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NAME Grade 7STUDENT NOTES FOR DIGITAL LESSONS
© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use.This work is a derivative of Open Up Resources’ 6-8 Math curriculum, used under the CC BY 4.0 license.Download the original for free at openupresources.orgZearn® is a registered trademark. Printed in the U.S.A.ISBN: 979-8-88868-884-7
Table of ContentsMISSION 1 Scale Drawings 1MISSION 2 Introducing Proportional Relationships 11MISSION 3 Measuring Circles 27MISSION 4 Proportional Relationships and Percentages 37MISSION 5 Rational Number Arithmetic 53MISSION 6 Expressions, Equations, and Inequalities 69MISSION 7 Angles, Triangles, and Prisms 93MISSION 8 Probability and Sampling 109
Grade 7Mission 1Scale Drawings
ZEARN MATH Student Notes for Digital LessonsG7M1 | Lesson 1Lesson 1: What Are Scaled Copies?Which is a scaled copy? Explain how you know.The scaled copy is .I know this becauseABoriginal© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.2
ZEARN MATH Student Notes for Digital Lessons G7M1 | Lesson 2Lesson 2: Corresponding Parts and Scale Factors1. What do we mean by corresponding parts? Use the triangles to identify at least 1 pair of corresponding parts.Corresponding parts refers to In these two triangles, the sides measuring and are corresponding parts.2. What is a scale factor? How can you create scaled copies using a scale factor?A scale factor isTo create scaled copiesOriginal Triangle15 cm12 cm36 cm45 cm21 cm7 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.3
ZEARN MATH Student Notes for Digital LessonsG7M1 | Lesson 3Lesson 3: Making Scaled CopiesOn the right of this grid is one side of a scaled copy of the rectangle. The side that corresponds to 5 units in the original rectangle is 15 units in the scaled copy. What is the scale factor used? Explain how you found the scale factor. Then complete the rest of the scaled copy.The scale factor is .I know this becauseOriginal RectangleScaled Copy© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.4
ZEARN MATH Student Notes for Digital Lessons G7M1 | Lesson 4Lesson 4: Scaled RelationshipsFigure 2 is a scaled copy of Figure 1.AFigure 1Figure 2CUS1. Identify the points in Figure 2 that correspond to the points A and C in Figure 1. Label them R and T. What is the distance between R and T?2. Identify the points in Figure 1 that correspond to the points S and U in Figure 2. Label them B and D. What is the distance between B and D?3. What is the scale factor that takes Figure 1 to Figure 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.5
ZEARN MATH Student Notes for Digital LessonsG7M1 | Lesson 5Lesson 5: The Size of the Scale FactorRectangles B, C, and D are all scaled copies of Rectangle A.• Which scaled copy has a scale factor greater than 1?• Which scaled copy has a scale factor equal to 1?• Which scaled copy has a scale factor less than 1?Explain how you know.ABCD© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.6
ZEARN MATH Student Notes for Digital Lessons G7M1 | Lesson 7Lesson 7: Scale DrawingsBelow are scale drawings of the Statue of Liberty, Golden Gate Bridge, and Washington Monument. Use the scale drawings below to answer the following questions.1. About how tall is the actual Golden Gate Bridge? Explain or show your reasoning.2. About how tall is the actual Washington Monument? Explain or show your reasoning.3. About how much taller is the actual Washington Monument than the actual Statue of Liberty? Explain or show your reasoning.100 m0© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M1 | Lesson 9Lesson 9: Creating Scale DrawingsThe actual dimensions for a handball court are 24 feet by 36 feet. Below is a scale drawing of the court. What is the scale? You could think about what you can multiply the dimensions of 8 inches12 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.8
ZEARN MATH Student Notes for Digital Lessons G7M1 | Lesson 10Lesson 10: Changing Scales in Scale DrawingsIf all the dimensions of a scale drawing are twice as long as in the original shape, will the area of the scaled copy be twice as large? Use an example to explain your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.9
ZEARN MATH Student Notes for Digital LessonsG7M1 | Lesson 12Lesson 12: Units in Scale DrawingsWhat does it mean when the scale on a scale drawing does not indicate any units?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.10
Grade 7Mission 2Introducing Proportional Relationships
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 1Lesson 1: One of These Things Is Not Like the OthersBelow are two tables that represent chocolate milk mixtures. Will these two recipes of chocolate milk taste the same? Explain your reasoning.Milk (Cups)Chocolate Powder (Tablespoons)3 91 32 65 15Milk (Cups)Chocolate Powder (Tablespoons)4 166 247 281 4The mixtures will taste the same/dierent 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.12
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 2Lesson 2: Introducing Proportional Relationships with TablesFor a birthday party, it’s recommended that there are 4 pitchers of lemonade for every 12 students. Find the constant of proportionality for the relationship between pitchers of the unknown value in the table.Pitchers of lemonadeNumber of students4 128 245 15118 ?The constant of proportionality isI can use the constant of proportionality to nd the unknown value in the table by© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 3Lesson 3: More about Constant of ProportionalityLook at the table below. What are the two constants of proportionality? What is the relationship between them? Explain in your notes.Feet Inches1 123 365 60The constants of proportionality are and .The relationship between them 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.14
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 4Lesson 4: Proportional Relationships and EquationsThe table represents a proportional relationship between the number of hours it snows, h, and the number of inches of now on the ground, s. Find the constant of proportionality and write an equation that represents the relationship.h s2 103 156 3011 55Constant of proportionality:Equation: s =© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.15
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 5Lesson 5: Two Equations for Each RelationshipA car can travel 400 miles in 8 hours at a constant speed. Using d for distance in miles and t for numbers of hours, an equation that represents this situation is d = 50t.1. What are two constants of proportionality for the relationship between distance in miles and numbers of hours? What is the relationship between these two values?2. Write another equation that relates d and t 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.16
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 6Lesson 6: Using Equations to Solve Problemsa) Write an equation or create a table that relates the number of bottles of water to the b) How much water is in 51 bottles?c) © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.17
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 7Lesson 7: Comparing Relationships with TablesOne of these relationships is proportional and the other is not. How could you determine which relationship is not proportional? Explain your reasoning and then determine which is proportional.ATime in Hours (h)Distance in Miles (m)2 1203 1804 2405 300BTime in Hours (h)Distance in Miles (m)2 1203 1404 1605 180© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.18
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 8Lesson 8: Comparing Relationships with EquationsUse the equation y = 5xx and y? Explain why or why not.x y236Use the equation y = 6xx and y? Explain why or why not.x y124© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 9Lesson 9: Solving Problems about Proportional RelationshipsMake your own example of a relationship between two quantities that is proportional. Describe the situation, write an equation, and create a table to model it. Explain why one quantity is proportional to the other.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.20
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 10Lesson 10: Introducing Graphs of Proportional RelationshipsAmaya is working at a summer camp. She earns $12 an hour. Plot the pairs from the table on the coordinate plane. Is the relationship proportional? Explain how you know.Hours, x Dollars, y0 01 122 243 364 485 60121 2 3HoursDollars4 52436486072yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 11Lesson 11: Interpreting Graphs of Proportional RelationshipsIn a recipe for marinara sauce, there is a proportional relationship between the amount of tomatoes, in cups, and the amount of salt, in teaspoons. The table below shows this relationship.Salt (teaspoons)Tomatoes (cups)4 86 128 1610 201. Plot the points on the coordinate plane.2. Interpret the point (8, 16). What does it tell you about the situation?3. What is the constant of proportionality? Describe what the constant of proportionality means in this situation.1 3 5 7 92 4 6 8 10403216824362812420Salt (teaspoons)Tomatoes (cups)xy© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.22
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 12Lesson 12: Using Graphs to Compare RelationshipsDeandre and Harper each ran at a constant rate at track practice. Deandre can run 80 meters in 20 seconds. Harper can run 75 meters in 25 seconds. The tables below show their running times and distances. 1. Plot both students’ points on one graph.2. What is Deandre’s constant of proportionality? What is Harper’s?3. Who is running faster?yx5010203040506070809010010 15 20 25 30 35 40 45 50Time (seconds)Distance (meters)DeandreTime in seconds, xDistance in meters, y20 8015 601HarperTime in seconds, xDistance in meters, y25 7530 901© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M2 | Lesson 13Lesson 13: Two Graphs for Each RelationshipIn this proportional relationship, there are two quantities: points scored and time in minutes. In each table, x and yTime in Minutes, xPoints Scored, y10 2020 4030 6040 8050 100 points scored per minutePoints Scored, xTime in Minutes, y20 1040 2060 3080 40100 50 points scored per minuteEquations:a) y = 2xb) y = 2x© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.24
ZEARN MATH Student Notes for Digital Lessons G7M2 | Lesson 14Lesson 14: Four RepresentationsThe equation c = 3.50b represents the cost of blackberries at a certain store. Use the equation Pounds of blackberries (b)Cost in dollars (c)17.506142.0015© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.25
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Grade 7Mission 3Measuring Circles
ZEARN MATH Student Notes for Digital LessonsG7M3 | Lesson 1Lesson 1: How Well Can You Measure?in the pool and the time that has passed in minutes. Do you think that there is a proportional relationship between the amount of water in gallons in the pool and the time that has passed? the points to solve.Water (gallons)Time (minutes)150 10310 20420 30600 40720 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.28
ZEARN MATH Student Notes for Digital Lessons G7M3 | Lesson 2Lesson 2: Exploring CirclesCircle the letter of the shape that is a circle. Then label the radius and diameter of the circle. A B C© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.29
ZEARN MATH Student Notes for Digital LessonsG7M3 | Lesson 3Lesson 3: Exploring CircumferenceComplete the table. Use the approximation 3.14 for pi. Explain your reasoning.Object Diameter (cm) Circumference (cm)Dart Board 18 inchesSoup Can 26 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.30
ZEARN MATH Student Notes for Digital Lessons G7M3 | Lesson 4Lesson 4: Applying Circumferenceyour thinking.A B C© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.31
ZEARN MATH Student Notes for Digital LessonsG7M3 | Lesson 6Lesson 6: Estimating AreasWhat’s a good estimate for the area of this shape? Draw on the shape to show how shapes you thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.32
ZEARN MATH Student Notes for Digital Lessons G7M3 | Lesson 7Lesson 7: Exploring the Area of a Circlearea of the circle.rr© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M3 | Lesson 8Lesson 8: Relating Area to CircumferenceHere’s a circle with radius of 4 inches. Which is the best estimate for the area of the circle? Explain your reasoning using estimation or calculations.a) 16 square inchesb) 25 square inchesc) 50 square inchesd) 200 square inches4 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.34
ZEARN MATH Student Notes for Digital Lessons G7M3 | Lesson 9Lesson 9: Applying Area of Circles10 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.35
ZEARN MATH Student Notes for Digital LessonsG7M3 | Lesson 10Lesson 10: Distinguishing Circumference and AreaFor each problem, decide whether the circumference of the circle or the area of the circle is a) A painter wants to paint a circular table. The diameter of the table is 65 inches. She wants to know how much paint she needs to cover the top of the table in paint.b) Parents want to build a fence around a circular playground that measures 30 feet in diameter.c) A roller coaster travels in a circle. The diameter of the circle is 30 meters. How far do riders travel in one rotation? d) A baker is greasing the bottom of a pie pan. His pan measures 9 inches in diameter. How much of his pan does he need to grease?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.36
Grade 7Mission 4Proportional Relationships and Percentages
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 1Lesson 1: Relative Areas of Scaled CopiesWhat percentage of the park below is the pool? Consider using a double number line to solve.10 m20 m15 m15 m© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.38
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 2Lesson 2: Ratios and Rates With FractionsDuring cross country practice, Tania runs at a constant rate of 40 meters every 16 seconds. At this rate, what is her speed in meters per second?Time (seconds) Distance (meters)16 401 ?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 3Lesson 3: Revisiting Proportional RelationshipsAhmir solved using the constant of proportionality, whereas Layla solved using the scale factor. using both Ahmir and Layla’s methods.Ahmir’s Method: Constant of ProportionalityNumber of pizzasPrice2 $205Layla’s Method: Scale FactorNumber of pizzasPrice2 $205x x x x © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.40
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 4Lesson 4: Half as Much Againx14 less miles than Duck A. Two students each wrote an x, and Duck B’s y. Do you agree with either of them? Explain your reasoning.Maryy = x14xBrycey = 34x© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 5Lesson 5: Say It With DecimalsSasha and Mihnkang are converting 19 to a decimal. Sasha says the answer is 0.1 and Mihnkang says its 0.1. Who is correct? What mistake did the other student make? Explain in your notes and use long division to support your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.42
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 6Lesson 6: Increasing and DecreasingA restaurant used a certain amount of vegetable oil last month. If the amount of oil the restaurant used increases by 40%, what percent of the original amount does the restaurant have? If the amount of oil decreases by 40%, what percent of the original amount does the restaurant have? Show your thinking on a double number line.Oil (cups)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 7Lesson 7: One Hundred PercentRepresent the problem on the double number line below. Then solve using the double number line or the percent formula.ounces. How much water can the new water container hold?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.44
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 8Lesson 8: Percent Increase and Decrease with EquationsRepresent this situation with an equation and solve. You can use a double number line to organize your thinking.Jimmy had $20 in his savings account at the beginning of the school year. He continued to add money to it and by July, the value of the savings accound had increased by 40%. How much money is in Jimmy’s account in July?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.45
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 9Lesson 9: More and Less than 1%Spot the error and correct the student’s work below. Explain your reasoning. 40% of 120 is 484% of 120 is 4.80.4% of 120 is 0.480.04% of 120 is 0.480© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.46
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 10Lesson 10: Tax and TipBelow is a receipt for a hat in a city where the sales tax rate is 8.5%. Find the sales tax and the total.January 30Sale #15HatSubtotalSales TaxTotal12.0012.00© 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.47
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 11Lesson 11: Percentage ContextsAlice solved a word problem with the following double number line but she lost the original problem. What problem could she have solved with this double number line? What equation could she have used to solve it? Explain your reasoning.28.80 360% 80% 100%Dollars© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.48
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 12Lesson 12: Find the PercentageJaylee bought a pair of shoes and received the receipt, shown below, from the store. She is 1.62 = kRECEIPTShoes 27.00Sales Tax 1.62Total 28.62© 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.49
ZEARN MATH Student Notes for Digital LessonsG7M4 | Lesson 13Lesson 13: Measurement ErrorBelow are two containers of milk from a grocery store along with their actual weight and listed weight, in pounds. Match the measurement errors and percent errors to each milk container. Then, explain why you would use a percent error rather than a measurement error to compare these two containers of milk.3.0 lb8.5 lb2.5lb8.0lbContainer: Container: Container A:• Measurement error = 0.5 pounds• Percent error = 6.25%Container B:• Measurement error = 0.5 pounds• Percent error = 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.50
ZEARN MATH Student Notes for Digital Lessons G7M4 | Lesson 14Lesson 14: Percent Error25 people attended an open house. A real estate agent expected 28% fewer people to attend. How many people did the real estate agent expect to attend? You can use a double number line or an equation to support your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.51
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Grade 7Mission 5Rational Number Arithmetic
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 1Lesson 1: Interpreting Negative NumbersHere is a set of signed numbers: 7, -3, 8, -6, 1, -2. Answer the questions about the numbers. Consider drawing a number line to help.1. Use two of the numbers to write an inequality.2. If these numbers represent temperatures in degrees Celsius, which is the coldest?3. If these numbers represent elevations in meters, which is the farthest away from sea level?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.54
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 2Lesson 2: Changing TemperaturesTianna is on a ski vacation in Colorado. In the morning, the temperature was -4 degrees Celsius. By noon, the temperature was 2 degrees. Use the number line to help you answer the following questions.What was the starting temperature?What is the change in temperature shown on the number line?-6-8-10 -2 0-4 2 4 6 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.55
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 3Lesson 3: Changing ElevationIsabelle said that when you add a positive and a negative number, the sum is always positive. Do you agree? Why or why not? Use at least 2 examples to support your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.56
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 4Lesson 4: Money and DebtsWrite a situation that this number line could represent. Consider using some of the vocabulary from the lesson such as deposit, withdrawal, debt, and account balance.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 5Lesson 5: Representing Subtractionnumber 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.58
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 6Lesson 6: Subtracting Rational NumbersShow each expression on the number line.-7 + 55 + (-7)543210-1-2-3-4-5-6-7-8-9-10-12 -11543210-1-2-3-4-5-6-7-8-9-10-12 -1154-1-2 1098763210-3-4-5-6-754-1-2 1098763210-3-4-5-6-7© 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.59
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 7Lesson 7: Adding and Subtracting to Solve ProblemsThe table below shows the amount of baked goods being made and sold at a school bake sale. Inventory ChangeMonday 50 -10Tuesday -20Wednesday 20Thursday 30 -20Friday 10 +10Saturday -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.60
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 8Lesson 8: Position, Speed, and DirectionUsing the example 3 · -8, prove that a positive times a negative number always equals a negative product. Show your work on the number line, write a phrase that describes 3 · -8, and groups of 3 · -8 = 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.61
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 9Lesson 9: Multiplying Rational NumbersSolve the following problems. Explain or show your thinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.62
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 11Lesson 11: Dividing Rational Numbers1. When you divide a positive number by a negative number, what sign is the quotient? Use a multiplication equation of your choice to explain why this makes sense.2. When you divide a negative number by a negative number, what sign is the quotient? Use a multiplication equation of your choice to explain why this makes sense.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.63
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 13Lesson 13: Expressions with Rational NumbersComplete the table below by writing an expression that is equivalent to the given expression. you.Expression -8 + -7 20 ÷ -4 20 • -4Equivalent ExpressionValue -15© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.64
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 14Lesson 14: Solving Problems with Rational Numbersrate of 9 gallons per minute. A drain in the pool can empty the pool at a constant rate of 9 gallons per minute. The expressions below can be used to determine how much water is in the 10,000 + 20 · 9 10,000 + 20 · -9What does each expression represent in the context of this situation? 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.65
ZEARN MATH Student Notes for Digital LessonsG7M5 | Lesson 15Lesson 15: Solving Equations With Rational NumbersWithout solving, explain how you could solve each problem below. You could consider rewriting these equations as the related subtraction or the related division equations to help you.1. x + (-7.2) = 5.42. y • (-7.2) = 5.4© 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.66
ZEARN MATH Student Notes for Digital Lessons G7M5 | Lesson 16Lesson 16: Representing Contexts with EquationsWrite an equation and solve for the number of hours it takes for the temperature to drop. Explain what your variable represents.The temperature has been dropping 3 degrees Fahrenheit every hour, and the current temperature is -12 degrees. How many hours ago was the temperature 0 degrees?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.67
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Grade 7Mission 6Expressions, Equations, and Inequalities
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 1Lesson 1: Relationships between Quantitiesrelationship between the number of pizzas ordered and the amount the restaurant charged? Explain your reasoning.Number of Pizzas Cost for Delivery ($)3 204 265 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.70
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 2Lesson 2: Reasoning about Contexts with Tape Diagrams (Part 1)Select all stories that the tape diagram can represent.a) groups.b) bracelets up between 5 friends.c) Hannah has a collection of 98 seashells. She gives 43 to her sister and shared the remaining seashells between herself and 4 friends.d) Marcus buys 5 packs of toothpicks with 43 toothpicks in each pack. Then he gives 98 toothpicks to his teacher.e) Randy’s family spends $98 on 5 tickets to the amusement park and $43 on lunch.98x x x x x43© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 3Lesson 3: Reasoning about Contexts with Tape Diagrams (Part 2)Draw a tape diagram to match each equation.a) 4(x + 6) = 40b) 4x + 6 = 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.72
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 4Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)Vandana is trying to solve the following word problem:A fair charges $7 for a car to park and x dollars per ticket to enter the fair. A family of 4 paid $65 to park one car and enter the fair. How much was each ticket?Vandana drew the tape diagram below and wrote an equation to represent the situation. Do you agree with the tape diagram and equation she used? If you agree, explain why. If you disagree, what should the tape diagram and equation look like? 657x + 4 = 65x x x x x x x 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.73
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 5Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)A student is trying to solve the following word problem:Elena has 45 ounces of hot chocolate. She pours equal amounts into 5 mugs, then adds 6 more ounces to each mug.Sandra drew the tape diagram below and wrote an equation to represent the situation. Do you agree with the tape diagram and equation Sandra used? If you agree, explain why. If you disagree, what should the tape diagram and equation look like?5(x + 6) = 45x + 6 x + 6 x + 6 x + 6 x + 645© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.74
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 6Lesson 6: Distinguishing between Two Types of SituationsConsider describing how each of the following are represented in the tape diagrams and equations: • equal groups• • the total3939a + 9a + 9 a + 9aa a93(a + 9) = 393a + 9 = 39© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 7Lesson 7: Reasoning about Solving Equations (Part 1)Circle the hanger diagram that represents the equation. Then, solve.5x + 2.3 = 17.8xxxxx2.317.8xxxxx17.82.3© 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.76
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 8Lesson 8: Reasoning about Solving Equations (Part 2)Write an equation to represent the hanger diagram. Solve and explain your reasoning.44418nnn© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 9Lesson 9: Dealing with Negative NumbersAndre and Kristen each solved the equation -3w + 7 = 1. Their teacher tells them that they both made a mistake!1. Circle and identify the mistake each student made.2. -3w + 7=1-7-7-3w-3= -6-3w=-2-3w + 7=1-7-7-3w-3= 8-3w =83-© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.78
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 10Lesson 10Consider the equation -15 = 4(x + 14)• Solve the equation using each method you practiced today.• If the equation is harder to solve using one of the methods, stop solving with that method.• Explain the reason you stopped. What made that method harder and the other method easier?Divide: -15 = 4(x + 14)Distribute: -15 = 4(x + 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.79
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 11Lesson 11: Using Tape Diagrams and Equations to Solve ProblemsWrite a story that could be represented by this tape diagram and then solve for y.52y + 3 y + 3 y + 3 y + 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.80
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 12Lesson 12: Solving Problems about Percent Increase or Decreaseof the reduced price. If Drew pays $36 for a pair of shoes, what was their original price before the sale and without the coupon? Finish drawing and labeling the tape diagram and write an PriceDrewpaidOriginalpricePriceaercoupon© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 13Lesson 13: Reintroducing InequalitiesThe table shows two inequalities and two possible values for x. Decide whether each value makes each inequality true, and complete the table with “true” or “false.”x = -50 x = 50xx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.82
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 14Lesson 14: Finding Solutions to Inequalities in ContextMonica has $140 saved in her bank account. She wants to have at least $200 in the account 6 months from now.a) Monica wrote the inequality 6xMonica puts into her account each month. What does 6x represent?b) Find some values of x that would work for Monica.c) You could express all the values that would work using an inequality symbol. Which symbol should you use?d) Write the answer to Monica’s question using mathematical notation.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 15Lesson 15ythinking.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.84
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 16Lesson 16: Inequalities in ContextWrite a word problem that could be represented by this inequality. Then, solve the inequality and explain what the solution means in your situation.8 + 2.50x > 63© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 17Lesson 17: Modeling with InequalitiesMs. Rodriguez has $149 to spend on a school pizza party. If each pizza costs $14, how many pizzas can she buy if she wants to have at least $30 remaining for decorations?a) Write an inequality to model the situation.b) Solve and graph the solution to the inequality on a number line.c) Interpret the solution in the context of the 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.86
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 18Lesson 18: Subtraction in Equivalent ExpressionsUse the distributive property to write equivalent expressions that represent the boxes below. You can use the boxes to help you organize your work. ( + + )( ) + ( ) + ( ) + + x-2y64© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 19Lesson 19: Expanding and FactoringUse the diagram below to write 10xyon the boxes. Then, explain how you can use the boxes to write an equivalent expression. Include the factored expression in your answer. Use the diagram to organize your thinking. 10x y210x -8y© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.88
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 20Lesson 20: Combining Like Terms (Part 1)Esme is doubtful that 8a + 3bab is equivalent to 3ab. How could you convince her that these expressions are equivalent? Show all of the steps you would take to prove to Esme that the expressions are equivalent.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.89
ZEARN MATH Student Notes for Digital LessonsG7M6 | Lesson 21Lesson 21: Combining Like Terms (Part 2)y + 4) as 2(2y + 4). Explain the error that Liam made.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.90
ZEARN MATH Student Notes for Digital Lessons G7M6 | Lesson 22Lesson 22: Combining Like Terms (Part 3)Fathia said that (10r + 6p) – (5r + 11p) is equivalent to 5(r – p). Is she correct? Explain why or why not.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.91
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Grade 7Mission 7Angles, Triangles, and Prisms
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 1Lesson 1: Relationships of AnglesHere are two pairs of adjacent angles.Which angle is a right angle, and which angle is a straight angle? Explain how you know.118°62°BDCA37°53°ZVXY© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.94
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 2Lesson 2: Adjacent AnglesLook at square ABCD. Name a pair of complementary angles and a pair of supplementary angles.A BD CE© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 3Lesson 3: Nonadjacent AnglesIf two angles are both vertical and supplementary, can we determine the angles? Is it possible to be both vertical and complementary? If so, can you determine the angles? 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.96
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 4Lesson 4: Solving for Unknown Anglesimage below.b°d°a°e°c°© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.97
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 5Lesson 5: Using Equations to Solve for Unknown AnglesSegments AB, DC, and EC intersect at point C. Angle DCE measures 136°. Find the value of y.y˚136˚Ay˚CBD E© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.98
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 6Lesson 6: Building Polygons (Part 1)A rectangle has side lengths of 4 units and 7 units. Could you make a quadrilateral that is not identical using the same four side lengths? If so, describe 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.99
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 7Lesson 7: Building Polygons (Part 2)Here are 3 side lengths. Could these be a triangle? Why or why not?8 inches, 9 inches, 20 inches© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.100
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 8Lesson 8: Triangles with 3 Common MeasuresExplain how a set of conditions could lead to a unique triangle. Explain how another set of conditions could lead to many possible triangles.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 11Lesson 11: Slicing Solidsexample. You can use the shapes below to support 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.102
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 12Lesson 12: Volume of Right PrismsThe hexagonal prism and hexagonal pyramid below both have a base with an area of 32 cm2, and a height of 7 cm. Khalid thinks the prism and pyramid have the same volume. Do you agree or disagree? Explain your reasoning.32 cm232 cm2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 13Lesson 13: Decomposing Bases for Areavolume of the prism? You may use the prism below, and the overhead view of its base, to support 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.104
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 14Lesson 14: Surface Area of Right Prismssurface area.1. For which of these shapes can she use this strategy?2. Explain why the new strategy works for that shape.3. 6 cm6 cm9 cm3 cm4 cm11 cm5 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.105
ZEARN MATH Student Notes for Digital LessonsG7M7 | Lesson 15Lesson 15: Distinguishing Volume and Surface Areasurface area and a strategy you could use to solve for volume.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.106
ZEARN MATH Student Notes for Digital Lessons G7M7 | Lesson 16Lesson 16: Applying Volume and Surface Areaexterior of the barn.Paint (m2) Cost ($)100 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.107
108
Grade 7Mission 8Probability and Sampling
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 1Lesson 1: Mystery Bags18 24 25 21 19 30 24in the last 7 throws in the table below.14 18 15 30 28 13 21reasoning.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.110
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 2Lesson 2: Chance ExperimentsWrite an example for each of the following types of events. For example, the weather report says there is a 10% chance of rain tomorrow. The chance of rain tomorrow is unlikely.impossibleunlikelyequally likely as notlikelycertain© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 3Lesson 3: What Are Probabilities?You randomly select a month of the year.a) What is the sample space?b) How many outcomes are in the sample space?c) What is the probability of selecting a random month of the year and getting a month that starts with the letter “J?”© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.112
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 4Lesson 4: Estimating Probabilities through Repeated Experimentsreally is 21proven that the theoretical probability is not 21? 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.113
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 5Lesson 5: More Estimating ProbabilitiesEdgar has a bag of purple and green blocks. He picks a block out of a bag and puts it back 80 times. He notes that 64 of them were purple.a) What should Edgar estimate for the experimental probability of picking out a purple block from this bag?b) Natasha looks in the bag and sees that there are 4 blocks in the bag. Should Edgar change his estimate based on this information? If so, what should the new estimate be? If not, 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.114
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 6Lesson 6: Estimating Probabilities Using SimulationThe weather forecast says there is an 80% chance it will snow in Anchorage, AK later today.a) Draw a spinner you could use to simulate this probability.b) Describe another way you could simulate this probability.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 7Lesson 7: Simulating Multi-Step ExperimentsSuppose that, on average, a professional bowler bowls a strike about 1 out of every 2 times he bowls. In other words, he has a 50% chance of bowling a strike. Jake used a number cube to simulate this event by specifying that the numbers 1, 2 or 3 represent a strike, and the numbers an estimate of the probability that the bowler bowls a strike at least 3 out of the 5 attempts.Location Roll 1 Roll 2 Roll 3 Roll 4 Roll 5 Did he bowl a strike at least 3 out of 5 attempts?Simulation 1 1 3 4 2 2Simulation 2 2 6 5 4 3Simulation 3 2 1 1 4 4Simulation 4 6 5 1 2 6Simulation 5 3 4 3 1 5Simulation 6 1 1 4 5 6Simulation 7 2 6 2 1 3Simulation 8 5 5 4 1 2Simulation 9 6 2 4 3 1Simulation 10 4 1 2 3 4© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.116
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 8Lesson 8: Keeping Track of All Possible OutcomesCameron picks one type of cheese and one topping to make a pizza.• Cheese: Parmesan or Mozzarella• Toppings: Peppers, Onions, MushroomsList the sample space and determine the number of pizzas that Cameron can make with one cheese and one topping from the lists above. You might consider using a table or tree to organize your sample space.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 9Lesson 9: Multi-Step ExperimentsCoralie has a bag that contains a green, a yellow, and a blue marble. She has a second bag that contains 5 cards, each labeled with a number 1-5. If she randomly picks one item from each bag, what is the probability of getting a blue marble and a card labeled with the number 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.118
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 10Lesson 10: Designing SimulationsHalfway through the season, Neonna’s team won 10% of the games they played. To see how likely it is that they will win at least 1 out of their next 5 games, the situation is going to be simulated. Which of these options is the best simulation? For others, explain why it is not a good simulation.a) Roll a standard cube 5 times. Each time a 1 appears, it represents Neonna’s team winning a game. Repeat this process 50 times and count the fraction of times at least one number 1 appears.b) Have a computer produce 5 random digits (0 through 9). If a 2 appears in the list of digits, it represents Neonna’s team winning a game. Repeat this process 500 times and count the fraction of times at least one number 2 appears.c) Create a spinner with 10 equal sections and mark one of them as a “win” for Neonna’s team. Spin the spinner 5 times to represent the next 5 games. Repeat this process 50 times and count the fraction of times that at least 1 “win” was spun.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 11Lesson 11: Comparing GroupsHere is the data for the test scores in two classes. The mean and MAD have been calculated for what that means about the data.Class 1 test scoresMean = 88 MAD = 3.48070 8272 8474 86 9088 9276 78 9694 98 100Class 2 test scoresMean = 79 MAD = 4.88070 8272 8474 86 9088 9276 78 9694 98 100© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.120
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 12Lesson 12: Larger PopulationsFor each sample given, list two possible populations they could belong to. Explain your reasoning.1. Sample: The number of hours students at your school spend on homework each week.2. Sample: The average income for teachers in your state.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 13Lesson 13: What Makes a Good Sample?This is a dot plot that shows the number of books read this school year for a population of 50 teenagers.The three dot plots together are the number of books teenagers read in three samples from this population. Which of the three samples is most representative of the population? Explain how you know.Number of Books6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38Number of BooksSample 1Sample 2Sample 36 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 386 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 386 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 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.122
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 14Lesson 14: Sampling in a Fair WayA farmer noticed that a few apple trees were rotten. She wants to know if it is a problem in the 1. What may be a good method that would produce a representative sample?2. Why would a random sample be useful in this situation?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.123
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 15Lesson 15: Estimating Population Measures of CenterThis dot plot shows the wingspans of a random sample of 20 birds in Section A at the zoo. The mean wingspan from this sample is 27.5 inches.This dot plot shows the wingspans of a random sample of 20 birds in Section B at the zoo. The mean wingspan from this sample is also 27.5 inches.If you were to choose a random bird from each sample, which bird’s wingspan is more likely to be close to the sample mean wingspan, 27.5 inches? The bird from Section A, or the bird from Section B? Explain your reasoning.Wingspan of birds (inches)305 3510 4015 45 5020 25Wingspan of birds (inches)305 3510 4015 45 5020 25© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.124
ZEARN MATH Student Notes for Digital Lessons G7M8 | Lesson 16Lesson 16: Estimating Population ProportionsAriella wants to know what proportion of students in her school like chocolate ice cream best. The population of her school is 640, so it would take her too long to ask every student. She decides to ask a random sample of 20 students. The data is shown below.a) What proportion of students in the sample said that chocolate ice cream is their favorite?b) Describe a way that Ariella could use her sample to make a prediction about the number of students in the entire school who like chocolate ice cream best. In your response, provide three values that are reasonable estimates.Favorite Ice Cream Flavor Number of ResponsesVanilla 4Chocolate 9Strawberry 2Other 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.125
ZEARN MATH Student Notes for Digital LessonsG7M8 | Lesson 18Lesson 18: Comparing Populations Using SamplesThese two dot plots show the heights of a random sample of men and women college basketball players.know.58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 8858 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88Height of players on the men’s basketball team (inches)Height of players on the women’s basketball team (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.126
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zearn org NAME Grade 7 Mission 1 Scale Drawings Mission 3 Measuring Circles Mission 4 Proportional Relationships and Percentages Mission 5 Rational Number Arithmetic Mission 6 Expressions Equations and Inequalities Mission 7 Angles Triangles and Prisms Student Notes for Digital Lessons Mission 2 Introducing Proportional Relationships Mission 8 Probability and Sampling Mission 9 Putting It All together Student Notes for Digital Lessons Grade 7 Grade 7