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STUDENT EDITION Grade 6 VOLUME 3 Mission 7 Rational Numbers Mission 8 Data Sets and Distributions Mission 9 Putting It All Together NAME

2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum used under the CC BY 4 0 license Download the original for free at openupresources org Zearn is a registered trademark Printed in the U S A ISBN 979 8 88868 096 4

Table of Contents Mission 7 Lesson 1 Positive and Negative Numbers 3 Lesson 2 Points on the Number Line 9 Lesson 3 Comparing Positive and Negative Numbers 15 Lesson 4 Ordering Rational Numbers 21 Lesson 5 Using Negative Numbers to Make Sense of Contexts 25 Lesson 6 Absolute Value of Numbers 31 Lesson 7 Comparing Numbers and Distance from Zero 37 Lesson 8 Writing and Graphing Inequalities 43 Lesson 9 Solutions of Inequalities 49 Lesson 10 Interpreting Inequalities 55 Lesson 11 Points on the Coordinate Plane 61 Lesson 12 Constructing the Coordinate Plane 67 Lesson 13 Interpreting Points on a Coordinate Plane 73 Lesson 14 Distances on a Coordinate Plane 79 Lesson 15 Shapes on the Coordinate Plane 85 Lesson 16 Common Factors 93 Lesson 17 Common Multiples 99 Lesson 18 Using Common Multiples and Common Factors 105 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license iii

Mission 8 iv Lesson 1 Got Data 113 Lesson 2 Statistical Questions 121 Lesson 3 Representing Data Graphically 127 Lesson 4 Dot Plots 133 Lesson 5 Using Dot Plots to Answer Statistical Questions 139 Lesson 6 Histograms 145 Lesson 7 Using Histograms to Answer Statistical Questions 153 Lesson 8 Describing Distributions on Histograms 161 Lesson 9 Interpreting the Mean as Fair Share 167 Lesson 10 Finding and Interpreting the Mean as the Balance Point 173 Lesson 11 Deviation from the Mean 181 Lesson 12 Using Mean and MAD to Make Comparisons 189 Lesson 13 The Median of a Data Set 195 Lesson 14 Comparing Mean and Median 201 Lesson 15 Quartiles and Interquartile Range 209 Lesson 16 Box Plots 217 Lesson 17 Using Box Plots 223 Lesson 18 Using Data to Solve Problems 229 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

Mission 9 Lesson 1 Fermi Problems 239 Lesson 2 If Our Class Were the World 241 Lesson 3 Rectangle Madness 243 Lesson 4 How Do We Choose 251 Lesson 5 More than Two Choices 255 Lesson 6 Picking Representatives 263 Terminology 273 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 6 Mission 7 Rational Numbers

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ZEARN MATH STUDENT EDITION G6M7 LESSON 1 Lesson 1 Positive and Negative Numbers Let s explore how we represent temperatures and elevations Warm Up 1 What do you notice What do you wonder 37 F 3 C Memphis TN Saturday 5pm Light Rain Showers 1 F 17 C Bangor ME Saturday 6pm Partly Cloudy Concept Exploration ACTIVITY 1 2 Here are three situations involving changes in temperature and three number lines Represent each change on a number line Then answer the questions a At noon the temperature was 5 degrees Celsius By late afternoon it has risen 6 degrees Celsius What was the temperature late in the afternoon b The temperature was 8 degrees Celsius at midnight By dawn it has dropped 12 degrees Celsius What was the temperature at dawn 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 1 c ZEARN MATH STUDENT EDITION Water freezes at 0 degrees Celsius but the freezing temperature can be lowered by adding salt to the water A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius What is the freezing temperature of the gallon of salt water 0 0 0 ACTIVITY 2 3 Here is a table that shows elevations of various cities a On the list of cities which city has the second highest elevation City Harrisburg PA b How would you describe the elevation of Coachella CA in relation to sea level c How would you describe the elevation of Death Valley CA in relation to sea level Elevation feet 320 Bethell IN 1 211 Denver CO 5 280 Coachella CA 22 Death Valley CA 282 New York City NY 33 Miami FL 0 d If you are standing on a beach right next to the ocean what is your elevation 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M7 LESSON 1 e How would you describe the elevation of Miami FL f A city has a higher elevation than Coachella CA Select all numbers that could represent the city s elevation Be prepared to explain your reasoning 11 feet 35 feet 4 feet 8 feet 0 feet 43 Here are two tables that show the elevations of highest points on land and lowest points in the ocean Distances are measured from sea level Mountain Continent Elevation meters Trench Ocean Elevation meters Everest Asia 8 848 Mariana Trench Pacific 11 033 Kilimanjaro Africa 5 895 Puerto Rico Trench Atlantic 8 600 Denali North America 6 168 Tonga Trench Pacific 10 882 Pikchu Pikchu South America 5 664 Sunda Trench Indian 7 725 a Which point in the ocean is the lowest in the world What is its elevation b Which mountain is the highest in the world What is its elevation c If you plot the elevations of the mountains and trenches on a vertical number line what would 0 represent What would points above 0 represent What about points below 0 d Which is farther from sea level the deepest point in the ocean or the top of the highest mountain in the world Explain 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 1 ZEARN MATH STUDENT EDITION Lesson Summary Positive numbers are numbers that are greater than 0 Negative numbers are numbers that are less than zero The meaning of a negative number in a context depends on the meaning of zero in that context For example if we measure temperatures in degrees Celsius then 0 degrees Celsius corresponds to the temperature at which water freezes 6 5 4 3 2 1 0 1 2 3 4 5 6 7 In this context positive temperatures are warmer than the freezing point and negative temperatures are colder than the freezing point A temperature of 6 degrees Celsius means that it is 6 degrees away from 0 and it is less than 0 This thermometer shows a temperature of 6 degrees Celsius Another example is elevation which is a distance above or below sea level An elevation of 0 refers to the sea level Positive elevations are higher than sea level and negative elevations are lower than sea level 5 elevation If the temperature rises a few degrees and gets very close to 0 degrees without reaching it the temperature is still a negative number 10 0 sea level 5 10 TERMINOLOGY Negative Number Positive Number 6 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G6M7 LESSON 1 Date GRADE 6 MISSION 7 LESSON 1 Exit Ticket State whether you agree with each of the following statements Explain your reasoning 1 A temperature of 35 degrees Fahrenheit is as cold as a temperature of 35 degrees Fahrenheit 2 A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of 10 meters 3 A city that has an elevation of 17 meters is closer to sea level than a city that has an elevation of 40 meters 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 7

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ZEARN MATH STUDENT EDITION G6M7 LESSON 2 Lesson 2 Points on the Number Line Let s plot positive and negative numbers on the number line Warm Up 1 Which of the following numbers could be B B 0 1 2 25 25 5 2 3 4 25 10 2 49 Concept Exploration ACTIVITY 1 2 Here are five thermometers The first four thermometers show temperatures in Celsius Write the temperatures in the blanks The last thermometer is missing some numbers Write them in the boxes a b c d e 5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 25 10 5 20 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 9

G6M7 LESSON 2 3 ZEARN MATH STUDENT EDITION Elena says that the thermometer shown here reads 2 5 C because the line of the liquid is above 2 C Jada says that it is 1 5 C Do you agree with either one of them Explain your reasoning 5 4 3 2 1 0 1 2 3 4 43 One morning the temperature in Phoenix Arizona was 8 C and the temperature in Portland Maine was 12 C cooler What was the temperature in Portland ACTIVITY 2 53 1 10 Your teacher will give you a sheet of tracing paper on which to draw a number line Follow the steps to make your own number line Then use your number line to answer the questions Follow the steps to make your own number line Use a straightedge or a ruler to draw a horizontal line Mark the middle point of the line and label it 0 To the right of 0 draw tick marks that are 1 centimeter apart Label the tick marks 1 2 3 10 This represents the positive side of your number line Fold your paper so that a vertical crease goes through 0 and the two sides of the number line match up perfectly Use the fold to help you trace the tick marks that you already drew onto the opposite side of the number line Unfold and label the tick marks 1 2 3 10 This represents the negative side of your 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 2 G6M7 LESSON 2 Use your number line to answer the questions a Which number is the same distance away from zero as is the number 4 b Which number is the same distance away from zero as is the number 7 c Two numbers that are the same distance from zero on the number line are called opposites Find another pair of opposites on the number line d Determine how far away the number 5 is from 0 Then choose a positive number and a negative number that is each farther away from zero than is the number 5 e Determine how far away the number 2 is from 0 Then choose a positive number and a negative number that is each farther away from zero than is the number 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 11

G6M7 LESSON 2 ZEARN MATH STUDENT EDITION Lesson Summary Here is a number line labeled with positive and negative numbers The number 4 is positive so its location is 4 units to the right of 0 on the number line The number 1 1 is negative so its location is 1 1 units to the left of 0 on the number line 5 4 3 2 1 0 1 2 We say that the opposite of 8 3 is 8 3 and that the opposite of equally far from 0 are called opposites 3 3 2 4 3 2 is 5 Any pair of numbers that are Points A and B are opposites because they are both 2 5 units away from 0 even though A is to the left of 0 and B is to the right of 0 A 5 4 3 B 2 1 0 1 2 C 3 4 5 A positive number has a negative number for its opposite A negative number has a positive number for its opposite The opposite of 0 is itself You have worked with positive numbers for many years All of the positive numbers you have seen whole and non whole numbers can be thought of as fractions and can be located on a number line To locate a non whole number on a number line we can divide the distance between two whole numbers into fractional parts and then count the number of parts For example 2 7 can be written as 7 2 10 The segment between 2 and 3 can be partitioned into 10 equal parts or 10 tenths From 2 we can count 7 of the tenths to locate 2 7 on the number line All of the fractions and their opposites are what we call rational numbers For example 4 1 1 8 3 8 3 32 and 32 are all rational numbers TERMINOLOGY Opposite Rational number 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 G6M7 LESSON 2 Name Date GRADE 6 MISSION 7 LESSON 2 Exit Ticket 1 Put these numbers in order from least to greatest If you get stuck consider using the number line 3 5 1 4 8 1 5 0 5 4 2 0 5 2 1 3 5 5 2 4 3 2 1 0 1 2 3 4 5 Write two numbers that are opposites and each more than 6 units away 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 13

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ZEARN MATH STUDENT EDITION G6M7 LESSON 3 Lesson 3 Comparing Positive and Negative Numbers Let s compare numbers on the number line Warm Up 1 Which inequality doesn t belong 54 2 8 5 0 95 8 5 7 10 00 100 Concept Exploration ACTIVITY 1 2 Here are the low temperatures in degrees Celsius for a week in Anchorage Alaska Day Mon Tues Wed Thurs Fri Sat Sun Temperature 5 1 5 5 2 3 4 0 1 Plot the temperatures on a number line Which day of the week had the lowest low temperature 2 The average winter temperature at the South Pole is 60 degrees Celsius The average temperature on Mars is about 55 degrees Celsius a Which is warmer the average winter temperature at the South Pole or the average temperature on Mars Explain how you know b Write an inequality to show your answer 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 15

G6M7 LESSON 3 3 ZEARN MATH STUDENT EDITION On a winter day the low temperature in Anchorage Alaska was 21 degrees Celsius and the low temperature in Minneapolis Minnesota was 14 degrees Celsius Jada said I know that 14 is less than 21 so 14 is also less than 21 This means that it was colder in Minneapolis than in Anchorage Do you agree Explain your reasoning ACTIVITY 2 3 1 Plot and compare numbers Plot the numbers 2 4 7 and 10 on the number line Label each point with its numeric value 0 2 1 Decide whether each inequality statement is true or false Be prepared to explain your reasoning 2 4 2 7 4 7 3 Andre says that 14 is less than Explain your reasoning 4 Answer each question Be prepared to explain how you know a Which number is greater b Which is farther from 0 c 3 4 1 4 1 4 Which number is greater d Which is farther from 0 3 4 because of the two numbers or 5 4 or 5 4 3 4 or 5 8 5 8 or 7 10 1 4 is closer to 0 Do you agree e Is the number that is farther from 0 always the greater number Explain your reasoning 16 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M7 LESSON 3 Lesson Summary We use the words greater than and less than to compare numbers on the number line For example the numbers 2 7 0 8 and 1 3 are shown on the number line 2 7 3 1 3 2 0 8 1 0 1 2 3 Because 2 7 is to the left of 1 3 we say that 2 7 is less than 1 3 We write 2 7 1 3 In general any number that is to the left of a number n is less than n We can see that 1 3 is greater than 2 7 because 1 3 is to the right of 2 7 We write 1 3 2 7 In general any number that is to the right of a number n is greater than n We can also see that 0 8 1 3 and 0 8 2 7 In general any positive number is greater than any negative number TERMINOLOGY Sign 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 3 Name Date GRADE 6 MISSION 7 LESSON 3 Exit Ticket 1 The elevation of Death Valley California is 282 feet The elevation of Tallahassee Florida is 203 feet The elevation of Westmorland California is 157 feet a Compare the elevations of Death Valley and Tallahassee using or b Compare the elevations of Death Valley and Westmorland 2 Here are the points A B C and 0 plotted on a number line A B 0 C The points B and C are opposites Decide whether each of the following statements is true a A is greater than B b A is farther from 0 than C c A is a less than C d B and C are equally far away from 0 e B and C are equal 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 4 Lesson 4 Ordering Rational Numbers Let s order rational numbers Warm Up 1 Use the symbols

G6M7 LESSON 4 ZEARN MATH STUDENT EDITION Lesson Summary To order rational numbers from least to greatest we list them in the order they appear on the number line from left to right For example we can see that the numbers 2 7 1 3 0 8 are listed from least to greatest because of the order they appear on the number line 2 7 3 22 1 3 2 0 8 1 0 1 2 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 G6M7 LESSON 4 Name Date GRADE 6 MISSION 7 LESSON 4 Exit Ticket 1 Place these numbers in order from least to greatest 16 5 2 3 6 3 1 2 5 1 4 34 38 2 Write a sentence to compare the two points shown on the number line 2 7 4 5 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 23

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ZEARN MATH STUDENT EDITION G6M7 LESSON 5 Lesson 5 Using Negative Numbers to Make Sense of Contexts Let s make sense of negative amounts of money Warm Up 1 What do you notice What do you wonder Activity Amount do my chores 30 00 babysit my cousin 45 00 buy my lunch 10 80 get my allowance 15 00 buy a shirt 18 69 pet my dog 0 00 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 5 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 The manager of the concession stand keeps records of all of the supplies she buys and all of the items she sells The table shows some of her records for Tuesday Item 26 Quantity Value in Dollars doughnuts 58 37 70 straws 3 000 10 35 hot dogs 39 48 75 pizza 13 116 87 apples 40 14 00 french fries 88 132 00 1 Which items did she sell Explain your reasoning 2 How can we interpret 58 in this situation 3 How can we interpret 10 35 in this situation 4 On which item did she spend the most amount of money Explain your reasoning 5 If the total amount of money spent on buying supplies equals the total amount received from selling items how much money would the concession stand make that day 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 5 ACTIVITY 2 3 A vending machine in an office building sells bottled beverages The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance This record shows the changes for every 5 minute period over one hour Time Number of Bottles 8 00 8 04 1 8 05 8 09 12 8 10 8 14 4 8 15 8 19 1 8 20 8 24 5 8 25 8 29 12 8 30 8 34 2 8 35 8 39 0 8 40 8 44 0 8 45 8 49 6 8 50 8 54 24 8 55 8 59 0 service 1 What might a positive number mean in this context What about a negative number 2 What would a 0 in the second column mean in this context 3 Which numbers positive or negative result in fewer bottles in the machine 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 5 ZEARN MATH STUDENT EDITION 4 At what time was there the greatest change to the number of bottles in the machine How did that change affect the number of remaining bottles in the machine 5 At which time period 8 05 8 09 or 8 25 8 29 was there a greater change to the number of bottles in the machine Explain your reasoning 6 The machine must be emptied to be serviced If there are 40 bottles in the machine when it is to be serviced what number will go in the second column in the table Lesson Summary Sometimes we represent changes in a quantity with positive and negative numbers If the quantity increases the change is positive If it decreases the change is negative Suppose 5 gallons of water is put in a washing machine We can represent the change in the number of gallons as 5 If 3 gallons is emptied from the machine we can represent the change as 3 It is especially common to represent money we receive with positive numbers and money we spend with negative numbers Suppose Clare gets 30 00 for her birthday and spends 18 00 buying lunch for herself and a friend To her the value of the gift can be represented as 30 00 and the value of the lunch as 18 00 Whether a number is considered positive or negative depends on a person s perspective If Clare s grandmother gives her 20 for her birthday Clare might see this as 20 because to her the amount of money she has increased But her grandmother might see it as 20 because to her the amount of money she has decreased In general when using positive and negative numbers to represent changes we have to be very clear about what it means when the change is positive and what it means when the change is negative 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 G6M7 LESSON 5 Name Date GRADE 6 MISSION 7 LESSON 5 Exit Ticket The table shows records of money related activities of a bakery owner over a period of a week Date Items Amount in dollars May 1 rent 850 00 May 2 order birthday cake and cookies 106 75 May 3 utilities electricity gas phone 294 50 May 5 order wedding cake and desserts 240 55 May 5 baking supplies 147 95 May 6 order anniversary cake 158 20 May 7 order breads and desserts for a conference 482 30 May 7 bakery sales 415 65 1 For which items did she receive money 2 What does the number 147 95 mean in this context 3 Did the bakery owner receive more or spend more money on May 5 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 29

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ZEARN MATH STUDENT EDITION G6M7 LESSON 6 Lesson 6 Absolute Value of Numbers Let s explore distances from zero more closely Warm Up For each pair of expressions decide mentally which one has a value that is closer to 0 1 9 11 or 15 11 1 5 or 1 9 1 25 or 5 4 0 01 or 001 Concept Exploration ACTIVITY 1 2 A flea is jumping around on a number line 0 1 a If the flea starts at 1 and jumps 4 units to the right where does it end up How far away from 0 is this b If the flea starts at 1 and jumps 4 units to the left where does it end up How far away from 0 is this c If the flea starts at 0 and jumps 3 units away where might it land d If the flea jumps 7 units and lands at 0 where could it have started 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 6 ZEARN MATH STUDENT EDITION e The absolute value of a number is the distance it is from 0 The flea is currently to the left of 0 and the absolute value of its location is 4 Where on the number line is it f If the flea is to the left of 0 and the absolute value of its location is 5 where on the number line is it g If the flea is to the right of 0 and the absolute value of its location is 2 5 where on the number line is it 3 We use the notation 2 to say the absolute value of 2 which means the distance of 2 from 0 on the number line a What does 7 mean and what is its value b What does 1 8 mean and what is its value ACTIVITY 2 43 1 Solve these problems about elevation and temperature A part of the city of New Orleans is 6 feet below sea level We can use 6 feet to describe its elevation and 6 feet to describe its vertical distance from sea level In the context of elevation what would each of the following numbers describe a 25 feet b 25 feet c 8 feet d 8 feet 2 32 The elevation of a city is different from sea level by 10 feet Name the two elevations that the city could have 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 3 G6M7 LESSON 6 We write 5 C to describe a temperature that is 5 degrees Celsius below freezing point and 5 C for a temperature that is 5 degrees above freezing In this context what do each of the following numbers describe a 1 C b 4 C c 12 C d 7 C 4 Compare the temperatures a Which temperature is colder 6 C or 3 C b Which temperature is closer to freezing temperature 6 C or 3 C c Which temperature has a smaller absolute value 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 33

G6M7 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary We compare numbers by comparing their positions on the number line the one farther to the right is greater the one farther to the left is less Sometimes we wish to compare which one is closer to or farther from 0 For example we may want to know how far away the temperature is from the freezing point of 0 C regardless of whether it is above or below freezing The absolute value of a number tells us its distance from 0 The absolute value of 4 is 4 because 4 is 4 units to the left of 0 The absolute value of 4 is also 4 because 4 is 4 units to the right of 0 Opposites always have the same absolute value because they both have the same distance from 0 4 units 5 4 3 2 4 units 1 0 1 2 3 4 5 The distance from 0 to itself is 0 so the absolute value of 0 is 0 Zero is the only number whose distance to 0 is 0 For all other absolute values there are always two numbers one positive and one negative that have that distance from 0 To say the absolute value of 4 we write 4 To say that the absolute value of 8 is 8 we write 8 8 TERMINOLOGY Absolute Value 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 Name G6M7 LESSON 6 Date GRADE 6 MISSION 7 LESSON 6 Exit Ticket 1 Write down a number that has the same value as each number a 5 b 12 9 2 Write down a number that has a value less than 4 7 3 Write down a number that has a value greater than 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 35

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ZEARN MATH STUDENT EDITION G6M7 LESSON 7 Lesson 7 Comparing Numbers and Distance from Zero Let s use absolute value and negative numbers to think about elevation Warm Up 1 1 Use the number line to help you solve a is a rational number Choose a value for a and plot it on the number line 0 2 a Based on where you plotted a plot a on the same number line b What is the value of a that you plotted 3 Noah said If a is a rational number a will always be a negative number Do you agree with Noah Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 37

G6M7 LESSON 7 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 A submarine is at an elevation of 100 feet 100 feet below sea level Compare the elevations of these four people to that of the submarine Clare s elevation is greater than the elevation of the submarine Clare is farther from sea level than the submarine Andre s elevation is less than the elevation of the submarine Andre is farther away from sea level than the submarine Han s elevation is greater than the elevation of the submarine Han is closer to sea level than is the submarine Lin s elevation is the same distance away from sea level as the submarine s 200 150 100 50 0 50 100 Complete the table as follows 150 a Write a possible elevation for each person 200 b Use or to compare the elevation of that person to that of the submarine c Use absolute value to tell how far away the person is from sea level elevation 0 As an example the first row has been filled with a possible elevation for Clare Clare Possible elevation Compare to submarine Distance from sea level 150 feet 150 100 150 or 150 feet Andre Han Lin 2 38 Priya says her elevation is less than the submarine s and she is closer to sea level Is this possible Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M7 LESSON 7 ACTIVITY 2 3 Use the numbers and symbols below to write true comparison statements 3 5 1 4 8 6 3 2 5 2 5 8 0 7 4 0 7 2 3 52 0 7 One partner should select two numbers and one comparison symbol and use them to write a true statement using symbols The other partner should write a sentence in words with the same meaning using the following phrases is equal to is the absolute value of is greater than is less than For example one partner could write 4 8 and the other would write 4 is less than 8 Switch roles until each partner has three true mathematical statements and three sentences written down Lesson Summary We can use elevation to help us compare two rational numbers or two absolute values Suppose an anchor has an elevation of 10 meters and a house has an elevation of 12 meters To describe the anchor having a lower elevation than the house we can write 10 12 and say 10 is less than 12 The anchor is closer to sea level than the house is to sea level or elevation of 0 To describe this we can write 10 12 and say the distance between 10 and 0 is less than the distance between 12 and 0 We can use similar descriptions to compare rational numbers and their absolute values outside of the context of elevation To compare the distance of 47 5 and 5 2 from 0 we can say 47 5 is 47 5 units away from 0 and 5 2 is 5 2 units away from 0 so 47 5 5 2 18 4 means that the absolute value of 18 is greater than 4 This is true because 18 is greater than 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 39

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ZEARN MATH STUDENT EDITION Name G6M7 LESSON 7 Date GRADE 6 MISSION 7 LESSON 7 Exit Ticket Mark each of the following as true or false and explain how you know 1 5 3 2 5 3 3 5 3 4 5 3 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 41

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ZEARN MATH STUDENT EDITION G6M7 LESSON 8 Lesson 8 Writing and Graphing Inequalities Let s write inequalities Warm Up 1 Here is a picture of Mr Sawicki a Name a number in feet that is clearly too high for his height b Name a number in feet that is clearly too low for his height c Make an estimate of his height 2 Here is a picture of Mr Sawicki standing next to a student Here is a picture of Mr Sawicki standing next to a student If Mr Sawicki s actual height is 5 feet 10 inches what can you say about the height of the student in this picture Be prepared to explain your reasoning Concept Exploration ACTIVITY 1 3 1 You ll get a set of paper slips with four stories and questions involving the number 9 Match each question to three representations of the solution a description or a list a number line or an inequality statement 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 8 2 ZEARN MATH STUDENT EDITION Compare your matching decisions with another group s If there are disagreements discuss until both groups come to an agreement Then record your final matching decisions here a A fishing boat can hold fewer than 9 people How many people x can it hold Description or list Number line 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Inequality b Lin needs more than 9 ounces of butter to make cookies for her party How many ounces of butter x would be enough Description or list Number line 0 c 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Inequality A magician will perform her magic tricks only if there are at least 9 people in the audience For how many people x will she perform her magic tricks Description or list Number line 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Inequality d A food scale can measure up to 9 kilograms of weight What weights x can the scale measure Description or list Number line 0 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Inequality 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 8 ACTIVITY 2 Here is a picture of Ms Taylor and a basketball hoop Based on the picture what do you think are reasonable estimates for the maximum and minimum heights of the basketball hoop 43 1 Complete the first blank in each sentence with an estimate and the second blank with taller or shorter a I estimate the minimum height of the basketball hoop to be feet this means the hoop cannot be than this height b I estimate the maximum height of the basketball hoop to be feet this means the hoop cannot be than this height 2 Write two inequalities one to show your estimate for the minimum height of the basketball hoop and another for the maximum height Use an inequality symbol and the variable to h represent the unknown height 3 Plot each estimate for minimum or maximum value on a number line Minimum 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Maximum 0 4 1 Suppose a classmate estimated the value of h to be 19 feet Does this estimate agree with your inequality for the maximum height Does it agree with your inequality for the minimum height Explain or show 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 45

G6M7 LESSON 8 5 ZEARN MATH STUDENT EDITION Ask a partner for an estimate of h Record the estimate and check if it agrees with your inequalities for maximum and minimum heights Lesson Summary An inequality tells us that one value is less than or greater than another value Suppose we knew the temperature is less than 3 F but we don t know exactly what it is To represent what we know about the temperature t in F we can write the inequality t 16 a 16 46 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G6M7 LESSON 8 Date GRADE 6 MISSION 7 LESSON 8 Exit Ticket Andre looks at a box of paper clips He says I think the number of paper clips in the box is less than 1 000 Lin also looks at the box She says I think the number of paper clips in the box is more than 500 1 Write an inequality to show Andre s statement using p for the number of paper clips 2 Write another inequality to show Lin s statement also using p for the number of paper clips 3 Do you think both Lin and Andre would agree that there could be 487 paperclips in the box Explain your reasoning 4 Do you think both Lin and Andre would agree that there could be 742 paperclips in the box 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 47

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ZEARN MATH STUDENT EDITION G6M7 LESSON 9 Lesson 9 Solutions of Inequalities Let s think about the solutions to inequalities Warm Up The number line shows several points each labeled with a letter 1 A B C D E F 0 1 Fill in each blank with a letter so that the inequality statements are true a b 2 Jada says that she found three different ways to complete the first question correctly Do you think this is possible Explain your reasoning 3 List a possible value for each letter on the number line based on its location 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 9 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 1 Priya finds these height requirements for some of the rides at an amusement park To ride the you must be High Bounce between 55 and 72 inches tall Climb A Thon under 60 inches tall Twirl O Coaster 58 inches minimum Write an inequality for each of the three height requirements Use h for the unknown height Then represent each height requirement on a number line High Bounce Climb A Thon Twirl O Coaster Pause here for additional instructions from your teacher 2 Han s cousin is 55 inches tall Han doesn t think she is tall enough to ride the High Bounce but Kiran believes that she is tall enough Do you agree with Han or Kiran Be prepared to explain your reasoning 3 Priya can ride the Climb A Thon but she cannot ride the High Bounce or the Twirl O Coaster Which if any of the following could be Priya s height Be prepared to explain your reasoning 59 inches 53 inches 56 inches 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

ZEARN MATH STUDENT EDITION G6M7 LESSON 9 4 Jada is 56 inches tall Which rides can she go on 5 Kiran is 60 inches tall Which rides can he go on 6 The inequalities h 75 and h 64 represent the height restrictions in inches of another ride Write three values that are solutions to both of these inequalities Lesson Summary Let s say a movie ticket costs less than 10 If c represents the cost of a movie ticket we can use c 10 to express what we know about the cost of a ticket Any value of c that makes the inequality true is called a solution to the inequality For example 5 is a solution to the inequality c 10 because 5 10 or 5 is less than 10 is a true statement but 12 is not a solution because 12 10 12 is less than 10 is not a true statement If a situation involves more than one boundary or limit we will need more than one inequality to express it For example if we knew that it rained for more than 10 minutes but less than 30 minutes we can describe the number of minutes that it rained r with the following inequalities and number lines r r 10 10 r 10 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 25 25 30 30 35 35 40 40 r 30 r 10 and any number less than 30 is a solution to r 30 But to meet the condition of more than 10 but less than 30 the solutions are limited to the numbers between 10 and 30 minutes not including 10 and 30 We can show the solutions visually by graphing the two inequalities on one number line 0 5 10 15 20 25 30 35 40 TERMINOLOGY Solution to an inequality 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G6M7 LESSON 9 Name Date GRADE 6 MISSION 7 LESSON 9 Exit Ticket 1 a Select all numbers that are solutions to the inequality w 1 A 5 B 5 C 0 D 0 9 E 1 3 b Draw a number line to represent this inequality 2 a Write an inequality for which 3 4 0 and 2 300 are solutions b How many total solutions are there to your inequality 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G6M7 LESSON 10 Lesson 10 Interpreting Inequalities Let s examine what inequalities can tell us Warm Up Is each equation true or false Be prepared to explain your reasoning 1 1 2 3 3 12 5 3 12 3 5 1 3 3 4 3 4 2 6 2 1 5 12 4 0 75 6 Concept Exploration ACTIVITY 1 2 Noah scored n points in a basketball game 1 What does 15 n mean in the context of the basketball game 2 What does n 25 mean in the context of the basketball game 3 Draw two number lines to represent the solutions to the two inequalities 4 Name a possible value for n that is a solution to both inequalities 5 Name a possible value for n that is a solution to 15 n but not a solution to n 25 6 Can 8 be a solution to n in this context 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 55

G6M7 LESSON 10 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Here is a diagram of an unbalanced hanger Jada says that the weight of one circle is greater than the weight of one pentagon a Write an inequality to represent her statement Let p be the weight of one pentagon and c be the weight of one circle b A circle weighs 12 ounces Use this information to write another inequality to represent the relationship of the weights Then describe what this inequality means in this context 43 Here is another diagram of an unbalanced hanger a Write an inequality to represent the relationship of the weights Let p be the weight of one pentagon and s be the weight of one square b One pentagon weighs 8 ounces Use this information to write another inequality to represent the relationship of the weights Then describe what this inequality means in this context c 56 Graph the solutions to this inequality on a 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 53 G6M7 LESSON 10 Based on your work so far can you tell the relationship between the weight of a square and the weight of a circle If so write an inequality to represent that relationship If not explain your reasoning 63 This is another diagram of an unbalanced hanger Andre writes the following inequality c p s Do you agree with his inequality Explain your reasoning 73 Jada looks at another diagram of an unbalanced hanger and writes s c 2t where t represents the weight of one triangle Draw a sketch of the diagram 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 57

G6M7 LESSON 10 ZEARN MATH STUDENT EDITION Lesson Summary When we find the solutions to an inequality we should think about its context carefully A number may be a solution to an inequality outside of a context but may not make sense when considered in context Suppose a basketball player scored more than 11 points in a game and we represent the number of points she scored s with the inequality s 11 By looking only at s 11 we can say that numbers such as 12 14 12 and 130 25 are all solutions to the inequality because they each make the inequality true 12 11 14 1 2 11 130 25 11 In a basketball game however it is only possible to score a whole number of points so fractional and decimal scores are not possible It is also highly unlikely that one person would score more than 130 points in a single game In other words the context of an inequality may limit its solutions Here is another example The solutions to r 30 can include numbers such as 27 34 18 5 0 and 7 But if r represents the number of minutes of rain yesterday and it did rain then our solutions are limited to positive numbers Zero or negative number of minutes would not make sense in this context To show the upper and lower boundaries we can write two inequalities 0 r r 30 Inequalities can also represent comparison of two unknown numbers 58 Let s say we knew that a puppy weighs more than a kitten but we did not know the weight of either animal We can represent the weight of the puppy in pounds with p and the weight of the kitten in pounds with k and write this inequality p k 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 10 Name Date GRADE 6 MISSION 7 LESSON 10 Exit Ticket 1 Lin says that the inequalities h 150 and h 160 describe her height in centimeters What do the inequalities tell us about her height 2 Andre notices that he is a little taller than Lin but is shorter than their math teacher who is 164 centimeters tall Write two inequalities to describe Andre s height Let a be Andre s height in centimeters 3 Select all heights that could be Andre s height in centimeters If you get stuck consider drawing a number line to help you a 150 b 154 5 c 160 d 162 5 e 164 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 59

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ZEARN MATH STUDENT EDITION G6M7 LESSON 11 Lesson 11 Points on the Coordinate Plane Let s explore and extend the coordinate plane Warm Up 1 Use the coordinate plane to complete the activity with a partner 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 Choose a horizontal or a vertical line on the grid Draw 4 points on the line and label each point with its coordinates 2 Tell your partner whether your line is horizontal or vertical and have your partner guess the locations of your points by naming coordinates If a guess is correct put an X through the point If your partner guessed a point that is on your line but not the point that you plotted say That point is on my line but is not one of my points Take turns guessing each other s points 3 guesses per turn 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 61

G6M7 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Use this coordinate plane to help you answer the questions 5 A 4 3 B 2 1 7 6 5 4 3 2 1 1 2 C 3 4 5 1 2 3 4 5 6 7 D 1 Label each point on the coordinate plane with an ordered pair 2 What do you notice about the locations and ordered pairs of B C and D How are they different from those for point A 3 Plot a point at 2 5 Label it E Plot another point at 3 4 5 Label it F 3 The coordinate plane is divided into four quadrants I II III and IV as shown here G 5 2 y Quadrant II H 1 5 Quadrant I x Quadrant III I 7 4 Quadrant IV a In which quadrant is G located H I b A point has a positive y coordinate In which quadrant could it be 62 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION c G6M7 LESSON 11 Finish completing the table below to show the signs of the coordinates for a point plotted in each quadrant Quadrant x coordinate I positive II y coordinate positive III negative IV negative ACTIVITY 2 43 The scores for hitting each target are listed below Use this information to answer the following questions y Heart 2 points 1 Moon 4 points 2 8 7 6 5 4 3 2 1 1 1 2 x Hexagon 6 points 2 Star 8 points 3 4 5 6 7 8 Name the coordinates for a possible landing point to score the following points 1 6 points 2 2 points 4 4 points 5 8 points 3 No points 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 11 ZEARN MATH STUDENT EDITION Lesson Summary Just as the number line can be extended to the left to include negative numbers the x and y axis of a coordinate plane can also be extended to include negative values The ordered pair x y can have negative x and y values For B 4 1 the x value of 4 tells us that the point is 4 units to the left of the y axis The y value of 1 tells us that the point is 1 unit above the x axis The same reasoning applies to the points A and C The x and y coordinates for point A are positive so A is to the right of the y axis and above the x axis The x and y coordinates for point C are negative so C is to the left of the y axis and below the x axis 7 6 5 4 B 4 1 3 2 1 7 6 5 4 3 2 1 1 2 C 3 5 3 3 4 5 6 7 A 2 3 1 2 3 4 5 6 7 TERMINOLOGY Quadrant 64 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 11 Name Date GRADE 6 MISSION 7 LESSON 11 Exit Ticket The scores for hitting one of the targets below are y Heart 2 points 4 Happy Face 4 points 5 3 Diamond 6 points 2 1 5 4 3 2 1 1 1 2 3 4 5 x Lightning bolt 8 points 2 3 4 5 1 Andre shot three darts and they landed at 3 4 5 3 and 1 1 What is his total score Show your reasoning 2 Jada threw a dart and scored 4 points She threw a second dart that landed directly below the first one and scored 6 points Name two coordinates that could be the landing points of her two darts 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 12 Lesson 12 Constructing the Coordinate Plane Let s investigate different ways of creating a coordinate plane Warm Up Some data were collected over one December afternoon in England Temperature C 0 5 1 3 2 4 3 2 4 1 5 2 6 3 7 4 A 5 4 temperature C Time after noon hours 3 2 1 1 B 3 4 5 6 7 8 9 6 4 2 2 2 2 8 2 time after noon hrs temperature C 1 4 4 6 8 10 time after noon hrs 4 6 b Explain why the other two sets of axes did not seem as appropriate as the one you chose C 30 temperature C a Which set of axes would you choose to represent these data Explain your reasoning 20 10 10 10 10 20 30 40 time after noon hrs 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 67

G6M7 LESSON 12 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 For each set of coordinates draw and label an appropriate pair of axes and plot the points a 1 2 3 4 5 2 0 2 5 b 50 50 0 0 10 30 35 40 68 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION c 14 3 4 54 1 2 G6M7 LESSON 12 1 14 34 14 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 69

G6M7 LESSON 12 ZEARN MATH STUDENT EDITION Lesson Summary The coordinate plane can be used to show information involving pairs of numbers When using the coordinate plane we should pay close attention to what each axis represents and what scale each uses Suppose we want to plot the following data about the temperatures in Minneapolis one evening We can decide that the x axis represents number of hours in relation to midnight and the y axis represents temperatures in degrees Celsius Time hours from midnight Temperature C 4 3 1 2 0 4 3 8 In this case x values less than 0 represent hours before midnight and x values greater than 0 represent hours after midnight On the y axis the values represent temperatures above and below the freezing point of 0 degrees Celsius The data involve whole numbers so it is appropriate that each square on the grid represents a whole number On the left of the origin the x axis needs to go as far as 4 or less farther to the left On the right it needs to go to 3 or greater Below the origin the y axis has to go as far as 8 or lower Above the origin it needs to go to 3 or higher temperature degrees C Here is a graph of the data with the axes labeled appropriately On this coordinate plane the point at 0 0 means a temperature of 0 degrees Celsius at midnight The point at 4 3 means a temperature of 3 degrees Celsius at 4 hours before midnight or 8 p m y 6 5 4 3 2 1 8 7 6 5 4 3 2 1 1 2 1 2 3 4 5 6 7 8 time hours from midnight 9 10 x 3 4 5 6 7 8 70 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M7 LESSON 12 Name Date GRADE 6 MISSION 7 LESSON 12 Exit Ticket Lin drew this set of axes and plotted the points A 1 2 B 3 5 C 5 7 D 4 3 and E 4 6 on them y E 10 9 8 7 6 5 4 3 2 1 6 5 4 3 2 1 1 2 3 D 4 B 5 C A 1 2 3 4 5 x Identify as many mistakes as you notice in Lin s graph 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 71

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ZEARN MATH STUDENT EDITION G6M7 LESSON 13 Lesson 13 Interpreting Points on a Coordinate Plane Let s examine what points on the coordinate plane can tell us Warm Up 1 Label each point on the coordinate plane with the appropriate letter and ordered pair A 7 5 5 B 8 4 C 3 2 D 3 5 0 2 y 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 1 1 2 3 4 5 6 7 8 9 10 x 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 73

G6M7 LESSON 13 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 The graph shows the balance in a bank account over a period of 14 days The axis labeled b represents account balance in dollars The axis labeled d represents the day b 400 350 300 250 200 150 100 50 1 2 3 4 5 6 7 8 9 10 11 50 12 13 14 d 100 150 74 1 Estimate the greatest account balance On which day did it occur 2 Estimate the least account balance On which day did it occur 3 What does the point 6 50 tell you about the account balance 4 How can we interpret 50 in the context 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 13 ACTIVITY 2 3 The coordinate plane shows the high and low temperatures in Nome Alaska over a period of 8 days The axis labeled T represents temperatures in degrees Fahrenheit The axis labeled d represents the day T 28 26 24 22 20 18 16 14 12 10 8 6 4 2 2 1 2 3 4 5 6 7 8 9 d 4 6 1 a What was the warmest high temperature b Write an inequality to describe the high temperatures H over the 8 day period 2 a What was the coldest low temperature b Write an inequality to describe the low temperatures L over the 8 day period 3 a On which day s did the largest difference between the high and low temperatures occur Write down this difference b On which day s did the smallest difference between the high and low temperatures occur Write down this difference 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 13 ZEARN MATH STUDENT EDITION Lesson Summary Points on the coordinate plane can give us information about a context or a situation One of those contexts is about money To open a bank account we have to put money into the account The account balance is the amount of money in the account at any given time If we put in 350 when opening the account then the account balance will be 350 Sometimes we may have no money in the account and need to borrow money from the bank In that situation the account balance would have a negative value If we borrow 200 then the account balance is 200 A coordinate grid can be used to display both the balance and the day or time for any balance This allows us to see how the balance changes over time or to compare the balances of different days Similarly if we plot on the coordinate plane data such as temperature over time we can see how temperature changes over time or compare temperatures of different times 76 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION Name G6M7 LESSON 13 Date GRADE 6 MISSION 7 LESSON 13 Exit Ticket The temperature in Princeton was recorded at various times during the day The times and temperatures are shown in the table 1 Label axes and plot points that represent the data Time hours before or after midnight Temperature degrees C 5 1 2 2 1 6 0 3 5 8 6 7 2 In the town of New Haven the temperature at midnight was 1 2 C Plot and label this point Which town was warmer at midnight Princeton or New Haven How many degrees warmer was it 3 If the point 3 2 5 was also plotted on the diagram what would it mean 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 77

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ZEARN MATH STUDENT EDITION G6M7 LESSON 14 Lesson 14 Distances on a Coordinate Plane Let s explore distance on the coordinate plane Warm Up 1 Plot points in your assigned quadrant and label them with their coordinates 5 4 3 2 1 7 6 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 6 7 Concept Exploration ACTIVITY 1 2 Answer the following questions using the coordinate plane below 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 14 1 ZEARN MATH STUDENT EDITION Write the coordinates of each point A 5 E B A 3 2 1 C 7 6 5 4 3 2 1 1 2 D 3 D E 2 4 1 4 5 2 3 4 5 6 7 B C Answer these questions for each pair of points How are the coordinates the same How are they different How far away are they from the y axis To the left or to the right of it How far away are they from the x axis Above or below it a A and B b B and D c 3 A and D Point F has the same coordinates as point C except its y coordinate has the opposite sign a Plot point F on the coordinate plane and label it with its coordinates b How far away are F and C from the x axis c 4 What is the distance between F and C Point G has the same coordinates as point E except its x coordinate has the opposite sign a Plot point G on the coordinate plane and label it with its coordinates b How far away are G and E from the y axis c 5 80 What is the distance between G and E Point H has the same coordinates as point B except its both coordinates have the opposite sign In which quadrant is point H 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 14 ACTIVITY 2 3 Answer the following questions using the coordinate plane below 5 4 A 3 B 2 1 7 6 5 4 3 2 1 1 2 3 E 4 5 1 2 3 4 5 6 7 C D 1 Label each point with its coordinates 2 Find the distance between each of the following pairs of points a Point B and C b Point D and B c Point D and E 3 Which of the points are 5 units from 1 5 3 4 Which of the points are 2 units from 0 5 4 5 5 Plot a point that is both 2 5 units from A and 9 units from E Label that point and write down its coordinates 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 14 ZEARN MATH STUDENT EDITION Lesson Summary The points A 5 2 B 5 2 C 5 2 and D 5 2 are shown in the plane Notice that they all have almost the same coordinates except the signs are different They are all the same distance from each axis but are in different quadrants 5 4 B 5 2 3 A 5 2 2 1 7 6 5 4 3 2 1 1 C 5 2 2 3 1 2 3 4 5 6 7 D 5 2 4 5 We can always tell which quadrant a point is located in by the signs of its coordinates x y Quadrant positive positive I negative positive II negative negative III positive negative IV y Quadrant II Quadrant I x Quadrant III Quadrant IV In general 82 If two points have x coordinates that are opposites like 5 and 5 they are the same distance away from the vertical axis but one is to the left and the other to the right If two points have y coordinates that are opposites like 2 and 2 they are the same distance away from the horizontal axis but one is above and the other below 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 14 Name Date GRADE 6 MISSION 7 LESSON 14 Exit Ticket Here are four points on a coordinate plane 5 4 3 C 2 1 7 6 5 4 3 2 1 1 A 2 3 4 5 1 What is the distance between points A and B 2 What is the distance between points C and D 3 Plot the point 3 2 Label it E 4 Plot the point 4 5 4 5 Label it F 1 2 3 4 5 6 7 B 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 83

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ZEARN MATH STUDENT EDITION G6M7 LESSON 15 Lesson 15 Shapes on the Coordinate Plane Let s use the coordinate plane to solve problems and puzzles Warm Up 1 Follow the directions to draw a figure on the coordinate plane 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 Draw a figure on the coordinate plane with at least three of the following properties 6 vertices 1 pair of parallel sides At least 1 right angle 2 sides with the same length Is your figure a polygon 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 85

G6M7 LESSON 15 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Plot the four polygons on the coordinate plane 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 Here are the coordinates for four polygons Plot them on the coordinate plane connect the points in the order that they are listed and label each polygon with its letter name 86 1 Polygon A 7 4 8 5 8 6 7 7 5 7 5 5 7 4 2 Polygon B 4 3 3 3 2 2 2 1 3 0 4 0 5 1 5 2 4 3 3 Polygon C 8 5 8 8 5 8 5 5 8 5 4 Polygon D 5 1 3 3 1 2 0 3 3 3 5 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 G6M7 LESSON 15 ACTIVITY 2 3 The following diagram shows Andre s route through a maze He started from the lower right entrance 11 15 11 15 11 15 11 15 1 a What are the coordinates of the first two and the last two points of his route b How far did he walk from his starting point to his ending point Show how you know 2 Jada went into the maze and stopped at 7 2 a Plot that point and other points that would lead her out of the maze through the exit on the upper left side b How far from 7 2 must she walk to exit the maze Show 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 87

G6M7 LESSON 15 ZEARN MATH STUDENT EDITION Lesson Synthesis 43 Create a drawing with a perimeter of 30 units using a continuous path of horizontal and vertical line segments y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 x 2 4 6 8 10 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 G6M7 LESSON 15 Lesson Summary We can use coordinates to find lengths of segments in the coordinate plane 2 2 y 4 3 4 2 2 1 7 6 5 4 3 2 1 1 2 1 2 3 1 1 4 5 6 7 x 4 1 3 2 4 4 5 1 4 6 For example we can find the perimeter of this polygon by finding the sum of its side lengths Starting from 2 2 and moving clockwise we can see that the lengths of the segments are 6 3 3 3 3 and 6 units The perimeter is therefore 24 units In general If two points have the same x coordinate they will be on the same vertical line and we can find the distance between them If two points have the same y coordinate they will be on the same horizontal line and we can find the distance between them 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 89

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ZEARN MATH STUDENT EDITION G6M7 LESSON 15 Name Date GRADE 6 MISSION 7 LESSON 15 Exit Ticket 1 Plot the following points on the coordinate plane and connect them to create a polygon A 1 3 B 3 3 C 3 2 D 2 2 E 2 0 F 0 0 G 0 2 H 1 2 I 1 3 5 4 3 2 1 7 6 5 4 3 2 1 1 1 2 3 4 5 6 7 2 3 4 5 2 Find the perimeter of the polygon 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 91

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ZEARN MATH STUDENT EDITION G6M7 LESSON 16 Lesson 16 Common Factors Let s use factors to solve problems Warm Up 1 How are the pairs of figures alike How are they different Concept Exploration ACTIVITY 1 2 Diego is preparing brownies and cookies for a bake sale He would like to make equal size bags for selling all of the 48 brownies and 64 cookies that he has Organize your answer to each question so that it can be followed by others 1 How can Diego package all the 48 brownies so that each bag has the same number of them How many bags can he make and how many brownies will be in each bag Find all the possible ways to package the brownies 2 How can Diego package all the 64 cookies so that each bag has the same number of them How many bags can he make and how many cookies will be in each bag Find all the possible ways to package the cookies 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 16 ZEARN MATH STUDENT EDITION 3 How can Diego package all the 48 brownies and 64 cookies so that each bag has the same combination of items How many bags can he make and how many of each will be in each bag Find all the possible ways to package both items 4 What is the largest number of combination bags that Diego can make with no left over Explain to your partner how you know that it is the largest possible number of bags ACTIVITY 2 3 Solve these problems about factors 1 The greatest common factor of 30 and 18 is 6 In your own words what is the greatest common factor 2 Find all of the factors of 21 and 6 Then identify the greatest common factor of 21 and 6 3 Find all of the factors of 28 and 12 Then identify the greatest common factor of 28 and 12 4 A rectangular bulletin board is 12 inches tall and 27 inches wide Elena plans to cover it with squares of colored paper that are all the same size The paper squares come in different sizes all of them have whole number inches for their side lengths a What is the side length of the largest square that Elena could use to cover the bulletin board completely without gaps and overlaps Explain or show your reasoning b How is the solution to this problem related to greatest common factor 94 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M7 LESSON 16 ACTIVITY 3 43 1 Use your understanding of factors to solve these problems Match the expressions on the left with an equivalent expression on the right 20 35 15 75 56 49 1 5 15 5 4 7 7 8 7 2 Fill in the blanks in the equations below to make the equations true a 6 b 4 15 c 7 18 42 60 44 9 5 18 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 95

G6M7 LESSON 16 ZEARN MATH STUDENT EDITION Lesson Summary A factor of a whole number n is a whole number that divides evenly without a remainder For example 1 2 3 4 6 and 12 are all factors of 12 because each of them divides 12 evenly and without a remainder A common factor of two whole numbers is a factor that they have in common For example 1 3 5 and 15 are factors of 45 they are also factors of 60 We call 1 3 5 and 15 common factors of 45 and 60 The greatest common factor sometimes written as GCF of two whole numbers is the greatest of all of the common factors For example 15 is the greatest common factor for 45 and 60 One way to find the greatest common factor of two whole numbers is to list all of the factors for each and then look for the greatest factor they have in common Let s try to find the greatest common factor of 18 and 24 First we list all the factors of each number Factors of 18 1 2 3 6 9 18 Factors of 24 1 2 3 4 6 8 12 24 The common factors are 1 2 3 and 6 Of these 6 is the greatest one so 6 is the greatest common factor of 18 and 24 TERMINOLOGY Common factor Greatest common factor 96 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 16 Date GRADE 6 MISSION 7 LESSON 16 Exit Ticket 1 What is the greatest common factor of 24 and 64 Show your reasoning 2 In your own words what is the greatest common factor of two whole numbers How can you find 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 97

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ZEARN MATH STUDENT EDITION G6M7 LESSON 17 Lesson 17 Common Multiples Let s use multiples to solve problems Warm Up 1 Find the multiples of 4 and 6 Look at your lists What do you notice What do you wonder Circle all the multiples of 4 in this list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Circle all the multiples of 6 in this list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Concept Exploration ACTIVITY 1 2 A florist can order roses in bunches of 12 and lilies in bunches of 8 Last month she ordered the same number of roses and lilies 1 If she ordered no more than 100 of each kind of flower how many bunches of each could she have ordered Find all the possible combinations 2 What is the smallest number of bunches of roses that she could have ordered What about the smallest number of bunches of lilies 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 99

G6M7 LESSON 17 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 100 Think about the statement The least common multiple of 6 and 8 is 24 1 What do you think the term least common multiple means 2 Find all of the multiples of 10 and 8 that are less than 100 Find the least common multiple of 10 and 8 3 Find all of the multiples of 7 and 9 that are less than 100 Find the least common multiple of 7 and 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 G6M7 LESSON 17 ACTIVITY 3 43 Lin s uncle is opening a bakery On the bakery s grand opening day he plans to give away prizes to the first 50 customers that enter the shop Every fifth customer will get a free bagel Every ninth customer will get a free blueberry muffin Every 12th customer will get a free slice of carrot cake 1 Diego is waiting in line and is the 23rd customer He thinks that he should get farther back in line in order to get a prize Is he right If so how far back should he go to get at least one prize Explain your reasoning 2 Jada is the 36th customer a Will she get a prize If so what prize will she get b Is it possible for her to get more than one prize How do you know Explain your reasoning 3 How many prizes total will Lin s uncle give away 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 101

G6M7 LESSON 17 ZEARN MATH STUDENT EDITION Lesson Summary A multiple of a whole number is a product of that number with another whole number For example 20 is a multiple of 4 because 20 5 4 A common multiple for two whole numbers is a number that is a multiple of both numbers For example 20 is a multiple of 2 and a multiple of 5 so 20 is a common multiple of 2 and 5 The least common multiple sometimes written as LCM of two whole numbers is the smallest multiple they have in common For example 30 is the least common multiple of 6 and 10 One way to find the least common multiple of two numbers is to list multiples of each in order until we find the smallest multiple they have in common Let s find the least common multiple for 4 and 10 First we list some multiples of each number Multiples of 4 4 8 12 16 20 24 28 32 36 40 44 Multiples of 10 10 20 30 40 50 20 and 40 are both common multiples of 4 and 10 as are 60 80 but 20 is the smallest number that is on both lists so 20 is the least common multiple TERMINOLOGY Common Multiple Least Common Multiple 102 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M7 LESSON 17 Date GRADE 6 MISSION 7 LESSON 17 Exit Ticket 1 What is the least common multiple of 6 and 9 Show your reasoning 2 In your own words what is the least common multiple of two whole numbers How can you find 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 103

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ZEARN MATH STUDENT EDITION G6M7 LESSON 18 Lesson 18 Using Common Multiples and Common Factors Let s use common factors and common multiple to solve problems Warm Up 1 We will establish a steady beat together One group will clap on every other beat Another group will say yeah on every third beat During the activity think about these questions When will the two sounds happen at the same time How does this activity relate to common factors or common multiples Concept Exploration ACTIVITY 1 2 Elena is buying cups and plates for her party Cups are sold in packs of 8 and plates are sold in packs of 6 She wants to have the same number of plates and cups a Find a number of plates and cups that meets her requirement b How many packs of each supply will she need to buy to get that number c Name two other quantities of plates and cups she could get to meet her requirement 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 18 3 ZEARN MATH STUDENT EDITION A restaurant owner is replacing the restaurant s bathroom floor with square tiles The tiles will be laid side by side to cover the entire bathroom with no gaps and none of the tiles can be cut The floor is a rectangle that measures 24 feet by 18 feet a What is the largest possible tile size she could use Write the side length in feet Explain how you know it s the largest possible tile b How many of these largest size tiles are needed c 43 Name more tile sizes that are whole number of feet that she could use to cover the bathroom floor Write the side lengths in feet of the square tiles To celebrate the first day of spring Lin is putting stickers on some of the 100 lockers along one side of her middle school s hallway She puts a skateboard sticker on every 4th locker starting with locker 4 and a kite sticker on every 5th locker starting with locker 5 a Name three lockers that will get both stickers b After Lin makes her way down the hall will the 30th locker have no stickers 1 sticker or 2 stickers Explain how you know 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 53 G6M7 LESSON 18 The school nurse is assembling first aid kits for the teachers She has 75 bandages and 90 throat lozenges All the kits must have the same number of each supply and all supplies must be used a What is the largest number of kits the nurse can make b How many bandages and lozenges will be in each kit 63 What kind of mathematical work was involved in each of the previous problems Put a check mark to show what the questions were about Problem Finding multiples Finding least common multiple Finding factors Finding greatest common factor Problem 1 Party Problem 2 Tiles Problem 3 Stickers Problem 4 Kits 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 LESSON 18 ZEARN MATH STUDENT EDITION Lesson Summary If a problem requires dividing two whole numbers by the same whole number solving it involves looking for a common factor If it requires finding the largest number that can divide into the two whole numbers we are looking for the greatest common factor Suppose we have 12 bagels and 18 muffins and want to make bags so each bag has the same combination of bagels and muffins The common factors of 12 and 18 tell us possible number of bags that can be made The common factors of 12 and 18 are 1 2 3 and 6 For these numbers of bags here are the number of bagels and muffins per bag 1 bag 12 bagels and 18 muffins 2 bags 6 bagels and 9 muffins 3 bags 4 bagels and 6 muffins 6 bags 2 bagels and 3 muffins We can see that the largest number of bags that can be made 6 is the greatest common factor If a problem requires finding a number that is a multiple of two given numbers solving it involves looking for a common multiple If it requires finding the first instance the two numbers share a multiple we are looking for the least common multiple Suppose forks are sold in boxes of 9 and spoons are sold in boxes of 15 and we want to buy an equal number of each The multiples of 9 tell us how many forks we could buy and the multiples of 15 tell us how many spoons we could buy as shown here Forks 9 18 27 36 45 54 63 72 81 90 Spoons 15 30 45 60 75 90 If we want as many forks as spoons our options are 45 90 135 and so on but the smallest number of utensils we could buy is 45 the least common multiple This means buying 5 boxes of forks 5 9 45 and 3 boxes of spoons 3 15 45 108 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 Name G6M7 LESSON 18 Date GRADE 6 MISSION 7 LESSON 18 Exit Ticket 1 For each problem tell whether finding the answer requires finding a greatest common factor or a least common multiple You do not need solve the problems a Elena has 20 apples and 35 crackers for making snack bags She wants to make as many snack bags as possible and wants each bag to have the same combination of apples and crackers What is the largest number of snack bags she could make b A string of holiday lights at a store have three colors that flash at different times Red lights flash every fifth second Blue lights flash every third second Green light flashes every four seconds The store owner turns on the lights After how many seconds will all three lights flash at the same time for the first time c A florist orders sunflowers every 6 days starting from the sixth day of the year and daisies every 4 days starting from the fourth day of the year When or on which day will she order both kinds of flowers on the same day d Noah has 12 yellow square cards and 18 green ones All the cards are the same size He would like to arrange the square cards into two rectangles one of each color He wants both the yellow and green rectangles to have the same height and to be as tall as possible What is the tallest possible height for the two rectangles 2 Explain how you know which problem s involves finding the greatest common 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 109

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Grade 6 Mission 8 Data Sets and Distributions

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ZEARN MATH STUDENT EDITION G6M8 LESSON 1 Lesson 1 Got Data Let s explore different kinds of data Warm Up 1 Answer the following questions about the dot plot Here is a dot plot for a data set 1 Determine if each of the following would be an appropriate label to represent the data in the dot plot Be prepared to explain your reasoning 0 1 2 3 4 a Number of children per class b Distance between home and school in miles c Hours spent watching TV each day d Weight of elephants in pounds e Points received on a homework assignment 2 Think of another label that can be used with the dot plot a Write it below the scale of the dot plot Be sure to include the unit of measurement b In your scenario what does one dot represent c In your scenario what would a data point of 0 mean What would a data point of 3 1 4 mean 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 113

G6M8 LESSON 1 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Below are some survey questions Your teacher will explain which questions can be used to learn more about the students in your group and how the responses will be collected The data that your group collects will be used in upcoming activities 1 How long does it usually take you to travel to school Answer to the nearest minute 2 How do you travel to school on most days Choose one Walk Car Public transport Bike School bus Other Scooter or skateboard 3 How tall are you without your shoes on Answer to the nearest centimeter 4 What is the length of your right foot without your shoe on Answer to the nearest centimeter 5 What is your arm span Stretch your arms open and measure the distance from the tip of your right hand s middle finger to the tip of your left hand s middle finger across your back Answer to the nearest centimeter 6 How important are the following issues to you Rate each on a scale from 0 not important to 10 very important a Reducing pollution 114 b Recycling Yes c Conserving water 7 Do you have any siblings No 8 How many hours of sleep per night do you usually get when you have school the next day Answer to the nearest half hour 9 How many hours of sleep per night do you usually get when you do not have school the next day Answer to the nearest half hour 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 1 10 Other than traveling from school what do you do right after school on most days Have a snack Practice a sport Do homework Do chores Read a book Use the computer Talk on the phone Participate in an extracurricular activity 11 If you could meet one of these celebrities who would you choose A city or state leader A musical artist A champion athlete A best selling author A movie star 12 Estimate how much time per week you usually spend on each of these activities Answer to the nearest quarter of an hour a Playing sports or doing outdoor activities c Doing homework b Using a screen for fun watching TV playing computer games etc d Reading ACTIVITY 2 3 1 Use the list of survey questions in the previous activity to help you complete the following questions The first survey question about travel time produces numerical data Identify two other questions that produce numerical data For each describe what was measured and its unit of measurement a Question Unit of measurement b Question 2 What was measured What was measured Unit of measurement The second survey question about travel method produces categorical data Identify two other questions that produce categorical data For each describe what characteristic or feature was being studied a Question Characteristic being studied b Question Characteristic being studied 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 1 3 ZEARN MATH STUDENT EDITION Think about the responses to these survey questions Do they produce numerical or categorical data Be prepared to explain how you know a How many pets do you have b How many years have you lived in this state c What is your favorite band d What kind of music do you like best e What is the area code of your school s phone number f Where were you born g How much does your backpack weigh 4 Name two characteristics you could investigate to learn more about your classmates Make sure one would give categorical data and the other would give numerical data Lesson Summary The table contains data about 10 dogs 116 Dog name Weight kg Breed Duke 36 German shepherd Coco 6 Pug Pierre 7 Pug Ginger 35 German shepherd Lucky 10 Beagle Daisy 10 Beagle Buster 35 German shepherd 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 1 Dog name Weight kg Breed Pepper 7 Pug Rocky 7 Beagle Lady 32 German shepherd The weights of the dogs are an example of numerical data which is data that are numbers quantities or measurements The weights of the dogs are measurements in kilograms The dog breeds are an example of categorical data which is data containing values that can be sorted into categories In this case there are three categories for dog breeds pug beagle and German shepherd ome data with numbers are categorical because the numbers are not quantities or measurements S For example telephone area codes are categorical data because the numbers are labels rather than quantities or measurements Numerical data can be represented with a dot plot sometimes called a line plot Here is a dot plot that shows the weights of the dogs 5 10 15 20 25 30 35 40 Dog Weights in Kilograms We can collect and study both kinds of data by doing surveys or taking measurements When we do it is important to think about what feature we are studying for example breeds of dogs or weights of dogs and what units of measurement are used TERMINOLOGY Categorical data Dot plot Numerical data 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 1 Name Date GRADE 6 MISSION 8 LESSON 1 Exit Ticket 1 Would each survey question produce categorical data or numerical data a What is your favorite vegetable b Have you been to the capital city of your state c How old is the youngest person in your family d In which zip code do you live e What is the first letter of your name f 2 How many hours do you spend outdoors each day Andre collected data measured in centimeters 8 5 10 5 7 8 9 5 8 1 9 0 10 2 9 6 11 2 10 9 12 7 9 8 What could he be investigating Select all that apply a The weight of a dozen eggs b The length of leaves from a tree c The height of cups and mugs in a cupboard d The length of songs in a music CD e The length of colored pencils in a box 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 119

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ZEARN MATH STUDENT EDITION G6M8 LESSON 2 Lesson 2 Statistical Questions Let s look more closely at data and the questions they can help to answer Warm Up 1 Measure the length of your pencil Then answer the question about pencil lengths in your class 1 4 1 Measure your pencil to the nearest inch Then plot your measurement on the class dot plot 2 What is the difference between the longest and shortest pencil lengths in the class 3 What is the most common pencil length 4 Find the difference in lengths between the most common length and the shortest pencil Concept Exploration ACTIVITY 1 2 Ten sixth grade students at a school were each asked five survey questions Their answers to each question are shown in the table below Data set A 0 1 1 3 0 0 0 2 1 1 Data set B 12 12 12 12 12 12 12 12 12 12 Data set C 6 5 7 6 4 5 3 4 6 8 Data set D 6 6 6 6 6 6 6 6 6 6 Data set E 3 7 9 11 6 4 2 16 6 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 121

G6M8 LESSON 2 1 2 ZEARN MATH STUDENT EDITION Here are the five survey questions Match each question to a data set that could represent the students answers Explain your reasoning Question 1 Flip a coin 10 times How many heads did you get Data set Reason Question 2 How many books did you read in the last year Data set Reason Question 3 What grade are you in Data set Reason Question 4 How many dogs and cats do you have Data set Reason Question 5 How many inches are in 1 foot Data set Reason Discuss with a partner How are Question 3 and Question 5 different from the other questions ACTIVITY 2 TASK 1 3 Use the examples of the statistical question and non statistical questions to discuss the following questions with your partner These three questions are examples of statistical questions 122 These three questions are not examples of statistical questions What is the most common color of the cars in the school parking lot What color is the principal s car What percentage of students in the school have a cell phone Does Elena have a cell phone Which kind of literature fiction or nonfiction is more popular among students in the school What kind of literature fiction or nonfiction does Diego prefer 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 1 G6M8 LESSON 2 Study the examples and non examples Discuss with your partner How are the three statistical questions alike What do they have in common How are the three non statistical questions alike What do they have in common How can you find answers to the statistical questions How about answers to non statistical questions What makes a question a statistical question ACTIVITY 2 TASK 2 43 Read each question Think about the data you might collect to answer it and whether you expect to see variability in the data Complete each blank with Yes or No a How many cups of water do my classmates drink each day Is variability expected in the data Is the question statistical b Where in town does our math teacher live Is variability expected in the data Is the question statistical c How many minutes does it take students in my class to get ready for school in the morning Is variability expected in the data Is the question statistical d How many minutes of recess do sixth grade students have each day Is variability expected in the data Is the question statistical e Do all students in my class know what month it is Is variability expected in the data Is the question statistical Lesson Summary We often collect data to answer questions about something The data we collect may show variability which means the data values are not all the same Some data sets have more variability than others Here are two sets of figures 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 123

G6M8 LESSON 2 ZEARN MATH STUDENT EDITION Set A has more figures with the same shape color or size Set B shows more figures with different shapes colors or sizes so set B has greater variability than set A Both numerical and categorical data can show variability Numerical sets can contain different numbers and categorical sets can contain different categories or types When a question can only be answered by using data and we expect that data to have variability we call it a statistical question Here are some examples Who is the most popular musical artist at your school When do students in your class typically eat dinner Which classroom in your school has the most books To answer the question about books we may need to count all of the books in each classroom of a school The data we collect would likely show variability because we would expect each classroom to have a different number of books In contrast the question How many books are in your classroom is not a statistical question If we collect data to answer the question for example by asking everyone in the class to count books the data can be expected to show the same value Likewise if we ask all of the students at a school where they go to school that question is not a statistical question because the responses will all be the same TERMINOLOGY statistical question variability 124 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 2 Date GRADE 6 MISSION 8 LESSON 2 Exit Ticket Here are two questions Question A Over the past 10 years what is the warmest temperature recorded in degrees Fahrenheit for the month of December in Miami Florida Question B At what temperature does water freeze in Miami Florida 1 Decide if each question is statistical or non statistical Explain your reasoning 2 If you decide that a question is statistical describe how you would find the answer What data would you collect 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 3 Lesson 3 Representing Data Graphically Let s represent data with dot plots and bar graphs Warm Up 1 Clare collects bottle caps and keeps them in plastic containers Write one statistical question that someone could ask Clare about her collection Be prepared to explain your reasoning Concept Exploration ACTIVITY 1 2 Answer the following questions 1 Write down the statistical question your class is trying to answer 2 Look at the dot plot that shows the data from your class Write down one thing you notice and one thing you wonder about the dot plot 3 Use the dot plot to answer the statistical question Be prepared to explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 127

G6M8 LESSON 3 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Priya wants to know if basketball players on a men s team and a women s team have had prior experience in international competitions She gathered data on the number of times the players were on a team before 2016 Men s team 3 0 0 0 0 1 0 0 0 0 0 0 Women s team 2 3 3 1 0 2 0 1 1 0 3 1 1 Did Priya collect categorical or numerical data 2 Organize the information on the two basketball teams into these tables Men s Basketball Team Players Number of prior competitions 3 Women s Basketball Team Players Frequency number 0 0 1 1 2 2 3 3 4 4 Frequency number Make a dot plot for each table Men s Basketball Team Players 0 1 2 3 Number of Prior Competitions 128 Number of prior competitions Women s Basketball Team Players 4 0 1 2 3 4 Number of Prior Competitions 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 3 Study your dot plots What do they tell you about the competition participation of a the players on the men s basketball team b the players on the women s basketball team 5 Explain why a dot plot is an appropriate representation for Priya s data Lesson Summary Weight in kilograms Frequency 6 1 7 3 10 2 32 1 35 2 36 1 When we analyze data we are often interested in the distribution which is information that shows all the data values and how often they occur In a previous lesson we saw data about 10 dogs We can see the distribution of the dog weights in a table such as this one The term frequency refers to the number of times a data value occurs In this case we see that there are three dogs that weigh 7 kilograms so 3 is the frequency for the value 7 kilograms Recall that dot plots are often used to represent numerical data Like a frequency table a dot plot also shows the distribution of a data set This dot plot which you saw in an earlier lesson shows the distribution of dog weights 5 10 15 20 25 30 35 40 Dog weights in kilograms 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 129

G6M8 LESSON 3 ZEARN MATH STUDENT EDITION A dot plot uses a horizontal number line We show the frequency of a value by the number of dots drawn above that value Here the two dots above the number 35 tell us that there are two dogs weighing 35 kilograms The distribution of categorical data can also be shown in a table This table shows the distribution of dog breeds Breed Frequency Pug 9 Beagle 9 German Shepherd 12 We often represent the distribution of categorical data using a bar graph A bar graph also uses a horizontal line Above it we draw a rectangle or bar to represent each category in the data set The height of a bar tells us the frequency of the category There are twelve German shepherds in the data set so the bar for this category is 12 units tall Below the line we write the labels for the categories In a dot plot a data value is placed according to its position on the number line A weight of 10 kilograms must be shown as a dot above 10 on the number line In a bar graph however the categories can be listed in any order The bar that shows the frequency of pugs can be placed anywhere along the horizontal line TERMINOLOGY Distribution Frequency 130 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 3 Name Date GRADE 6 MISSION 8 LESSON 3 Exit Ticket 1 Noah gathered information on the home states of the swimmers on Team USA He organized the data in a table Would a dot plot be appropriate to display his data Explain your reasoning 2 This dot plot shows the ages of students in a swimming class How many students are in the class 16 18 20 22 24 26 28 30 32 34 36 Age in months Based on the dot plot do you agree with each of the following statements Explain your reasoning a The class is an adult swimming class b Half of the students are between 2 and 3 years old 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 4 Lesson 4 Dot Plots Let s investigate what dot plots and bar graphs can tell us Warm Up 1 Fifteen customers in a pizza shop were asked How many toppings did you add to your cheese pizza Their responses are shown in the table 1 2 1 3 0 1 1 2 0 3 0 1 Could you use a dot plot to represent the data Explain your reasoning 2 Complete the table Number of Toppings 0 1 2 2 Frequency Number 0 1 2 3 Concept Exploration ACTIVITY 1 2 1 Solve the following problems in your notes Use the tables from the warm up to display the number of toppings as a dot plot Label your drawing clearly 0 1 2 3 4 5 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 133

G6M8 LESSON 4 2 ZEARN MATH STUDENT EDITION Use your dot plot to study the distribution for number of toppings What do you notice about the number of toppings that this group of customers ordered Write 2 3 sentences summarizing your observations ACTIVITY 2 3 Twenty five sixth grade students answered the question How many hours do you generally spend on homework each week Answer the following questions 1 Why is this question a statistical question 2 This dot plot shows the number of hours per week that these 25 students reported spending on homework 0 1 2 3 4 5 6 7 8 9 10 Hours Spent on Homework Per Week Use the dot plot to answer the following questions For each show or explain your reasoning a What percentage of the students reported spending 1 hour on homework each week b What percentage of the students reported spending 4 or fewer hours on homework each week 3 134 Would 6 hours per week be a good description of the number of hours this group of students spends on homework per week What about 1 hour per week Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 4 4 What value do you think would be a good description of the homework time of the students in this group Explain your reasoning 5 Someone said In general these students spend roughly the same number of hours doing homework Do you agree Explain your reasoning Lesson Summary We often collect and analyze data because we are interested in learning what is typical or what is common and can be expected in a group Sometimes it is easy to tell what a typical member of the group is For example we can say that a typical shape in this set is a large circle Just looking at the members of a group doesn t always tell us what is typical however For example if we are interested in the side length typical of squares in this set it isn t easy to do so just by studying the set visually In a situation like this it is helpful to gather the side lengths of the squares in the set and look at their distribution as shown in this dot plot 1 2 3 4 5 6 7 8 Side Lengths in Centimeters 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 135

G6M8 LESSON 4 ZEARN MATH STUDENT EDITION We can see that many of the data points are between 2 and 4 so we could say that side lengths between 2 and 4 centimeters or close to these lengths are typical of squares in this set 136 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 4 Name Date GRADE 6 MISSION 8 LESSON 4 Exit Ticket A group of students was asked How many children are in your family The responses are displayed in the dot plot 0 1 2 3 4 5 6 Number of Children 1 How many students responded to the questions 2 What percentage of the students have more than one child in the family 3 Write a sentence that describes the distribution of the data shown on the dot plot 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 137

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ZEARN MATH STUDENT EDITION G6M8 LESSON 5 Lesson 5 Using Dot Plots to Answer Statistical Questions Let s use dot plots to describe distributions and answer questions Warm Up 1 This dot plot shows the weights of backpacks in kilograms of 50 sixth grade students at a school in New Zealand Use the dot plot to answer the following questions in your notes 0 2 4 6 8 10 12 14 16 Weight in kilograms 1 The dot plot shows several dots at 0 kilograms What could a value of 0 mean in this context 2 Clare and Tyler studied the dot plot Clare said I think we can use 3 kilograms to describe a typical backpack weight of the group because it represents 20 or the largest portion of the data Tyler disagreed and said I think 3 kilograms is too low to describe a typical weight Half of the dots are for backpacks that are heavier than 3 kilograms so I would use a larger value 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 139

G6M8 LESSON 5 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Twenty five sixth grade students were asked to estimate how many hours a week they spend talking on the phone This dot plot represents their reported number of hours of phone usage per week Use the dot plot to answer the following questions 1 a How many of the students reported not talking on the phone during the week Explain how you know 0 1 2 3 4 5 6 7 8 9 10 Hours on the phone per week b What percentage of the students reported not talking on the phone 2 a What is the largest number of hours a student spent talking on the phone per week b What percentage of the group reported talking on the phone for this amount of time 3 a How many hours would you say that these students typically spend talking on the phone b How many minutes per day would that be 4 a How would you describe the spread of the data Would you consider these students amounts of time on the phone to be alike or different Explain your reasoning b Here is the dot plot from an earlier activity It shows the number of hours per week the same group of 25 sixth grade students reported spending on homework Overall are these students more alike in the amount of time they spend talking on the phone or in the amount of time they spend on homework Explain your reasoning 140 0 1 2 3 4 5 6 7 8 9 10 Hours spent on homework per week 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 5 G6M8 LESSON 5 Suppose someone claimed that these sixth grade students spend too much time on the phone Do you agree Use your analysis of the dot plot to support your answer ACTIVITY 2 3 Answer the following questions 1 A keyboarding teacher wondered Do typing speeds of students improve after taking a keyboarding course Explain why her question is a statistical question 2 The teacher recorded the number of words that her students could type per minute at the beginning of a course and again at the end The two dot plots show the two data sets Beginning of course 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 28 30 32 34 36 Number of words per minute End of course 8 10 12 14 16 18 20 22 24 26 Number of words per minute Based on the dot plots do you agree with each of the following statements about this group of students Be prepared to explain your reasoning a Overall the students typing speed did not improve They typed at the same speed at the end of the course as they did at the beginning b 20 words per minute is a good estimate for how fast in general the students typed at the beginning of the course c 20 words per minute is a good description of the center of the data set at the end of the course d There was more variability in the typing speeds at the beginning of the course than at the end so the students typing speeds were more alike at the end 3 Overall how fast would you say that the students typed after completing the course What would you consider the center of the end of course data 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 5 ZEARN MATH STUDENT EDITION Lesson Summary One way to describe what is typical or characteristic for a data set is by looking at the center and spread of its distribution Let s compare the distribution of cat weights and dog weights shown on these dot plots 2 3 4 5 6 7 8 9 10 11 12 Cat weights in kilograms The collection of points for the cat data is further to 2 3 4 5 6 7 8 9 10 11 Dog weights in kilograms the left on the number line than the dog data Based on the dot plots we may describe the center of the distribution for cat weights to be between 4 and 5 kilograms and the center for dog weights to be between 7 and 8 kilograms 12 We often say that values at or near the center of a distribution are typical for that group This means that a weight of 4 5 kilograms is typical for a cat in the data set and weight of 7 8 kilograms is typical for a dog We also see that the dog weights are more spread out than the cat weights The difference between the heaviest and lightest cats is only 4 kilograms but the difference between the heaviest and lightest dogs is 6 kilograms A distribution with greater spread tells us that the data have greater variability In this case we could say that the cats are more similar in their weights than the dogs In future lessons we will discuss how to measure the center and spread of a distribution TERMINOLOGY Center Spread 142 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 5 Name Date GRADE 6 MISSION 8 LESSON 5 Exit Ticket A farmer sells tomatoes in packages of ten She would like the tomatoes in each package to all be about the same size and close to 5 5 ounces in weight The farmer is considering two different tomato varieties Variety A and Variety B She weighs 25 tomatoes of each variety These dot plots show her data Variety A 5 35 5 4 5 45 5 5 5 55 5 6 5 55 5 6 Weight in ounces Variety B 5 35 5 4 5 45 5 5 Weight in ounces 1 What would be a good description for the weight of Variety A tomatoes in general What about for the weight of Variety B tomatoes in general 2 Which tomato variety should the farmer choose 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 143

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ZEARN MATH STUDENT EDITION G6M8 LESSON 6 Lesson 6 Histograms Let s explore how histograms represent data sets Warm Up 1 Here is a dot plot showing the weights in pounds of 40 dogs at a dog show 60 70 80 90 100 110 120 130 140 150 160 170 180 Weight in pounds 1 Write two statistical questions that can be answered using the dot plot 2 What would you consider a typical weight for a dog at this dog show 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 145

G6M8 LESSON 6 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Here is a histogram that shows some dog weights in pounds 14 12 10 8 6 4 2 0 60 80 100 120 140 160 180 Weight in pounds Each bar includes the left end value but not the right end value For example the first bar includes dogs that weigh 60 pounds and 68 pounds but not 80 pounds 1 Use the histogram to answer the following questions a How many dogs weigh at least 100 pounds b How many dogs weigh exactly 70 pounds c How many dogs weigh at least 120 and less than 160 pounds d How much does the heaviest dog at the show weigh e What would you consider a typical weight for a dog at this dog show Explain your reasoning 2 146 Discuss with a partner If you used the dot plot to answer the same five questions you just answered how would your answers be different How are the histogram and the dot plot alike How are they different 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 6 ACTIVITY 2 3 The dot plot shows the population data from the 2010 census for each of the fifty states and the District of Columbia DC Every ten years the United States conducts a census which is an effort to count the entire population 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Population of states in millions 1 Here are some statistical questions about the population of the fifty states and DC How difficult would it be to answer the questions using the dot plot In the middle column rate each question with an E easy to answer H hard to answer or I impossible to answer Be prepared to explain your reasoning Statistical question Using the dot plot Using the histogram a How many states have populations greater than 15 million b Which states have populations greater than 15 million c How many states have populations less than 5 million d What is a typical state population e Are there more states with fewer than 5 million people or more states with between 5 and 10 million people f How would you describe the distribution of state populations 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 6 2 ZEARN MATH STUDENT EDITION Here are the population data for all states and the District of Columbia from the 2010 census Use the information to complete the table Alabama 4 78 Indiana 6 48 Nevada 2 70 Tennessee 6 35 Alaska 0 71 Iowa 3 05 New Hampshire 1 32 Texas 25 15 Arizona 6 39 Kansas 2 85 New Jersey 8 79 Utah 2 76 Arkansas 2 92 Kentucky 4 34 New Mexico 2 06 Vermont 0 63 California 37 25 Louisiana 4 53 New York 19 38 Virginia 8 00 Colorado 5 03 Maine 1 33 North Carolina 9 54 Washington 6 72 Connecticut 3 57 Maryland 5 77 North Dakota 0 67 West Virginia 1 85 Delaware 0 90 Massachusetts 6 55 Ohio 11 54 Wisconsin 5 69 District of Columbia 0 60 Michigan 9 88 Oklahoma 3 75 Wyoming 0 56 Florida 18 80 Minnesota 5 30 Oregon 3 83 Georgia 9 69 Mississippi 2 97 Pennsylvania 12 70 Hawaii 1 36 Missouri 5 99 Rhode Island 1 05 Idaho 1 57 Montana 0 99 South Carolina 4 63 Illinois 12 83 Nebraska 1 83 South Dakota 0 81 Population millions Frequency 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 148 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 3 G6M8 LESSON 6 Use the grid and the information in your table to create a histogram 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 25 30 35 40 Population of states in millions 4 Return to the statistical questions at the beginning of the activity Which ones are now easier to answer In the last column of the table rate each question with an E easy H hard and I impossible based on how difficult it is to answer 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 149

G6M8 LESSON 6 ZEARN MATH STUDENT EDITION Lesson Summary In addition to using dot plots we can also represent distributions of numerical data using histograms Here is a dot plot that shows the weights in kilograms of 30 dogs followed by a histogram that shows the same distribution 10 15 20 25 Dog weights in kilograms In a histogram data values are placed in groups or bins of a certain size and each group is represented with a bar The height of the bar tells us the frequency for that group 35 30 For example the height of the tallest bar is 10 and the bar represents weights from 20 to less than 25 kilograms so there are 10 dogs whose weights fall in that group Similarly there are 3 dogs that weigh anywhere from 25 to less than 30 kilograms 10 8 6 4 Notice that the histogram and the dot plot have a similar shape The dot plot has the advantage of showing all of the data values but the histogram is easier to draw and to interpret when there are a lot of values or when the values are all different 2 0 10 15 20 25 30 35 Dog weights in kilograms Here is a dot plot showing the weight distribution of 40 dogs The weights were measured to the nearest 0 1 kilogram instead of the nearest kilogram 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 Dog weights in kilograms Here is a histogram showing the same distribution In this case it is difficult to make sense of the distribution from the dot plot because the dots are so close together and all in one line The histogram of the same data set does a much better job showing the distribution of weights even though we can t see the individual data values 12 10 8 6 4 2 0 10 20 25 30 15 Dog weights in kilograms 35 TERMINOLOGY Histogram 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 G6M8 LESSON 6 Name Date GRADE 6 MISSION 8 LESSON 6 Exit Ticket The table shows the average amount of rainfall in inches for each month in Miami Florida 1 Month Rainfall inches Month Rainfall inches January 1 61 July 6 5 February 2 24 August 8 9 March 2 99 September 9 84 April 3 14 October 6 34 May 5 35 November 3 27 June 9 69 December 2 06 Complete the table and use it to make a histogram Rainfall inches 0 2 2 4 4 6 6 8 Frequency 6 5 4 3 2 1 0 0 8 10 2 2 4 6 8 10 Rainfall in inches What is a typical amount of rainfall in one month in Miami 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 7 Lesson 7 Using Histograms to Answer Statistical Questions Let s draw histograms and use them to answer questions Warm Up Here are four questions about the population of Alaska Which question does not belong Be prepared to explain your reasoning 1 1 In general at what age do Alaska residents retire 2 At what age can Alaskans vote 3 What is the age difference between the youngest and oldest Alaska residents with a full time job 4 Which age group is the largest part of the population 18 years or younger 19 24 years 25 34 years 35 44 years 45 54 years 55 64 years or 65 years or older Concept Exploration ACTIVITY 1 An earthworm farmer set up several containers of a certain species of earthworms so that he could learn about their lengths The lengths of the earthworms provide information about their ages The farmer measured the lengths of 25 earthworms in one of the containers Each length was measured in millimeters 2 1 a Using a ruler draw a line segment for each length 20 millimeters 40 millimeters 60 millimeters 80 millimeters 100 millimeters b Here are the lengths in millimeters of the 25 earthworms 6 11 18 19 20 23 23 25 25 26 27 27 28 29 32 33 41 42 48 52 54 59 60 77 93 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 7 ZEARN MATH STUDENT EDITION Complete the table for the lengths of the 25 earthworms Length Frequency 0 millimeters to less than 20 millimeters 20 millimeters to less than 40 millimeters 40 millimeters to less than 60 millimeters 60 millimeters to less than 80 millimeters 80 millimeters to less than 100 millimeters 2 Use the grid and the information in the table to draw a histogram for the worm length data Be sure to label the axes of your histogram 14 12 10 8 6 4 2 0 154 10 20 30 40 50 60 70 80 90 100 3 Based on the histogram what is a typical length for these 25 earthworms Explain how you know 4 Write 1 2 sentences to describe the spread of the data Do most of the worms have a length that is close to your estimate of a typical length or are they very different in length 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 7 ACTIVITY 2 3 1 The earthworm farmer measured the lengths of 25 earthworms from a different container Each length was measured in millimeters Here are the lengths in millimeters of the 25 earthworms 19 27 35 40 44 46 49 55 57 61 64 65 65 68 72 75 75 75 75 77 79 80 88 92 97 Complete the stem plot below to show the lengths of the 25 earthworms The length of the first earthworm is shown Stem Leaf 1 9 2 3 4 5 6 7 8 9 Key 1 9 represents 19 2 Based on the stem plot what is a typical length for these 25 earthworms Explain how you know 3 Write 1 2 sentences to describe the spread of the data 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 7 ZEARN MATH STUDENT EDITION ACTIVITY 3 Professional basketball players tend to be taller than professional baseball players Here are two histograms that show height distributions of 50 male professional baseball players and 50 male professional basketball players 43 1 Decide which histogram shows the heights of baseball players and which shows the heights of basketball players Be prepared to explain your reasoning a b 20 20 16 16 12 12 8 8 4 4 0 66 68 70 72 74 76 78 80 Height in inches 156 82 84 86 88 90 0 66 68 70 72 74 76 78 80 82 84 86 88 90 Height in inches 2 Write 2 3 sentences that describe the distribution of the heights of the basketball players Comment on the center and spread of the data 3 Write 2 3 sentences that describe the distribution of the heights of the baseball players Comment on the center and spread of the data 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 7 Lesson Summary Here are the weights in kilograms of 30 dogs 10 11 12 12 13 15 16 16 17 18 18 19 20 20 20 21 22 22 22 23 24 24 26 26 28 30 32 32 34 34 Before we draw a histogram let s consider a couple of questions What are the smallest and largest values in our data set This gives us an idea of the distance on the number line that our histogram will cover In this case the minimum is 10 and the maximum is 34 so our number line needs to extend from 10 to 35 at the very least Remember the convention we use to mark off the number line for a histogram we include the left boundary of a bar but exclude the right boundary If 34 is the right boundary of the last bar it won t be included in that bar so the number line needs to go a little greater than the maximum value What group size or bin size seems reasonable here We could organize the weights into bins of 2 kilograms 10 12 14 5 kilograms 10 15 20 25 10 kilograms 10 20 30 or any other size The smaller the bins the more bars we will have and vice versa Let s use bins of 5 kilograms for the dog weights The boundaries of our bins will be 10 15 20 25 30 35 We stop at 35 because it is greater than the maximum Weight in kilograms Frequency 10 to less than 15 5 15 to less than 20 7 20 to less than 25 10 25 to less than 30 3 30 to less than 35 5 Next we find the frequency for the values in each group It is helpful to organize the values in a table Now we can draw the histogram 12 10 8 6 4 2 0 10 15 20 25 30 Dog weights in kilograms 35 The histogram allows us to learn more about the dog weight distribution and describe its center and spread 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G6M8 LESSON 7 Name Date GRADE 6 MISSION 8 LESSON 7 Exit Ticket The two histograms show the points scored per game by a college basketball player in 2012 and 2016 12 12 10 10 8 8 6 6 4 4 2 2 0 5 10 15 20 25 30 35 40 Points per game in 2012 45 0 5 10 15 20 25 30 35 40 45 Points per game in 2016 1 What is a typical number of points per game scored by this player in 2012 What about in 2016 Explain your reasoning 2 Write 2 3 sentences that describe the spreads of the two distributions including what spreads might tell us in this context 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 159

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ZEARN MATH STUDENT EDITION G6M8 LESSON 8 Lesson 8 Describing Distributions on Histograms Let s describe distributions displayed in histograms Warm Up Which histogram does not belong Be prepared to explain your reasoning 1 A B 30 30 25 25 20 20 15 15 10 10 5 5 0 C 45 55 65 75 85 95 105 115 125 135 145 0 155 D 30 25 20 20 15 15 10 10 5 5 45 55 65 75 85 95 105 115 125 135 145 155 55 65 75 85 95 105 115 125 135 145 155 30 25 0 45 0 45 55 65 75 85 95 105 115 125 135 145 155 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 8 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Follow the directions and answer the questions about your histogram cards 1 Your teacher will give your group a set of histogram cards Sort them into two piles one for histograms that are approximately symmetrical and another for those that are not 2 Discuss your sorting decisions with another group Do both groups agree which cards should go in each pile If not discuss the reasons behind the differences and see if you can reach agreement Record your final decisions 3 Histograms that are approximately symmetrical Histograms that are not approximately symmetrical Histograms are also described by how many major peaks they have Histogram A is an example of a distribution with a single peak that is not symmetrical Which other histograms have this feature 4 Some histograms have a gap a space between two bars where there are no data points For example if some students in a class have 7 or more siblings but the rest of the students have 0 1 or 2 siblings the histogram for this data set would show gaps between the bars because no students have 3 4 5 or 6 siblings Which histograms do you think show one or more gaps 5 Sometimes there are a few data points in a data set that are far from the center Histogram A is an example of a distribution with this feature Would you describe any of the other histograms as having this feature If so which ones 162 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 8 ACTIVITY 2 3 1 One partner will create a bar graph to represent the data on the class s travel methods and the other will create a histogram to represent the data on travel times Then answer the questions together Use the data to draw a histogram that shows your class s travel times 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Travel time in minutes 2 Write a couple of sentences to describe the distribution of travel times Comment on the center and spread of the data as well as the shape and features 3 Use the data on methods of travel to draw a bar graph Include labels for the horizontal axis 4 Write 2 3 sentences to describe what you learned about your class s methods of transportation to school Comment on any patterns you noticed 5 Compare the histogram and the bar graph that you drew Discuss your thinking with your partner How are they alike How are they different 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 163

G6M8 LESSON 8 ZEARN MATH STUDENT EDITION Lesson Summary We can describe the shape and features of the distribution shown on a histogram Here are two distributions with very different shapes and features B A 6 6 5 5 4 4 3 3 2 2 1 1 0 10 12 14 16 18 20 22 24 26 28 30 0 10 12 14 16 18 20 22 24 26 28 30 Histogram A is very symmetrical and has a peak near 21 Histogram B is not symmetrical and has two peaks one near 11 and one near 25 Histogram B has two clusters A cluster forms when many data points are near a particular value or a neighborhood of values on a number line Histogram B also has a gap between 20 and 22 A gap shows a location with no data values Here is a bar graph showing the breeds of 30 dogs and a histogram for their weights 10 12 8 9 6 6 4 3 2 0 Pugs Beagles German Shepherds 0 10 15 20 25 30 35 Dog weights in kilograms Bar graphs and histograms may seem alike but they are very different 164 Bar graphs represent categorical data Histograms represent numerical data Bar graphs have spaces between the bars Histograms show a space between bars only when no data values fall between the bars Bars in a bar graph can be in any order Histograms must be in numerical order In a bar graph the number of bars depends on the number of categories In a histogram we choose how many bars to use 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 8 Name Date GRADE 6 MISSION 8 LESSON 8 Exit Ticket Here is a histogram that shows the number of points scored by a college basketball player during the 2008 season Describe the shape and features of the data 12 10 8 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 Points per game 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 165

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ZEARN MATH STUDENT EDITION G6M8 LESSON 9 Lesson 9 Interpreting the Mean as Fair Share Let s explore the mean of a data set and what it tells us Warm Up 1 Use the digits 0 9 to write an expression with a value as close as possible to 4 Each digit can be used only one time in the expression 4 Concept Exploration ACTIVITY 1 2 The kittens in a room at an animal shelter are placed in five crates as shown a The manager of the shelter wants the kittens distributed equally among the crates How might that be done How many kittens will end up in each crate b The number of kittens in each crate after they are equally distributed is called the mean number of kittens per crate or the average number of kittens per crate Explain how the expression 10 5 is related to the average 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 9 c ZEARN MATH STUDENT EDITION A different room in the shelter has 6 crates No two crates contain the same number of kittens and there is an average of 3 kittens per crate Draw or describe at least two different arrangements of kittens that match this description 3 Five servers were scheduled to work the number of hours shown in the table They decided to share the workload so each one would work equal hours Hours worked Server A Server B Server C Server D Server E 3 6 11 7 4 a On the grid on the left draw 5 bars whose heights represent the hours worked by servers A B C D and E 12 12 10 10 8 8 6 6 4 4 2 2 0 0 b Think about how you would rearrange the hours so that each server gets a fair share Then on the grid on the right draw a new graph to represent the rearranged hours Be prepared to explain your reasoning c Based on your second graph what is the average or mean number of hours that the servers will work d Explain why we can also find the mean by finding the value of 31 5 e Which server will see the biggest change to work hours Which server will see the least change 168 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 9 ACTIVITY 2 43 For the past 12 school days Mai has recorded how long her bus rides to school take in minutes The times she recorded are shown in the table 9 8 6 9 10 7 6 12 9 8 10 8 a Find the mean for Mai s data Show your reasoning b In this situation what does the mean tell us about Mai s trip to school 53 For 5 days Tyler recorded how long his walks to school take in minutes The mean for his data is 11 minutes a Without calculating predict if each of the data sets shown could be Tyler s Explain your reasoning Data set A 11 8 7 9 8 Data set B 12 7 13 9 14 Data set C 11 20 6 9 10 Data set D 8 10 9 11 11 b Determine which data set is Tyler s 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 169

G6M8 LESSON 9 ZEARN MATH STUDENT EDITION Lesson Summary Sometimes a general description of a distribution does not give enough information and a more precise way to talk about center or spread would be more useful The mean or average is a number we can use to summarize a distribution We can think about the mean in terms of fair share or leveling out That is a mean can be thought of as a number that each member of a group would have if all the data values were combined and distributed equally among the members The table and diagram show how many liters of water are in each of five bottles 1 4 2 3 0 To find the mean first we add up all of the values which we can think of as putting all of the water together 1 4 2 3 0 10 To find the fair share we divide the 10 liters equally into the 5 containers 10 5 2 Suppose the quiz scores of a student are 70 90 86 and 94 We can find the mean or average score by finding the sum of the scores 70 90 86 94 340 and dividing the sum by four 340 4 85 We can then say that the student scored on average 85 points on the quizzes In general to find the mean of a data set with values we add all of the values and divide the sum by n TERMINOLOGY Average Mean 170 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 9 Date GRADE 6 MISSION 8 LESSON 9 Exit Ticket 1 Last week the daily low temperatures for a city in degrees Celsius were 5 8 6 5 10 7 and 1 What was the average low temperature Show your reasoning 2 The mean of four numbers is 7 Three of the numbers are 5 7 and 7 What is the fourth number 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 171

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ZEARN MATH STUDENT EDITION G6M8 LESSON 10 Lesson 10 Finding and Interpreting the Mean as the Balance Point Let s look at another way to understand the mean of a data set Warm Up 1 Which expression does not belong Be prepared to explain your reasoning 8 8 4 4 4 10 10 4 4 6 6 6 6 6 5 9 9 5 5 4 Concept Exploration ACTIVITY 1 2 1 This data set shows how long it takes for Diego to walk to school in minutes over 5 days The mean number of minutes was 11 Represent Diego s data on a dot plot Mark the location of the mean with a triangle 12 7 13 9 14 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 173

G6M8 LESSON 10 3 ZEARN MATH STUDENT EDITION The mean can also be seen as a measure of center that balances the points in a data set If we find the distance between every point and the mean add the distances on each side of the mean and compare the two sums we can see this balancing a Record the distance between each point and 11 and its location relative to 11 Time in minutes Distance from 11 Left of 11 or right of 11 12 7 13 9 14 b Sum of distances left of 11 Sum of distances right of 11 What do you notice about the two sums 43 Can another point that is not the mean produce similar sums of distances Let s investigate whether 10 can produce similar sums as those of 11 a Complete the table with the distance of each data point from 10 Time in minutes Distance from 10 Left of 10 or right of 10 12 7 13 9 14 b Sum of distances left of 10 Sum of distances right of 10 What do you notice about the two sums 174 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 10 ACTIVITY 2 53 Here are dot plots showing how long Diego s trips to school took in minutes which you studied earlier and how long Andre s trips to school took in minutes The dot plots include the means for each data set marked by triangles 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 18 19 20 21 22 Diego s travel time in minutes 7 8 9 10 11 12 13 14 15 16 17 Andre s travel time in minutes a Which of the two data sets has a larger mean In this context what does a larger mean tell us b Which of the two data sets has larger sums of distances to the left and right of the mean What do these sums tell us about the variability in Diego s and Andre s travel times 63 Here is a dot plot showing lengths of Lin s trips to school 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Travel time in minutes a Calculate the mean of Lin s travel times 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 175

G6M8 LESSON 10 ZEARN MATH STUDENT EDITION b Complete the table with the distance between each point and the mean as well as whether the point is to the left or right of the mean Time in minutes Distance from the mean Left or right of the mean 22 18 11 8 11 c Find the sum of distances to the left of the mean and the sum of distances to the right of the mean d Use your work to compare Lin s travel times to Andre s What can you say about their average travel times What about the variability in their travel times 176 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 10 Lesson Summary The mean is often used as a measure of center of a distribution This is because the mean of a distribution can be seen as the balance point for the distribution Why is this a good way to think about the mean Let s look at a very simple set of data on the number of cookies that each of eight friends baked shown in the table and dot plot 18 19 19 20 20 21 20 22 21 23 21 22 22 23 24 Number of cookies The distribution shown is completely symmetrical The mean number of cookies is 21 because 19 20 20 21 21 22 22 23 8 21 If we mark the location of the mean on the dot plot we can see that the data points could balance at 21 In this plot each point on either side of the mean has a mirror image For example the two points at 20 and the two at 22 are the same distance from 21 but each pair is located on either side of 21 We can think of them as balancing each other around 21 18 19 20 21 22 23 24 Number of cookies Similarly the points at 19 and 23 are the same distance from 21 but are on either side of it They too can be seen as balancing each other around 21 We can say that the distribution of the cookies has a center at 21 because that is its balance point and that the eight friends on average baked 21 cookies 18 19 20 21 22 23 24 Number of cookies Even when a distribution is not completely symmetrical the distances of values below the mean on the whole balance the distances of values above the mean 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 177

G6M8 LESSON 10 ZEARN MATH STUDENT EDITION TERMINOLOGY Measure of center 178 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 10 Name Date GRADE 6 MISSION 8 LESSON 10 Exit Ticket The three data sets show the number of text messages sent by Jada Diego and Lin over 6 days One of the data sets has a mean of 4 one has a mean of 5 and one has a mean of 6 Jada 4 Diego 4 4 6 6 6 4 Lin 5 5 6 8 8 1 1 2 2 9 9 1 Which data set has which mean What does this tell you about the text messages sent by the three students 2 Which data set has the greatest variability Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 179

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ZEARN MATH STUDENT EDITION G6M8 LESSON 11 Lesson 11 Deviation from the Mean Let s study distances between data points and the mean and see what they tell us Warm Up 1 Elena Jada and Lin enjoy playing basketball during recess Lately they have been practicing free throws They record the number of baskets they make out of 10 attempts Here are their data sets for 12 school days Elena 4 5 1 6 9 7 2 8 3 3 5 7 Jada 2 4 5 4 6 6 4 7 3 4 8 7 Lin 3 6 6 4 5 5 3 5 4 6 6 7 1 Calculate the mean number of baskets each player made and compare the means What do you notice 2 What do the means tell us in this context 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 11 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 Here are the dot plots showing the number of baskets Elena Jada and Lin each made over 12 school days 2 1 On each dot plot mark the location of the mean with a triangle Then contrast the dot plot distributions Write 2 3 sentences to describe the shape and spread of each distribution 0 1 2 3 4 5 6 7 8 9 10 8 9 10 8 9 10 Number of baskets Elena made 0 1 2 3 4 5 6 7 Number of baskets Jada made 0 1 2 3 4 5 6 7 Number of baskets Lin made 2 Discuss the following questions with your group Explain your reasoning a Would you say that all three students play equally well b Would you say that all three students play equally consistently c 182 If you could choose one player to be on your basketball team based on their records who would you choose 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 11 ACTIVITY 2 3 1 The tables show Elena Jada and Lin s basketball data from an earlier activity Recall that the mean of Elena s data as well as that of Jada s and Lin s data was 5 Record the distance between each of Elena s scores and the mean Elena 4 5 1 6 9 7 2 8 3 3 5 7 Distance from 5 Now find the average of the distances in the table Show your reasoning and round your answer to the nearest tenth This value is the mean absolute deviation MAD of Elena s data Elena s MAD 2 Find the mean absolute deviation of Jada s data Round it to the nearest tenth Jada 2 4 5 4 6 6 4 7 3 4 8 7 6 7 Distance from 5 Jada s MAD 3 Find the mean absolute deviation of Lin s data Round it to the nearest tenth Lin 3 6 6 4 5 5 3 5 4 6 Distance from 5 Lin s MAD 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 11 4 ZEARN MATH STUDENT EDITION Compare the MADs and dot plots of the three students data Do you see a relationship between each student s MAD and the distribution on her dot plot Explain your reasoning 0 1 2 3 4 5 6 7 8 9 10 8 9 10 8 9 10 Number of baskets Elena made 0 1 2 3 4 5 6 7 Number of baskets Jada made 0 1 2 3 4 5 6 7 Number of baskets Lin made Lesson Summary We use the mean of a data set as a measure of center of its distribution but two data sets with the same mean could have very different distributions This dot plot shows the weights in grams of 22 cookies 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie weights in grams The mean weight is 21 grams All the weights are within 3 grams of the mean and most of them are even closer These cookies are all fairly close in weight This dot plot shows the weights in grams of a different set of 30 cookies 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie weights in grams The mean weight for this set of cookies is also 21 grams but some cookies are half that weight and others are one and a half times that weight There is a lot more variability in the weight 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 G6M8 LESSON 11 There is a number we can use to describe how far away or how spread out data points generally are from the mean This measure of spread is called the mean absolute deviation MAD Here the MAD tells us how far cookie weights typically are from 21 grams To find the MAD we find the distance between each data value and the mean and then calculate the mean of those distances For instance the point that represents 18 grams is 3 units away from the mean of 21 grams We can find the distance between each point and the mean of 21 grams and organize the distances into a table as shown 3 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie weights in grams Weight in grams 18 19 19 19 20 20 20 20 21 21 21 21 21 22 22 22 22 22 22 23 23 24 Distance 3 from mean 2 2 2 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 2 2 3 The values in the first row of the table are the cookie weights for the first set of cookies Their mean 21 grams is the mean of the cookie weights The values in the second row of the table are the distances between the values in the first row and 21 The mean of these distances is the MAD of the cookie weights What can we learn from the averages of these distances once they are calculated In the first set of cookies the distances are all between 0 and 3 The MAD is 1 2 grams which tells us that the cookie weights are typically within 1 2 grams of 21 grams We could say that a typical cookie weighs between 19 8 and 22 2 grams In the second set of cookies the distances are all between 0 and 13 The MAD is 5 6 grams which tells us that the cookie weights are typically within 5 6 grams of 21 grams We could say a typical cookie weighs between 15 4 and 26 6 grams The MAD is also called a measure of the variability of the distribution In these examples it is easy to see that a higher MAD suggests a distribution that is more spread out showing more variability TERMINOLOGY Mean absolute deviation MAD 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 11 GRADE 6 MISSION 8 LESSON 11 Exit Ticket These three data sets show the number of text messages sent by Jada Diego and Lin over 6 days as well as the mean number of text messages sent by each student per day Jada mean 5 4 4 4 6 6 6 5 6 8 8 2 2 9 9 Diego mean 6 4 5 Lin mean 4 1 1 1 Predict which data set has the largest MAD and which has the smallest MAD 2 Compute the MAD for each data set to check your prediction 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 187

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ZEARN MATH STUDENT EDITION G6M8 LESSON 12 Lesson 12 Using Mean and MAD to Make Comparisons Let s use mean and MAD to describe and compare distributions Warm Up 1 Find the value of each expression mentally 1 42 12 2 2 4 12 3 44 4 12 4 46 8 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 189

G6M8 LESSON 12 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 TASK 1 2 1 Andre and Noah joined Elena Jada and Lin in recording their basketball scores They all recorded their scores in the same way the number of baskets made out of 10 attempts Each collected 12 data points Andre s mean number of baskets was 5 25 and his MAD was 2 6 Noah s mean number of baskets was also 5 25 but his MAD was 1 Here are two dot plots that represent the two data sets The triangle indicates the location of the mean data set A 0 1 2 0 1 2 3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10 data set B Number of baskets made a Without calculating decide which dot plot represents Andre s data and which represents Noah s Explain how you know b If you were the captain of a basketball team and could use one more player on your team would you choose Andre or Noah Explain your reasoning 2 An eighth grade student decided to join Andre and Noah and kept track of his scores His data set is shown here The mean number of baskets he made is 6 Eighth grade student 6 5 4 7 6 5 7 8 5 6 5 8 Distance from 6 a Calculate the MAD Show your reasoning 190 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 12 b Draw a dot plot to represent his data and mark the location of the mean with a triangle c Compare the eighth grade student s mean and MAD to Noah s mean and MAD What do you notice d Compare their dot plots What do you notice about the distributions e What can you say about the two players shooting accuracy and consistency ACTIVITY 2 TASK 1 3 In 1984 the mean age of swimmers on the U S women s swimming team was 18 2 years and the MAD was 2 2 years In 2016 the mean age of the swimmers was 22 8 years and the MAD was 3 years 1 How has the average age of the women on the U S swimming team changed from 1984 to 2016 Explain your reasoning 2 Are the swimmers on the 1984 team closer in age to one another than the swimmers on the 2016 team are to one another 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

G6M8 LESSON 12 3 ZEARN MATH STUDENT EDITION Here are dot plots showing the ages of the women on the U S swimming team in 1984 and in 2016 Use them to make two other comments about how the women s swimming team has changed over the years 1984 2016 14 16 14 16 18 20 22 24 26 28 30 18 20 22 24 26 28 30 Age of swimmers years Lesson Summary Sometimes two distributions have different means but the same MAD Pugs and beagles are two different dog breeds The dot plot shows two sets of weight data one for pugs and the other for beagles X X X X X X X X X X X X X X X X X X X X 6 7 Pug weights in kilograms 8 9 10 11 Beagle weights in kilograms The mean weight for pugs is 7 kilograms and the MAD is 0 5 kilogram The mean weight for beagles is 10 kilograms and the MAD is 0 5 kilogram We can say that in general the beagles are heavier than pugs A typical weight for the beagles in this group is about 3 kilograms heavier than a typical weight for the pugs The variability of pug weights however is about the same as the variability of beagle weights In other words the weights of pugs and the weights of beagles are equally spread out 192 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 12 Name Date GRADE 6 MISSION 8 LESSON 12 Exit Ticket Ten sixth grade students in five different countries United States Australia South Africa Canada and New Zealand were asked about their travel times to school Their responses were organized into five data sets The mean and MAD of each data set are shown in the table 1 Which group of students has the greatest variability in their travel times Explain your reasoning Mean minutes MAD minutes United States 9 4 2 Australia 18 1 7 9 South Africa 23 5 16 2 Canada 11 8 New Zealand 12 3 5 5 2 a The mean of the data set for New Zealand is close to that of Canada What does this tell us about the travel times of students in those two data sets b The MAD of the data set for New Zealand is quite different than that of Canada What does this tell us about the travel times of students in those two data sets 3 The data sets for Australia and Canada have very different means 18 1 and 11 minutes but very similar MADs What can you say about the travel times of the students in those two data sets 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G6M8 LESSON 13 Lesson 13 The Median of a Data Set Let s explore the median of a data set and what it tells us Warm Up 1 Here are two dot plots and two stories Match each story with a dot plot that could represent it Be prepared to explain your reasoning Data set A Data set A Data set B Data set B 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 60 65 65 70 70 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 60 60 65 65 70 70 Age in years Age in years Twenty people high school students parents guardians and teachers attended a rehearsal for a high school musical The mean age was 38 5 years and the MAD was 16 5 years High school soccer team practice is usually watched by family members of the players One evening twenty people watched the team practice The mean age was 38 5 years and the MAD was 12 7 years 2 Another evening twenty people watched the soccer team practice The mean age was similar to that from the first evening but the MAD was greater about 20 years Make a dot plot that could illustrate the distribution of ages in this story 10 15 20 25 30 35 40 45 50 55 60 65 70 Age in years 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 13 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 TASK 1 3 Here is a table that shows the numbers of siblings of ten students in Tyler s class 1 0 2 1 7 0 2 0 1 10 1 Represent the data shown in the table with a dot plot 2 Based on your dot plot estimate the center of the data without making any calculations What is your estimate of a typical number of siblings of these sixth grade students Mark the location of that number on your dot plot 3 Find the mean Show your reasoning 4 a How does the mean compare to the value that you marked on the dot plot as a typical number of siblings Is the mean that you calculated a little larger a lot larger exactly the same a little smaller or a lot smaller than your estimate b Do you think the mean summarizes the data set well Explain your reasoning 196 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 13 ACTIVITY 2 TASK 1 43 Here is the data set on numbers of siblings from an earlier activity 1 0 2 1 7 0 2 0 1 10 a Sort the data from least to greatest and then find the median b In this situation do you think the median is a good measure of a typical number of siblings for this group Explain your reasoning ACTIVITY 2 TASK 2 53 Here is the dot plot showing the travel time in minutes of Elena s bus rides to school 5 6 7 8 9 10 11 12 13 14 Travel time in minutes a Find the median travel time Be prepared to explain your reasoning b What does the median tell us in this context 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 197

G6M8 LESSON 13 ZEARN MATH STUDENT EDITION Lesson Summary The median is another measure of center of a distribution It is the middle value in a data set when values are listed in order Half of the values in a data set are less than or equal to the median and half of the values are greater than or equal to the median To find the median we order the data values from least to greatest and find the number in the middle Suppose we have 5 dogs whose weights in pounds are shown in the table The median weight for this group of dogs is 32 pounds because three dogs weigh less than or equal to 32 pounds and three dogs weigh greater than or equal to 32 pounds 20 32 25 40 55 Now suppose we have 6 cats whose weights in pounds are as shown in the table Notice that there are two values in the middle 7 and 8 The median weight must be between 7 and 8 pounds because half of the cats weigh less or equal to 7 pounds and half of the cats weigh greater than or equal to 8 pounds 4 6 7 8 10 10 In general when we have an even number of values we take the number exactly in between the two middle values In this case the median cat weight is 7 5 pounds because 7 8 2 7 5 TERMINOLOGY Median 198 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 13 Name Date GRADE 6 MISSION 8 LESSON 13 Exit Ticket Jada and Diego are practicing the piano for an upcoming rehearsal The tables list the number of minutes each of them practiced in the past few weeks Jada s practice times 10 10 20 15 25 25 8 15 20 20 35 25 40 Diego s practice times 25 10 15 30 15 20 20 25 30 45 1 Find the median of each data set 2 Explain what the medians tell you about Jada s and Diego s piano practice 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

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ZEARN MATH STUDENT EDITION G6M8 LESSON 14 Lesson 14 Comparing Mean and Median Let s compare the mean and median of data sets Warm Up 1 Here are two dot plots The first dot plot shows the heights of the first 22 U S presidents The second dot plot shows the heights of the next 22 presidents 1st 22nd presidents 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 23rd 44th presidents 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 height in centimeters Based on the two dot plots decide if you agree or disagree with each of the following statements Be prepared to explain your reasoning 1 The median height of the first 22 presidents is 178 centimeters 4 U S presidents have become taller over time 2 The mean height of the first 22 presidents is about 183 centimeters 5 The heights of the first 22 presidents are more alike than the heights of the second 22 presidents 3 A typical height for a president in the second group is about 182 centimeters 6 The MAD of the second data set is greater than the MAD of the first set 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 14 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Your teacher will provide the height data for your class Use the data to complete the questions 1 Find the mean height of your class in centimeters 2 Find the median height in centimeters Show your reasoning 3 Suppose that the world s tallest adult who is 251 centimeters tall joined your class a Discuss the following questions with your group and explain your reasoning How would the mean height of the class change How would the median height change b Find the new mean c Find the new median d Which measure of center the mean or the median changed more when this new person joined the class Explain why the value of one measure changed more than the other 202 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION 4 G6M8 LESSON 14 The world s smallest adult is 63 centimeters tall Suppose that the world s tallest and smallest adults both joined your class a Discuss the following questions with your group and explain your reasoning How would the mean height of the class change from the original mean How would the median height change from the original median b Find the new mean c Find the new median d How did the measures of center the mean and the median change when these two people joined the class Explain why the values of the mean and median changed the way they did ACTIVITY 2 3 Your teacher will give you six cards Each has either a dot plot or a histogram Use the cards to answer the questions 1 Sort the cards into two piles based on the distributions shown Be prepared to explain your reasoning 2 Discuss your sorting decisions with another group Did you have the same cards in each pile If so did you use the same sorting categories If not how are your categories different 3 Use the information on the cards to answer the following questions a Card A What is a typical age of the dogs being treated at the animal clinic b Card B What is a typical number of people in the Irish households c Card C What is a typical travel time for the New Zealand students 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 203

G6M8 LESSON 14 ZEARN MATH STUDENT EDITION d Card D Would 15 years old be a good description of a typical age of the people who attended the birthday party e Card E Is 15 minutes or 24 minutes a better description of a typical time it takes the students in South Africa to get to school f 4 Card F Would 21 3 years old be a good description of a typical age of the people who went on a field trip to Washington D C How did you decide which measure of center to use for the dot plots on Cards A C What about for those on Cards D F Lesson Summary Both the mean and the median are ways of measuring the center of a distribution They tell us slightly different things however The dot plot shows the weights of 30 cookies The mean weight is 21 grams marked with a triangle The median weight is 20 5 grams marked with a diamond 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie Weights in Grams The mean tells us that if the weights of all cookies were distributed so that each one weighed the same that weight would be 21 grams We could also think of 21 grams as a balance point for the weights of all of the cookies in the set The median tells us that half of the cookies weigh more than 20 5 grams and half weigh less than 20 5 grams In this case both the mean and the median could describe a typical cookie weight because they are fairly close to each other and to most of the data points 204 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 14 Here is a different set of 30 cookies It has the same mean weight as the first set but the median weight is 23 grams 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie Weights in Grams In this case the median is closer to where most of the data points are clustered and is therefore a better measure of center for this distribution That is it is a better description of a typical cookie weight The mean weight is influenced in this case pulled down by a handful of much smaller cookies so it is farther away from most data points In general when a distribution is symmetrical or approximately symmetrical the mean and median values are close But when a distribution is not roughly symmetrical the two values tend to be farther apart 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 205

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ZEARN MATH STUDENT EDITION G6M8 LESSON 14 Name Date GRADE 6 MISSION 8 LESSON 14 Exit Ticket For each dot plot or histogram 1 Predict if the mean is greater than less than or approximately equal to the median Explain your reasoning Which measure of center the mean or the median better describes a typical value for the following distributions Heights of 50 NBA basketball players 20 15 10 5 0 2 66 68 70 72 74 76 Height in Inches 78 80 Backpack weights of 55 sixth grade students 0 2 4 6 8 10 12 14 16 Backpack Weight in Kilograms 3 Ages of 30 people at a family dinner party 12 10 8 6 4 2 0 5 10 15 20 25 30 35 40 45 50 55 Age in Years 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 207

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ZEARN MATH STUDENT EDITION G6M8 LESSON 15 Lesson 15 Quartiles and Interquartile Range Let s look at other measures for describing distributions Warm Up 1 Here are two dot plots including the mean marked with a triangle Each shows the ages of partygoers at a party What do you notice and wonder about the distributions in the two dot plots data set A 5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45 data set B age in years 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 15 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 7 Here are the ages of a group of the 20 partygoers you saw earlier shown in order from least to greatest Use this table to answer the question below 8 9 10 10 11 12 15 16 20 20 22 23 24 28 30 33 35 38 42 1 a Find and mark the median on the table and label it 50th percentile The data is now partitioned into an upper half and a lower half b Find and mark the middle value of the lower half of the data excluding the median If there is an even number of values find and write down the average of the middle two Label this value 25th percentile c Find and mark the middle value of the upper half of the data excluding the median If there is an even number of values find and write down the average of the middle two Label the value 75th percentile d You have now partitioned the data set into four pieces Each of the three values that cut the data is called a quartile The first or lower quartile is the 25th percentile mark Write Q1 next to 25th percentile The second quartile is the median Write Q2 next to that label The third or upper quartile is the 75th percentile mark Write Q3 next to that label e Label the least value in the set minimum and the greatest value maximum 2 Record the five values that you have just identified They are the five number summary of the data Minimum 210 Q1 Q2 Q3 Maximum 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 15 The median or Q2 value of this data set is 20 This tells us that half of the partygoers are 20 or younger and that the other half are 20 or older What does each of the following values tell us about the ages of the partygoers a Q3 b Minimum c Maximum ACTIVITY 2 3 This dot plot shows how long Elena s bus rides to school took in minutes over 12 days 5 6 7 8 9 10 11 12 13 14 Travel time in minutes 1 Write the five number summary for this data set by finding the minimum Q1 Q2 Q3 and the maximum Show your reasoning 2 The range of a data set is one way to describe the spread of values in a data set It is the difference between the greatest and least data values What is the range of Elena s data 3 Another number that is commonly used to describe the spread of values in a data set is the interquartile range IQR which is the difference between Q1 the lower quartile and Q3 the upper quartile a What is the interquartile range IQR of Elena s data b What fraction of the data values are between the lower and upper quartiles Use your answer to complete the following statement c The interquartile range IQR is the length that contains the middle a data set of the values in 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 211

G6M8 LESSON 15 43 1 Here are two dot plots that represent two data sets Use the dot plots to answer the questions below Without doing any calculations predict a Which data set has the smaller IQR Explain your reasoning b Which data set has the smaller range Explain your reasoning 2 ZEARN MATH STUDENT EDITION data set A 14 16 18 20 22 24 26 28 14 16 18 20 22 24 26 28 data set B Check your predictions by calculating the IQR and range for the data in each dot plot Lesson Summary Earlier we learned that the mean is a measure of the center of a distribution and the MAD is a measure of the variability or spread that goes with the mean There is also a measure of spread that goes with the median called the interquartile range IQR Finding the IQR involves partitioning a data set into fourths Each of the three values that cut the data into fourths is called a quartile The median which cuts the data into a lower half and an upper half is the second quartile Q2 The first quartile Q1 is the middle value of the lower half of the data The third quartile Q3 is the middle value of the upper half of the data Here is a set of data with 11 values The median Q2 is 33 Q1 Q2 The first quartile Q1 is 20 the median of the numbers less than 33 The third quartile Q3 is 40 the median of the numbers greater than 33 212 12 19 20 21 22 33 34 35 40 40 49 Q3 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 15 The difference between the minimum and maximum values of a data set is the range The difference between Q1 and Q3 is the interquartile range IQR Because the distance between Q1 and Q3 includes the middle two fourths of the distribution the values between those two quartiles are sometimes called the middle half of the data The bigger the IQR the more spread out the middle half of the data are The smaller the IQR the closer the middle half of the data are We consider the IQR a measure of spread for this reason A five number summary which includes the minimum Q1 Q2 Q3 and the maximum can be used to summarize a distribution The five numbers in this example are 12 20 33 40 and 49 Their locations are marked with diamonds in the following dot plot Different data sets could have the same five number summary For instance the following data has the same maximum minimum and quartiles as the one above 10 15 20 25 30 35 40 45 50 10 15 20 25 30 35 40 45 50 TERMINOLOGY Interquartile range IQR Quartile Range 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 213

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ZEARN MATH STUDENT EDITION G6M8 LESSON 15 Name Date GRADE 6 MISSION 8 LESSON 15 Exit Ticket Diego wondered how far sixth grade students could throw a ball He decided to collect data to find out He asked 10 friends to throw a ball as far as they could and measured the distance from the starting line to where the ball landed The table shows the distances he recorded in feet 40 76 40 63 47 57 49 55 50 53 1 Find the median and IQR of the data set 2 On a later day he asked the same group of 10 friends to throw a ball again and collected another set of data The median of the second data set is 49 feet and the IQR is 6 feet a Did the 10 friends as a group perform better or throw farther in the second round compared to the first round Explain how you know b Were the distances in the second data set more variable or less variable compared to those in the first round 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 215

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ZEARN MATH STUDENT EDITION G6M8 LESSON 16 Lesson 16 Box Plots Let s explore how box plots can help us summarize distributions Warm Up 1 Here are the birth weights in ounces of all the puppies born at a kennel in the past month What do you notice and wonder about the distribution of puppy weights 13 14 15 15 16 16 16 16 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 19 20 Concept Exploration ACTIVITY 1 2 Your teacher will give you the data on the lengths of names of students in your class Write the five number summary by finding the data set s minimum Q1 Q2 Q3 and the maximum 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 16 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 Twenty people participated in a study about blinking The number of times each person blinked while watching a video for one minute was recorded The data values are shown here in order from smallest to largest 3 6 8 11 11 13 14 14 14 14 16 18 20 20 20 22 24 32 36 51 1 a Use the grid and axis to make a dot plot of this data set 0 5 10 15 20 25 30 35 Number of blinks 40 45 50 55 b Find the median Q2 and mark its location on the dot plot c Find the first quartile Q1 and the third quartile Q3 Mark their locations on the dot plot d What are the minimum and maximum values 2 A box plot can be used to represent the five number summary graphically Let s draw a box plot for the number of blinks data On the grid above the dot plot a Draw a box that extends from the first quartile Q1 to the third quartile Q3 Label the quartiles b At the median Q2 draw a vertical line from the top of the box to the bottom of the box Label the median 218 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 c 3 G6M8 LESSON 16 From the left side of the box Q1 draw a horizontal line a whisker that extends to the minimum of the data set On the right side of the box Q3 draw a similar line that extends to the maximum of the data set You have now created a box plot to represent the number of blinks data What fraction of the data values are represented by each of these elements of the box plot a The left whisker b The box c The right whisker Lesson Summary A box plot represents the five number summary of a data set It shows the first quartile Q1 and the third quartile Q3 as the left and right sides of a rectangle or a box The median Q2 is shown as a vertical segment inside the box On the left side a horizontal line segment a whisker extends from Q1 to the minimum value On the right a whisker extends from Q3 to the maximum value The rectangle in the middle represents the middle half of the data Its width is the IQR The whiskers represent the bottom quarter and top quarter of the data set Earlier we saw dot plots representing the weights of pugs and beagles The box plots for these data sets are shown above the corresponding dot plots x x x x x x x x x x x x x x x x x x x x 6 7 8 Pug weights in kilograms 9 10 11 Beagle weights in kilograms We can tell from the box plots that in general the pugs in the group are lighter than the beagles the median weight of pugs is 7 kilograms and the median weight of beagles is 10 kilograms Because 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 219

G6M8 LESSON 16 ZEARN MATH STUDENT EDITION two box plots are on the same scale and the rectangles have similar widths we can also tell that the IQRs for the two breeds are very similar This suggests that the variability in the beagle weights is very similar to the variability in the pug weights TERMINOLOGY Box Plot 220 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 16 Name Date GRADE 6 MISSION 8 LESSON 16 Exit Ticket 1 Here are two box plots that summarize two data sets Do you agree with each of the following statements Box plot A Box plot B 0 2 4 6 8 10 12 14 16 a Both data sets have the same range b Both data sets have the same minimum value c The IQR shown in box plot B is twice the IQR shown in box plot A d Box plot A shows a data set that has a quarter of its values between 2 and 5 Data set 1 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Data set 2 2 These dot plots show the same data sets as those represented by the box plots Decide which box plot goes with each dot plot 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 221

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ZEARN MATH STUDENT EDITION G6M8 LESSON 17 Lesson 17 Using Box Plots Let s use box plots to make comparisons Warm Up 1 Ten sixth grade students were asked how much sleep in hours they usually get on a school night Here is the five number summary of their responses Minimum 5 hours First quartile 7 hours Third quartile 8 hours Maximum 9 hours Median 7 5 hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Hours of sleep 1 On the grid draw a box plot for this five number summary 2 What questions could be answered by looking at this box plot 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M8 LESSON 17 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Your teacher will give you either a Problem Card or a Data Card about sea turtles that nest on the Outer Banks of North Carolina Do not show or read your card to your partner If your teacher gives you the problem card If your teacher gives you the data card 1 1 Silently read the information on your card 2 Ask your partner What specific information do you need Wait for your partner to ask for information Only give information that is on your card Do not figure out anything for your partner 3 Before telling your partner the information ask Why do you need that information 4 After your partner solves the problem ask them to explain their reasoning Listen to their explanation Silently read your card and think about what information you need to answer the question 2 Ask your partner for the specific information that you need 3 Explain to your partner how you are using the information to solve the problem 4 Solve the problem and explain your reasoning to your partner Pause here so your teacher can review your work Ask your teacher for a new set of cards and repeat the activity trading roles with your partner 224 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 17 ACTIVITY 2 3 Andre Lin and Noah each designed and built a paper airplane They launched each plane several times and recorded the distance of each flight in yards Work with your group to summarize the data sets with numbers and box plots 1 Andre 25 26 27 27 27 28 28 28 29 30 30 Lin 20 20 21 24 26 28 28 29 29 30 32 Noah 13 14 15 18 19 20 21 23 23 24 25 Write the five number summary for the data for each airplane Then calculate the interquartile range for each data set Min Q1 Q2 median Q3 Max IQR Andre Lin Noah 2 Draw three box plots one for each paper airplane Label the box plots clearly 10 15 20 25 Distance in yards 30 35 3 How are the results for Andre s and Lin s planes the same How are they different 4 How are the results for Lin s and Noah s planes the same How are they different 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 225

G6M8 LESSON 17 ZEARN MATH STUDENT EDITION Lesson Summary Box plots are useful for comparing different groups Here are two sets of plots that show the weights of some berries and some grapes 1 2 3 4 5 6 7 1 8 2 3 4 5 6 7 8 Grape weights in grams Berry weights in grams Notice that the median berry weight is 3 5 grams and the median grape weight is 5 grams In both cases the IQR is 1 5 grams Because the grapes in this group have a higher median weight than the berries we can say a grape in the group is typically heavier than a berry Because both groups have the same IQR we can say that they have a similar variability in their weights These box plots represent the length data for a collection ladybugs and a collection of beetles Ladybugs Beetles 4 6 8 10 12 14 16 Lengths in millimeters The medians of the two collections are the same but the IQR of the ladybugs is much smaller This tells us that a typical ladybug length is similar to a typical beetle length but the ladybugs are more alike in their length than the beetles are in their length 226 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 17 Name Date GRADE 6 MISSION 8 LESSON 17 Exit Ticket Humpback whales are one of the larger species of whales that can be seen off the coast of California Suppose that researchers measured the lengths in feet of 20 male humpback whales and 20 female humpback whales Then the researchers drew two box plots to summarize the data Male Female 38 40 42 44 46 48 50 Length in feet 52 54 56 1 How long was the longest whale measured Was this whale male or female 2 What was a typical length for the male humpback whales that were measured 3 Do you agree with each of the following statements about the whales that were measured Explain your reasoning a More than half of male humpback whales measured were longer than 46 feet b The male humpback whales tended to be longer than female humpback whales c The lengths of the male humpback whales tended to vary more than the lengths of the female humpback whales 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 18 Lesson 18 Using Data to Solve Problems Let s compare data sets using visual displays Warm Up 1 1 In one study on wild bears researchers measured the head lengths and head widths in inches of 143 wild bears The ages of the bears ranged from newborns 0 years to 15 years The box plots summarize the data from the study Write four statistical questions that could be answered using the box plots two questions about the head length and two questions about the head width Male bears Female bears 2 4 6 8 10 12 14 16 18 20 14 16 18 20 Head length in inches Male bears Female bears 2 4 6 8 10 12 Head width in inches 2 Trade questions with your partner a Decide if each question is a statistical question b Use the box plots to answer each question 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 229

G6M8 LESSON 18 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Over a two week period Mai had the following number of math homework problems each school day 2 1 15 20 0 5 25 1 0 10 12 Calculate the following Show your reasoning a The mean number of math homework problems b The mean absolute deviation MAD 2 Interpret the mean and MAD What do they tell you about the number of homework problems Mai had over these two weeks 3 Find or calculate the following values and show your reasoning a The median quartile maximum and minimum of the same data on Mai s math homework problems b The interquartile range IQR 4 230 Which pair of measures of center and variability mean and MAD or median and IQR do you think summarize the distribution of Mai s math homework assignments better Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M8 LESSON 18 ACTIVITY 2 3 Jada wanted to know whether a dot plot a histogram or a box plot would best summarize the center variability and other aspects of her homework data 2 1 15 20 0 5 25 1 0 10 12 Use the axis to make a dot plot to represent the data Mark the position of the mean which you calculated earlier on the dot plot using a triangle From the triangle draw a horizontal line segment to the left and right sides to represent the MAD 0 2 4 6 8 10 12 14 16 18 20 22 24 18 20 22 26 Number of math problems 2 Use the five number summary from the previous task and the grid to draw a box plot that represents Jada s homework data 0 2 4 6 8 10 12 14 16 24 26 Number of math problems 3 Work with your group to draw three histograms to represent Jada s homework data The width of the bars in each histogram should represent a different number of homework problems as specified a One bar represents 10 problems 5 4 3 2 1 0 10 20 30 Number of math problems b One bar represents 5 problems 5 4 3 2 1 0 5 10 15 20 25 30 Number of math 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 231

G6M8 LESSON 18 c ZEARN MATH STUDENT EDITION One bar represents 2 problems 5 4 3 2 1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Number of math problems 4 Which of the five representations should Jada use to summarize her data Should she use a dot plot box plot or one of the histograms Explain your reasoning ACTIVITY 3 43 Read the information below about yellow perch Then use the table to answer the questions Scientists studying the yellow perch a species of fish believe that the length of a fish is related to its age This means that the longer the fish the older it is Adult yellow perch vary in size but they are usually between 10 and 25 centimeters Length of fish in centimeters Scientists at the Great Lakes Water Institute caught measured and released yellow perch at several locations in Lake Michigan The following summary is based on a sample of yellow perch from one of these locations 1 Number of fish 0 to less than 5 5 5 to less than 10 7 10 to less than 15 14 15 to less than 20 20 20 to less than 25 24 25 to less than 30 30 Use the data to make a histogram that shows the lengths of the captured yellow perch Each bar should contain the lengths shown in each row in the table 30 25 20 15 10 5 0 5 10 15 20 25 30 Fish length in centimeters 232 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 How many fish were measured How do you know 3 Use the histogram to answer the following questions G6M8 LESSON 18 a How would you describe the shape of the distribution b Estimate the median length for this sample Describe how you made this estimate c Predict whether the mean length of this sample is greater than less than or nearly equal to the median length for this sample of fish Explain your prediction d Would you use the mean or the median to describe a typical length of the fish being studied Explain your reasoning 4 Based on your work so far a Would you describe a typical age for the yellow perch in this sample as young adult or old Explain your reasoning b Some researchers are concerned about the survival of the yellow perch Do you think the lengths or the ages of the fish in this sample are something to worry about 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 233

G6M8 LESSON 18 ZEARN MATH STUDENT EDITION Lesson Summary The dot plot shows the distribution of 31 cookie weights in grams 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie weights in grams The mean cookie weight marked by the triangle is 21 grams This tells us that if the weights of all of the cookies were redistributed so they all had the same weight each cookie would weigh 21 grams The MAD is 5 6 grams which suggests that a cookie typically weighs between 15 4 grams and 26 6 grams The box plot for the same data set is shown above the dot plot The median shows that half of the weights are greater than or equal to 20 5 grams and half are less than or equal to 20 5 grams The box shows that the IQR is 10 and that the middle half of the cookies weigh between 16 and 26 grams In this case the median weight is very close to the mean weight and the IQR is about twice the MAD This tells us that the two pairs of measures of center and spread are very similar Now let s look at another example of 30 different cookies 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Cookie weights in grams Here the mean is 21 grams and the MAD is 3 4 grams This suggests that a cookie typically weighs between 17 6 and 24 4 grams The median cookie weight is 23 grams and the box plot shows that the middle half of the data are between 20 and 24 grams These two pairs of measures paint very different pictures of the variability of the cookie weights The median 23 grams is closer to the middle of the big cluster of values If we were to ignore the smaller cookies the median and IQR would give a more accurate picture of how much a cookie typically weighs When a distribution is not symmetrical the median and IQR are often better measures of center and spread than the mean and MAD However the decision on which pair of measures to use depends on what we want to know about the group we are investigating 234 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M8 LESSON 18 Name Date GRADE 6 MISSION 8 LESSON 18 Exit Ticket Lin surveyed her classmates on the number of hours they spend doing chores each week She represented her data with a dot plot and a histogram 0 1 2 3 4 5 6 Hours spent on chores per week 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 Hours spent on chores per week 1 Lin thinks that she could find the median the minimum and the maximum of the data set using both the dot plot and the histogram Do you agree Explain your reasoning 2 Should Lin use the mean and MAD or the median and IQR to summarize her data 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 235

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Grade 6 Mission 9 Putting It All Together

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ZEARN MATH STUDENT EDITION G6M9 LESSON 1 Lesson 1 Fermi Problems Let s make some estimates Warm Up 1 How long would it take an ant to run from Los Angeles to New York City The distance between Los Angeles and New York City is about 3 944 km An ant can run about 18 mm per second Concept Exploration ACTIVITY 1 2 Imagine a warehouse that has a rectangular floor and that contains all of the boxes of breakfast cereal bought in the United States in one year If the warehouse is 10 feet tall what could the side lengths of the floor be Every year people in the U S buy 2 7 billion boxes of breakfast cereal A typical cereal box has dimensions of 2 5 inches by 7 75 inches by 11 75 inches 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 239

G6M9 LESSON 1 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 How many tiles would it take to cover the Washington Monument Standard sizes for square tiles side lengths of 1 inch 6 inches 8 inches 1 foot and 1 12 feet 55 feet 35 feet 500 feet 55 feet 240 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M9 LESSON 2 Lesson 2 If Our Class Were the World Let s use math to better understand our world Warm Up 1 Use the information below to answer the following questions There are 7 4 billion people in the world If the whole world were represented by a 30 person class 14 people would eat rice as their main food 12 people would be under the age of 20 5 people would be from Africa 1 How many people in the class would not eat rice as their main food 2 What percentage of the people in the class would be under the age of 20 3 Based on the number of people in the class representing people from Africa how many people live in Africa 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 2 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 With the members of your group write a list of questions about the people in the world Your questions should begin with How many Then choose several questions on the list that you find most interesting ACTIVITY 2 3 Suppose your class represents all the people in the world Choose several characteristics about the world s population that you have investigated Find the number of students in your class that would have the same characteristics Create a visual display that includes a diagram that represents this information Give your display the title If Our Class Were the World 242 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M9 LESSON 3 Lesson 3 Rectangle Madness Let s cut up rectangles Warm Up 1 1 Answer the questions about the 3 rectangles below A F D B E C Rectangle ABCD is not a square Rectangle ABEF is a square a Suppose segment AF were 5 units long and segment FD were 2 units long How long would segment AD be b Suppose segment BC were 10 units long and segment BE were 6 units long How long would segment EC be c Suppose segment AF were 12 units long and segment FD were 5 units long How long would segment FE be d Suppose segment AD were 9 units long and segment AB were 5 units long How long would segment FD be 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 243

G6M9 LESSON 3 2 ZEARN MATH STUDENT EDITION Rectangle JKXW has been decomposed into squares J K S T U W G H I L M O N Q R V P X Segment JK is 33 units long and segment JW is 75 units long Find the areas of all of the squares in the diagram 3 Rectangle ABCD is 16 units by 5 units D C A B a In the diagram draw a line segment that decomposes ABCD into two regions a square that is the largest possible and a new rectangle b Draw another line segment that decomposes the new rectangle into two regions a square that is the largest possible and another new rectangle c Keep going until rectangle ABCD is entirely decomposed into squares d List the side lengths of all the squares in your diagram 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 G6M9 LESSON 3 ENRICHMENT Z U T V 1 The diagram shows that rectangle VWYZ has been decomposed into three squares What could the side lengths of this rectangle be S 2 How many different side lengths can you find for rectangle VWYZ Y 3 X W What are some rules for possible side lengths of rectangle VWYZ Concept Exploration ACTIVITY 1 2 1 Answer the questions about rectangles and fractions Draw a rectangle that is 21 units by 6 units a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until the diagram shows that your original rectangle has been entirely decomposed into squares b How many squares of each size are in your diagram c What is the side length of the smallest square 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 3 2 ZEARN MATH STUDENT EDITION Draw a rectangle that is 28 units by 12 units a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until the diagram shows that your original rectangle has been decomposed into squares b How many squares of each size are in your diagram c 3 4 246 What is the side length of the smallest square Write each of these fractions as a mixed number with the smallest possible numerator and denominator a 16 5 b 21 6 c 28 12 What do the fraction problems have to do with the previous rectangle decomposition 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

ZEARN MATH STUDENT EDITION G6M9 LESSON 3 ACTIVITY 2 3 1 Answer the questions about rectangles factors and fractions Accurately draw a rectangle that is 9 units by 4 units a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until your original rectangle has been entirely decomposed into squares b How many squares of each size are there c What are the side lengths of the last square you drew d Write 2 9 4 as a mixed number Accurately draw a rectangle that is 27 units by 12 units a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until your original rectangle has been entirely decomposed into squares b How many squares of each size are there c What are the side lengths of the last square you drew 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 3 ZEARN MATH STUDENT EDITION d Write 27 12 as a mixed number e Compare the diagram you drew for this problem and the one for the previous problem How are they alike How are they different 3 What is the greatest common factor of 9 and 4 What is the greatest common factor of 27 and 12 What does this have to do with your diagrams of decomposed rectangles ENRICHMENT We have seen some examples of rectangle tilings A tiling means a way to completely cover a shape with other shapes without any gaps or overlaps For example here is a tiling of rectangle KXWJ with 2 large squares 3 medium squares 1 small square and 2 tiny squares J K S U W G H I L M O N Q R T V P X Some of the squares used to tile this rectangle have the same size Might it be possible to tile a rectangle with squares where the squares are all different sizes If you think it is possible find such a rectangle and such a tiling If you think it is not possible explain why it is not possible ACTIVITY 3 Write a fraction that is equal to each expression 43 1 248 3 1 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 2 1 3 1 5 3 2 3 53 1 G6M9 LESSON 3 1 1 5 Answer the questions about rectangles factors and fractions Accurately draw a 37 by 16 rectangle Use graph paper if possible a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until your original rectangle has been entirely decomposed into squares b How many squares of each size are there c What are the dimensions of the last square you drew d What does this have to do with 2 3 2 1 1 5 Consider a 52 by 15 rectangle a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until your original rectangle has been entirely decomposed into squares b Write a fraction equal to this expression 3 2 1 1 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 249

G6M9 LESSON 3 c ZEARN MATH STUDENT EDITION Notice some connections between the rectangle and the fraction d What is the greatest common factor of 52 and 15 3 Consider a 98 by 21 rectangle a In your rectangle draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible Continue until your original rectangle has been entirely decomposed into squares b Write a fraction equal to this expression 4 1 c 1 7 14 Notice some connections between the rectangle and the fraction d What is the greatest common factor of 98 and 21 4 Consider a 121 by 38 rectangle a Use the decomposition into squares process to write a continued fraction for 121 38 Verify that it works b What is the greatest common factor of 121 and 38 250 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M9 LESSON 4 Lesson 4 How Do We Choose Let s vote and choose a winner Warm Up 1 Two sixth grade classes A and B voted on whether to give the answers to their math problems in poetry The yes choice was more popular in both classes Yes No Class A 24 16 Class B 18 9 1 Was one class more in favor of math poetry or were they equally in favor 2 Find three or more ways to answer the question 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 251

G6M9 LESSON 4 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 The school will be painted over the summer Students get to vote on whether to change the color to purple a yes vote or keep it a beige color a no vote The principal of the school decided to analyze voting results by class The table shows some results In both classes a majority voted for changing the paint color to purple Which class was more in favor of changing Yes No Class A 26 14 Class B 31 19 ACTIVITY 2 3 252 A school is voting to change their school s color and school s mascot Answer the following questions about this school 1 A school is voting on whether to change their school s color to purple Their rules require a 23 supermajority to change the colors A total of 240 people voted and 153 voted to change to purple Were there enough votes to make the change 2 This school also is thinking of changing their mascot to an armadillo To change mascots a 55 supermajority is needed How many of the 240 students need to vote yes for the mascot to change 3 At this school which requires more votes to pass a change of mascot or a change of color 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M9 LESSON 4 ACTIVITY 3 43 A town s newspaper held a contest to decide the best restaurant in town Use the information below to answer the question about Darnell s sign Only people who subscribe to the newspaper can vote 25 of the people in town subscribe to the newspaper 20 of the subscribers voted 80 of the people who voted liked Darnell s BBQ Pit best Darnell put a big sign in his restaurant s window that said 80 say Darnell s is the best Do you think Darnell s sign is making an accurate statement Support your answer with Some calculations An explanation in words A diagram that accurately represents the people in town the newspaper subscribers the voters and the people who liked Darnell s best 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 4 254 ZEARN MATH STUDENT EDITION 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M9 LESSON 5 Lesson 5 More than Two Choices Let s explore different ways to determine a winner Warm Up 1 Students in a sixth grade class were asked What activity would you most like to do for field day The results are shown in the table Use the results to answer the questions Activity Number of votes softball game 16 scavenger hunt 10 dancing talent show 8 marshmallow throw 4 no preference 2 1 What percentage of the class voted for softball 2 What percentage did not vote for softball as their first choice 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 5 ZEARN MATH STUDENT EDITION Concept Exploration ACTIVITY 1 2 Suppose students at our school are voting for the lunch menu over the course of one week The following is a list of options provided by the caterer To vote draw one of the following symbols next to each menu option to show your first second third and last choices A Meat Lovers Meat loaf Hot dogs Pork cutlets Beef stew Liver and onions B Vegetarian Vegetable soup and peanut butter sandwich Hummus pita and veggie sticks Veggie burgers and fries Chef s salad Cheese pizza every day double desserts every day 1st choice 2nd choice C Something for Everyone Chicken nuggets Burgers and fries Pizza Tacos Leftover day all the week s leftovers made into a casserole Bonus side dish pea jello green gelatin with canned peas 3rd choice D Concession Stand Choice of hamburger or hot dog with fries every day 4th choice A Meat Lovers C Something for Everyone B Vegetarian D Concession Stand Here are two voting systems that can be used to determine the winner 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 3 G6M9 LESSON 5 Use the class data to answer the questions about plurality voting Voting System 1 Plurality The option with the most first choice votes stars wins Use the class data to answer the questions about plurality voting 1 How many people in our class are voting How many votes does it take to win a majority 2 How many votes did the top option receive Was this a majority of the votes 43 1 Use the class data to answer questions about voter satisfaction People tend to be more satisfied with election results if their top choices win For how many and what percentage of people was the winning option a their first choice b their second choice c d their last choice 53 their third choice Use the class data on runoff voting to answer the questions Voting System 2 Runoff If no choice received a majority of the votes leave out the choice that received the fewest first choice votes stars Then have another vote If your first vote is still a choice vote for that If not vote for your second choice that you wrote down If there is still no majority leave out the choice that got the fewest votes and then vote again Vote for your first choice if it s still in and if not vote for your second choice If your second choice is also out vote for your third choice 1 After the second round of voting did any choice get a majority If so is it the same choice that got a plurality in Voting System 1 2 Which choice won 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 5 63 1 2 ZEARN MATH STUDENT EDITION Use the class data to answer questions about voter satisfaction How satisfied were the voters by the election results For how many and what percentage of people was the winning option a their first choice b their second choice c d their last choice their third choice Compare the satisfaction results for the plurality voting rule and the runoff rule Did one produce satisfactory results for more people than the other ACTIVITY 2 73 In another class there are four clubs Everyone in each club agrees to vote for the lunch menu exactly the same way as shown in this table Barbecue club 21 members Garden club 13 members Sports boosters 7 members Film club 9 members A Meat Lovers B Vegetarian C Something for everyone D Concession Stand 258 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 1 G6M9 LESSON 5 Figure out which option won the election by answering these questions a On the first vote when everyone voted for their first choice how many votes did each option get Did any choice get a majority b Which option is removed from the next vote c On the second vote how many votes did each of the remaining three menu options get Did any option get a majority d Which menu option is removed from the next vote e On the third vote how many votes did each of the remaining two options get Which option won 2 Estimate how satisfied all the voters were a For how many people was the winner their first choice b For how many people was the winner their second choice c For how many people was the winner their third choice d For how many people was the winner their last choice 3 Compare the satisfaction results for the plurality voting rule and the runoff rule Did one produce satisfactory results for more people than the other 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 259

G6M9 LESSON 5 ZEARN MATH STUDENT EDITION ACTIVITY 3 83 260 Our class will vote using the instant runoff system Use the class data for questions 1 For our class which choice received the most points 2 Does this result agree with that from the runoff election in an earlier activity 3 For the other class which choice received the most points 4 Does this result agree with that from the runoff election in an earlier activity 5 The runoff method uses information about people s first second third and last choices when it is not clear that there is a winner from everyone s first choices How does the instant runoff method include the same information 6 After comparing the results for the three voting rules plurality runoff instant runoff and the satisfaction surveys which method do you think is fairest Explain 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6M9 LESSON 5 ENRICHMENT Numbering your choices 0 through 3 might not really describe your opinions For example what if you really liked A and C a lot and you really hated B and D You might want to give A and C both a 3 and B and D both a 0 1 Design a numbering system where the size of the number accurately shows how much you like a choice Some ideas The same 0 to 3 scale but you can choose more than one of each number or even decimals between 0 and 3 A scale of 1 to 10 with 10 for the best and 1 for the worst 2 Try out your system with the people in your group using the same school lunch options for the election 3 Do you think your system gives a more fair way to make choices 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 261

G6M9 LESSON 5 ZEARN MATH STUDENT EDITION ACTIVITY 4 93 262 Clare Han Mai Tyler and Noah are deciding what to do on the weekend Their options are cooking hiking and bowling Here are the points for their instant runoff vote Each first choice gets 2 points the second choice gets 1 point and the last choice gets 0 points Cooking Hiking Bowling Clare 2 1 0 Han 2 1 0 Mai 2 1 0 Tyler 0 2 1 Noah 0 2 1 1 Which activity won using the instant runoff method Show your calculations and use expressions or equations 2 Which activity would have won if there was just a vote for their top choice with a majority or plurality winning 3 Which activity would have won if there was a runoff election 4 Explain why this happened 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M9 LESSON 6 Lesson 6 Picking Representatives Let s think about fair representation Warm Up 1 1 A program gives computers to families with school aged children They have a certain number of computers to distribute fairly between several families How many computers should each family get One month the program has 8 computers The families have these numbers of school aged children 4 2 6 2 2 a How many children are there in all b Counting all the children in all the families how many children would use each computer This is the number of children per computer Call this number A c Fill in the third column of the table Decide how many computers to give to each family if we use A as the basis for distributing the computers Family Number of children Baum 4 Chu 2 Davila 6 Eno 2 Farouz 2 Number of computers using A d Check that 8 computers have been given out 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 263

G6M9 LESSON 6 2 ZEARN MATH STUDENT EDITION The next month they again have 8 computers There are different families with these numbers of children 3 1 2 5 1 8 a How many children are there in all b Counting all the children in all the families how many children would use each computer This is the number of children per computer Call this number B c Does it make sense that B is not a whole number Why d Fill in the third column of the table Decide how many computers to give to each family if we use B as the basis for distributing the computers Family Number of children Gray 3 Hernandez 1 Ito 2 Jones 5 Krantz 1 Lo 8 Number of computers using B Number of computers your way Number of children per computer your way e Check that 8 computers have been given out in all f Does it make sense that the number of computers for one family is not a whole number Explain your reasoning g Find and describe a way to distribute computers to the families so that each family gets a whole number of computers Fill in the fourth column of the table h Compute the number of children per computer in each family and fill in the last column of the table i 264 Do you think your way of distributing the computers is fair Explain your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6M9 LESSON 6 Concept Exploration ACTIVITY 1 2 A school is deciding on a school mascot The table shows how three classes voted They have narrowed the choices down to the Banana Slugs or the Sea Lions The principal decided that each class gets one vote Each class held an election and the winning choice was the one vote for the whole class Banana Slugs Sea Lions Class vote Class A 9 3 Banana Slug Class B 14 10 Class C 6 30 1 Which mascot won according to the principal s plan What percentage of the votes did the winner get under this plan 2 Which mascot received the most student votes in all What percentage of the votes did this mascot receive 3 The students thought this plan was not very fair They suggested that bigger classes should have more votes to send to the principal Make up a proposal for the principal where there are as few votes as possible but the votes proportionally represent the number of students in each class 4 Decide how to assign the votes for the results in the class Do they all go to the winner Or should the loser still get some votes 5 In your system which mascot is the winner 6 In your system how many representative votes are there How many students does each vote represent 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M9 LESSON 6 ZEARN MATH STUDENT EDITION ACTIVITY 2 3 School Number of students D 48 E 12 F 24 G 36 Number of advisors A students per advisor 1 How many students are in this district in all 2 If the advisors could represent students at different schools how many students per advisor should there be Call this number A Show your reasoning 3 Using A students per advisor how many advisors should each school have Complete the table with this information for schools D E F and G 43 Another district has four schools some are large others are small The district wants 10 advisors in all Each school should have at least one advisor School Number of students Dr King School 48 O Connor School 12 Science Magnet School 24 Trombone Academy 36 1 266 In a very small school district there are four schools D E F and G The district wants a total of 10 advisors for the students Each school should have at least one advisor Number of advisors B students per advisor Number of advisors your way Number of students per advisor your way How many students are in this district 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

ZEARN MATH STUDENT EDITION G6M9 LESSON 6 2 If the advisors didn t have to represent students at the same school how many students per advisor should there be Call this number 3 Using students per advisor how many advisors should each school have Give your quotients to the tenths place Fill in the first number of advisors column of the table Does it make sense to have a tenth of an advisor 4 Decide on a consistent way to assign advisors to schools so that there are only whole numbers of advisors for each school and there is a total of 10 advisors among the schools Fill in the your way column of the table 5 How many students per advisor are there at each school Fill in the last row of the table 6 Do you think this is a fair way to assign advisors Explain your reasoning ACTIVITY 3 53 The whole town gets interested in choosing a mascot Here is a map of the town with preferences shown The mayor of the town decides to choose representatives to vote There are 50 blocks in the town and the people on each block tend to have the same opinion about which mascot is best Dark gray blocks like sea lions and light gray blocks like banana slugs The mayor decides to have 5 representatives each representing a district of 10 blocks 1 Suppose there were an election with each block getting one vote How many votes would be for banana slugs For sea lions What percentage of the vote would be for banana slugs 2 Suppose the districts are shown in the next map What did the people in each district prefer What did their representative vote Which mascot would win the election 1 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 267

G6M9 LESSON 6 ZEARN MATH STUDENT EDITION Complete the table with this election s results District Number of blocks for Banana Slugs Number of blocks for Sea Lions 1 10 0 Percentage of blocks for Banana Slugs Representative s vote Banana Slugs 2 3 4 5 3 Suppose instead that the districts are shown in the new map below What did the people in each district prefer What did their representative vote Which mascot would win the election 1 2 3 4 5 Complete the table with this election s results District Number of blocks for Banana Slugs Number of blocks for Sea Lions Percentage of blocks for Banana Slugs Representative s vote 1 2 3 4 5 4 Suppose the districts are designed in yet another way as shown in the next map What did the people in each district prefer What did their representative vote Which mascot would win the election 1 4 268 2 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

ZEARN MATH STUDENT EDITION G6M9 LESSON 6 Complete the table with this election s results District Number of blocks for Banana Slugs Number of blocks for Sea Lions Percentage of blocks for Banana Slugs Representative s vote 1 2 3 4 5 5 Write a headline for the local newspaper for each of the ways of splitting the town into districts 6 Which systems on the three maps of districts do you think are more fair Are any totally unfair ACTIVITY 4 Smallville s map is shown with opinions shown by block in dark gray and light gray Decompose the map to create three connected equal area districts in two ways 63 1 Smallville s map is shown with opinions shown by block in dark gray and light gray Decompose the map to create three connected equal area districts in two ways a Design three districts where dark gray will win at least two of the three districts Record results in Table 1 Table 1 District Number of blocks for dark gray Number of blocks for light gray Percentage of blocks for dark gray Representative s vote 1 2 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 269

G6M9 LESSON 6 ZEARN MATH STUDENT EDITION b Design three districts where light gray will win at least two of the three districts Record results in Table 2 Table 2 District Number of blocks for dark gray Number of blocks for light gray Percentage of blocks for dark gray Representative s vote Percentage of blocks for dark gray Representative s vote 1 2 3 2 Squaretown s map is shown with opinions by block shown in dark gray and light gray Decompose the map to create five connected equal area districts in two ways a Design five districts where dark gray will win at least three of the five districts Record the results in Table 3 Table 3 District Number of blocks for dark gray Number of blocks for light gray 1 2 3 4 5 270 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 G6M9 LESSON 6 b Design five districts where light gray will win at least three of the five districts Record the results in Table 4 Table 4 District Number of blocks for dark gray Number of blocks for light gray Percentage of blocks for dark gray Representative s vote 1 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 271

G6M9 LESSON 6 3 ZEARN MATH STUDENT EDITION Mountain Valley s map is shown with opinions by block shown in dark gray and light gray This is a town in a narrow valley in the mountains Can you decompose the map to create three connected equal area districts in the two ways described here a Design three districts where dark gray will win at least two of the three districts Record the results in Table 5 Table 5 District Number of blocks for dark gray Number of blocks for light gray Percentage of blocks for dark gray Representative s vote Percentage of blocks for dark gray Representative s vote 1 2 3 b Design three districts where light gray will win at least two of the three districts Record the results in Table 6 Table 6 District Number of blocks for dark gray Number of blocks for light gray 1 2 3 272 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6V3 Terminology Absolute Value The absolute value of a number is its distance from 0 on the number line 5 7 7 5 3 1 0 1 3 5 7 The absolute value of 7 is 7 because it is 7 units away from 0 The absolute value of 5 is 5 because it is 5 units away from 0 Average The average is another name for the mean of a data set For the data set 3 5 6 8 11 12 the average is 7 5 3 5 6 8 11 12 45 45 6 7 5 Box Plot A box plot is a way to represent data on a number line The data is divided into four sections The sides of the box represent the first and third quartiles A line inside the box represents the median Lines outside the box connect to the minimum and maximum values For example this box plot shows a data set with a minimum of 2 and a maximum of 15 The median is 6 the first quartile is 5 and the third quartile is 10 0 2 4 6 8 10 12 14 16 Number of books Categorical data A set of categorical data has values that are words instead of numbers For example Han asks 5 friends to name their favorite color Their answers are blue blue green blue orange 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6V3 ZEARN MATH STUDENT EDITION Center The center of a set of numerical data is a value in the middle of the distribution It represents a typical value for the data set For example the center of this distribution of cat weights is between 4 5 and 5 kilograms 2 3 4 5 6 7 8 9 10 11 12 Cat weights in kilograms Common factor A common factor of two numbers is a number that divides evenly into both numbers For example 5 is a common factor of 15 and 20 because 15 5 3 and 20 5 4 Both of the quotients 3 and 4 are whole numbers The factors of 15 are 1 3 5 and 15 The factors of 20 are 1 2 4 5 10 and 20 Common Multiple A common multiple of two numbers is a product you can get by multiplying each of the two numbers by some whole number For example 30 is a common multiple of 3 and 5 because 3 10 30 and 5 6 30 Both of the factors 10 and 6 are whole numbers The multiples of 3 are 3 6 9 12 15 18 21 24 27 30 33 The multiples of 5 are 5 10 15 20 25 30 35 40 The common multiples of 3 and 5 are 15 30 45 60 Distribution The distribution tells how many times each value occurs in a data set For example in the data set blue blue green blue orange the distribution is 3 blues 1 green and 1 orange Here is a dot plot that shows the distribution for the data set 6 10 7 35 7 36 32 10 7 35 5 10 15 20 25 30 35 40 Dog weights in kilograms 274 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6V3 Dot plot A dot plot is a way to represent data on a number line Each time a value appears in the data set we put another dot above that number on the number line For example in this dot plot there are three dots above the 9 This means that three different plants had a height of 9 cm 1 2 3 4 5 6 7 8 9 10 11 12 Plant height centimeters Frequency The frequency of a data value is how many times it occurs in the data set For example there were 20 dogs in a park The table shows the frequency of each color color frequency white 4 brown 7 black 3 multi color 6 Greatest common factor The greatest common factor of two numbers is the largest number that divides evenly into both numbers Sometimes we call this the GCF For example 15 is the greatest common factor of 45 and 60 The factors of 45 are 1 3 5 9 15 and 45 The factors of 60 are 1 2 3 4 5 6 10 12 15 20 30 and 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 275

G6V3 ZEARN MATH STUDENT EDITION Histogram 14 A histogram is a way to represent data on a number line Data values are grouped by ranges The height of the bar shows how many data values are in that group 12 10 8 6 For example this histogram shows there were 10 people who earned 2 or 3 tickets We can t tell how many of them earned 2 tickets or how many earned 3 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of tickets Interquartile range IQR The interquartile range is one way to measure how spread out a data set is We sometimes call this the IQR To find the interquartile range we subtract the first quartile from the third quartile 22 29 30 31 Q1 32 43 44 45 Q2 50 50 59 Q3 For example the IQR of this data set is 20 because 50 30 20 Least Common Multiple The least common multiple of two numbers is the smallest product you can get by multiplying each of the two numbers by some whole number Sometimes we call this the LCM For example 30 is the least common multiple of 6 and 10 The multiples of 6 are 6 12 18 24 30 36 42 48 54 60 The multiples of 10 are 10 20 30 40 50 60 70 80 Mean The mean is one way to measure the center of a data set We can think of it as a balance point For example for the data set 7 9 12 13 14 the mean is 11 To find the mean add up all the numbers in the data set Then divide by how many numbers there are 7 9 12 13 14 55 and 55 5 11 276 3 4 2 2 7 8 9 1 10 11 12 13 14 15 16 17 18 19 20 21 22 Travel time in minutes 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH STUDENT EDITION G6V3 Mean absolute deviation MAD The mean absolute deviation is one way to measure how spread out a data set is Sometimes we call this the MAD For example for the data set 7 9 12 13 14 the MAD is 2 4 This tells us that these travel times are typically 2 4 minutes away from the mean which is 11 To find the MAD add up the distance between each data point and the mean Then divide by how many numbers there are 4 2 1 2 3 12 and 12 5 2 4 Measure of center A measure of center is a value that seems typical for a data distribution Mean and median are both measures of center Median The median is one way to measure the center of a data set It is the middle number when the data set is listed in order For the data set 7 9 12 13 14 the median is 12 For the data set 3 5 6 8 11 12 there are two numbers in the middle The median is the average of these two numbers 6 8 14 and 14 2 7 Negative Number A negative number is a number that is less than zero On a horizontal number line negative numbers are usually shown to the left of 0 7 5 3 1 0 1 3 5 7 Numerical data A set of numerical data has values that are numbers For example Han lists the ages of people in his family 7 10 12 36 40 67 Opposite Two numbers are opposites if they are the same distance from 0 and on different sides of the number line For example 4 is the opposite of 4 and 4 is the opposite of 4 They are both the same distance from 0 One is negative and the other is positive 5 4 3 2 1 0 1 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 277

G6V3 ZEARN MATH STUDENT EDITION Positive Number A positive number is a number that is greater than zero On a horizontal number line positive numbers are usually shown to the right of 0 7 5 3 1 0 1 3 5 7 Quadrant The coordinate plane is divided into 4 regions called quadrants The quadrants are numbered using Roman numerals starting in the top right corner and moving counter clockwise Quartile Quartiles are the numbers that divide a data set into four sections that each have the same number of values For example in this data set the first quartile is 20 The second quartile is the same thing as the median which is 33 The third quartile is 40 12 19 20 Q1 21 22 33 34 Q2 35 40 40 49 Q3 Range The range is the distance between the smallest and largest values in a data set For example for the data set 3 5 6 8 11 12 the range is 9 because 12 3 9 Rational number A rational number is a fraction or the opposite of a fraction For example 8 and 8 are rational numbers because they can be written as 81 and 81 75 75 Also 0 75 and 0 75 are rational numbers because they can be written as 100 and 100 278 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 G6V3 Sign The sign of any number other than 0 is either positive or negative For example the sign of 6 is positive The sign of 6 is negative Zero does not have a sign because it is not positive or negative Solution to an inequality A solution to an inequality is a number that can be used in place of the variable to make the inequality true For example 5 is a solution to the inequality c 10 because it is true that 5 10 Some other solutions to this inequality are 9 9 0 and 4 Spread The spread of a set of numerical data tells how far apart the values are For example the dot plots show that the travel times for students in South Africa are more spread out than for New Zealand New Zealand 0 10 20 0 10 20 30 40 50 60 30 40 50 60 South Africa Travel time in minutes Statistical question A statistical question can be answered by collecting data that has variability Here are some examples of statistical questions How many minutes do sixth grade students spend on homework each week What is the typical bedtime of a seventh grade student How many pets does an eighth grade student have 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 279

G6V3 ZEARN MATH STUDENT EDITION Variability Variability means having different values For example data set B has more variability than data set A Data set B has many different values while data set A has more of the same values 32 34 36 38 40 42 44 46 48 50 42 44 46 48 50 A 32 34 36 38 40 B 280 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

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zearn org NAME Grade 6 Student Edition Vol 1 Mission 1 Area and Surface Area Mission 2 Introducing Ratios Mission 3 Unit Rates and Percentages Mission 4 Dividing Fractions Mission 5 Arithmetic in Base Ten Mission 6 Expressions and Equations Student Edition Vol 2 Vol 3 Mission 7 Rational Numbers Mission 8 Data Sets and Distributions Mission 9 Putting It All Together G6 Vol 3 Zearnmath_SE_Grade6_Vol3 indd 1 Grade 6 Volume 3 MISSIONS 1 2 3 4 5 6 7 8 9 12 15 22 11 44 AM