## Alignment: Overall Summary

The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for alignment. The instructional materials meet expectations for focus and coherence by assessing grade-level content, devoting the majority of class time to the major work of the grade, and being coherent and consistent with the progressions in the Standards. The instructional materials partially meet expectations for rigor and the mathematical practices. The instructional materials partially meet the expectations for rigor by attending to conceptual understanding and procedural skill and fluency, and they also partially meet expectations for practice-content connections by identifying the mathematical practices and using them to enrich grade-level content.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## Gateway 3:

### Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

+
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Gateway One Details

The instructional materials reviewed for JUMP Math Grade 8 meet expectations for Gateway 1. The instructional materials meet expectations for focus within the grade by assessing grade-level content and spending the majority of class time on the major work of the grade. The instructional materials meet expectations for being coherent and consistent with the Standards as they connect supporting content to enhance focus and coherence, have an amount of content that is viable for one school year, and foster coherence through connections at a single grade.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
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Criterion Rating Details

The instructional materials reviewed for JUMP Math Grade 8 meet expectations for not assessing topics before the grade level in which the topic should be introduced.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 8 meet expectations for assessing grade-level content. The Sample Unit Quizzes and Tests along with Scoring Guides and Rubrics were reviewed for this indicator. Examples of grade-level assessment items include:

• Teacher Resource, Part 1, Sample Quizzes and Tests, Unit 2 Test, Item 6, “John thinks 6 + 6 + 6 + 6 = 64 . Is he correct? Explain.” Students apply the properties of exponents to solve the problem. (8.EE.1)
• Teacher Resource, Part 1, Sample Quizzes and Tests, Unit 7 Test, Item 4, “a. Draw a scatter plot for data. b. Circle the cluster. c. Describe the association in as much detail as possible. d. Identify the outlier(s). Explain.” Students construct and interpret scatter plots and describe the patterns and outliers. (8.SP.1)
• Teacher Resource, Part 2, Sample Quizzes and Tests, Unit 1 Test, Item 6, “The graph shows the cost of renting an e-bike per hour. a. What is the y-intercept? What is the flat rate? b. Find the slope and write an equation for the line. Slope = riserun = ____= y=_______ c. Jack has 22. For how many hours can he rent an e-bike?” Students find the slope and y-intercept of a graph and write an equation. (8.F.6) • Teacher Resource, Part 2, Sample Quizzes and Tests, Unit 3 Quiz, Item 4, “A cube has volume 0.512 m$$^3$$. What is the length of one side of the cube?” Students find the cube root of a number. (8.EE.2) • Teacher Resource, Part 2, Sample Quizzes and Tests, Unit 4 Test, Item 6, “An engineer stands 200 m away from the base of a building. The distance to the top of the building is 350 m. a. What is the height of the building to nearest tenth of a meter? b. If the engineer stands 100 m from the base of the building, what will be the distance to the top of the building to the nearest tenth of a meter?” Students apply the Pythagorean Theorem to find a missing side length in a right triangle. (8.G.7) ### Criterion 1b Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade. 4/4 + - Criterion Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for students and teachers using the materials as designed and devoting the majority of class time to the major work of the grade. Overall, instructional materials spend approximately 80 percent of class time on the major clusters of the grade. ### Indicator 1b Instructional material spends the majority of class time on the major cluster of each grade. 4/4 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 80 percent of class time is devoted to major work of the grade. The materials for Grade 8 include 14 units. In the materials, there are 156 lessons, and of those, 29 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-56), so the number of lessons examined for this indicator is 127 lessons. The supporting clusters were also reviewed to determine if they could be factored in due to how strongly they support major work of the grade. There were connections found between supporting clusters and major clusters, and due to the strength of the connections found, the number of lessons addressing major work was increased from the approximately 101 lessons addressing major work as indicated by the materials themselves to 103.5 lessons. Three perspectives were considered: the number of units devoted to major work, the number of lessons devoted to major work, and the number of instructional days devoted to major work including days for unit assessments. The percentages for each of the three perspectives follow: • Units – Approximately 71 percent, 10 out of 14; • Lessons – Approximately 81 percent, 103.5 out of 127; and • Days – Approximately 80 percent, 113.5 out of 141. The number of instructional days, approximately 80 percent, devoted to major work is the most reflective for this indicator because it represents the total amount of class time that addresses major work. ### Criterion 1c - 1f Coherence: Each grade's instructional materials are coherent and consistent with the Standards. 7/8 + - Criterion Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for being coherent and consistent with the Standards. The instructional materials connect supporting content to enhance focus and coherence, include an amount of content that is viable for one school year, and foster connections at a single grade. However, the instructional materials contain off-grade-level material and do not relate grade-level concepts explicitly to prior knowledge from earlier grades. ### Indicator 1c Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade level. Examples where connections are present include the following: • Teacher Resource, Part 2, Unit 4, Lessons G8-46, G8-47, and G8-48 connect 8.NS.2 with 8.G.7,8 as students are expected to use rational approximations of irrational numbers in order to apply the Pythagorean Theorem to real-world and mathematical problems or find the distance between two points in the coordinate plane. • Teacher Resource, Part 2, Unit 6, Lessons G8-53 and G8-54 connect 8.G.7 with 8.G.9 as students use the Pythagorean Theorem in real-world and mathematical problems in order to find the volumes of cones and spheres. • Teacher Resource, Part 2, Unit 7, Lessons SP8-7 and SP8-8 connect 8.F.4 with 8.SP.2 as students construct a linear model for a relationship between two quantities because a scatterplot of the two quantities suggests a linear association between them. ### Indicator 1d The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for having an amount of content designated for one grade level that is viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is approximately 141 days which is appropriate for a school year of approximately 140-190 days. • The materials are written with 14 units containing a total of 156 lessons. • Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 156 lessons, and of those, 29 are Bridging lessons. These 29 Bridging lessons have been removed from the count because the Teacher Resource states that they are not counted as part of the work for the year, so the number of lessons examined for this indicator is 127 lessons. • There are 14 unit tests which are counted as 14 extra days of instruction. • There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction. ### Indicator 1e Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades. 1/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 partially meet the expectation for being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade level and provide all students with extensive work on grade-level problems. The materials make connections to content in future grades, but they do not explicitly relate grade-level concepts to prior knowledge from earlier grades. The materials develop according to the grade-by-grade progressions in the Standards, and content from prior or future grades is clearly identified and related to grade-level work. The Teacher Resource contains sections that highlight the development of the grade-by-grade progressions in the materials, identify content from prior or future grades, and state the relationship to grade-level work. • At the beginning of each unit, "This Unit in Context" provides a description of prior concepts and standards students have encountered during the grade levels before this one. The end of this section also makes connections to concepts that will occur in future grade levels. For example, "This Unit in Context" from Teacher Resource, Part 1, Unit 6, Functions: Defining, Evaluating, and Comparing Functions describes the topics from Operations and Algebraic Thinking that students encountered in Grades 4 and 5, specifically generating patterns given rules, and from Equations and Expressions in Grade 6, specifically analyzing the relationship between dependent and independent variables. The description then includes topics from Functions, specifically the graph of a function along with its rate of change and initial value, and it concludes with how the work of this unit builds to the study of functions in high school. The materials give all students extensive work with grade-level problems. The lessons also include "Extensions," and the problems in these sections are on grade level. • Whole class instruction is used in the lessons, and all students are expected to do the same work throughout the lesson. Individual, small-group, or whole-class instruction occurs in the lessons. • The problems in the Assessment & Practice books align to the content of the lessons, and they provide on-grade-level problems that "were designed to help students develop confidence, fluency, and practice." (page A-54, Teacher Resource) • In the Advanced Lessons, students get the opportunity to engage with more difficult problems, but the problems are still aligned to grade-level standards. For example, the problems in Teacher Resource, Part 1, Unit 2, Lesson EE8-23 engage students in estimation with numbers written in scientific notation and the four operations, and these problems still align to 8.EE.3,4. Also, in Teacher Resource, Part 2, Unit 5, Lesson EE8-55, the problems align to 8.EE.8. The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of missing explicit connections include: • Every lesson identifies “Prior Knowledge Required” even though the prior knowledge identified is not aligned to any grade-level standards. For example, Teacher Resource, Part 2, Unit 1, Lesson F8-15 states that its goals are to introduce the y-intercept and find the y-intercept by graphing and draw a line using the slope and y-intercept. The prior knowledge required is adding, subtracting, and dividing integers and plotting points on a grid. • There are 29 lessons identified as Bridging lessons, but these lessons are not explicitly aligned to standards from prior grades even though they do state for which grade-level standards they are preparation. For example, in Teacher Resource, Part , Unit 1, all fourteen lessons are Bridging Lessons and are labeled as "preparation for" various standards in 8.EE and 8.F.3. However, none of these fourteen Bridging lessons are explicitly aligned to standards prior to Grade 8. Also, Teacher Resource, Part 2, Unit 1, Lessons F8-13 and F8-14 are Bridging lessons labeled as "preparation for 8.G.1, 8.G.3, and 8.F.4" that have students plotting points in coordinate grids and finding the lengths of horizontal and vertical line segments, but the lessons are not explicitly aligned to standards prior to Grade 8. ### Indicator 1f Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and make connections within and across domains. In the materials, the units are organized by domains and are clearly labeled. For example, Teacher Resource, Part 1, Unit 7 is titled Statistics and Probability: Patterns in Scatter Plots, and Teacher Resource, Part 2, Unit 4 is titled Geometry: Pythagorean Theorem. Within the units, there are goals for each lesson, and the language of the goals is visibly shaped by the CCSSM cluster headings. For example, in Teacher Resource, Part 1, Unit 5, one of the goals for Lesson EE8-44 states "Students will review the concept of unit rate and find the unit rate in proportional relationships represented in different ways, including on the line of a graph." The language of this goal is visibly shaped by 8.EE.B, "Understand the connections between proportional relationships, lines, and linear equations." The instructional materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples of these connections include the following: • In Teacher Resource, Part 2, Unit 1, Lessons F8-15 through F8-19 and F8-23, the materials connect 8.F.B with 8.F.A as students are expected to be able to interpret the equation y=mx+b as defining a linear function and construct a function to model a linear relationship between two quantities. • In Teacher Resource, Part 2, Unit 2, Lessons G8-37 and G8-38, the materials connect 8.EE.B with 8.G.A as students use an understanding of similar triangles in order to explain why the slope is the same between any two points on a line and derive the equation of a line through the origin or any other point on the vertical axis. • In Teacher Resource, Part 2, Unit 4, Lessons G8-42 and G8-43, the materials connect 8.EE.A with 8.G.B as students work with radicals, specifically square root and cube root symbols, in order to represent solutions of equations that arise from developing an understanding of and being able to apply the Pythagorean Theorem. ### Gateway Two ## Rigor & Mathematical Practices #### Partially Meets Expectations + - Gateway Two Details The instructional materials reviewed for JUMP Mathematics Grade 8 partially meet expectations for Gateway 2. The instructional materials partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency. The instructional materials partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics. ### Criterion 2a - 2d Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. 6/8 + - Criterion Rating Details The instructional materials reviewed for JUMP Mathematics Grade 8 partially meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and spending some time working with routine applications. The instructional materials do not always treat the three aspects of rigor together or separately, but they do place heavier emphasis on procedural skill and fluency. ### Indicator 2a Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include lessons designed to support students’ conceptual understanding. Examples include: • Teacher Resource, Part 2, Unit 2, Lesson G8-31 focuses on similarity; the student proves figures are similar by showing that the ratios of the side lengths are proportional. Similarity is introduced before students learn dilations. The two topics are connected in Teacher Resource, Part 2, Unit 2, Lesson G8-35. • Teacher Resource, Part 1, Unit 3, Lesson G8-9, Exercises, “The triangles are congruent. a. Sketch the triangles. Mark the equal sides with hash marks (p. D-58).” Transformations are mentioned briefly when teachers are directed to say, “I need to turn the second triangle 90 clockwise to get it to the same position as the first triangle.” • Teacher Resource, Part 2, Unit 1, Lesson F8-16, “The y-intercept of lines that go through the origin is zero. Remind students that lines that go through the origin represent a proportional relationship between x and y. For example, in y = 3x. SAY: the coordinates of the origin is (0,0), so one row in the table of values is (0,0). ASK: If a line goes through the origin, what is the y-value when x is equal to zero? (0) What is the y-intercept for the line that goes through the origin? (0) Ask a volunteer to circle the y intercept in the equations y = x + 2 and y = 2x - 3. (+2, -3) Explain that in the equation y = 1.5x, the y-intercept is 0 because you can write the equation as y = 1.5x + 0.” ### Indicator 2b Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for attending to those standards that set an expectation of procedural skill and fluency. The materials place an emphasis on fluency, giving many opportunities to practice standard algorithms and to work on procedural knowledge. Standard 8.EE.7 expects students to develop procedural skills when solving linear equations in one variable. Lessons that include on-grade-level practice to develop fluency with linear equations with one variable include: • Teacher Resource, Part 1, Unit 4, Lesson EE8-35, Exercises, “Solve the equation. a. 3x + 3 − x = 5 b. 7x + 2 = 4x + 11.” Students solve equations with the distributive property and combine like terms. • Teacher Resource, Part 1, Unit 4, Lesson EE8-37, Exercises, “Solve the equation. If there is no solution, write ‘no solution’. a. x + 15 = 33 b. 9x = 18 c. 0x =7.” Students must know if the equations have one solution, no solution, or infinitely many solutions. • Teacher Resource, Part 2, Unit 3, Lesson NS8-1, “x = 4 SAY: To isolate x, we need to undo the square root. ASK: What operation does this? (squaring) SAY: To keep our equation balanced, we need to square both sides. Continue writing on the board: (√x)$$^2$$ = 4$$^2$$.” Students are reminded how to undo operations when solving equations and relate this idea to equations with radicals and exponents and practice similar equations. Standard 8.G.9 expects students to know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems with procedural skill. Examples include: • Teacher Resource, Part 2, Unit 6, Lesson G8-50, students find the volume of a cylinder given the radius or diameter. For example, students are given exercises with pictures of cylinders that have various measures and are asked to calculate the volume. • Book 2 Unit 6 Lesson G8-53, Exercises, Item 1, “A paper cup in the shape of a cone has a radius of 1.5 inches and a height of 4 inches. What is the volume of water that the cup can hold? (p. Q-42).” Students solve problems with the volume of cones, cylinders, and spheres. ### Indicator 2c Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade 1/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics without losing focus on the major work of each grade. Overall, many of the application problems are routine in nature and replicate the examples given during guided practice, and problems given for independent work are heavily scaffolded. Examples include: • Teacher Resource, Part 2, Unit 1, Lesson F8-23, Exercises, “There is some water in the bathtub. Sam pulls out the plug from the bathtub to let the water drain. After 10 seconds, there are 14 gallons of water left in the tub. After 30 seconds, there are 10 gallons of water left. a. Use two points, A (10, 14) and B (30, 10), and find the slope of the line. b. When Sam pulls out the plug, how much water was there? c). Write an equation for the number of gallons (g) left in the tub after s seconds. d. How many gallons are there after 20 seconds? e. How long does it take for all the water to drain from the tub? f. Find the y-intercept and the x-intercept of the equation and compare them to the answers to parts a and d. What did you notice? g. What does the slope represent?” (8.F.B) This problem misses the opportunity to have students apply the mathematics of using functions to model relationships between quantities. The questions include multiple prompts, guiding students along step by step for each question, rather than allowing students to attempt to apply the math and solve the problems independently. • Student Resource, Assessment & Practice Book, Part 2, Lesson EE8-52, Item 4, “Write the equations for the word problem. Then solve by graphing. The intersection point may have fractions or decimals. a. Two trains left Union Station at different times. Train A is 12 km from the station and is traveling 60 km/h. Train B is 27 km from the station and is traveling 50 km/h. When will Train A catch up to Train B? How far will they be from the station?” (8.EE.8c) Students solve real-world problems by writing two linear equations for the word problems and finding the solution by graphing them. • Teacher Resource, Part 2, Unit 5, Lesson EE8-52, Exercises, “Write a formula for the word problem. a. A gravel company charges25 per cubic yard and a delivery charge of $75. b. A yearbook company charges$500 plus $15 per yearbook.” (8.EE.8c) All questions in the lesson are structured as a “flat fee” plus a rate. The application questions follow given examples closely. Non-routine problems are occasionally found in the materials. For example, • Teacher Resource, Part 2, Unit 5, Lesson EE8-55, Extensions, Item 1, “Alex is four times as old as Clara. In 5 years, Alex will only be three times as old as Clara. How old are Alex and Clara today?” Students are solving a non-routine problem leading to two linear equations in two variables. (8.EE.8c) ### Indicator 2d Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. 1/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency. The curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials emphasize fluency, procedures, and algorithms. Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include: • Conceptual Understanding: Teacher Resource, Part 2, Unit 2, Lesson G8-37, Extensions, Item 1, “Use the fact that dilations produce similar triangles to explain why a line AB and its dilation A*B*have the same slope. Hint: Draw an example. Construct a triangle ABC used to find the slope of AB. Use similarity rules and cross multiplication instead of counting grid squares.” Students develop conceptual understanding of slope. • Application: Student Resource, Assessment and Practice, Part 2, Lesson G8-53, Item 11, “The Mayon volcano in the Philippines is cone shaped. The diameter of its base is 20km and the distance up the curved side, from the base to the apex , is 10.3km. Find the height of the volcano.” Students engage in application when solving the word problem. • Procedural Skills and Fluency: Teacher Resource, Part 1, Unit 4, Lesson EE8-35, Exercises, “Solve the equation. a. 3x + 3 − x = 5 b. 7x + 2 = 4x + 11.” Students use the distributive property to solve equations. Examples of where conceptual understanding, procedural skill and fluency, and application are presented together in the materials include: • Teacher Resource, Part 1, Unit 2, Lesson EE8-16, Exercises, “Simplify the expression to as few powers as possible by multiplying powers with the same base. a. 4$$^2$$x 7$$^2$$x 7$$^4$$x 4$$^3$$.” Conceptual understanding is developed while also practicing procedural skill. • Teacher Resource, Part 2, Unit 3, Lesson NS8-6, Exercises, Item 2, “Alex plays baseball. Last month, he was at bat 33 times and got 19 hits. How many hits did Alex get as a percentage of the number of times he was at bat?” Students develop both procedural skill and application. ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 6/10 + - Criterion Rating Details The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for practice-content connections. Although the instructional materials meet expectations for identifying and using the MPs to enrich mathematics content, they partially attend to the full meaning of each practice standard. The instructional materials partially attend to the specialized language of mathematics. ### Indicator 2e The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level. All 8 MPs are clearly identified throughout the materials, with few or no exceptions. Examples include: • The Mathematical Practices are identified at the beginning of each unit in the “Mathematical Practices in this Unit.” • “Mathematical Practices in this Unit” gives suggestions on how students can show they have met a Mathematical Practice. For example, in Teacher Resource, Part 2, Unit 5, Mathematical Practices in this Unit, “MP.4: EE8-49 Extension 6, EE8-50 Extension 5, EE8-53 Extension 1, EE8-54 Extensions 2-3, EE8-55 Extensions 1-4 In EE8-53 Extension 1, students make sense of and persevere in solving a non-routine problem when they find the area of a triangle given the equations of the lines that form the triangle by finding the base and height. STudents need to recognize the horizontal side as the base and the vertical distance to the intersection of the other two lines as the height.” • “Mathematical Practices in this Unit” gives the Mathematical Practices that can be assessed in the unit. For example, in Teacher Resources, Part 1, Unit 7, Mathematical Practices in this Unit, “In this unit, you will have the opportunity to assess MP.2, MP.3, MP.5, and MP.8.” • The Mathematical Practices are also identified in the materials in the lesson margins. • In optional Problem Solving Lessons designed to develop specific problem-solving strategies, MPs are identified in specific components/ problems in the lesson. ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 1/2 + - Indicator Rating Details The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MP4. Examples of the materials carefully attending to the meaning of some MPs include: • MP1: Teacher Resource, Part 1, Unit 3, Lesson G8-15, Extensions, Item 3, “Which is larger, 2$$^{75}$$ or 3$$^{50}$$? Do not use a calculator. Explain how you know your answer is correct.” Students would have to persevere when solving the problem as they would likely need to try multiple strategies to determine which is larger.” • MP2: Teacher Resource, Part 1, Unit 5, Lesson EE8-44, Extensions, Item 7, “When Amy cut $$\frac{3}{4}$$ of a foot off the bottom of her curtain, the curtain became $$\frac{3}{4}$$ of the length it originally was. How long was the curtain originally? Write your answer as a full sentence.” Students decontextualize the problem to solve the equation they write, and they put their answer back in context at the end when they write the answer as a full sentence. • MP5: Teacher Resource, Part 2, Unit 3, Lesson NS8-1, Extensions, Item 2, “Alice buys a house for$200,000. The price of her house goes up by $8,000 every 3 years. Ken buys a house for$100,000. The price of his house doubles every 10 years. When will the two houses be worth the same amount of money? Use any tool you think will help.” Students can use any tool which will help solve the problem.
• MP6: Teacher Resource, Part 1, Unit 2, Lesson EE8-23, Extensions, Item 2, “a. If a year is 365.2422 days, and the universe is about 13.8 billion years old, about how many seconds old is the universe? Write your answer using scientific notation. b. What decimal hundredths might have been rounded to 13.8? c. What range of values might the number of seconds actually be, given the range of decimal hundredths that round to 13.8? d. What place value does it make sense to round your answer from part a to? Explain.” Students attend to precision as they work with scientific notation to solve the problem.
• MP7: Teacher Resource, Part 1, Unit 2, Lesson EE8-17, Extensions, Item 3, “Give students an easier problem: write 10$$^3$$ x 8 + 10$$^3$$ x 2 as a single power of 10. Encourage students to compute it first, and then to look back and explain why the result happened. Then encourage students to use the same technique for the harder problem.” By redirecting students in this way, students make use of the structure.
• MP8: Teacher Resource, Part 2, Unit 1, Lesson F8-19, Extensions, Item 1, “b. Describe what you are always doing the same in part a. c. Find a formula for finding the x-intercept of the line y = mx + b.” Students are given four equations in slope intercept form and calculate the x-intercept of the line. Students use repeated reasoning to find the formula as a generalization.

Examples of the materials not carefully attending to the meaning of MP4 include:

• Teacher Resource, Part 2, Unit 7, Lesson SP8-11, Extensions, Item 1, students are given a set of data about late phone charges and create a two-way table for the data. Students answer follow-up questions, “b. How many landline customers did not pay on time this year? Make a row two-way relative frequency table for the data. c. Based on the data, is there an association between the type of phone and repeated lateness? Explain.” By scaffolding the questions into a step-by-step process, students do not model with mathematics.
• Teacher Resource, Part 2, Unit 4, Performance Task, Fire Department Ladder Problems, Item 5, “Two firefighters need to reach the top of a building. The building is 20 feet high and has a stone wall around it. The stone wall is: 8 feet high, 4 feet out from the building, 1 foot thick. The firefighters need to bring a ladder (not one mounted on the truck). The firefighters have two options.” Students are shown pictures of the two options, one with the ladder between the wall and the building, and the other with the ladder outside of the wall. Students complete the following: “a. Label each picture with the distances given. b. What is the slope of the ladder in each option? c. To be safe to climb, the absolute value of the slope of the ladder has to be less than 4. Circle the option(s) that are safe.” By asking each question separately, students do not model with mathematics independently.

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

Students explain their thinking, compare answers with a partner, or understand the error in a problem. However, this is done sporadically within extension questions, and often the materials identify questions as MP3 when there is not an opportunity for students to analyze situations, make conjectures, and justify conclusions. At times, the materials prompt students to construct viable arguments and critique the reasoning of others. Examples that demonstrate this include:

• Teacher Resource, Part 1, Unit 4, Lesson EE8-34, Extensions, Item 5, “a. Glen says that the expression -5x - 3 is always negative because both the coefficient and the constant terms are negative. Do you agree with Glen? Why or why not? b. In pairs, discuss your answers to part a). Do you agree with each other? Discuss why or why not.”
• In Teacher Resource, Part 1, Unit 6, Lesson F8-15, Extensions, Item 1, students make an argument about where a y-intercept would be given a point and a slope. “A line passes through A (1, 2) with a negative slope. Can the y-intercept be negative? Why? Hint: Draw lines with negative slope from point A.”
• Teacher Resource, Part 2, Unit 2, Lesson G8-26, Extensions, Item 4, “A Transformation takes the point (x, y) to the point (2x, y+3). Does the transformation take the line y = 2x + 1 to another line? Explain how you know.”
• Teacher Resource, Part 1, Unit 6, Lesson F8-10, Extensions, Item 2, “Tessa says that when you find the rate of change from point A to point B, you always get the same answer as when you find the rate of change from point B to point A. a. Do you agree with Tessa? Why or why not? b. In pairs, explain your answers to part a. Do you agree with each other? Discuss why or why not.”

In questions where students must explain an answer or way of thinking, the materials identify the exercise as MP3. As a result, questions identified as MP3 are not arguments and not designed to establish conjectures and build a logical progression of a statement to explore the truth of the conjecture. Examples include:

• Teacher Resource, Part 1, Unit 4, Lesson EE8-32, Extensions, Item 5, “a. Find a positive number x that makes the equation true: 125$$^8$$ = x$$^6$$. Explain how you got your answer? b). In pairs, compare your answers. Do you agree with each other? Discuss why or why not. c. Is your answer to part a) greater or less than 125? Explain why this makes sense.”
• Teacher Resource, Part 1, Unit 4, Lesson EE8-37, Extensions, Item 1, “Simplify the equation. Does the equation have one unique solution, no solution, or infinitely many solutions? a. 6x + 3 = 6x + 6 b. 7x + 1 = 43 c. 9(x+1) = 9x + 9”
• Many MP3 problems in the extension sections follow a similar structure. Students are given a problem and “explain.” Then, students compare their answers with a partner and discuss if they agree or not. This one dimensional approach does not offer guidance to students on how to construct an argument or critique the reasoning of others. For example, Teacher Resource, Part 2, Unit 3, Lesson NS8-6, Extensions, Item 6, “b. Explain why, in a right triangle, the side opposite the right angle is always the longest side. Use any tool you think would help. c. In pairs, explain your answers to part b. Do you agree with each other? Discuss why or why not.”
• Students are given extension questions when they are asked to analyze the math completed by a fictional person. For example, Teacher Resource, Part 1, Unit 4, Lesson EE8-33, Extensions, Item 4, “Marta says that the expression 5x + 20 is always a multiple of 5 because 5 and 20 are both multiples of 5. Do you agree with Marta? Why or why not?” These problems begin to develop students’ ability to analyze the mathematical reasoning of others but do not fully develop this skill. Students analyze an answer given by another, but do not develop an argument or present counterexamples.

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Some guidance is provided to teachers to initiate students in constructing arguments and critiquing others; however, the guidance lacks depth and structure, and there are multiple missed opportunities to assist students to engage in constructing and critiquing mathematical arguments.

The materials have limited support for the teacher to develop MP3. Generally, the materials encourage students to work with a partner as a way to construct arguments and critique each other. In the teacher information section, teachers are provided with the following information:

• Page A-14: “Promote communication by encouraging students to work in pairs or in small groups. Support students to organize and justify their thinking by demonstrating how to use mathematical terminology symbols, models and manipulatives as they discuss and share their ideas. Student grouping should be random and vary throughout the week.” The material provides no further guidance on thoughtful ways to group students and only limited structures that would encourage collaboration.
• Page A-49: “Classroom discussion in the lesson plans include prompts such as SAY, ASK and PROMPT. SAY is used to provide a sample wording of an explanation, concept or definition that is at grade level, precise, and that will not lead to student misconceptions. ASK is used for probing questions, followed by sample answers in parentheses. Allow students time to think before providing a PROMPT, which can be a simple re-wording of the question or a hint to guide students in the correct direction to answer the question….You might also have students discuss their thinking and explain their reasoning with a partner, or write down their explanations individually. This opportunity to communicate thinking, either orally or in writing, helps students consolidate their learning and facilitates the assessment of many Standards for Mathematical Practice.” While this direction would help teachers facilitate discussion in the classroom, it would not help teachers to develop student’s ability to construct arguments or critique the reasoning of others.
• Page A-49: There are sentence starters that are referenced that mostly show teachers how to facilitate discussions among students. The materials state, “When students work with a partner, many of them will benefit from some guidance, such as displaying question or sentence stems on the board to encourage partners to understand and challenge each other’s thinking, use of vocabulary, or choice of tools or strategies. For example:
• I did ___ the same way but got a different answer. Let’s compare our work.
• What does ___ mean?
• Why is ___ true?
• Why do you think that ___ ?
• I don’t understand ___. Can you explain it a different way?
• Why did you use ___? (a particular strategy or tool)
• How did you come up with ___? (an idea or strategy)”

Once all students have answered the ASK question, have volunteers articulate their thinking to the whole class so other students can benefit from hearing their strategies” While this direction would help teachers facilitate discussion in the classroom, it would not help them to develop student’s ability to construct arguments or critique the reasoning of others.

• A rubric for the Mathematical Practices is provided for teachers on page K-91. For MP3, a Level 3 is stated as, “Is able to use objects, drawings, diagrams, and actions to construct an argument” and “Justifies conclusions, communicates them to others, and responds to the arguments of others.” This rubric would provide some guidance to teachers about what to look for in student answers but no further direction is provided about how to use it to coach students to improve their arguments or critiques.
• In the Math Practices in this Unit Sections, MP3 is listed multiple times. The explanation of MP3 in the unit often consists of a general statement. For example, in Teacher Resource, Part 1, Unit 4, the MP3 portion of the section states, “In EE8-37 Extension 4, students critique an argument when they explain where the mistake is in a fictional student’s argument. Students construct an argument when they explain how to correct the mistake.” These explanations do not provide guidance to teachers in how to get students to construct arguments or critique the reasoning of others.

There are limited times when specific guidance is provided to teachers for specific problems. Examples include:

• Some guidance is provided to teachers for constructing a viable argument when teachers are provided solutions to questions labeled as MP3 in the extension questions. Some of these questions include wording that could be used as an exemplar response about what a viable argument is. For example, in Teacher Resource, Part 1, Unit 5, Lesson EE8-46, Extensions, Item 5, students are given the work of another student and asked if they agree. Teachers are provided with a sample solution, “a. I do not agree with Kyle. I solved the equation and got x = −13. In this case, 2x + 6 = − 20 and 2x + 1 = −25. It is true that 5 > 4 and −20 > −25, but it is not true that when you multiply two greater numbers, you always get a greater answer. Indeed, 5 × (−20) = −100 and 4 × (−25) = −100. Kyle would be correct if 2x + 6 and 2x + 1 were positive numbers; then it would be true that 5(2x + 6) > 5(2x + 1) > 4(2x + 1), but since 2x + 1 is negative and 5 > 4, you get 5(2x + 1) < 4(2x + 1), so the inequalities become 5(2x + 6) > 5(2x + 1) < 4(2x + 1).” In addition to the sample solution that could be used as an exemplar, teachers are also given the note, “Encourage students to not only explain why Kyle’s answer is incorrect, but why his reasoning is incorrect (when you multiply both sides of the inequality 5 > 4 by the same negative number, the inequality changes direction).” This guidance would help teachers develop students’ arguments and emphasizes the importance of not just explaining an answer but looking specifically at the mathematical reasoning.
• In Teacher Resource, Part 2, Unit 7, Lesson SP8-6, Extensions, Item 3, students construct an argument to explain why a sphere with a given volume will or will not fit inside a box with a given, larger, volume. Students have the opportunity to critique a partner’s argument. For example, if one student argues incorrectly that the ball will fit into the cube because 11.3 < 20, their partner will need to explain that they need to compare the diameter, not the radius, to the width of the box.

Frequently, problems are listed as providing an opportunity for students to engage in MP3, but miss the opportunity to give detail on how a teacher will accomplish this. Examples include:

• In Teacher Resource, Part 2, Unit 3, Lesson NS8-6, Extension, a sample answer is provided but no support on engaging students in how to analyze the reasoning of others: “b. Explain why, in a right triangle, the side opposite the right angle is always the longest side. Use any tool you think will help. c. In pairs, explain your reasoning from part b. Do you agree with each other? Discuss why or why not.”
• In Teacher Resource, Part 1, Unit 4, Lesson EE8-31, Extensions, Item 4, students are given the question, “Without using a calculator, show that 2$$^{100}$$ has at least 31 digits.” Teachers are provided with the answer, “2$$^{10}$$ = 1,024 > 10$$^3$$, so 2$$^{100}$$ = (2$$^{10}$$)$$^{10}$$ > (10$$^3$$)$$^{10}$$= 10$$^{30}$$ , which is the smallest number with 31 digits, so 2$$^100$$ has at least 31 digits.” This sample answer does not provide any assistance for developing students ability to construct viable arguments.
• In Teacher Resource, Part 2, Unit 1, Lesson 8F-15, MP3 is identified in the section titled, “Drawing a line using the y-intercept and the slope (page L-18).” In this section, teachers are told to ask students a series of questions about drawing lines. “ASK: But how can we use the slope to find another point? SAY: As an example, let’s draw a line with y-intercept = 2 and slope = $$\frac{1}{3}$$. First, mark the y-intercept on the y-axis. SAY: The y-intercept is 2, so we mark (0, 2) on the grid. The slope is $$\frac{1}{3}$$. ASK: What does the slope fraction stand for? ($$\frac{rise}{run}$$) SAY: The fraction of rise over run is 1 over 3, so I can say the rise is 1 and the run is 3. ASK: Do the rise and run have to be 1 and 3? (no) What other numbers would work? (2 and 6, or 3 and 9).” These questions are not developing students’ abilities to construct arguments or to critique the reasoning of others.

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for JUMP Math Grade 8 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials, however, while vocabulary is identified throughout the materials, there is no explicit directions for instruction of the vocabulary in the teacher materials of the lesson. Examples include, but are not limited to:

• Vocabulary is identified in the Terminology section at the beginning of each unit.
• Vocabulary is identified at the beginning of each lesson.
• The vocabulary words and definitions are bold within the lesson.
• There is not a glossary.
• There is not a place for the students to practice the new vocabulary in the lessons.

## Usability

#### Not Rated

+
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Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
N/A

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

### Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2020/09/17

Report Edition: 2019

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.