Supplemental Materials: Assess Embedded Opportunities to Inform Instruction 6-9 by General

Supplemental Materials Assess Embedded Opportunities to Inform Instruction, 6–9 A Story of Ratios® A Story of Functions®

Supplemental Materials Assess: Embedded Opportunities to Inform Instruction, 6 9 © Great Minds PBC 2 Contents Connect Assessment to Key Content 3 Grade 6 Module 3 Overview 3 Collect Data from Multiple Perspectives ..................................................................................................... 5 Proficiency Indicators for 6.Mod3.AD4 and 6.Mod3.AD5 5 Measure Progress over Time ....................................................................................................................... 6 Lesson 10 ................................................................................................................................................. 6 Lesson 11 ................................................................................................................................................. 7 Lesson 12 ................................................................................................................................................. 8 Lesson 13 ................................................................................................................................................. 9 Lesson 14 ............................................................................................................................................... 10 Grade 6 Module 3 Topic C Quiz Scoring Guide 11 6.Mod3.AD4, AD5, AD7 .......................................................................................................................... 12 Scored Sample Topic Quiz ...................................................................................................................... 13 Grade 6 Module 3 Topic D ......................................................................................................................... 16 Topic Overview 16 Progression of Lessons 17 Credits ........................................................................................................................................................ 18 Works Cited ............................................................................................................................................... 18

Before This Module Grade 3 Module 5 Grade

above freezing

Topic B Ordering and Magnitude Students apply their understanding of rational numbers on the number line to compare and order sets of rational numbers in topic B. They observe that a number and its opposite are the same distance from 0 and use this understanding to calculate absolute value. Students use rational numbers to describe and compare real-world quantities. They apply the concept of magnitude to describe the distance between two rational numbers. a b 4 5 Beginning in grade 3, students understand fractions as numbers on the number line and use the number line to locate and compare Infractions.grade4, when students learn to express decimal fractions as decimals, they locate and compare decimals on the number line. 5 Module 6 Students are first introduced to the coordinate plane in grade 5 module 6. They recognize the plane as the intersection of a pair of perpendicular number lines at 0 on each line. Students locate and plot points in Quadrant I, including points with coordinates that are fractions and decimals.

In topic A, students use positive and negative numbers and 0 to describe real-world quantities such as elevation and temperature. They plot whole numbers and opposites of whole numbers on horizontal and vertical number lines and discover that these numbers are called integers Then students extend their understanding of integers to locate positive and negative rational numbers on the number line, and they represent opposite quantities in real-world situations by using rational numbers. They choose appropriate scales for a number line to plot a set of rational numbers. Celsius Temperat Celsius

Topic A Integers and Rational Numbers

Module

6789 10–10 –6–7–8–9 –5 –4 –3 –2 –1 0 1 2 3 4 5 3 degrees Celsius below freezing 3 degrees

0ba

Grade

ure water freezes in deg rees

321 456789 10−6 −5−10 −8−9 −7 −2−3−4 −1−10−7−8−1−2−3−4−5−6101298765430−9 y x (–2, 6.5) (–5, 3) (3, –9) (–2, –6.5) (–8.5, –1) (7, 3) y x 264 810−6−8 −4 −2−10 −10−2−4−8−61024860( 3,7) (3,7) ( 3, 6) (3, 6)

Topic C The Coordinate Plane

EUREKAMATH2 6 ▸ CopyrightM3 ©GreatMindsPBC3

In topic C, students apply their understanding of rational numbers to discover the four quadrants of the coordinate plane. Students plot and locate points with rational number coordinates in all four quadrants. Students explore the structure of the coordinate plane by reflecting points across one or both axes, noticing patterns in the coordinates of those points. They choose appropriate scales for the x- and y-axes for a given set of points. In a modeling task, students create a time graph by using real-world data about an underwater vehicle’s descent to the bottom of the Mariana Trench.

Topic D Solving Problems in the Coordinate Plane

Students use all four quadrants of the coordinate plane to graph figures and solve problems in topic D. They calculate the lengths of horizontal and vertical line segments in the coordinate plane, both by counting units and by applying their understanding of absolute value. Students graph geometric figures and apply their understanding of distance and symmetry to solve problems such as finding unknown vertices of rectangles or calculating perimeter and area. Lastly, they encounter real-world problems related to the coordinate plane, such as street maps on a grid and the geographic coordinate system.

After This Module Grade 6 Module 5 In module 5, students draw a variety of polygons in the coordinate plane and solve real-world and mathematical problems by applying their understanding of rational number coordinates and determining the distance between points. Grade 7 Module 2 In grade 7, students apply the properties of operations to add, subtract, multiply, and divide rational numbers. They solve real-world and mathematical problems involving the four operations with rational numbers. Grade 8 Modules 2 and 3 Students perform transformations of points, lines, and figures on the coordinate plane in grade 8.

Supplemental Materials Assess: Embedded Opportunities to Inform Instruction, 6 9 © Great Minds PBC 5 Collect Data from Multiple Perspectives Proficiency Indicators for 6.Mod3.AD4 and 6.Mod3.AD5

In this lesson, students first play a guessing game and must identify a classmate’s point from only a verbal description. By using their recent knowledge that all positive numbers have opposites, students extend the x-axis to the left of the origin and the y-axis below the origin to show the four quadrants of the coordinate plane.

Lesson at a Glance

Use ordered pairs to identify the locations of points in the coordinate plane. Relate the signs of x- and y-coordinates to each of the four quadrants of the coordinate plane.

10 EUREKACopyright©GreatMindsPBC MATH2 6 ▸ M3 ▸ TC ▸ CopyrightLesson10 ©GreatMindsPBC125 Consider the graph. 1234 5−4−5 −3−2−1 −2 C D A −1−3−5−40345 y x 12 B Write the ordered pairs of points A, B, C, and D. In which quadrant is each point located? Point A: (−4, 3) Quadrant II Point B (3, 5), Quadrant I Point C: (−2, −3), Quadrant III Point D: (3, −4), Quadrant IV Name Date TICKETEXIT 10 LESSON 10 The Four Quadrants of the Coordinate Plane

Students recognize the importance of the signs and the order of the coordinates of a point. They realize that the signs are useful for identifying the quadrant in which the point is located and that the order allows them to find the exact location of the point. Students revisit the game and recognize the usefulness of a coordinate plane in determining precise locations of points. This lesson introduces the term quadrant.

Key Question • How do the x- and y-coordinates of a point tell us the location of the point in the coordinate plane?

(6.NS.C.6.b)

Achievement Descriptor 6.Mod3.AD4 Identify relationships between the signs of the numbers in an ordered pair and the point’s location in a coordinate plane.

•

Key

Achievement Descriptors

Using a given set of integers, students create ordered pairs of points in the four quadrants by reasoning about the signs of the coordinates.

6.Mod3.AD4 Identify relationships between the signs of the numbers in an ordered pair and the point’s location in a coordinate plane. (6.NS.C.6.b) 6.Mod3.AD7 Plot and write ordered pairs of numbers to describe points in a coordinate plane. (6.NS.C.6.c)

11 EUREKACopyright©GreatMindsPBC MATH2 6 ▸ M3 ▸ TC ▸ CopyrightLesson11 ©GreatMindsPBC141 Use the ordered pairs in the table to plot and label each point in the coordinate plane. Indicate the quadrant in which each point is located. If the point does not lie in a quadrant, write “none.” Point Ordered Pair Quadrant A (3, 2) I B (0, 7) none C (−5, −8) III D (6, −4) IV E (−4, 5) II F (−9, 0) none 5432 678 910−5−6−7−8−9 −4−3−2−1−10 −10−1−2−3−4−9−8−7−6−510123459876 y x 0 1 B A D C F E Name Date TICKETEXIT 11 LESSON 11 Plotting Points in the Coordinate Plane Use ordered pairs to plot points in the coordinate plane. Lesson at a Glance

•

Students connect what they learned about plotting points on horizontal and vertical number lines to plotting points in the coordinate plane.

Students plot points by using the x- and y-coordinates to determine how far to move to the right or left of the origin and then how far to move up or down from there. In pairs, students look for patterns in the coordinates of points that lie between quadrants on the x- or y-axis. When given a star map of the Ursa Major constellation, students identify and plot points with rational coordinates that represent the locations of stars in the constellation. Questions How do we use the x- and y-coordinates of a point to plot the point in the coordinate plane? What is true about points that lie on the x-axis? On the y-axis?

12 EUREKACopyright©GreatMindsPBC MATH2 6 ▸ M3 ▸ TC ▸ CopyrightLesson12 ©GreatMindsPBC151 1. Point A is plotted at (8, −2). Use the graph to answer parts (a)–(c). 123 4 5687−8−7−4−3−2−1 −1−7−8−5−6−3−4−2 y x 0−6−5 78651243 A a. Write the ordered pair of the reflection of point A across the x-axis. (8, 2) b. Write the ordered pair of the reflection of point A across the y-axis. (−8, −2) c. Write the ordered pair of the reflection of point A across the x-axis and then across the y-axis. (−8, 2) Name Date 12TICKETEXIT LESSON 12 Reflections in the Coordinate Plane Graph points and their reflections in the coordinate plane. Recognize that when two ordered pairs differ only by the sign of one or both coordinates, the locations of the points are related by reflections across one or both axes. 6 ▸ M3 ▸ TC ▸ Lesson12EUREKAMATH2 152Copyright©GreatMindsPBC EXIT TICKET 2. Which points are reflections of the point (2, 1) across one or both axes? Choose all that apply. A. (2, 2) B. (−2, 1) C. (−2, −1) D. (−1, 1) E. (2, −1) F. (−2, 0)

13 EUREKACopyright©GreatMindsPBC MATH2 6 ▸ M3 ▸ TC ▸ CopyrightLesson13 ©GreatMindsPBC171 For parts (a) and (b), consider the points (3, 2), (0.5, −1.5), (−2, −3.25), (0.5, −2.5) a. Determine appropriate scales for the x and y-axes. Label the coordinate plane. b. Plot and label the points. Sample: (–2, –3.25) (0.5, –1.5) (3, 2) (0.5, –2.5) 2.52 131.5–2.5–3 –2 –1.5 –1 –0.5–0.5–1.5–2.50.51.52.5213–3–2–1 y x 0 0.5 Name Date TICKETEXIT 13 LESSON 13 Constructing the Coordinate Plane Draw and label a coordinate plane, choosing a reasonable scale for a given set of points. Plot points and describe how a graph changes when the scale changes. Lesson at a Glance In this lesson, students first consider which graphs have an appropriate scale for different real-world situations. Through a digital interactive, students see how points appear in the coordinate plane when the interval lengths for the x- and y-axes change. In groups, students plot points in coordinate planes with different scales for the axes. Given a graph of the same set of points with an interval length of 1 for both axes, they describe how their graphs compare when the interval length for one axis changes and when the interval lengths for both axes change. Students then choose scales for both the x- and y-axes, construct coordinate planes, and plot sets of points.

• Why does changing interval lengths change the way the graph looks?

Achievement Descriptors

Key Questions • What must we consider when choosing scales for the x- and y-axes?

14 6Copyright©GreatMindsPBC ▸ M3 ▸ TC ▸ Lesson14EUREKAMATH2 188Copyright©GreatMindsPBC EXIT TICKET a. Did the temperature increase or decrease between 8:00 a.m. and 11:00 a.m.? Explain. The temperature increased because the graph goes up from left to right during that time. b. What was the approximate temperature at 10:00 p.m.? The approximate temperature was 14°F c. At about what times during the day was the temperature exactly 0°F? The temperature was exactly 0°F at about 3:45 a.m., about 9:30 a.m., and about 6:30 p.m. LESSON 14 Modeling with the Coordinate Plane Create time graphs in the coordinate plane. Solve real-world problems by using time graphs. EUREKAMATH2 6 ▸ M3 ▸ TC ▸ CopyrightLesson14 ©GreatMindsPBC187 The graph shows the temperatures in degrees Fahrenheit in a city in Colorado over a 24-hour period. 12:00a.m. a.m.4:00 a.m.8:00 12:00p.m. p.m.4:00 p.m.8:00 12:00a.m. x y –10–15–20–505101520(°F)Temperature Time since 12:00 a.m. Name Date TICKETEXIT 14

If you administer this assessment on paper, you can see each student’s adjusted score by keying the student’s responses into the digital platform. To do so, navigate to the Assign section of the digital platform. View the target assessment and select Score. Select Complete on Paper to access the digital version of the assessment. Key in the student’s response for each item. The student’s adjusted score appears in the Analyze section. To score the assessment and compute a student’s raw score by hand, use this scoring guide and the answer key. The table shows how scale factors based on an item’s target level of proficiency are applied to each item, as well as how to use that information to determine each item’s possible points. Weighting items differently allows you to use a student’s level of proficiency to determine their grade. Score the assessment by using the notes in the table to determine how many of the possible points to award for each item. After scoring all items, divide the total number of points earned by the total number of possible points (i.e., 15 total possible points for this Topic Quiz) to determine a percentage grade.

Notes 1 6.Mod3.AD4 P 1 × 2 = 2 Polytomous Each correct response is worth 25 points. 2 Part A 6.Mod3.AD4 P 1 × 2 = 2 Polytomous Each correct response is worth 25 points. 2 Part B 6.Mod3.AD4 P 1 × 2 = 2 Polytomous Each correct response is worth 23 points. 2 Part C 6.Mod3.AD5 P 1 × 2 = 2 Dichotomous Both correct responses must be identified to earn 2 points. 3 6.Mod3.AD7 P 1 × 2 = 2 Polytomous Each correct response is worth 14 point. 4 Part A 6.Mod3.AD5 P 1 × 2 = 2 Polytomous Each correct response is worth 23 points. 4 Part B 6.Mod3.AD7 P 1 × 2 = 2 Dichotomous All eight responses must be correct to earn 2 points. 5 6.Mod3.AD5 HP 1 × 1 = 1 Polytomous Each correct response is worth 14 point. Module 3 Topic C Quiz

This assessment has five items. No partial credit is given unless otherwise indicated in the notes.

NumberItem AchievementDescriptor ProficiencyIndicator PointsRaw FactorScale PossiblePoints ScoringType

Supplemental Materials Assess: Embedded Opportunities to Inform Instruction, 6 9 © Great Minds PBC 12 6.Mod3.AD4, AD5, AD7

Supplemental Materials Assess: Embedded Opportunities to Inform Instruction, 6 9 © Great Minds PBC 13 Scored Sample Topic Quiz

3 142 56789 10−6 −5−10−8−9 −7 −2−3−4 −1−10−7−8−1−2−3−4−5−6101298765430−9 y x (4, 5)(–2, 5) –2, –3 21 4, –3 21 ))))

In lesson 15, students first calculate the lengths of horizontal and vertical line segments in the coordinate plane through exploration with digital interactives. Then students reason about the coordinates of two endpoints to determine whether a line segment is horizontal or vertical. Students use absolute value to find the distance between two points. For example, students recognize that the line segment with endpoints (−3, −5) and (−3, 7) is a vertical line segment because the x-coordinates are the same. They recognize that they can add the lengths 5 units and 7 units to determine the distance between the two points.

In topic D, students extend these understandings when they use all four quadrants of the coordinate plane to solve both geometric and real-world problems.

In lesson 16, students graph geometric figures in all four quadrants and apply their understanding of distance and symmetry to solve geometric problems. First, students identify the symmetry of line segments. When given an endpoint and the length of a line segment, students find that there are two possible horizontal line segments and two possible vertical line segments with the given endpoint and length. Then students generalize patterns in the x- and y-coordinates of points that lie on horizontal and vertical line segments. Finally, students apply their understanding to solve problems involving perimeter and area of rectangles graphed in the coordinate plane. At the end of the topic in lesson 17, students complete a series of collaborative problem-solving tasks. Students compare street maps on grids and then use a set of criteria to design a map of a town in the coordinate plane. Students extend their understanding of distance and symmetry when they create figures in the coordinate plane from a set of clues. To complete the lesson, students examine the geographic coordinate system and compare it to the coordinate plane. Students revisit the coordinate plane in module 5 when they solve more geometric problems, including problems involving geometric figures composed of triangles graphed in the coordinate plane.

In topic C, students plot points with rational number coordinates and identify ordered pairs in all four quadrants of the coordinate plane. Students reflect points across one or both axes and recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Students learn to choose appropriate scales for the x- and y-axes.

EUREKAMATH2 6 ▸ M3 ▸ CopyrightTD ©GreatMindsPBC279 Progression of Lessons Lesson 15 Distance in the Coordinate Plane Lesson 16 Figures in the Coordinate Plane Lesson 17 Problem Solving with the Coordinate Plane

Supplemental Materials Assess: Embedded Opportunities to Inform Instruction, 6 9 © Great Minds PBC 18 Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgement in all future editions and reprints of this handout. Works Cited Great Minds. Eureka Math2TM. Washington, DC: Great Minds, 2021. https://greatminds.org/math.