 9 Date GRADE 7 MISSION 6 LESSON 9 Exit Ticket Solve each equation Show your work or explain your reasoning 1 3x 5 16 2 4 y 2 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 251

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ZEARN MATH STUDENT EDITION G7M6 LESSON 10 Lesson 10 Different Options for Solving One Equation Let s think about which way is easier when we solve equations with parentheses Warm Up 1 Solve each equation 100 x 3 1 000 500 x 3 5 000 0 03 x 3 0 3 0 72 x 2 7 2 1 7 x 2 10 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 253

G7M6 LESSON 10 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Three students each attempted to solve the equation 2 x 9 10 but got different solutions Here are their methods Do you agree with any of their methods and why Noah s method 2 x 9 10 2 x 9 9 10 9 2x 19 2x 2 19 2 x add 9 to each side divide each side by 2 19 2 Elena s method 2 x 9 10 2x 18 10 2x 18 18 10 18 2x 8 2x 2 8 2 x 4 apply the distributive property subtract 18 from each side divide each side by 2 Andre s method 2 x 9 10 2x 18 10 2x 18 18 10 18 2x 28 2x 2 28 2 x 14 254 apply the distributive property add 18 to each side divide each side by 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 G7M6 LESSON 10 ACTIVITY 2 3 For each equation try to solve the equation using each method dividing each side first or applying the distributive property first Some equations are easier to solve by one method than the other When that is the case stop doing the harder method and write down the reason you stopped 1 2 000 x 0 03 6 000 2 2 x 1 25 3 5 3 1 4 4 x 4 3 4 10 x 1 7 3 5 5 4 0 3 x 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 255

G7M6 LESSON 10 ZEARN MATH STUDENT EDITION Lesson Summary Equations can be solved in many ways In this lesson we focused on equations with a specific structure and two specific ways to solve them Suppose we are trying to solve the equation 4 5 x 27 16 Two useful approaches are 4 5 divide each side by apply the distributive property In order to decide which approach is better we can look at the numbers and think about which would be easier to compute We notice that 45 27 will be hard because 27 isn t divisible by 5 But 16 45 gives us 16 54 and 16 is divisible by 4 Dividing each side by 45 gives 5 4 4 5 4 5 x 27 16 x 27 16 x 27 20 x 7 5 4 Sometimes the calculations are simpler if we first use the distributive property Let s look at the 21 equation 100 x 0 06 21 If we first divide each side by 100 we get 100 or 0 21 on the right side of the equation But if we use the distributive property first we get an equation that only contains whole numbers 100 x 0 06 21 100x 6 21 100x 15 15 x 100 256 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 Name G7M6 LESSON 10 Date GRADE 7 MISSION 6 LESSON 10 Exit Ticket Solve each equation Show or explain your method 1 8 88 4 44 x 7 2 5 y 2 5 13 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 257

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ZEARN MATH STUDENT EDITION G7M6 LESSON 11 Lesson 11 Using Tape Diagrams and Equations to Solve Problems Let s use tape diagrams equations and reasoning to solve problems Warm Up 1 Use the tape diagram to answer the questions 24 a a 2 2 a 2 a 2 a 2 a 2 1 Write a story that could be represented by this tape diagram 2 Write an equation that could be represented by this tape diagram 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 259

G7M6 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Tyler is making invitations to the state fair He has already made some of the invitations and he wants to finish the rest of them within a week He is trying to spread out the remaining work to make the same number of invitations each day Tyler draws a diagram to represent the situation Answer the questions below 122 x x x x x x x 66 a Explain how each part of the situation is represented in Tyler s diagram How many total invitations Tyler is trying to make How many invitations he has made already How many days he has to finish the invitations b How many invitations should Tyler make each day to finish his goal within a week Explain or show your reasoning c Use Tyler s diagram to write an equation that represents the situation Explain how each part of the situation is represented in your equation d Show how to solve your equation 260 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 11 Noah and his sister are making prize bags for a game at the fair Noah is putting 7 pencil erasers in each bag His sister is putting in some number of stickers After filling 3 of the bags they have used a total of 57 items Answer the questions below 57 x 7 x 7 x 7 a Explain how the diagram represents the situation b Noah writes the equation 3 x 7 57 to represent the situation Do you agree with him Explain your reasoning c 43 How many stickers is Noah s sister putting in each prize bag Explain or show your reasoning A family of 6 is going to the fair They have a coupon for 1 50 off each ticket If they pay 46 50 for all their tickets how much does a ticket cost without the coupon Explain or show your reasoning If you get stuck consider drawing a diagram or writing an equation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 11 ZEARN MATH STUDENT EDITION ACTIVITY 2 53 1 Priya Han and Elena are members of the running club at school Answer the question s below Priya was busy studying this week and ran 7 fewer miles than last week She ran 9 times as far as Elena ran this week Elena only had time to run 4 miles this week a How many miles did Priya run last week 1 b Elena wrote the equation 9 x 7 4 to describe the situation She solved the equation by multiplying each side by 9 and then adding 7 to each side How does her solution compare to the way you found Priya s miles 262 5 2 One day last week 6 teachers joined 7 of the members of the running club in an after school run Priya counted a total of 31 people running that day How many members does the running club have 3 Priya and Han plan a fundraiser for the running club They begin with a balance of 80 because of expenses In the first hour of the fundraiser they collect equal donations from 9 parents which brings their balance to 44 How much did each parent give 4 The running club uses the money they raised to pay for a trip to a canyon At one point during a run in the canyon the students are at an elevation of 128 feet After descending at a rate of 50 feet per minute they reach an elevation of 472 feet How long did the descent take 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 11 Lesson Summary Many problems can be solved by writing and solving an equation Here is an example Clare ran 4 miles on Monday Then for the next six days she ran the same distance each day She ran a total of 22 miles during the week How many miles did she run on each of the 6 days One way to solve the problem is to represent the situation with an equation 4 6x 22 where x represents the distance in miles she ran on each of the 6 days Solving the equation gives the solution to this problem 4 6x 22 6x 18 x 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 263

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 11 Date GRADE 7 MISSION 6 LESSON 11 Exit Ticket Diego scored 9 points less than Andre in the basketball game Noah scored twice as many points as Diego If Noah scored 10 points how many points did Andre score 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 265

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ZEARN MATH STUDENT EDITION G7M6 LESSON 12 Lesson 12 Solving Problems about Percent Increase or Decrease Let s use tape diagrams equations and reasoning to solve problems with negatives and percents Warm Up 1 An item costs x dollars and then a 20 discount is applied Select all the expressions that could represent the price of the item after the discount 4 100 20 100 x 2 20 100 x 20 x 100 x 5 0 80x 3 1 0 20 x 6 100 20 x 1 Concept Exploration ACTIVITY 1 2 Mai started a new exercise program On the second day she walked 5 minutes more than on the first day On the third day she increased her walking time from day 2 by 20 and walked for 42 minutes Mai drew a diagram to show her progress day 1 d day 2 d 5 day 3 42 1 Explain how the diagram represents 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 267

G7M6 LESSON 12 2 Noah said the equation 1 20 d 5 42 also represents the situation Do you agree with Noah Explain your reasoning 3 Find the number of minutes Mai walked on the first day Did you use the diagram the equation or another strategy Explain or show your reasoning 3 1 268 ZEARN MATH STUDENT EDITION Mai has been walking indoors because of cold temperatures On Day 4 at noon Mai hears a report that the temperature is only 9 degrees Fahrenheit She remembers the morning news reporting that the temperature had doubled since midnight and was expected to rise 15 degrees by noon Mai is pretty sure she can draw a diagram to represent this situation but isn t sure if the equation is 9 15 2t or 2 t 15 9 What would you tell Mai about the diagram and the equation and how they might be useful to find the temperature t at midnight 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 12 ACTIVITY 2 43 A store is having a sale where all shoes are discounted by 20 1 Diego has a coupon for 3 off of the regular price for one pair of shoes The store first applies the coupon and then takes 20 off of the reduced price If Diego pays 18 40 for a pair of shoes what was their original price before the sale and without the coupon 2 Before the sale the store had 100 pairs of flip flops in stock After selling some they notice that 35 of the flip flops they have left are blue If the store has 39 pairs of blue flip flops how many pairs of flip flops any color have they sold 3 When the store had sold 29 of the boots that were on display they brought out another 34 pairs from the stock room If that gave them 174 pairs of boots out how many pairs were on display originally 4 On the morning of the sale the store donated 50 pairs of shoes to a homeless shelter Then they sold 64 of their remaining inventory during the sale If the store had 288 pairs after the donation and the sale how many pairs of shoes did they have at the start 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary We can solve problems where there is a percent increase or decrease by using what we know about equations For example a camping store increases the price of a tent by 25 A customer then uses a 10 coupon for the tent and pays 152 50 We can draw a diagram that shows first the 25 increase and then the 10 coupon original price p 25p 25 increase 10 10 coupon 152 50 The price after the 25 increase is p 0 25p or 1 25p An equation that represents the situation could be 1 25p 10 152 50 To find the original price before the increase and discount we can add 10 to each side and divide each side by 1 25 resulting in p 130 The original price of the tent was 130 270 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G7M6 LESSON 12 Date GRADE 7 MISSION 6 LESSON 12 Exit Ticket The track team is trying to reduce their time for a relay race First they reduce their time by 2 1 minutes Then they are able to reduce that time by 101 If their final time is 3 96 minutes what was their beginning time Show or 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 271

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ZEARN MATH STUDENT EDITION G7M6 LESSON 13 Lesson 13 Reintroducing Inequalities Let s work with inequalities Warm Up 1 The number line shows values of x that make the inequality x 1 true 5 1 4 3 2 1 0 1 2 3 4 5 Select all the values of x from this list that make the inequality x 1 true a 3 b 3 c 1 d 700 e 1 05 2 Name two more values of x that are solutions to the inequality Concept Exploration ACTIVITY 1 2 1 A sign next to a roller coaster at an amusement park says You must be at least 60 inches tall to ride Noah is happy to know that he is tall enough to ride Answer the following questions Noah is x inches tall Which of the following can be true x 60 x 60 or x 60 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 273

G7M6 LESSON 13 2 Noah s friend is 2 inches shorter than Noah Can you tell if Noah s friend is tall enough to go on the ride Explain or show your reasoning 3 List one possible height for Noah that means that his friend is tall enough to go on the ride and another that means that his friend is too short for the ride 4 On the number line below show all the possible heights that Noah s friend could be 52 5 274 ZEARN MATH STUDENT EDITION 54 56 58 60 62 64 66 68 Noah s friend is y inches tall Use y and any of the symbols to express this height 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 13 ACTIVITY 2 3 The table shows four inequalities and four possible values for x Decide whether each value makes each inequality true and complete the table with true or false Discuss your thinking with your partner If you disagree work to reach an agreement x 0 100 100 25 x 25 100 4x 3x 75 10 35 x 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 275

G7M6 LESSON 13 ZEARN MATH STUDENT EDITION Lesson Summary We use inequalities to describe a range of numbers In many places you are allowed to get a driver s license when you are at least 16 years old When checking if someone is old enough to get a license we want to know if their age is at least 16 If h is the age of a person then we can check if they are allowed to get a driver s license by checking if their age makes the inequality h 16 they are older than 16 or the equation h 16 they are 16 true The symbol pronounced greater than or equal to combines these two cases and we can just check if h 16 their age is greater than or equal to 16 The inequality h 16 can be represented on a number line 0 276 4 8 12 16 20 24 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 Name G7M6 LESSON 13 Date GRADE 7 MISSION 6 LESSON 13 Exit Ticket Here is an inequality 2x 10 1 List some values for x that would make this inequality true Consider substituting values of x to see which values make the inequality true For example you could substitute 10 5 0 5 10 2 How are the solutions to the inequality 2x 10 different from the solutions to 2x 10 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 277

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ZEARN MATH STUDENT EDITION G7M6 LESSON 14 Lesson 14 Finding Solutions to Inequalities in Context Let s solve more complicated inequalities Warm Up 1 Answer the following questions 1 Solve x 10 2 Find 2 solutions to x 10 3 Solve 2x 20 4 Find 2 solutions to 2x 20 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 279

G7M6 LESSON 14 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Andre has a summer job selling magazine subscriptions He earns 25 per week plus 3 for every subscription he sells Andre hopes to make at least enough money this week to buy a new pair of soccer cleats a Let n represent the number of magazine subscriptions Andre sells this week Write an expression for the amount of money he makes this week b The least expensive pair of cleats Andre wants costs 68 Write and solve an equation to find out how many magazine subscriptions Andre needs to sell to buy the cleats c If Andre sold 16 magazine subscriptions this week would he reach his goal Explain your reasoning d What are some other numbers of magazine subscriptions Andre could have sold and still reached his goal e Write an inequality expressing that Andre wants to make at least 68 f 280 Write an inequality to describe the number of subscriptions Andre must sell to reach his goal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 3 G7M6 LESSON 14 Diego has budgeted 35 from his summer job earnings to buy shorts and socks for soccer He needs 5 pairs of socks and a pair of shorts The socks cost different amounts in different stores The shorts he wants cost 19 95 a Let x represent the price of one pair of socks Write an expression for the total cost of the socks and shorts b Write and solve an equation that says that Diego spent exactly 35 on the socks and shorts c List some other possible prices for the socks that would still allow Diego to stay within his budget d Write an inequality to represent the amount Diego can spend on a single pair of socks 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G7M6 LESSON 14 ZEARN MATH STUDENT EDITION ACTIVITY 2 43 Kiran has 100 saved in a bank account The account doesn t earn interest He asked Clare to help him figure out how much he could take out each month if he needs to have at least 25 in the account a year from now a Clare wrote the inequality 12x 100 25 where x represents the amount Kiran takes out each month What does 12x represent b Find some values of x that would work for Kiran c We could express all the values that would work using either x one should we use or x Which d Write the answer to Kiran s question using mathematical notation 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 53 G7M6 LESSON 14 A teacher wants to buy 9 boxes of granola bars for a school trip Each box usually costs 7 but many grocery stores are having a sale on granola bars this week Different stores are selling boxes of granola bars at different discounts a If x represents the dollar amount of the discount then the amount the teacher will pay can be expressed as 9 7 x In this expression what does the quantity 7 x represent b The teacher has 36 to spend on the granola bars The equation 9 7 x 36 represents a situation where she spends all 36 Solve this equation c What does the solution mean in this situation d The teacher does not have to spend all 36 Write an inequality relating 36 and 9 7 x representing this situation e The solution to this inequality must either look like x 3 or x 3 Which do you think it is 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 283

G7M6 LESSON 14 ZEARN MATH STUDENT EDITION Lesson Summary Suppose Elena has 5 and sells pens for 1 50 each Her goal is to save 20 We could solve the equation 1 5x 5 20 to find the number of pens x that Elena needs to sell in order to save exactly 20 Adding 5 to both sides of the equation gives us 1 5x 15 and then dividing both sides by 1 5 gives the solution x 10pens What if Elena wants to have some money left over The inequality 1 5x 5 20 tells us that the amount of money Elena makes needs to be greater than 20 The solution to the previous equation will help us understand what the solutions to the inequality will be We know that if she sells 10 pens she will make 20 Since each pen gives her more money she needs to sell more than 10 pens to make more than 20 So the solution to the inequality is x 10 284 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 14 Date GRADE 7 MISSION 6 LESSON 14 Exit Ticket It is currently 0 degrees outside and the temperature is dropping 4 degrees every hour The temperature after h hours is 4h 1 Explain what the equation 4h 14 represents 2 What value of h makes the equation true 3 Explain what the inequality 4h 14 represents 4 What values of h make the inequality true 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G7M6 LESSON 15 Lesson 15 Efficiently Solving Inequalities Let s solve more complicated inequalities Warm Up 1 Answer the questions about the inequality Here is an inequality x 4 1 Predict what you think the solutions on the number line will look like 2 Select all the values that are solutions to x 4 3 a 3 d 4 b 3 e 4 001 c f 4 4 001 Graph the solutions to the inequality on the number line 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 287

G7M6 LESSON 15 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Let s investigate the inequality x 3 2 x 4 x 3 7 3 2 1 0 1 5 2 3 1 4 1 a Complete the table b For which values of x is it true that x 3 2 c For which values of x is it true that x 3 2 d Graph the solutions to x 3 2 on the number line 3 Here is an inequality 2x 6 a Predict which values of x will make the inequality 2x 6 true b Complete the table Does it match your prediction x 4 3 2 1 0 1 2 3 4 2x c 288 Graph the solutions to 2x 6 on the number line 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 43 G7M6 LESSON 15 Here is an inequality 2x 6 a Predict which values of x will make the inequality 2x 6 true b Complete the table Does it match your prediction x 4 3 2 1 0 1 2 3 4 2x c Graph the solutions to 2x 6 on the number line d How are the solutions to 2x 6 different from the solutions to 2x 6 ACTIVITY 2 53 Let s investigate 4x 5 25 a Solve 4x 5 25 b Is 4x 5 25 true when x is 0 What about when x is 7 What about when x is 7 c Graph the solutions to 4x 5 25 on the number line 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 289

G7M6 LESSON 15 Let s investigate 63 a Solve b Is c 4 3 x 3 23 3 x 3 23 3 x 3 23 3 true when x is 0 Graph the solutions to 73 290 4 3 4 3 ZEARN MATH STUDENT EDITION 4 3 x 3 23 3 on the number line Solve each inequality Then graph each solution on a number line 1 Solve the inequality 3 x 4 17 4 and graph the solutions on the number line 2 Solve the inequality 3 x 4 3 6 and graph the solutions on the number line 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G7M6 LESSON 15 Lesson Summary Here is an inequality 3 10 2x 18 The solution to this inequality is all the values you could use in place of x to make the inequality true In order to solve this we can first solve the related equation 3 10 2x 18 to get the solution x 2 That means 2 is the boundary between values of x that make the inequality true and values that make the inequality false To solve the inequality we can check numbers greater than 2 and less than 2 and see which ones make the inequality true Let s check a number that is greater than 2 x 5 Replacing x with 5 in the inequality we get 3 10 2 5 18 or just 0 18 This is true so x 5 is a solution This means that all values greater than 2 make the inequality true We can write the solutions as x 2 and also represent the solutions on a number line 3 2 1 0 1 2 3 4 5 Notice that 2 itself is not a solution because it s the value of x that makes 3 10 2x equal to 18 and so it does not make 3 10 2x 18 true For confirmation that we found the correct solution we can also test a value that is less than 2 If we test x 0 we get 3 10 2 0 18 or just 30 18 This is false so x 0 and all values of x that are less than 2 are not solutions 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 291

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ZEARN MATH STUDENT EDITION G7M6 LESSON 15 Name Date GRADE 7 MISSION 6 LESSON 15 Exit Ticket For each inequality decide whether the solution is represented by x 2 5 or x 2 5 1 4x 5 5 2 25 5 x 2 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 293

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ZEARN MATH STUDENT EDITION G7M6 LESSON 16 Lesson 16 Inequalities in Context Let s write inequalities Warm Up 1 For each inequality find the value or values of x that make it true 1 8x 21 56 2 56 7 7 x Concept Exploration ACTIVITY 1 2 1 Choose the inequality that best matches each given situation Explain your reasoning The Garden Club is planting fruit trees in their school s garden There is one large tree that needs 5 pounds of fertilizer The rest are newly planted trees that need 12 pound fertilizer each a 25x 5 1 2 b 1 2 x 5 25 c 1 2 x 25 5 d 5x 1 2 25 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 295

G7M6 LESSON 16 2 The Chemistry Club is experimenting with different mixtures of water with a certain chemical sodium polyacrylate to make fake snow To make each mixture the students start with some amount of water and then add 17 of that amount of the chemical and then 9 more grams of the chemical The chemical is expensive so there can t be more than a certain number of grams of the chemical in any one mixture a 1 7 x 9 26 25 b 9x c d 3 ZEARN MATH STUDENT EDITION 1 7 26 25 26 25x 9 1 7 1 7 x 26 25 9 The Hiking Club is on a hike down a cliff They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute a 37x 3 12 b 3x 37 12 c 12 3x 37 d 12x 37 3 4 The Science Club is researching boiling points They learn that at high altitudes water boils at lower temperatures At sea level water boils at 212 With each increase of 500 feet in elevation the boiling point of water is lowered by about 1 1 a 212 500 e 195 b 1 500 e 195 212 c 1 195 212e 500 1 d 212 195e 500 296 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 16 ACTIVITY 2 3 Your teacher will assign your group one of the situations from the last activity Create a visual display about your situation In your display Explain what the variable and each part of the inequality represent Write a question that can be answered by the solution to the inequality Show how you solved the inequality Explain what the solution means in terms of 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 297

G7M6 LESSON 16 ZEARN MATH STUDENT EDITION Lesson Summary We can represent and solve many real world problems with inequalities Writing the inequalities is very similar to writing equations to represent a situation The expressions that make up the inequalities are the same as the ones we have seen in earlier lessons for equations For inequalities we also have to think about how expressions compare to each other which one is bigger and which one is smaller Can they also be equal For example a school fundraiser has a minimum target of 500 Faculty have donated 100 and there are 12 student clubs that are participating with different activities How much money should each club raise to meet the fundraising goal If n is the amount of money that each club raises then the solution to 100 12n 500 is the minimum amount each club has to raise to meet the goal It is more realistic though to use the inequality 100 12n 500 since the more money we raise the more successful the fundraiser will be There are many solutions because there are many different amounts of money the clubs could raise that would get us above our minimum goal of 500 298 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 16 Date GRADE 7 MISSION 6 LESSON 16 Exit Ticket Andre is making paper cranes to decorate for a party He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane He will only have 30 minutes to make the paper cranes once he gets home 1 Andre wrote the inequality 3x 10 30 to plan his time Describe what x 3x 10 and 30 represent in this inequality 2 Solve Andre s inequality and explain what the solution means 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 299

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ZEARN MATH STUDENT EDITION G7M6 LESSON 17 Lesson 17 Modeling with Inequalities Let s look at solutions to inequalities Warm Up 1 The stage manager of the school musical is trying to figure out how many sandwiches he can order with the 83 he collected from the cast and crew Sandwiches cost 5 99 each so he lets x represent the number of sandwiches he will order and writes 5 99x 83 He solves this to 2 decimal places getting x 13 86 Which of these are valid statements about this situation Select all that apply 1 He can call the sandwich shop and order exactly 13 86 sandwiches 2 He can round up and order 14 sandwiches 3 He can order 12 sandwiches 4 He can order 9 5 sandwiches 5 He can order 2 sandwiches 6 He can order 4 sandwiches Concept Exploration ACTIVITY 1 2 A mover is loading an elevator with many identical 48 pound boxes The mover weighs 185 pounds The elevator can carry at most 2000 pounds 1 Write an inequality that says that the mover will not overload the elevator on a particular ride Check your inequality with your partner 2 Solve your inequality and explain what the solution means 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 301

G7M6 LESSON 17 ZEARN MATH STUDENT EDITION 3 Graph the solution to your inequality on a number line 4 If the mover asked How many boxes can I load on this elevator at a time what would you tell them ACTIVITY 2 3 Your teacher will give you either a problem card or a data card Do not show or read your card to your partner If your teacher gives you the problem card 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 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 Silently read your card and think about what information you need to answer the question 2 Ask your partner for the specific information you need 3 Explain to your partner how you are using the information to solve the problem 3 Solve the problem and explain your reasoning to your partner 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 4 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 302 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 17 Lesson Summary We can represent and solve many real world problems with inequalities Whenever we write an inequality it is important to decide what quantity we are representing with a variable After we make that decision we can connect the quantities in the situation to write an expression and finally the whole inequality As we are solving the inequality or equation to answer a question it is important to keep the meaning of each quantity in mind This helps us to decide if the final answer makes sense in the context of the situation For example Han has 50 centimeters of wire and wants to make a square picture frame with a loop to hang it that uses 3 centimeters for the loop This situation can be represented by 3 4s 50 where s is the length of each side if we want to use all the wire We can also use 3 4s 50 if we want to allow for solutions that don t use all the wire In this case any positive number that is less or equal to 11 75 cm is a solution to the inequality Each solution represents a possible side length for the picture frame since Han can bend the wire at any point In other situations the variable may represent a quantity that increases by whole numbers such as with numbers of magazines loads of laundry or students In those cases only whole number solutions make sense 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 303

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 17 Date GRADE 7 MISSION 6 LESSON 17 Exit Ticket Elena is trying to figure out how many movies she can download to her hard drive The hard drive is supposed to hold 500 gigabytes of data but 58 gigabytes are already taken up by other files Each movie is 8 gigabytes Elena wrote the inequality 8x 58 500 and solved it to find the solution x 55 25 1 Explain how you know Elena made a mistake based on her solution 2 Fix Elena s inequality and explain what each part of the inequality means 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 305

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ZEARN MATH STUDENT EDITION G7M6 LESSON 18 Lesson 18 Subtraction in Equivalent Expressions Let s find ways to work with subtraction in expressions Warm Up 1 Find each sum or difference mentally 30 10 10 30 30 10 10 30 Concept Exploration ACTIVITY 1 2 Lin and Kiran are trying to calculate 7 34 3 56 1 34 Here is their conversation Lin I plan to first add 7 34 and 3 56 so I will have to start by finding equivalent fractions with a common denominator Kiran It would be a lot easier if we could start by working with the 1 Can we rewrite it like 7 34 1 34 3 56 3 4 and 7 34 Lin You can t switch the order of numbers in a subtraction problem like you can with addition 2 3 is not equal to 3 2 Kiran That s true but do you remember what we learned about rewriting subtraction expressions using addition 2 3 is equal to 2 3 3 4 3 5 6 1 3 4 1 Write an expression that is equivalent to 7 that uses addition instead of subtraction 2 If you wrote the terms of your new expression in a different order would it still be equivalent 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 307

G7M6 LESSON 18 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Write two expressions for the area of the big rectangle 1 2 43 308 x 12 Use the distributive property to write an expression that is equivalent to 1 8y x 12 The boxes can help you organize your work 2 1 2 53 8y 8y x 12 Use the distributive property to write an expression that is equivalent to 1 2 8y x 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 G7M6 LESSON 18 Lesson Summary Working with subtraction and signed numbers can sometimes get tricky We can apply what we know about the relationship between addition and subtraction that subtracting a number gives the same result as adding its opposite to our work with expressions Then we can make use of the properties of addition that allow us to add and group in any order This can make calculations simpler For example 5 8 2 3 5 8 2 3 1 8 5 8 1 8 2 3 4 8 2 3 1 8 We can also organize the work of multiplying signed numbers in expressions The product 32 6y 2x 8 can be found by drawing a rectangle with the first factor 32 on one side and the three terms inside the parentheses on the other side 3 2 Multiply by each term across the top and perform the multiplications Reassemble the parts to get the expanded version of the original expression 3 2 3 2 3 2 3 2 6y 2x 6y 2x 8 3 2 6y 6y 9y 3 2 2x 8 3 2 8 2x 8 3x 12 6y 2x 8 9y 3x 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 309

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 18 Date GRADE 7 MISSION 6 LESSON 18 Exit Ticket 1 Select all the expressions that are equivalent to 4 x a x 4 b 4 x c x 4 d 4 x e 4 x 2 Use the distributive property to write an expression that is equivalent to 5 2x 3 You may consider using the boxes to help organize your work 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 311

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ZEARN MATH STUDENT EDITION G7M6 LESSON 19 Lesson 19 Expanding and Factoring Let s use the distributive property to write expressions in different ways Warm Up 1 Find the value of each expression mentally 2 3 4 2 3 4 2 3 4 2 3 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 313

G7M6 LESSON 19 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 In each row write the equivalent expression If you get stuck use a diagram to organize your work The first row is provided as an example Diagrams are provided for the first three rows 3 5 2y 15 6y a 6 5 2 Factored Expanded 3 5 2y 15 6y 6a 2b 5 a 6 6a 2b 4 2w 5z 2x 3y 20x 10y 15z k 4 17 10a 13a 2x 3y z ab bc 3bd x 3y z 4w 314 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 19 Lesson Summary We can use properties of operations in different ways to rewrite expressions and create equivalent expressions We have already seen that we can use the distributive property to expand an expression for example 3 x 5 3x 15 We can also use the distributive property in the other direction and factor an expression for example 8x 12 4 2x 3 We can organize the work of using distributive property to rewrite the expression 12x 8 In this case we know the product and need to find the factors The terms of the product go inside 12x 8 12x 8 3x 2 12x 8 We look at the expressions and think about a factor they have in common 12x and 8 each have a factor of 4 We place the common factor on one side of the large rectangle 4 Now we think 4 times what is 12x 4 times what is 8 and write the other factors on the other side of the rectangle So 12x 8 is equivalent to 4 3x 2 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 315

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 19 Date GRADE 7 MISSION 6 LESSON 19 Exit Ticket You may consider drawing a diagram to organize your work 1 Expand to write an equivalent expression 12 2x 4y 2 Factor to write an equivalent expression 26a 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 317

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ZEARN MATH STUDENT EDITION G7M6 LESSON 20 Lesson 20 Combining Like Terms Part 1 Let s see how we can tell that expressions are equivalent Warm Up 1 Explain why each statement is true 1 5 2 3 5 2 3 2 9a is equivalent to 11a 2a 3 7a 4 2a is equivalent to 7a 2a 4 4 8a 8a 8 is equivalent to 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 319

G7M6 LESSON 20 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Diego and Jada are both trying to write an expression with fewer terms that is equivalent to 7a 5b 3a 4b Jada thinks 10a 1b is equivalent to the original expression Diego thinks 4a 9b is equivalent to the original expression 2 We can show expressions are equivalent by writing out all the variables Explain why the expression on each row after the first row is equivalent to the expression on the row before it 7a 5b 3a 4b a a a a a a a b b b b b a a a b b b b a a a a a a a b b b b b a a a b b b b a a a a b b b b b a a a a a a b b b b a a a a b b b b b b b b b a a a a b b b b b b b b b 4a 9b 320 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 3 G7M6 LESSON 20 Here is another way we can rewrite the expressions Explain why the expression on each row after the first row is equivalent to the expression on the row before it 7a 5b 3a 4b 7a 5b 3a 4b 7a 3a 5b 4b 7 3 a 5 4 b 4a 9b ACTIVITY 2 43 Replace each with an expression that will make the left side of the equation equivalent to the right side Check your results from Set A with your partner and resolve any disagreements Then move on to Set B Set A Set B 1 6x 10x 1 6x 2x 2 6x 2x 2 6x 10x 3 6x 10x 3 6x x 4 6x 0 4 6x 6 5 6x 10 5 6x 4x 10 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 321

G7M6 LESSON 20 ZEARN MATH STUDENT EDITION Lesson Summary There are many ways to write equivalent expressions that may look very different from each other We have several tools to find out if two expressions are equivalent Two expressions are definitely not equivalent if they have different values when we substitute the same number for the variable For example 2 3 x 8 and 2x 5 are not equivalent because when x is 1 the first expression equals 4 and the second expression equals 7 If two expressions are equal for many different values we substitute for the variable then the expressions may be equivalent but we don t know for sure It is impossible to compare the two expressions for all values To know for sure we use properties of operations For example 2 3 x 8 is equivalent to 2x 2 because 2 3 x 8 6 2x 8 by the distributive property 2x 6 8 by the commutative property 2x 6 8 by the associative property 2x 2 322 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G7M6 LESSON 20 Date GRADE 7 MISSION 6 LESSON 20 Exit Ticket Write each expression with fewer terms Show your work or explain your reasoning 1 10x 2x 2 10x 3y 2x 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 323

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ZEARN MATH STUDENT EDITION G7M6 LESSON 21 Lesson 21 Combining Like Terms Part 2 Let s see how to use properties correctly to write equivalent expressions Warm Up 1 Select all the statements that are true Be prepared to explain your reasoning 1 4 2 3 7 4 2 3 2 7 2 4 2 3 7 4 2 3 2 7 3 4 2 3 7 4 2 3 2 7 4 4 2 3 7 4 2 3 2 7 Concept Exploration ACTIVITY 1 2 Some students are trying to write an expression with fewer terms that is equivalent to 8 3 4 9x Noah says I worked the problem from left to right and ended up with 20 45x Lin says I started inside the parentheses and ended up with 23x 8 3 4 9x 8 3 4 9x 5 4 9x 8 3 5x 20 45x 8 15x 23x Jada says I used the distributive property and ended up with 27x 4 Andre says I also used the distributive property but I ended up with 4 27x 8 3 4 9x 8 3 4 9x 8 12 27x 8 12 27x 8 12 27x 4 27x 27x 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 325

G7M6 LESSON 21 1 Do you agree with any of them Explain your reasoning 2 For each strategy that you disagree with find and describe the errors ZEARN MATH STUDENT EDITION ACTIVITY 2 3 326 Diego was taking a math quiz There was a question on the quiz that had the expression 8x 9 12x 5 Diego s teacher told the class there was a typo and the expression was supposed to have one set of parentheses in it 1 Where could you put parentheses in 8x 9 12x 5 to make a new expression that is still equivalent to the original expression How do you know that your new expression is equivalent 2 Where could you put parentheses in 8x 9 12x 5 to make a new expression that is not equivalent to the original expression List as many different answers 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

ZEARN MATH STUDENT EDITION G7M6 LESSON 21 Lesson Summary Combining like terms allows us to write expressions more simply with fewer terms But it can sometimes be tricky with long expressions parentheses and negatives It is helpful to think about some common errors that we can be aware of and try to avoid 6x x is not equivalent to 6 While it might be tempting to think that subtracting x makes the x disappear the expression is really saying take 1x away from 6x s and the distributive property tells us that 6x x is equivalent to 6 1 x 7 2x is not equivalent to 5x The expression 7 2x tells us to double an unknown amount and subtract it from 7 This is not always the same as taking 5 copies of the unknown 7 4 x 2 is not equivalent to 3 x 2 The expression tells us to subtract 4 copies of an amount from 7 not to take 7 3 copies of the amount If we think about the meaning and properties of operations when we take steps to rewrite expressions we can be sure we are getting equivalent expressions and are not changing their value in the process 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 327

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 21 Date GRADE 7 MISSION 6 LESSON 21 Exit Ticket Select all expressions that are equivalent to 16x 12 24x 4 Show or explain your reasoning 1 4 16x 12 1 2x 2 40x 16 3 16x 24x 4 12 4 8x 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 329

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ZEARN MATH STUDENT EDITION G7M6 LESSON 22 Lesson 22 Combining Like Terms Part 3 Let s see how we can combine terms in an expression to write it with fewer terms Warm Up 1 Select all expressions that are equal to 8 12 6 4 1 8 6 12 4 2 8 12 6 4 3 8 12 6 4 4 8 12 6 4 5 8 4 12 6 Concept Exploration ACTIVITY 1 2 Match each expression in column A with an equivalent expression from column B Be prepared to explain your reasoning A B a 9x 5y 3x 7y 1 12 x y b 9x 5y 3x 7y 2 12 x y c 3 6 x 2y d 9x 7y 3x 5y 4 9x 5y 3x 7y e 9x 7y 3x 5y 5 9x 5y 3x 7y f 6 9x 3x 5y 7y 9x 5y 3x 7y 9x 7y 3x 5y 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 331

G7M6 LESSON 22 ZEARN MATH STUDENT EDITION ACTIVITY 2 Write each expression with fewer terms Explain your reasoning 3 332 1 3 15 4 15 5 15 2 3x 4x 5x 3 3 x 2 4 x 2 5 x 2 4 3 5 2 x 6 1 2 4 5 2 x 6 1 2 5 5 2 x 6 1 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 G7M6 LESSON 22 Lesson Summary Combining like terms is a useful strategy that we will see again and again in our future work with mathematical expressions It is helpful to review the things we have learned about this important concept Combining like terms is an application of the distributive property For example 2x 9x 2 9 x 11x It often also involves the commutative and associative properties to change the order or grouping of addition For example 2a 3b 4a 5b 2a 4a 3b 5b 2a 4a 3b 5b 6a 8b We can t change order or grouping when subtracting so in order to apply the commutative or associative properties to expressions with subtraction we need to rewrite subtraction as addition For example 2a 3b 4a 5b 2a 3b 4a 5b 2a 4a 3b 5b 2a 8b 2a 8b Since combining like terms uses properties of operations it results in expressions that are equivalent The like terms that are combined do not have to be a single number or variable they may be longer expressions as well Terms can be combined in any sum where there is a common factor in all the terms For example each term in the expression 5 x 3 0 5 x 3 2 x 3 has a factor of x 3 We can rewrite the expression with fewer terms by using the distributive property 5 x 3 0 5 x 3 2 x 3 5 0 5 2 x 3 6 5 x 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 333

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ZEARN MATH STUDENT EDITION Name G7M6 LESSON 22 Date GRADE 7 MISSION 6 LESSON 22 Exit Ticket Match each expression in column A with an equivalent expression from column B Show or explain your reasoning Column A Column B a 12r t 4r 6t 1 8 r t b 12r 2t 4r 10t 2 8 r t c 12 r t 6 r t 4 r t 2 r t 3 8r 7t 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 335

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ZEARN MATH STUDENT EDITION G7V2 Terminology Deposit When you put money into an account it is called a deposit For example a person added 60 to their bank account Before the deposit they had 435 After the deposit they had 495 because 435 60 495 Measurement Error Measurement error is the positive difference between a measured amount and the actual amount For example Diego measures a line segment and gets 5 3 cm The actual length of the segment is really 5 32 cm The measurement error is 0 02 cm because 5 32 5 3 0 02 Percent Error Percent error is a way to describe error expressed as a percentage of the actual amount For example a box is supposed to have 150 folders in it Clare counts only 147 folders in the box This is an error of 3 folders The percent error is 2 because 3 is 2 of 150 3 150 0 02 Percentage Decrease A percentage decrease tells how much a quantity went down expressed as a percentage of the starting amount 100 48 16 75 25 Percentage Increase A percentage increase tell how much a quantity went up expressed as a percentage of the starting amount 100 12 50 6 112 Repeating Decimal A repeating decimal has digits that keep going in the same pattern over and over The repeating digits are marked with a line above them For example the decimal representation for 13 is 0 3 which means 0 3333333 The decimal representation for 25 22 is 1 136 which means 1 136363636 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 337

G7V2 ZEARN MATH STUDENT EDITION Withdrawal When you take money out of an account it is called a withdrawal For example a person removed 25 from their bank account Before the withdrawal they had 350 After the withdrawal they had 325 because 350 25 325 338 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 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 2 Zearnmath_SE_Grade7_Vol2 indd 1 Grade 7 Volume 2 MISSIONS 1 2 3 4 5 6 7 8 9 12 15 22 2 28 PM