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NAME Grade 8STUDENT 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: 979-8-88868-880-9

Table of ContentsMISSION 1 Rigid Transformations and Congruence 1MISSION 2 Dilations, Similarity, and Introducing Slope 17MISSION 3 Linear Relationships 31MISSION 4 Linear Equations and Linear Systems 45MISSION 5 Functions and Volume 61MISSION 6 Associations in Data 81MISSION 7 Exponents and Scientic Notation 93MISSION 8 Pythagorean Theorem and Irrational Numbers 109

Grade 8Mission 1Rigid Transformations and Congruence

ZEARN MATH Student Notes for Digital LessonsG8M1 | Lesson 1Lesson 1: Moving in the PlaneThe six frames show a shape’s dierent positions. Describe how the shape moves to get from its position in each frame to the next.To get from frame 1 to frame 2,To get from frame 2 to frame 3,To get from frame 3 to frame 4,To get from frame 4 to frame 5,To get from frame 5 to frame 6,Frame 1 Frame 2 Frame 3Frame 4 Frame 5 Frame 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.2

ZEARN MATH Student Notes for Digital Lessons G8M1 | Lesson 2Lesson 2: Naming the MovesLabel each set of 2 frames as a translation, rotation, or reection and explain how you decided.Frame 1 to Frame 2 shows a , becauseFrame 3 to Frame 4 shows a , becauseFrame 5 to Frame 6 shows a , 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

ZEARN MATH Student Notes for Digital LessonsG8M1 | Lesson 3Lesson 3: Grid MovesReect gure A across line ℓ.ℓFGAD 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.4

ZEARN MATH Student Notes for Digital Lessons G8M1 | Lesson 4Lesson 4: Making the MovesDescribe a sequence of translations, rotations, and reections that takes Polygon A to Polygon J.AEDBCMNJKL© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M1 | Lesson 5Lesson 5: Coordinate MovesAnswer the questions about the points on both coordinate planes below.1. What are the coordinates of A, B, and C aer a translation to the right 5 units and down 3 units? Plot these on the grid, and label them A’, B’, and C’.2. What are the coordinates of D, E, and F aer a reection over the y-axis? Plot these points on the grid, and label them D’, E’, and F’.-10 -8 -6 -4 -2 2 4 6 8 10yx108642-2-4-6-8-1000ABC-10 -8 -6 -4 -2 2 4 6 8 10yx108642-2-4-6-8-1000FDE© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M1 | Lesson 6Lesson 6: Describing TransformationsHere is triangle ABC in the coordinate plane. Draw triangle AʹBʹCʹ, the image of triangle ABC aer each sequence of transformations below.1. On the le plane, draw the image of triangle ABC aer a reection over the x-axis. Label the image triangle A’B’C’. Then, translate triangle A’B’C’ 3 units down, and label the image triangle A’’B’’C’’.2. On the right plane, draw the image of triangle ABC aer a translation of 3 units down. Label the image triangle A’B’C’. Then, reect triangle A’B’C’ using the x-axis as the line of reection, and label the image triangle A’’B’’C’’.3. Did the order matter for this sequence of transformations? 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.7

ZEARN MATH Student Notes for Digital LessonsG8M1 | Lesson 7Lesson 7: No Bending or StretchingExplain why the following is not an example of a rigid transformation. TQ© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M1 | Lesson 8Lesson 8: Rotation PatternsFor the gure shown below, describe where the image would be if you:a) rotated segment AB 180° around point Bb) rotated segment AB 180° around point Jc) rotated segment AB 180° around point TJBTA© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M1 | Lesson 9Lesson 9: Moves in ParallelThe diagram shows two lines that intersect at point B. Use the diagram to nd the measures of each angle. Explain your reasoning.a) Find the measure of angle ABCb) Find the measure of angle CBDc) Find the measure of angle DBE85ºAB CDE© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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

ZEARN MATH Student Notes for Digital Lessons G8M1 | Lesson 11Lesson 11: What Is the Same?1. If two rectangles have the same perimeter, do they have to be congruent? Explain how you know.2. If two rectangles are congruent, do they have to have the same perimeter? 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.11

ZEARN MATH Student Notes for Digital LessonsG8M1 | Lesson 12Lesson 12: Congruent PolygonsIf two shapes are congruent, do they have the same side lengths? If two shapes have the same side lengths, are they denitely congruent? Explain your thinking. Consider drawing shapes 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.12

ZEARN MATH Student Notes for Digital Lessons G8M1 | Lesson 14Lesson 14: Alternate Interior AnglesLines m and n are parallel, and the measure of angle b is 27 degrees.a) Explain why the measure of angle f is 27 degrees.b) What is the measure of angle h? Explain or show your thinking.bamncefgdh© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M1 | Lesson 15Lesson 15: Adding the Angles in a TriangleExplain what you observed about the angle measurements of a triangle made from a straight 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.14

ZEARN MATH Student Notes for Digital Lessons G8M1 | Lesson 16Lesson 16: Parallel Lines and the Angles in a Trianglea) Find the measure of the missing angle in triangle GHJ, shown below.b) Explain how you can nd the measure of a missing angle in any triangle if you know the measures of the other two angles.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.15

16

Grade 8Mission 2Dilations, Similarity, and Introducing Slope

ZEARN MATH Student Notes for Digital LessonsG8M2 | Lesson 1Lesson 1: Projecting and ScalingRectangle D has a length of 8 units and a width of 6 units. Rectangle E has a length of 12 units and a width of 9 units. Rectangle F has a length of 24 units and a width of 20 units.a) Is Rectangle D a scaled copy of Rectangle E? If so, what is the scale factor?b) Is Rectangle E a scaled copy of Rectangle D? If so, what is the scale factor?c) Explain how you know that Rectangle F is not a scaled copy of Rectangle 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.18

ZEARN MATH Student Notes for Digital Lessons G8M2 | Lesson 2Lesson 2: Circular GridDilate each vertex of polygon XYZ using point P as the center of dilation and a scale factor of 3. What do you notice about this new polygon? You may consider discussing the side lengths and/or the angles.PYZX© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M2 | Lesson 3Lesson 3: Dilations with no GridLook at the following gure.1. If point X is the center of dilation, which point is the dilation of point Y with a scale factor of 4? Explain your reasoning.2. If point X is the center of dilation, which point is the dilation of point W with a scale factor of 31? Explain your reasoning.WZYX© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M2 | Lesson 4Lesson 4: Dilations on a Square GridDilate points P and Q below using a scale factor of 41 and the origin as the center of dilation. Complete the table with the coordinates of the original points and their images, Pʹ and Qʹ.Original point Dilated pointP PʹQ Qʹ-10-8-6-4-224681010864-10 -8 -6 -4 -2 2yxPQ© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M2 | Lesson 5Lesson 5: More DilationsQuadrilateral ABCD is dilated with center, P, at (-1, 2), taking B to Bʹ.a) What is the scale factor?b) Draw quadrilateral AʹBʹCʹDʹ.-10 -8 -6 -4 -2 2 4 6 8 10yxAPBCD108642-2-4-6-8-1000B'© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M2 | Lesson 6Lesson 6: SimilarityPolygons ABCD and EFGH are similar. What does it mean that they are similar? Polygons ABCD and IJKL are also congruent. What does it mean that they are congruent?mFGEHL IJKBA DC© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M2 | Lesson 7Lesson 7: Similar PolygonsThese gures are not similar. Explain why they are not similar.57°57°123°123°6 cm6 cm6 cm6 cm80°80°100°100°12 cm12 cm12 cm12 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.24

ZEARN MATH Student Notes for Digital Lessons G8M2 | Lesson 8Lesson 8: Similar TrianglesAre these two triangles similar? Do you think two equilateral triangles will always, sometimes, or never be similar? Explain your reasoning.60˚AB C60˚ 60˚GH K60˚60˚ 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.25

ZEARN MATH Student Notes for Digital LessonsG8M2 | Lesson 9Lesson 9: Side Length Quotients in Similar TrianglesThese two triangles are similar. What is the value of ba ?ab7.5486© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.26

ZEARN MATH Student Notes for Digital Lessons G8M2 | Lesson 10Lesson 10: Meet SlopeOne of these lines has a slope of 4, and one has a slope of 21. Label each line with its slope and 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.27

ZEARN MATH Student Notes for Digital LessonsG8M2 | Lesson 11Lesson 11: Writing Equations for LinesWrite an expression that represents the slope of this line. You can draw a slope triangle to help you. Explain how you know your expression represents the slope of this line.102 3 4 5 6 7 8 9 10 1211123456789101211yx(x, y)(3, 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.28

ZEARN MATH Student Notes for Digital Lessons G8M2 | Lesson 12Lesson 12: Using Equations for LinesLine r is shown on the graph below. The points (1, 4), (x, y), and (3, 10) all lie on line r.a) Write an expression to represent the slope of line r.b) Find the slope of line r.c) Write an equation for line r.d) Does the point (7, 18) lie on the line? Explain your reasoning.1 10 119873 65421101198736542yx(1, 4)(3, 10)(x, y)r© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M2 | Lesson 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.30

Grade 8Mission 3Linear Relationships

ZEARN MATH Student Notes for Digital LessonsG8M3 | Lesson 1Lesson 1: Understanding Proportional RelationshipsArleth and Gafar were biking at a constant rate. The tables below show their distances at dierent times.a) Graph the relationship between distance traveled and time for Arleth and Gafar’s bike rides.b) Write an equation to represent each relationship.c) Who is going faster? Use the tables, graph, or equations to prove your thinking.Arleth’s Bike RideDistance traveled (km), xElapsed time (min), y0 02 44 85 10Gafar’s Bike RideDistance traveled (km), xElapsed time (min), y0 02 64 125 151 22468101214163 4 5 6Distance traveled (km)Elapsed time (min)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.32

ZEARN MATH Student Notes for Digital Lessons G8M3 | Lesson 2Lesson 2: Graphs of Proportional RelationshipsToyosi was running at a constant rate. The graph shows the relationship between distance and time for Toyosi’s run.Distance (mi), xElapsed time (min), y234a) Use the graph to complete the table.b) Write an equation to represent the relationship.xy0 1 2 3 4 5.15.30.45.60.75.901.051.20Elapsed time (min)Distance (mi)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M3 | Lesson 3Lesson 3: Representing Proportional RelationshipsAnthony is typing at a constant rate. The table and graph below show the number of pages, p, that Anthony has typed aer m minutes.5 10 15Time in minutes20 25 30 35yx28162024128400Number of pagesTime in minutes, mNumber of pages, p0 010 425 1035 14a) What is the rate of change?b) Explain how you can nd the rate of change using the table.c) Explain how you can nd the rate of change using the graph.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.34

ZEARN MATH Student Notes for Digital Lessons G8M3 | Lesson 4Lesson 4: Comparing Proportional RelationshipsAlexcy and Samantha each have part time jobs. Alexcy’s earnings can be represented by the equation y = 9x, where y is the amount of money she earns for working x hours. Some information about Samantha’s earnings are shown in the table.Alexcy’s Earningsy = 9xSamantha’s EarningsTime Worked (hr)Money Earned ($)5 5010 10015 15020 200a) What is the rate of change for each student’s earnings?b) What does the rate of change mean?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.35

ZEARN MATH Student Notes for Digital LessonsG8M3 | Lesson 5Lesson 5: Introduction to Linear RelationshipsEmma is starting a kayak rental company. She is going to charge $20 to rent the kayak plus $5 per hour of rental.1. How much would it cost to rent a kayak for 2 hours? For 5 hours? Plot these two points on the graph. Explain your thinking.2. Draw a line representing the relationship between the number of hours of rental, and the total cost of rental.3. Find the slope of the line. What is the meaning of the slope in this context?2 4Number of hours of rental6 8 101 3 5 7 9yx556050454035302520151050Cost of rental (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.36

ZEARN MATH Student Notes for Digital Lessons G8M3 | Lesson 6Lesson 6: More Linear RelationshipsA plumber charges $25 for a service call plus $50 per hour of service.1. What’s the vertical intercept?2. What does the vertical intercept mean in this context?2 4Number of hours6 8 10 111 3 5 7 9yx2502753002001501005022517512575250Cost of service (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.37

ZEARN MATH Student Notes for Digital LessonsG8M3 | Lesson 7Lesson 7: Representations of Linear RelationshipsThe graph shows the height in centimeters, h, of a bamboo plant m months aer it was planted. This equation represents the line: h = 40 + 5m. Explain what 40 and 5 represent in the equation and graph.01 2 3 4 5 6 7 8 9 10102030405060708090100110120Number of months, mHeight (cm), h© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.38

ZEARN MATH Student Notes for Digital Lessons G8M3 | Lesson 8Lesson 8: Translating to y = mx + bTwo friends, Damien and Eliora, are mountain climbing. Damien starts at sea level, which has an elevation of 0 meters, and climbs up at a constant rate of 40 meters per hour. Eliora starts at 60 meters above sea level and climbs up at a constant rate of 40 meters per hour.a) Write an equation to represent each line on the graph.b) Name one thing that is the same and one thing that is dierent about the two lines.1204060801001201401601802002202402602802 3 4 5Number of hours, xElevation, eElioraDamien© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M3 | Lesson 9Lesson 9: Slopes Don’t Have to be PositiveThe elevation in feet of a certain airplane can be represented with the variable e and its time in minutes can be represented with the variable t. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.1. The plane is cruising at an altitude of 35,000 feet above sea level.2. The plane is descending at a rate of 1,500 feet per minute.3. This plane is ascending at a rate of 2,500 feet per minute.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.40

ZEARN MATH Student Notes for Digital Lessons G8M3 | Lesson 10Lesson 10: Calculating SlopeNeha was trying to nd the slope of line q using the coordinates of point A and point B. You can see her work below.xy109873 6542198736542A (2, 7)B (5, 3)Slope = 2 − 53 − 7= -3-4= 34a) Explain the error that Neha made.b) Calculate the slope of line q.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.41

ZEARN MATH Student Notes for Digital LessonsG8M3 | Lesson 11Lesson 11: Equations of All Kinds of LinesLines f and g are graphed below. Write an equation for each line. Explain your reasoning for each equation.246810-2-4-6-8-10-2-4-6-8-10 2 4 6 8 10xyfg© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M3 | Lesson 12Lesson 12: Solutions to Linear EquationsAt the local produce market, apricots cost $1.50 per pound and raspberries cost $3 per pound. Imagine you want to spend exactly $45 on apricots and raspberries. The equation and graph below represent this situation.1.5a + 3r = 45Manoushka thinks the coordinate pair (5, 10) is a solution to this problem. In other words, Manoushka thinks that if you buy 5 pounds of apricots and 10 pounds of raspberries, you would spend exactly $45. Use an equation or a graph to determine whether or not you agree with Manoushka.r3530252015510105 15Pounds of apricots20 25 30 35a0Pounds of raspberries© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M3 | Lesson 13Lesson 13: More Solutions to Linear EquationsTrue or false: The points (1, 8) and (3, 14) lie on the line with the equation y − 3x = 5. Explain or show your reasoning. It can be helpful to substitute the x- and y-values to see if they make the equation true.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.44

Grade 8Mission 4Linear Equations and Linear Systems

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 2Lesson 2: Keeping the Equation BalancedWrite an equation that represents this hanger diagram. Then, solve for the value of p. Explain how you know your value for p is correct.p p424pppp© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M4 | Lesson 3Lesson 3: Balanced MovesName 3 dierent moves you could make to the equation below while maintaining equality. Then, solve the equation.8x − 3 = 5x + 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.47

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 4Lesson 4: More Balanced MovesConsider the equation below. Name two dierent ways you could start solving the equation. Then, solve the equation using one of the choices you named.5(y – 9) – 15 = 10(2y – 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.48

ZEARN MATH Student Notes for Digital Lessons G8M4 | Lesson 5Lesson 5: Solving Any Linear EquationSolve the equation. Explain or show your reasoning.4(x + 5) = 3x + 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.49

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 6Lesson 6: Strategic SolvingExplain how you could rewrite this equation to make it easier to work with. Then, solve for the value of y.32(6 + 2y) = 15 + 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.50

ZEARN MATH Student Notes for Digital Lessons G8M4 | Lesson 7Lesson 7: All, Some, or No SolutionsDoes the equation below have one solution, innitely many solutions, or no solutions? Explain how you know.6x + 24 = 3(2x + 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.51

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 8Lesson 8: How Many Solutions?A student is trying to gure out how many solutions 4x + 6x + 9 = 2(5x + 3) + 1 has. Her work is shown below. This student says there are innitely many solutions because the coeicients on the le and right sides of the equation are the same and the constants are dierent. Do you agree or disagree with this thinking? Explain.4x + 6x + 9 = 2(5x + 3) + 110x + 9 = 10x + 6 + 110x + 9 = 10x + 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.52

ZEARN MATH Student Notes for Digital Lessons G8M4 | Lesson 9Lesson 9: When Are They the Same?Jake and Mia are both scuba diving. Jake starts at an elevation of -120 feet and is swimming up at a rate of 5 feet per minute. Mia is at an elevation of -40 feet and is diving down at a rate of 3 feet per minute. When will Jake and Mia be at the same elevation? At what elevation will they meet?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 10a) How many hours do they have to work until they have the same amount of money?Lesson 10: On or O the Line?Rico has $30 in his savings, and he also makes $10 per hour babysitting. Tayo does not have any money in his savings, and he earns $20 per hour refereeing. You can see some information about the total amount of money each person has in the tables and graph below.Number of hours workedTotal amount0 302 505 80Number of hours workedTotal amount0 02 405 100number of hourstotal amount of moneyyx102 3 4 5102030405060708090100trb) How much money will they each have when they have the same amount of money? Explain where this solution can be seen in the tables of values, graph, or equations that represent Rico’s total amount of money and Tayo’s total amount of money.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.54

ZEARN MATH Student Notes for Digital Lessons G8M4 | Lesson 11Lesson 11: On Both of the LinesJayvon is comparing the heights of two plants over time. The pepper plant starts at a height of 5 inches and grows 3 inches per week. The tomato plant starts at a height of 1 inch and grows 4 inches per week. Is there a time when both plants will be the same height? If yes, what is that time and how tall will they be? If not, why not?You may consider writing equations, making tables, or graphing to help you answer this question.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.55

ZEARN MATH Student Notes for Digital LessonsG8M4 | Lesson 12Lesson 12: Systems of EquationsChristian and Dominic are both drinking smoothies. Christian’s smoothie starts at 24 ounces, and he drinks it at a rate of 2 ounces every minute. Dominic’s smoothie starts at 18 ounces, and he drinks his smoothie at a rate of 2 ounces every minute.• Is there a time when both smoothies will have the same amount remaining?• If yes, what is that time and how many ounces are le? If not, why not?You may consider writing equations, making a table, or graphing to help you answer this question.Time Passed (min)Amount of Christian’s Smoothie (oz)Amount of Dominic’s Smoothie (oz)yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M4 | Lesson 13Lesson 13: Solving Systems of EquationsBelow is a graph of a system of equations.a) Describe how to nd the solution to this system of equations by looking at the graph.b) Describe how to nd the solution to this system of equations by using the equations.-10-8-6-4-224681010y = -4 – xy = 1 + 3x864-10 -8 -6 -4 -2 2yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M4 | Lesson 14Lesson 14: Solving More SystemsShayannah wants to nd the solution to this system of equations. She starts by solving for the value of y by using the substitution method. Her work is shown below. What has Shayannah done wrong?⎰ x = 3y + 7 ⎱ y = 2x − 10 y = 2(3y + 7) − 10 y = 2 ∙ 3y + 7 − 10 y = 6y − 3 -6y -6y -5y = -3 -5 -5 y = 53 © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M4 | Lesson 15Lesson 15: Writing Systems of EquationsAt a baseball game, a concession stand is selling corn dogs and sodas. Each corn dog costs $1.50 and each soda costs $0.50. At the end of the night, the owner of the concession stand saw that she made a total of $78.50 and sold 87 corn dogs and sodas.1. Create a system of equations to represent this problem. Use c to represent the number of corn dogs and s to represent the number of sodas.2. Without solving, interpret what the solution to the system would tell you about the situation.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.59

60

Grade 8Mission 5Functions and Volume

ZEARN MATH Student Notes for Digital LessonsG8M5 | Lesson 1Lesson 1: Inputs and OutputsWrite your own input-output rule in the box, or choose from one of the options below. Then, write 4 input-output pairs that follow this rule.Multiply by 3.If odd, subtract 8. If even, add 4.Write 9.Divide by 2, then subtract 6. input outputInput Output© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 2Lesson 2: Introduction to FunctionsAt a spelling bee, each student gets 5 points for each correctly spelled word. Is each statement true or false? Explain your reasoning.1. The total number of points is a function of the number of correctly spelled words.2. The number of correctly spelled words is a function of the total number of points.3. The total number of points is a function of the number of students.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.63

ZEARN MATH Student Notes for Digital LessonsG8M5 | Lesson 3Lesson 3: Equations for FunctionsStella is 40 miles from home. She continues driving away from home at a rate of 60 miles per hour. Stella’s distance from home is a function of time, and we can represent the function with the equation d = 40 + 60t, where t is the time in hours and d is her distance from home.a) Complete the input and output table to nd Stella’s distance from home for the given times.b) Describe what the independent and dependent variables are in this situation and how you know.t d40 + 60tTime in hours, t Distance in miles, d458© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 4Lesson 4: Tables, Equations, and Graphs of FunctionsGraphs A and B below both show the relationship between Shon’s distance from home, x, and the elapsed time in hours, y, on 2 dierent days. Which one is a function and which one is not? Explain how you know.Graph ADistance from home (mi)Elapsed Time (hrs)10 20 30 40 50 60 70 80 90 10012345678910xyGraph BDistance from home (mi)Elapsed Time (hrs)10 20 30 40 50 60 70 80 90 10012345678910xy© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M5 | Lesson 5Lesson 5: More Graphs of FunctionsThe graph below shows the percentage of households in the US that owned a cat between 1987 and 2016.a) When was the percentage of households that owned a cat increasing?b) When was the percentage of households that owned a cat decreasing?c) Tell the story of the change in the percentage of households owning a cat over this time period. Consider including the terms “increasing” and “decreasing,” and specic years in your response.20%1987Percentage of US households that own a catYear19961991 2001 2006 2011 201625%30%35%40%yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 7Lesson 7: Connecting Representations of FunctionsThe graph below shows the distance traveled by a car as a function of time. The table shows the distance traveled by a motorcycle as a function of time. MotorcycleTime in hours, xDistance in miles, y1 752 1353 1804 2455 3206 3857 4058 4351. Did the car or the motorcycle travel farther aer 4 hours? Aer 8 hours?2. Approximately how long did it take the car to travel as far as the motorcycle had traveled aer 6 hours?yx551101652202753303854404955502 4 6 8 10 12 141816 20Time in hoursDistance in milesCar© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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

ZEARN MATH Student Notes for Digital LessonsG8M5 | Lesson 8Lesson 8: Linear FunctionsAlana has 24 dollars on her cafeteria card. Every time she orders a meal, 4 dollars are deducted from the value on her card.1. Write an equation to represent the relationship between the amount of money Alana has on her cafeteria card and the number of meals she orders.2. Make a graph to show that the amount of money on Alana’s cafeteria card is a function of the number of meals she orders.3. How can you tell if a linear function is decreasing from an equation? From a graph?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.68

ZEARN MATH Student Notes for Digital Lessons G8M5 | Lesson 9Lesson 9: Linear ModelsA baby grows each year. Aer 2 years, she is 30 inches tall. Aer 4 years, she is 40 inches tall.Number of yearsHeight (inches)2 304 40a) Graph the two data points that we know from the problem.b) Let’s assume that height is a linear function of the number of years since birth. Write an equation that represents this relationship.c) Could the linear equation you wrote be used to reasonably predict her height 4 years since birth? What about 50 years since birth? Explain your reasoning.Number of years since birthHeight (inches)yx1102030405060702 3 4 5 6© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.69

ZEARN MATH Student Notes for Digital LessonsG8M5 | Lesson 10Lesson 10: Piecewise Linear FunctionsThis graph shows the water in a pool as a function of time. How would you describe what a person might see happening during this time?yxTime (hours)Water in pool (liters)© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 11Lesson 11: Filling ContainersTwo cylinders, M and N, each started empty and were lled with water at the same rate. The graph shows how the height of the water changed as the volume of the water increased in each cylinder. Match the graphs of lines a and b to cylinders M and N. Explain your reasoning.Volume in mLHeight in cmhVbaM N© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M5 | Lesson 13Lesson 13: The Volume of a CylinderFind the volume of the rectangular prism and cylinder below. For the cylinder, leave your answer in terms of pi. Then, explain how nding the volume of a cylinder is like nding the volume of a prism.8 in6 in5 in8 in4 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.72

ZEARN MATH Student Notes for Digital Lessons G8M5 | Lesson 14Lesson 14: Finding Cylinder DimensionsEach row of the table has some information about a particular cylinder. Complete the table with the missing dimensions.Radius (units)Height (units)Volume (cubic units)3 63 45π10 250πhrV = πr2 . h© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.73

ZEARN MATH Student Notes for Digital LessonsG8M5 | Lesson 15Lesson 15: The Volume of a ConeIf you know the volume of a cylinder, how can you use it to nd the volume of a cone that has the same height and base area, or radius? Find the volume of each gure and use these examples to support your thinking.63 36V = πr2hV = πr2h13© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 16Lesson 16: Finding Cone DimensionsEach row of the table has some information about a particular cone. Complete the table with the missing dimensions.Radius (units) Height (units) Volume (cubic units)3 53 48π30 90πrhV = πr2h 31© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M5 | Lesson 17Lesson 17: Scaling One DimensionLook at the cylinder below.V = πr2∙h1. If we scale the height by a factor of 2, how will the volume of the cylinder change?2. What if we scale the height by a factor of 21? How will the volume of the cylinder change?3. How could you summarize what you learned about the relationship between the height of a cylinder and its volume?5 in4 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.76

ZEARN MATH Student Notes for Digital Lessons G8M5 | Lesson 18Lesson 18: Scaling Two DimensionsHow does the volume of a rectangular prism change when 2 dimensions are scaled by a factor of a? You can use the formula V = lwh to determine the volume of a rectangular prism.How does the volume of a cylinder change when the radius is scaled by a factor of a? You can use the formula V = πr2h to determine the volume of a cylinder. 3543a54a533a5© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M5 | Lesson 20Lesson 20: The Volume of a SphereA cone, sphere, and cylinder all have the same radius, 4 cm, and the same height. The volume of the cone is approximately 134 cm3 and the volume of the cylinder is approximately 402 cm3. Find an approximation of the volume of the sphere. You can use 3.14 as an approximation for π. You could use the volumes of the cone and cylinder or you could use the formula for the volume of a sphere to help you solve.4 cm4 cm4 cmVolume of a sphere = 34πr3© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M5 | Lesson 21Lesson 21: Cylinders, Cones, and SpheresYou just found which gure would hold the most water.1. In the beginning of the lesson, you predicted which gure would hold the most water. Which gure did you predict would hold the most water? Explain how you made your prediction.2. Was your prediction of which gure held the most water right or wrong?3. Whether you were right or wrong, did any of the volumes surprise you? Why or why not?3 inV ≈ 113.04 in3V ≈ 254.34 in3V ≈ 94.2 in3 10 in3 inV = 108 in3 3 in4 in3 in9 in9 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.79

80

Grade 8Mission 6Associations in Data

ZEARN MATH Student Notes for Digital LessonsG8M6 | Lesson 1Lesson 1: Organizing DataThe table below shows the average amount of light that a plant received during each day and the amount that the plant grew over a year for 7 dierent plants.1. Make a scatter plot to represent the data. 2. Based on this data, what would you predict the growth to be for a plant that received 800 lumens of light?Amount of light (lumens)Plant growth (cm)900 45350 20200 15600 35700 35600 30100 501020304050601,000800600400200yxAmount of light (lumens)Plant growth (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.82

ZEARN MATH Student Notes for Digital Lessons G8M6 | Lesson 2Lesson 2: Plotting DataThe data below shows the number of pages read each day on average by 10 students of dierent ages. If you wanted to predict about how many pages a 14-year-old read, would you make a histogram or a scatter plot to help you? Explain why you chose that representation. Make that representation now and then use your representation to make your prediction.Age Pages read per day9 108 1010 1516 3515 3518 5011 2013 2510 2017 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.83

ZEARN MATH Student Notes for Digital LessonsG8M6 | Lesson 3Lesson 3: What a Point in a Scatter Plot MeansThis scatter plot shows a company’s ice cream sales and the temperature in degrees Celsius on 12 dierent days.a) What does the point (22, 820) represent?b) On another day, it was 20 degrees Celsius and the company sold $800 in ice cream sales. Plot a point on the graph to show this information.c) How would you describe the general trend of this data?Sales (dollars)Temperature (°C)yx10121418202224261,00090080070060040030050016© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M6 | Lesson 4Lesson 4: Fitting a Line to DataHere is a scatter plot that compares points scored to shots attempted for dierent players in a basketball game. The model, represented by y = x + 0.5, is graphed with the scatter plot. Here, x represents the number of shot attempts, and y represents the number of points scored in the game.a) One of the players attempted 4 shots and scored 7 points. How does this compare to what the model predicts for this player?b) Circle a point that appears to be an outlier. What does it mean for this point to be an outlier in this situation?2 4 6 8 10 12 1448121620Shots attemptedPoints scoredyx0© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M6 | Lesson 5Lesson 5: Describing Trends in Scatter PlotsFour scatter plots with the same data are shown below. Which scatter plot shows a best t line for the given data? Explain why each of the other three is not a best t line for this 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.86

ZEARN MATH Student Notes for Digital Lessons G8M6 | Lesson 6Lesson 6: The Slope of a Fitted LineThe scatter plot below shows the relationship between a person’s age in years, x, and the number of sit-ups they could complete in a row before resting, y. The linear model is shown, and its equation is y = −1.1x + 82.What is the slope, and what does it mean in the context of this problem?yx1020 30 40 50 60 700102030405060AgeNumber of sit-ups© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M6 | Lesson 7Lesson 7: Observing More Patterns in Scatter PlotsThe scatter plot shows the number of minutes students spend playing video games per week and the number of hours they spend outdoors in their free time.Select all of the ways you could describe the data in the scatter plot:a) Linear associationb) Non-linear associationc) Clusteringd) Positive associatione) Negative associationyx0 5 10 15 20 25 302468Time spent outdoors (hours per week)Time spent playing video games (hours 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.88

ZEARN MATH Student Notes for Digital Lessons G8M6 | Lesson 8Lesson 8: Analyzing Bivariate DataBelow are the ages and heights of 10 trees.Age (years) Tree Height (feet)5 308 333 2210 367 328 349 367 3312 286 281. Draw a scatter plot of this data. Label the axes.2. Are there any outliers? Explain your reasoning.3. If there is a relationship between the variables, explain what it is.3. Draw a line you think is a best t line for the data. You can ignore the outlier and focus on the trend of the rest of the data when you draw this line.36353433323130292827262524232234567 8 9 10 11 12yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M6 | Lesson 9Lesson 9: Looking for AssociationsA group of people are surveyed about their use of laptops and tablet computers. The frequency table below compares customers who use a laptop and customers who do not use a laptop.Uses a tablet computerDoes not use a tablet computerTotalUses a laptop 77% 23% 100%Does not use a laptop36% 64% 100%1. Who is more likely to use a tablet computer: someone who uses a laptop or someone who does not use a laptop?2. Is there evidence of an association between using a laptop and using a tablet computer?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M6 | Lesson 10Lesson 10: Using Data Displays to Find AssociationsA publishing company is interested in teachers’ reading habits. The company takes a survey of teachers and records the subject that they teach and whether they prefer paper books or E-books. The results are recorded in a table and shown in a segmented bar graph. Is there evidence of an association between subject taught and reading paper books or E-books?English Algebra TotalPaper books13% 87% 100%E-books 46% 54% 100%100%9080706050403020100Paper books E-booksAlgebraEnglish© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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

92

Grade 8Mission 7Exponents and Scientic Notation

ZEARN MATH Student Notes for Digital LessonsG8M7 | Lesson 1Lesson 1: Exponent ReviewComplete the table to represent the missing values.Expanded Exponent Value3 ∙ 3 ∙ 3 ∙ 3 814 ∙ 4 ∙ 4 4331 ∙ 31(31)2623641 ∙ 41 ∙ 41641© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M7 | Lesson 2Lesson 2: Multiplying Powers of TenComplete the table.Expression Expanded Single power of 10(10 ∙ 10 ∙ 10) (10 ∙ 10 ∙ 10 ∙ 10 ∙ 10) 108104 ∙ 102(10 ∙ 10 ∙ 10 ∙ 10 ∙ 10) (10 ∙ 10)10n ∙ 10m© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M7 | Lesson 3Lesson 3: Powers of Powers of 10Write each of the following expressions in expanded form. Then write each with a single exponent. Explain the dierences between the two expressions.105 ∙ 102(105)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.96

ZEARN MATH Student Notes for Digital Lessons G8M7 | Lesson 4Lesson 4: Dividing Powers of 10Jamirra wrote an equivalent expression to 108 ÷ 102 as 104. She said when you’re dividing powers of 10, you can just divide the exponents to rewrite the expression as a single exponent. Use expanded form to show why 104 is not equivalent to 108 ÷ 102. Then nd an equivalent expression with a single power of 10, and explain or show your reasoning.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.97

ZEARN MATH Student Notes for Digital LessonsG8M7 | Lesson 5Lesson 5: Negative Exponents with Powers of 10Think about the meaning of exponents. How are 10-9 and 109 similar? How are they dierent? Consider using the following words in your explanation: base, multiplication, repeated, exponent.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M7 | Lesson 6Lesson 6: What about Other Bases?Rewrite each expression below using a single, positive exponent. You might choose to write expressions in expanded form to help simplify.Exponent form Single power76 ∙ 791281214(65)318-5750© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M7 | Lesson 7Lesson 7: Practice with Rational BasesKellan claims that 32 ∙ 35 is equal to 310. Explain his mistake. In your explanation, include:• A justication for why the equation 32 ∙ 35 = 310 is false.• An exponential expression equivalent to 32 ∙ 35, written with a single exponent.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M7 | Lesson 8Lesson 8: Combining BasesCara thinks that 74 ∙ 34 = 218. Do you agree? Use expanded form to explain your reasoning.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.101

ZEARN MATH Student Notes for Digital LessonsG8M7 | Lesson 9Lesson 9: Describing Large and Small Numbers Using Powers of 101. What is the value of this expression? Rewrite it using an integer.8.127 ∙ 103 = 2. Rewrite this expression as a multiple of a power of 10.524,700 = ∙ © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M7 | Lesson 10Lesson 10: Representing Large Numbers on the Number LineCircle the number that is greater. Then estimate how many times greater it is than the other number. Explain or show your reasoning.3.1 ∙ 106 or 6 ∙ 107 © 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M7 | Lesson 11Lesson 11: Representing Small Numbers on the Number LineThe diameter of a blood cell is 0.0006 cm. The diameter of a grain of salt is 0.03 cm. How many times as long is the diameter of a blood cell compared to the diameter of a grain of salt?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M7 | Lesson 12Lesson 12: Applications of Arithmetic with Powers of 10In 1790, the population of the city of Boston was 18,320. In the year 2000, the population had grown to 589,141. Approximately how many times greater was the population in the year 2000 compared to the population in 1790?© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M7 | Lesson 13Lesson 13: Denition of Scientic NotationWrite the numbers below in scientic notation.95,000,000,0000.00000034598 ∙ 1080.079 ∙ 10-5© 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.106

ZEARN MATH Student Notes for Digital Lessons G8M7 | Lesson 14Lesson 14: Multiplying, Dividing, and Estimating with Scientic NotationThe table below shows the number of computer programmers and doctors in the United States. Chanel thinks there are more doctors than computer programmers. Do you agree? Why or why not? In your answer, include the profession with the greater number of workers, and state how many times larger that number is than the number of people working in the other profession.Profession Number in U.S.Computer Programmer 1.36 × 106Doctor 69 × 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.107

ZEARN MATH Student Notes for Digital LessonsG8M7 | Lesson 15Lesson 15: Adding and Subtracting with Scientic NotationColson added 4.2 × 103 + 5.3 × 104 and found a sum of 9.5 × 107. Identify his mistake and explain how he could correct his work. Be sure to identify the correct answer to the addition 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.108

Grade 8Mission 8Pythagorean Theorem and Irrational Numbers

ZEARN MATH Student Notes for Digital LessonsG8M8 | Lesson 1Lesson 1: The Areas of Squares and Their Side LengthsFind the area of each square. Each grid square represents 1 square unit.ABC© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M8 | Lesson 2Lesson 2: Side Lengths and Areasa) Write the exact value of the side length of a square with an area of 44 square units. b) Estimate the side length. Between what two consecutive whole numbers is the side length of this square?A = 44 units2© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M8 | Lesson 3Lesson 3: Rational and Irrational Numbersa) Is √64 rational or irrational? Explain why.b) Is √10 rational or irrational? Explain why.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.112

ZEARN MATH Student Notes for Digital Lessons G8M8 | Lesson 4Lesson 4: Square Roots on the Number LineIs √14 rational or irrational? If it’s rational, what is the value? If it’s irrational, name the two consecutive whole numbers that √14 is between. 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.113

ZEARN MATH Student Notes for Digital LessonsG8M8 | Lesson 5Lesson 5: Reasoning about Square RootsExplain how you know that √40 is between 6 and 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.114

ZEARN MATH Student Notes for Digital Lessons G8M8 | Lesson 6Lesson 6: Finding Side Lengths of TrianglesYessenia thinks that 6 + 8 = 10 represents the relationship between the side lengths of this right triangle. Chongmi thinks that 62 + 82 = 102 represents the relationship. Based on the right triangles that you explored in today’s lesson, do you agree with either of them? Explain your reasoning.c = 10b = 8a = 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.115

ZEARN MATH Student Notes for Digital LessonsG8M8 | Lesson 7Lesson 7: A Proof of the Pythagorean TheoremBelow are two triangles. Circle the triangle that you can use the Pythagorean Theorem, a2 + b2 = c2, to nd the missing side length. Then use the Pythagorean Theorem to nd the missing side length.88??33© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M8 | Lesson 8Lesson 8: Finding Unknown Side LengthsFind the exact value of a in the gure below. Write your answer using the square root symbol. Keep in mind that the Pythagorean Theorem says that if a, b, and c are the sides of a right triangle, where c is the hypotenuse, then: a2 + b2 = c2.a3© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M8 | Lesson 9Lesson 9: The ConverseWhich of these triangles are right triangles? Explain how you know. (Note that not all triangles are drawn to scale.) 8612.53.51211Triangle A Triangle BTriangle 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.118

ZEARN MATH Student Notes for Digital Lessons G8M8 | Lesson 10Lesson 10: Applications of the Pythagorean TheoremCassius and Lorenzo are both trying to get from the library to the basketball court. Cassius walks along the trail, and Lorenzo rides his bike along the sidewalks.1. What is the length of the trail that Cassius takes?2. How much longer is Lorenzo’s route than Cassius’ route?BasketballcourtLibrar ySidewalk1.2 milesTrailSidewalk1.6 miles© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up Resources’ 6-8 Math curriculum, which is available to download for free at openupresources.org and used under the CC BY 4.0 license.119

ZEARN MATH Student Notes for Digital LessonsG8M8 | Lesson 11Lesson 11: Finding Distances in the Coordinate PlaneA right triangle is drawn in the coordinate plane below, and the coordinates of the vertices are labeled. Label each side of the right triangle with its length.0246-2-4-602 4 6 8 10-2-4A (-3, 5)B (-3, -3)C (8, 5)yx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 G8M8 | Lesson 12Lesson 12: Edge Lengths and Volumes1. Represent the edge lengths, x, of each of the cubes using cube root notation.2. Find the value of each edge length. If the value is not a whole number, write between which two whole numbers the value is.xV = 36 units3V = 64 units3V = 27 units3xx© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 LessonsG8M8 | Lesson 13Lesson 13: Cube RootsFind the positive solution to each equation. If the value is not a whole number, estimate between which two consecutive whole numbers the value is.a) b3 = 125b) g3 = 27c) a3 = 64d) y3 = 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.122

ZEARN MATH Student Notes for Digital Lessons G8M8 | Lesson 14Lesson 14: Decimal Representations of Rational Numbers1. Write each of these rational numbers as a fraction.a) √64b) 0.92. Write each of these rational numbers as a decimal.a) 83b) 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.123

ZEARN MATH Student Notes for Digital LessonsG8M8 | Lesson 15Lesson 15: Innite Decimal ExpansionsHow are the numbers 0.52 and 0.52 the same? How are they dierent? Think about whether you could express each number as a fraction.© 2023 Zearn. Licensed to you pursuant to Zearn’s Terms of Use. This work is a derivative of Open Up 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 org NAME Grade 8 Mission 1 Rigid Transformations and Congruence Mission 3 Linear Relationships Mission 4 Linear Equations and Linear Systems Mission 5 Functions and Volume Mission 6 Associations in Data Mission 7 Exponents and Scientific Notation Student Notes for Digital Lessons Mission 2 Dilations Similarity and Introducing Slope Mission 8 Pythagorean Theorem and Irrational Numbers Mission 9 Putting It All Together Student Notes for Digital Lessons Grade 8 Zearnmath_IDL_Grade8 indd 1 Grade 8 12 14 22 3 37 PM