STUDENT NOTES FOR DIGITAL LESSONS Grade 6 NAME

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Table of Contents MISSION 1 Area and Surface Area 1 MISSION 2 Introducing Ratios 19 MISSION 3 Unit Rates and Percentages 36 MISSION 4 Dividing Fractions 51 MISSION 5 Arithmetic in Base Ten 68 MISSION 6 Expressions And Equations 84 MISSION 7 Rational Numbers 101 MISSION 8 Data Sets and Distributions 120

Grade 6 Mission 1 Area and Surface Area

G6M1 Lesson 1 ZEARN MATH Student Notes for Digital Lessons Lesson 1 Tiling the Plane Marvin says that there are more white triangles than black squares so the white triangles must cover more area than the black squares Do you agree or disagree with Marvin Explain your reasoning I agree disagree with Marvin because 2 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M1 Lesson 2 Lesson 2 Finding Area by Decomposing and Rearranging This is the figure from the last problem Explain how you found the area Key 1 square 1 sq unit 2 small triangles 1 sq unit 1 medium triangle 2 small triangles 1 sq unit The area of this figure is square units I know this because 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 3

G6M1 Lesson 3 ZEARN MATH Student Notes for Digital Lessons Lesson 3 Reasoning to Find Area Without solving explain the steps you would take to find the area of the shaded region in the figure 6 cm 3 cm 6 cm 2 cm First I would Then I would Finally I would 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 Notes for Digital Lessons G6M1 Lesson 4 Lesson 4 Parallelograms This is a parallelogram Without calculating write how you would explain to a friend the steps to take to find the area Consider using either the decompose and rearrange or the enclose and subtract strategies To find the area First I would Then I would Finally I would 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M1 Lesson 5 ZEARN MATH Student Notes for Digital Lessons Lesson 5 Bases and Heights of Parallelograms Draw a height that corresponds to the base labeled on the parallelogram b Explain how you identified the height I know the height needs to be perpendicular parallel to the base so first I 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 Notes for Digital Lessons G6M1 Lesson 6 Lesson 6 Area of Parallelograms Which side could be the base for this parallelogram What would be the corresponding height Label a base and height and then use the measurements to find the area 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 7

G6M1 Lesson 7 ZEARN MATH Student Notes for Digital Lessons Lesson 7 From Parallelograms to Triangles Draw one line to decompose the parallelogram into 2 identical triangles 8 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M1 Lesson 8 Lesson 8 Area of Triangles Without calculating explain the steps you would take to find the area of this triangle Consider using pictures and words to 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 9

G6M1 Lesson 9 ZEARN MATH Student Notes for Digital Lessons Lesson 9 Formula for the Area of a Triangle Circle the triangle that has the height labeled correctly Then explain how to find the area of the triangle height height base 10 base height base 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M1 Lesson 10 Lesson 10 Bases and Heights of Triangles r p q If you needed to find the area of this triangle which side would you choose as the base Explain how you made your choice I would choose side p q r for the base I would choose this side because How would you determine the height of the triangle To determine the height of the triangle first I 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M1 Lesson 11 ZEARN MATH Student Notes for Digital Lessons Lesson 11 Polygons Clara decomposed the polygon into these two triangles and added their areas to find the area of the polygon Find the area in a different way Explain the strategy you would use and draw on the polygon to help you explain I could use the decompose and add the parts enclose and subtract strategy to find the area First I would Then I would Finally I would 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 Notes for Digital Lessons G6M1 Lesson 12 Lesson 12 What Is Surface Area 1 What is the surface area of a three dimensional figure The surface area of a three dimensional figure is 2 Explain how you would find the surface area of any prism To find the surface area of a prism first I would Next I would 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M1 Lesson 13 ZEARN MATH Student Notes for Digital Lessons Lesson 13 Polyhedra Is this polyhedron a prism a pyramid or neither Explain how you know How many faces does it have 14 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M1 Lesson 14 Lesson 14 Nets and Surface Area How can you use a net to find the surface area of a polyhedron Consider drawing a picture of a net to help you explain 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

G6M1 Lesson 15 ZEARN MATH Student Notes for Digital Lessons Lesson 15 More Nets More Surface Area 4 units 6 units 3 units 1 Circle the net that matches the polyhedron above The side length of a grid square is 1 unit 2 What s the surface area of the polyhedron Show 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 Notes for Digital Lessons G6M1 Lesson 17 Lesson 17 Squares and Cubes What does it mean to square a number What does it mean to cube a number Consider using pictures notations and words to help you 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 17

G6M1 Lesson 18 ZEARN MATH Student Notes for Digital Lessons Lesson 18 Surface Area of a Cube The side length of the cube is labeled in the net below 2 in 3 Describe what surface area is using this net of a cube as an example Without calculating write an expression that represents the surface area of this cube Consider using an exponent in your expression Describe what volume is using this cube as an example Then without calculating write an expression that represents the volume of this cube Consider using an exponent in your expression 18 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

Grade 6 Mission 2 Introducing Ratios

G6M2 Lesson 1 ZEARN MATH Student Notes for Digital Lessons Lesson 1 Introducing Ratios and Ratio Language In your own words explain a ratio You may choose to support your thinking with a picture A ratio is 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

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 2 Lesson 2 Representing Ratios with Diagrams These two diagrams show the same ratio of circles to triangles Diagram A Diagram B What is the ratio of circles to triangles Which diagram was more helpful to you in describing the ratio Why The ratio of circles to triangles is Diagram A Diagram B was more helpful to me in describing the ratio because 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 21

G6M2 Lesson 3 ZEARN MATH Student Notes for Digital Lessons Lesson 3 Recipes Cheryl makes a chocolate milk recipe that uses 2 cups of milk and 7 tablespoons of chocolate powder Draw a diagram to represent double the recipe Write a ratio to describe the quantities The ratio of milk to chocolate powder is 22 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 4 Lesson 4 Color Mixtures To make 1 batch of pink paint Joe mixes 2 liters of red paint with 1 gallon of white paint Make a diagram of an equivalent ratio Consider doubling or tripling this mixture to find an equivalent ratio Diagram Equivalent ratio The ratio of liters of red paint to gallons of white paint is 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 23

G6M2 Lesson 5 ZEARN MATH Student Notes for Digital Lessons Lesson 5 Defining Equivalent Ratios What are equivalent ratios Explain how you could find a ratio that is equivalent to 3 5 24 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 6 Lesson 6 Introducing Double Number Line Diagrams Water cups Lemonade mix tsp 0 1 Water cups Lemonade mix tsp 0 1 Complete the double number line diagram to show the amount of each ingredient in 1 2 3 4 and 5 batches of lemonade 2 How are these two representations 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 25

G6M2 Lesson 7 ZEARN MATH Student Notes for Digital Lessons Lesson 7 Creating Double Number Line Diagrams The ratio of apples to oranges needed to make a smoothie is 12 apples to 6 oranges Explain how you can determine how many apples are needed per orange to make a smoothie that tastes the same Consider using a double number line to support your thinking 26 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 8 Lesson 8 How Much for One The cost of 9 boxes of cereal is 36 What is the unit price Create a visual representation that shows your solution 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M2 Lesson 9 ZEARN MATH Student Notes for Digital Lessons Lesson 9 Constant Speed Evan ran 20 meters in 5 8 seconds Yelena ran 20 meters in 5 4 seconds Who ran faster Explain how you know 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 Notes for Digital Lessons G6M2 Lesson 10 Lesson 10 Comparing Situations by Examining Ratios Tracy rides her bike 5 meters in 5 seconds Peter rides his scooter 10 meters in 10 seconds Both travel at a constant rate Peter says I traveled faster because I went a greater distance Do you agree with Peter Explain or show your reasoning Consider using a double number line to help I agree disagree with Peter because 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 29

G6M2 Lesson 11 ZEARN MATH Student Notes for Digital Lessons Lesson 11 Representing Ratios with Tables Fill in the table and explain the strategies you used to fill it in Choc chips oz Pretzels oz 2 6 24 14 40 120 20 30 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 12 Lesson 12 Navigating a Table of Equivalent Ratios A printer prints 8 sheets of paper in 16 seconds Explain how you could find each unknown in the table Paper sheets Seconds 8 16 1 13 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 31

G6M2 Lesson 13 ZEARN MATH Student Notes for Digital Lessons Lesson 13 Tables and Double Number Line Diagrams The double number line shows how much sour cream and how much seasoning to mix to make different amounts of onion dip 0 0 5 1 1 5 0 2 4 6 Sour cream cups Seasoning tablespoons 1 Make a table to represent the same situation 2 What does the number 4 represent 32 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M2 Lesson 14 Lesson 14 Solving Equivalent Ratio Problems Jayson reads the first 48 pages of a 480 page book in 3 days Marcus reads the first 50 pages of a 400 page book in 4 days Nina reads the first 120 pages of a 600 page book in 5 days 1 If they continue to read at these rates who will finish first 2 How many days will each student take to finish his or her book 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M2 Lesson 15 ZEARN MATH Student Notes for Digital Lessons Lesson 15 Part Part Whole Ratios The ratio of students wearing sandals to those wearing sneakers is 5 1 If there are 30 students in the class and all of them are wearing either sandals or sneakers how many of them are wearing sandals Draw a tape diagram to support your thinking 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 Notes for Digital Lessons G6M2 Lesson 16 Lesson 16 Solving More Ratio Problems Write a word problem that could describe this situation Red paint ml 0 5 10 15 20 25 0 3 6 9 12 15 0 8 16 24 32 40 Blue paint ml Purple paint ml Red paint ml Blue paint ml Purple paint ml 5 3 8 25 15 40 Red paint ml 5 5 5 Blue paint ml 5 5 5 5 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 35

Grade 6 Mission 3 Unit Rates and Percentages

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 1 Lesson 1 Using Unit Rate to Solve Problems Sam does 11 jumping jacks in 8 seconds If he does the jumping jacks at a constant rate how many jumping jacks can he do in 20 seconds How would you solve this problem Think about explaining what values you may need to find in a table to solve this problem You do not need to actually solve 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M3 Lesson 3 ZEARN MATH Student Notes for Digital Lessons Lesson 3 Measuring with Different Sized Units Jack says This gymnasium is 30 meters long A meter is longer than a yard so if I measure the length of the gymnasium in yards I will get less than 30 yards Do you agree with Jack Explain your reasoning 38 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 4 Lesson 4 Converting Units Stacy knows that there are 8 ounces in a cup She wants to convert 12 ounces to cups but got stuck She cannot decide if there are 96 cups in 12 ounces or if there are 1 12 cups in 12 ounces Help Stacy out Consider drawing a double number line to support your reasoning 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 39

G6M3 Lesson 5 ZEARN MATH Student Notes for Digital Lessons Lesson 5 Comparing Speeds and Prices 1 Central Market sells 5 jars of jam for 3 00 Valley Market sells jars of jam at 59 cents per jar Yasmin bought 10 jars from Central Market and Nadia bought 10 jars from Valley Market Who spent less money How much less did she spend 2 These signs show the price of juice at two different markets 2 bottles of juice for 5 6 bottles of juice for 12 Kadir thinks the bottles of juice at Green Market are less expensive Explain how you know he is incorrect You may consider setting up a table and calculating the unit price to help prove your answer 40 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 6 Lesson 6 Interpreting Rates The table shows different quantities of red and blue paint for the same shade of purple Use the table to explain how you would find the missing value Red paint cups Blue paint cups 5 4 5 4 1 1 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 41

G6M3 Lesson 7 ZEARN MATH Student Notes for Digital Lessons Lesson 7 Equivalent Ratios Have the Same Unit Rates This table shows the amounts of chocolate powder and milk in different sized batches of chocolate milk Sam notices that if she takes the number in the milk column and divides it by the corresponding number in the chocolate powder column she always get the same result Chocolate powder tablespoons Milk ounces 2 14 4 28 6 42 a What number does Sam get when she divides b What s the meaning of this number 42 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 8 Lesson 8 More about Constant Speed A lion can run 4 kilometers in 3 minutes The table shows the 2 unit rates related to this situation Distance kilometers Time minutes 4 3 1 3 4 1 3 1 1 1 Explain how you would figure out how long it takes the lion to run 9 kilometers 2 Explain how you would figure out how far the lion can travel in 7 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 43

G6M3 Lesson 9 ZEARN MATH Student Notes for Digital Lessons Lesson 9 Solving Rate Problems Andrew thinks that The Corner Store is the better deal because you re only spending 20 88 while at The General Store you have to spend 24 70 Yasmin says The General Store is the better deal because the unit price is lower Who do you agree with Explain your reasoning The Corner Store 44 The General Store Bottles Price Bottles Price 12 20 88 15 24 70 1 1 74 1 1 65 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 11 Lesson 11 Percentages and Double Number Lines Leah has a goal to make cookies for a school bake sale This double number line represents her goal Explain what each of the numbers on the double number line mean 0 18 72 90 0 25 100 125 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 45

G6M3 Lesson 12 ZEARN MATH Student Notes for Digital Lessons Lesson 12 Percentages and Tape Diagrams Partition the tape diagram to show 60 of 30 Then label the value of 60 100 30 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 Notes for Digital Lessons G6M3 Lesson 13 Lesson 13 Benchmark Percentages You can think of percentages in terms of fractions Describe how you can think about 10 25 and 75 by using fractions Consider using tape diagrams to support your explanation 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 47

G6M3 Lesson 14 ZEARN MATH Student Notes for Digital Lessons Lesson 14 Solving Percentage Problems Use the double number line to help you answer the questions 0 60 120 180 240 0 25 50 75 100 1 What is 25 of 240 2 75 of the whole is 180 What is the whole 3 120 is what percent of 240 48 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M3 Lesson 15 Lesson 15 Finding This Percent of That Use two different strategies to explain how to find 30 of 600 Consider using a table a double number line a tape diagram or multiplication 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M3 Lesson 16 ZEARN MATH Student Notes for Digital Lessons Lesson 16 Finding the Percentage Today you learned a strategy for finding percentages If C is the part and B is the whole then to find what percentage C is of B you divide C by B and then multiply by 100 C B 100 Without calculating explain how you could find what percentage 60 is of 80 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

Grade 6 Mission 4 Dividing Fractions

G6M4 Lesson 1 ZEARN MATH Student Notes for Digital Lessons Lesson 1 Size of Divisor and Size of Quotient What happens to the quotient when you divide by smaller and smaller numbers You may want to use these 3 examples from the lesson to support your thinking 100 7 600 100 101 1 and 100 2 12 52 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 2 Lesson 2 Meanings of Division A math classroom needs 260 to pay for new calculators All calculators cost the same amount What could 260 20 mean in this context Describe two interpretations of the expression You may consider using a tape diagram to help 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 53

G6M4 Lesson 3 ZEARN MATH Student Notes for Digital Lessons Lesson 3 Interpreting Division Situations Without solving determine what is known and unknown in this word problem and draw a tape diagram that represents the problem Then write a multiplication and division equation to represent your diagram Word problem Marcus has 16 47 ounces of pretzels that he wants to split equally among 4 people How many ounces of pretzels will each person get Tape diagram Equations 54 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 4 Lesson 4 How Many Groups Part 1 How many 1 4 s are in 6 a Draw a tape diagram to represent the problem b What equations can you write to represent this problem 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 55

G6M4 Lesson 5 ZEARN MATH Student Notes for Digital Lessons Lesson 5 How Many Groups Part 2 How could you explain what 2 divided by thinking 56 1 3 means in words Draw a diagram to show your 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 6 Lesson 6 Using Diagrams to Find the Number of Groups How many 5 6 s are in 3 Label the tape diagram to solve this problem What number represents the total What number represents the size of the group What number represents the number of groups 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 57

G6M4 Lesson 7 ZEARN MATH Student Notes for Digital Lessons Lesson 7 What Fraction of a Group Answer the following questions about this division sentence 1 2 5 What are two ways you could interpret this division sentence is what fraction of How many groups of are in Draw a tape diagram to represent this problem 58 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 8 Lesson 8 How Much in Each Group Part 1 After walking 15 mile from home Anthony is 14 of the way to soccer practice What is the distance between home and soccer practice Use the tape diagram to help you answer the questions Mark up and label it as needed 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 59

G6M4 Lesson 9 ZEARN MATH Student Notes for Digital Lessons Lesson 9 How Much in Each Group Part 2 Janiyah can fill 15 bottle with 3 liters of water How many liters of water will fill 1 whole bottle Label the tape diagram and use it to help you solve 60 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 10 Lesson 10 Dividing by Unit and Non Unit Fractions Describe the steps you could take to find the quotient for each problem You may use the tape diagram to support your answer a 8 1 4 b 8 3 4 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 61

G6M4 Lesson 11 ZEARN MATH Student Notes for Digital Lessons Lesson 11 Using an Algorithm to Divide Fractions 3 4 1 2 Describe how you could solve this problem without drawing a tape diagram 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 Notes for Digital Lessons G6M4 Lesson 12 Lesson 12 Fractional Lengths A piece of paper is 10 12 inches long If you put of the paper how many sticky notes will fit 3 2 inch sticky notes end to end across the length First circle the tape diagram that represents the equation Then write a division equation that represents the problem Finally write a multiplication expression you could use to help you solve 10 12 inches 3 2 inch 10 12 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 63

G6M4 Lesson 13 ZEARN MATH Student Notes for Digital Lessons Lesson 13 Rectangles with Fractional Lengths Suppose we know that the width of a rectangle is 3 34 cm and the area is 15 square cm Write and solve a division equation to help you find the length of the rectangle 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 Notes for Digital Lessons G6M4 Lesson 14 Lesson 14 Fractional Lengths in Triangles and Prisms Without solving describe a method that you could use to find the volume of this rectangular prism 3 cm 8 1 2 cm 2 cm 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 65

G6M4 Lesson 15 ZEARN MATH Student Notes for Digital Lessons Lesson 15 Volume of Prisms Carlos packed this rectangular prism with 12 inch cubes Francine packed it with Who will need to use more cubes Will they find the same volume 1 4 inch cubes 4 in 2 12 in 6 12 in 66 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M4 Lesson 16 Lesson 16 Solving Problems Involving Fractions Look back at your notes from this mission What are some of the methods you can use to divide fractions Try to give two examples and explain those methods as if you were talking to a younger student 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 67

Grade 6 Mission 5 Arithmetic in Base Ten

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 1 Lesson 1 Using Decimals in a Shopping Context Solve 23 49 31 70 using a place value chart Then record the sum tens ones tenths hundredths 23 49 31 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 69

G6M5 Lesson 2 ZEARN MATH Student Notes for Digital Lessons Lesson 2 Using Diagrams to Represent Addition and Subtraction Solve each problem using the place value chart or the algorithm Choose whichever strategy works best for you 1 2 70 4 032 2 079 2 463 1 749 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 3 Lesson 3 Adding and Subtracting Decimals with Few NonZero Digits The work below shows how a student solved 5 408 1 07 5 408 1 0 7 1 301 What error did the student make Explain why this student s work is incorrect and show the correct solution using the subtraction algorithm or place value chart 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M5 Lesson 4 ZEARN MATH Student Notes for Digital Lessons Lesson 4 Adding and Subtracting Decimals with Many Non Zero Digits How could you solve this using subtraction 0 391 72 0 4017 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 5 Lesson 5 Decimal Points in Products Solve 102 103 You might think of this as 102 of 103 Consider using an area model to explain your answer 1 Whole 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M5 Lesson 6 ZEARN MATH Student Notes for Digital Lessons Lesson 6 Methods for Multiplying Decimals Place the decimal in the product Explain how you know where to place it using estimation fractions or the rule you learned today 4 52 1 219 550 988 4 52 12 19 74 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 7 Lesson 7 Using Diagrams to Represent Multiplication How are the numbers in the vertical calculations below related to those in the area diagram Use specific examples in the models below to prove your thinking 2 0 7 0 3 0 6 0 21 1 2 0 7 2 7 1 3 0 8 1 2 7 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 75

G6M5 Lesson 8 ZEARN MATH Student Notes for Digital Lessons Lesson 8 Calculating Products of Decimals 7 5 3 8 Choose a strategy you just practiced to solve this problem Then explain how you used the strategy to help you solve 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 Notes for Digital Lessons G6M5 Lesson 9 Lesson 9 Using the Partial Quotients Method The following place value chart shows how Melei divided 846 by 2 846 2 Describe the steps Melei took to divide Explain what the answer means hundreds tens ones 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M5 Lesson 10 ZEARN MATH Student Notes for Digital Lessons Lesson 10 Using Long Division How is the division algorithm similar to and different from dividing on the place value chart Use these two examples to support your thinking 672 3 hundreds 78 tens ones 224 3 672 6 07 6 12 12 0 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 11 Lesson 11 Dividing Numbers that Result in Decimals hundreds tens ones 31 4 126 12 06 4 2 Tamaya thinks she is done dividing Explain how you could continue dividing on the place value chart and the algorithm 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M5 Lesson 12 ZEARN MATH Student Notes for Digital Lessons Lesson 12 Dividing Decimals by Whole Numbers In this example of 0 6 4 what can you do with the remainder of 2 tenths in order to get a more precise answer ones 80 tenths 0 1 4 0 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 Notes for Digital Lessons G6M5 Lesson 13 Lesson 13 Dividing Decimals by Decimals A student said To find the value of 96 divided by 0 06 I can divide 960 by 6 Do you agree with this statement Why or why not 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 81

G6M5 Lesson 14 ZEARN MATH Student Notes for Digital Lessons Lesson 14 Using Operations on Decimals to Solve Problems In this lesson you reviewed adding subtracting multiplying and dividing using a standard algorithm In your notes choose two of the following problems and solve using an algorithm 3 187 2 654 9 321 4 162 1 5 3 2 4 5 0 5 82 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M5 Lesson 15 Lesson 15 Volume of Prisms Carlos packed this rectangular prism with 12 inch cubes Francine packed it with Who will need to use more cubes Will they find the same volume 1 4 inch cubes 4 in 2 12 in 6 12 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 83

Grade 6 Mission 6 Expressions And Equations

ZEARN MATH Student Notes for Digital Lessons G6M6 Lesson 1 Lesson 1 Tape Diagrams and Equations Draw a tape diagram for each equation Then solve 1 21 3 t 2 21 3 p Tape diagram Tape diagram Solve for t Solve for p 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M6 Lesson 2 ZEARN MATH Student Notes for Digital Lessons Lesson 2 Truth and Equations Harmony thinks 448 is a solution to the equation 8b 56 Is Harmony correct Explain why or why not 86 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M6 Lesson 3 Lesson 3 Staying in Balance Match the equation to the correct hanger and solve for y in each equation 3 y 10 3y 10 10 y y 3 y 10 y 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 87

G6M6 Lesson 4 ZEARN MATH Student Notes for Digital Lessons Lesson 4 Practice Solving Equations and Representing Situations with Equations Explain how you could find the value of y Consider explaining the operations you might use or drawing a hanger diagram to support your thinking 2y 7 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 Notes for Digital Lessons G6M6 Lesson 5 Lesson 5 A New Way to Interpret a over b Deliana is solving the equation 1 6 y 5 Her teacher wrote the first step to help get her started 1 6 1 6 y 5 1 6 Deliana thinks she needs to solve 5 6 Do you agree with her Explain why or why not Then solve for y 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 89

G6M6 Lesson 6 ZEARN MATH Student Notes for Digital Lessons Lesson 6 Write Expressions Where Letters Stand for Numbers Jin sells cookies to fundraise for her school She sells the cookies for 1 50 per cookie 1 Write an expression to represent how much money she collects if she sells c cookies 2 Without solving explain how your expression could help you solve if you knew Jin sold 45 cookies 90 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M6 Lesson 7 Lesson 7 Revisit Percentages Today you learned the equation px q Without solving how would you use this equation to solve the following 45 of 300 is equal to what 45 of what number is 300 Then explain how these are similar and 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 91

G6M6 Lesson 8 ZEARN MATH Student Notes for Digital Lessons Lesson 8 Equal and Equivalent Circle the pair of equivalent expressions Then explain what it means for two expressions to be equivalent b 0 and b 4a and a 4 92 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M6 Lesson 9 Lesson 9 The Distributive Property Part 1 Write three equivalent expressions using the distributive property to represent the area of the entire large rectangle Then use one of the expressions to find the area of the large rectangle 20 3 7 Area 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 93

G6M6 Lesson 10 ZEARN MATH Student Notes for Digital Lessons Lesson 10 The Distributive Property Part 2 Jade thinks the area is m 6 m 8 Arianna thinks the area is m 6 8 How can they both be correct Use the distributive property to support your answer 6 8 m 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 Notes for Digital Lessons G6M6 Lesson 12 Lesson 12 Meaning of Exponents 6 6 6 6 1 296 Using exponents write two more expressions that also have the value 1 296 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 95

G6M6 Lesson 13 ZEARN MATH Student Notes for Digital Lessons Lesson 13 Expressions with Exponents Without evaluating circle the expressions that are equivalent to each other Explain how you know they are equivalent 1 148 14 8 2 28 28 28 283 3 644 64 64 64 64 3 67 76 3 51 51 51 51 513 51 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 Notes for Digital Lessons G6M6 Lesson 14 Lesson 14 Evaluating Expressions with Exponents Jovany and Jada solved the following problem in different ways Do you agree with either of them Explain your reasoning Jovany Kenya 12 23 4 12 23 4 12 8 4 12 8 4 12 2 14 20 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 97

G6M6 Lesson 15 ZEARN MATH Student Notes for Digital Lessons Lesson 15 Equivalent Exponential Expressions Explain how you would figure out if c 4 is a solution to c2 5 13 98 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M6 Lesson 16 Lesson 16 Two Related Quantities Part 1 You represented the relationship between the cups of pineapple juice and the cups of cranberry juice with three different representations a table equations and a graph How are these representations similar and how are they different Cups of apple juice p Cups of cranberry juice c 1 4 y 40 36 2 8 5 20 10 40 3 12 cranberry juice cups 32 28 24 20 16 12 8 p 1 4 4 1 2 3 4 5 6 7 pineapple juice cups 8 9 10 x c c 4 p 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M6 Lesson 17 ZEARN MATH Student Notes for Digital Lessons Lesson 17 Two Related Quantities Part 2 Dominic works on the weekends mowing lawns in his neighborhood For every lawn he mows he charges 12 Write an equation to show the relationship between the number of lawns Dominic mows and the money he makes where d is the total amount of dollars he makes and m is the number of lawns he mows The use the equation and table to find how many lawns Dominic needs to mow if he needs to make 240 100 Lawns m Dollars d 1 12 2 24 3 36 4 48 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

Grade 6 Mission 7 Rational Numbers

G6M7 Lesson 1 ZEARN MATH Student Notes for Digital Lessons Lesson 1 Positive and Negative Numbers What is a positive number Where are positive numbers located on the number line What is a negative number Where are negative numbers located on the number line 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 Notes for Digital Lessons G6M7 Lesson 2 Lesson 2 Points on the Number Line What is the opposite of 181 Draw a number line and use the definition of an opposite to 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 103

G6M7 Lesson 3 ZEARN MATH Student Notes for Digital Lessons Lesson 3 Comparing Positive and Negative Numbers 0 1 Compare the smiley face and the star a Is less than b Write an inequality to compare and 2 Compare the smiley face and the heart a Is less than b Write an inequality to compare and 3 If you plot two numbers on the number line how can you tell which is greater 104 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 4 Lesson 4 Ordering Rational Numbers How can you tell if one number is greater than or less than another How do you write it with symbols 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 5 ZEARN MATH Student Notes for Digital Lessons Lesson 5 Using Negative Numbers to Make Sense of Contexts What other situations can you think of where you gain or lose an amount that you could use negative numbers to talk about What would positive and negative changes mean in those situations 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 Notes for Digital Lessons G6M7 Lesson 6 Lesson 6 Absolute Value of Numbers What is the difference between a number s opposite and a number s absolute value 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 107

G6M7 Lesson 7 ZEARN MATH Student Notes for Digital Lessons Lesson 7 Comparing Numbers and Distance from Zero How do you say 112 What does 112 mean in an elevation situation What does 112 mean on a number line What is the value of 112 108 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 Notes for Digital Lessons G6M7 Lesson 8 Lesson 8 Writing and Graphing Inequalities 1 2 3 4 5 6 7 8 9 10 11 Think about if the number line shows more than or less than 4 Then write a scenario that matches the number line Choose a variable for your scenario and write an inequality statement for your scenario using your variable 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 Lesson 9 ZEARN MATH Student Notes for Digital Lessons Lesson 9 Solutions of Inequalities A sign on the road says Speed limit 35 miles per hour A speed limit tells drivers the fastest speed they can drive so drivers can drive 35 miles per hour but they cannot go faster Name a speed you can drive Name a speed you cannot drive Use words an inequality and or a number line to explain your reasoning 110 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 10 Lesson 10 Interpreting Inequalities Think about the number of books you ve read so far this year Have you read more than 2 books More than 5 books More than 10 books Write an inequality for the number of books that you ve read so far this year Do solutions that are not whole numbers make sense in this situation Do solutions that are negative numbers make sense in this situation 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 111

G6M7 Lesson 11 ZEARN MATH Student Notes for Digital Lessons Lesson 11 Points on the Coordinate Plane Plot and label a point where the x value is negative and the y value is positive Explain how you know the x value is negative and the y value is positive y 10 8 6 4 2 10 8 6 4 2 2 2 4 6 8 10 x 4 6 8 10 112 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 12 Lesson 12 Constructing the Coordinate Plane When plotting 12 1 and 32 3 how would you make your graph Explain using words and then set up your coordinate plane Then plot the 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 113

G6M7 Lesson 13 ZEARN MATH Student Notes for Digital Lessons Lesson 13 Interpreting Points on a Coordinate Plane Account Balance Suppose two people open their own bank accounts on the same day Graphing their account balances over several days one person s situation is represented by 6 225 and the other person s is represented by 6 13 What does this mean in the situation How do their account balances compare Days 114 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 14 Lesson 14 Distances on a Coordinate Plane Without graphing what can you say about the points 6 2 and 6 2 on the coordinate plane You may want to point out what quadrant they are in how many units they are from the x axis how many units away they are from the y axis or how far apart they are 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

G6M7 Lesson 15 ZEARN MATH Student Notes for Digital Lessons Lesson 15 Shapes on the Coordinate Plane Record the coordinates of JKLM in the table Then find the perimeter of the polygon y 10 Points 8 J K 6 x y J 4 K 2 10 8 6 4 2 M 2 2 4 4 6 8 10 x L L M 6 8 10 116 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 16 Lesson 16 Common Factors Is the greatest common factor of a pair of numbers ever equal to one of the numbers Explain with an example 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 117

G6M7 Lesson 17 ZEARN MATH Student Notes for Digital Lessons Lesson 17 Common Multiples What is the least common multiple of 7 and 12 Show your work 118 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M7 Lesson 18 Lesson 18 Using Common Multiples and Common Factors Ruby s Flyers Ruby is putting flyers on some of the 50 lockers along one side of her school s hallway She puts a flyer for the music club on every 3rd locker starting with locker 3 and a flyer for the art club on every 5th locker starting with locker 5 1 Name 3 lockers that will get both flyers 2 After Ruby makes her way down the hall will the 50th locker have no flyers 1 flyer or 2 flyers Explain how you know Pencils and Erasers Mr Rodriguez is assembling supply kits for his students He has 24 pencils and 32 erasers All the kits must have the same number of each item and all items must be used 2 What is the largest number of kits Mr Rodriguez can make 3 How many pencils and erasers will be in each kit 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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

Grade 6 Mission 8 Data Sets and Distributions

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 1 Lesson 1 Got Data Give 3 examples of categorical and 3 examples of 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 121

G6M8 Lesson 2 ZEARN MATH Student Notes for Digital Lessons Lesson 2 Statistical Questions Give 2 examples of statistical and 2 examples of non statistical questions Keep in mind which ones would require collecting data with variability 122 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 3 Lesson 3 Representing Data Graphically In what ways might dot plots be more useful than lists and tables 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license 123

G6M8 Lesson 4 ZEARN MATH Student Notes for Digital Lessons Lesson 4 Dot Plots What s the typical age of members of the audience who attended each movie Which dot plot has the wider spread Explain your reasoning 10 15 20 25 30 35 40 45 50 55 40 45 50 55 Ages at Movie X 10 15 20 25 30 35 Ages at Movie Y 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 Notes for Digital Lessons G6M8 Lesson 5 Lesson 5 Using Dot Plots to Answer Statistical Questions In your own words explain what the center of a distribution is Explain what the spread of a distribution is Use the dot plot below to support your explanations 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 125

G6M8 Lesson 6 ZEARN MATH Student Notes for Digital Lessons Lesson 6 Histograms This histogram shows the number of students in each class at school What does the bar between 25 and 30 tell you 10 9 8 7 6 5 4 3 2 1 0 5 10 15 20 25 30 35 40 45 Number of students in each class 126 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 7 Lesson 7 Using Histograms to Answer Statistical Questions What does the horizontal axis of this histogram tell you What does the vertical axis tell you What does the height of each bar tell you 10 8 6 4 2 0 5 10 15 20 25 Dog height 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 127

G6M8 Lesson 8 ZEARN MATH Student Notes for Digital Lessons Lesson 8 Describing Distributions on Histograms This is a histogram that shows the number of books read by a class of students in a school year What do the features of this histogram tell you about the data For example you could mention Does this histogram have symmetrical distribution Are there any peaks and what do the peaks tell you Are there any gaps and what do the gaps tell you 7 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 Number of books read 128 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 9 Lesson 9 Interpreting the Mean as Fair Share For 5 days Sebastian has recorded how many minutes it takes for him to walk from school to the library The mean of his data set is 6 minutes Which data set could be Sebastian s Explain how you know You may choose to explain your reasoning using calculations or your knowledge of mean Data set A 5 4 8 8 5 Data set B 8 7 9 8 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 129

G6M8 Lesson 10 ZEARN MATH Student Notes for Digital Lessons Lesson 10 Finding and Interpreting the Mean as the Balance Point Kendall walks to school every weekday The table and dot plot below show the time in minutes it took for Kendall to walk to school every day last week She put a triangle on the dot plot where she thought the mean was Do you agree with Kendall Explain your reasoning 8 130 9 10 11 Day Minutes Monday 17 Tuesday 12 Wednesday 17 Thursday 10 Friday 13 12 13 14 15 16 17 18 19 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

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 11 Lesson 11 Deviation from the Mean Match the store with its dot plot Use your knowledge of Mean Absolute Deviation and your knowledge of the variability of a data set to explain how you matched each dot plot to the correct store Store A Store B Mean Number of Dollars Spent 23 Mean Number of Dollars Spent 23 MAD 16 MAD 7 5 5 10 15 20 25 30 35 40 45 50 55 60 5 10 15 20 25 30 35 40 45 50 55 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 131

G6M8 Lesson 12 ZEARN MATH Student Notes for Digital Lessons Lesson 12 Using Mean and MAD to Make Comparisons Imagine you and a friend are reading the same book You both decide to record how many pages you read each day for the next week After a week you and your friend calculate the mean and MAD for your data sets Explain in your notes how you could have the same mean but different MADs and how you could have the same MADs but different means 132 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 13 Lesson 13 The Median of a Data Set Here s a table that shows students scores on the last math test Jordyn thinks the median is 81 Marvion thinks the median is 84 because the median has to be a number in the data set close to the middle Who do you think is correct Why 64 65 74 78 84 88 97 98 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 14 ZEARN MATH Student Notes for Digital Lessons Lesson 14 Comparing Mean and Median Explain why the mean and median are the same in the dot plot showing cat ages compared to the dot plot showing dog ages Consider discussing whether or not the distribution is symmetrical 1 2 3 4 5 6 7 8 9 10 11 8 9 10 11 Ages of Dogs at the Vet Median 5 Mean 6 1 2 3 4 5 6 7 Ages of Cats at the Vet Median 5 Mean 5 134 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up Resources 6 8 Math curriculum which is available to download for free at openupresources org and used under the CC BY 4 0 license

ZEARN MATH Student Notes for Digital Lessons G6M8 Lesson 15 Lesson 15 Quartiles and Interquartile Range The dot plot and box plot below show the distribution of competitors ages at a weightlifting competition Find the range and the interquartile range IQR using the information provided Minimum 30 30 10 Q1 35 30 20 30 40 30 Q2 55 40 40 50 Q3 82 5 60 50 70 60 80 85 70 Maximum 90 85 80 90 90 Ages of Weightlifters 2023 Zearn Licensed to you pursuant to Zearn s Terms of Use This work is a derivative of Open Up 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 16 ZEARN MATH Student Notes for Digital Lessons Lesson 16 Box Plots Below is a box plot that shows the number of canned goods a school collected for their annual food donation drive Draw a line to match each shape to the correct term in your notes Then write the definition of each term next to the term Finally name one thing this box plot tells you about the shape center and spread of the number of cans collected 20 30 40 50 60 70 80 90 Number of canned goods collected for a food drive Minimum Maximum Q1 Median Q3 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 Notes for Digital Lessons G6M8 Lesson 17 Lesson 17 Using Box Plots The box plots below summarize the number of books students read in two different classes this year Use the box plots to compare the number of books the two classes have read Class 1 Class 2 8 10 12 14 16 18 20 22 24 26 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 137

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zearn org NAME 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 Mission 7 Rational Numbers Mission 8 Data Sets and Distributions Mission 9 Putting It All Together Student Notes for Digital Lessons Grade 6 Grade 6 Student Notes for Digital Lessons Grade 6