## Alignment: Overall Summary

The instructional materials for Eureka Grade 7 meet the expectation for alignment to the CCSS. In Gateway 1, the instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of class time on the major clusters of the grade, and they are coherent and consistent with the Standards. In Gateway 2, the instructional materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, and they partially connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## Gateway 3:

### Usability

0
22
31
38
25
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 for Eureka Grade 7 meet the expectation for focusing on the major work of the grade and having a sequence of topics that is consistent with the logical structure of mathematics. The materials do not assess topics before the grade level indicated, spend at least 65% of class time on the major clusters of the grade, and are coherent and consistent with the Standards.

### 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 for Eureka Grade 7 meet the expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content.

### 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 Eureka Grade 7 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 7 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 1, Mid-Module Assessment: Students use a table to analyze a proportional relationship (7.RP.2a). Question 1 states, “Josiah and Tillery have new jobs at YumYum’s Ice Cream Parlor. Josiah is Tillery’s manager. In their first year, Josiah will be paid $14 per hour, and Tillery will be paid$7 per hour. They have been told that after every year with the company, they will each be given a raise of $2 per hour. Is the relationship between Josiah’s pay and Tillery’s pay rate proportional? Explain your reasoning using a table.” • In Module 2, End-of-Module Assessment: Students determine if a number, when written in decimal form, would be a repeating decimal or a terminating decimal. The students justify their answer using long division (7.NS.2d). Question 1c states, “The water level in Ricky Lake changes at an average of -7/16 inch every 3 years. 1c. When written in decimal form, is your answer to part (b) a repeating decimal or a terminating decimal? Justify your answer using long division.” • In Module 3, End-of-Module Assessment: Students use their knowledge of supplementary angles to solve equations (7.EE.4a). Questions 5b states, “Marcus drew two adjacent angles. If the measure of angle CBD is 9(8x + 11) degrees, then what is the value of x?” • In Module 4, End-of-Module Assessment: Students solve a multi-step percent and ratio problem (7.RP.3). Question 1 states, “Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck was in the amount of$6,500, including her salary of $1,000. Her sales for the week totaled$45,000. Express her rate of commission as a percent, rounded to the nearest whole number.”

### 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
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Criterion Rating Details

The instructional materials for Eureka Grade 7 meet the expectation for students and teachers using the materials as designed devoting the majority of class time to the major work of the grade. Overall, the instructional materials spend at least 65% 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
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 7.RP, 7.NS and 7.EE.

• More than 65 percent of the lessons are explicitly focused on major work, with major work often included within supporting-work lessons as well.
• Of the six modules, Modules 1, 2, and 4 focus on major work. Module 3 contains lessons related to the major work.
• Of the 180 days, 145 days (81 percent) are spent on major clusters of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

The instructional materials for Eureka Grade 7 meet the expectation for being coherent and consistent with the Standards. Overall, the instructional materials have supporting content that enhances focus and coherence, are consistent with the progressions in the Standards, and foster coherence through connections at a single grade, where appropriate and required by the Standards.

### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade. For example:

• In Module 3, Lesson 10: 7.G.5 supports the major work of 7.EE. Students find the measure of angles using an expression with multiple steps.
• In Module 3, Lesson 11: 7.G.5 supports the major work of 7.EE.4. Students write an equation for the angle relationship and then solve for the angle measure.
• In Module 3, Lessons 19-26: 7.G.6 supports the major work of 7.EE.2. Students use properties of operations to generate equivalent expressions as they solve area and volume problems using numerical and algebraic expressions and equations.
• In Module 5, Lessons 5-7: 7.EE.3 supports the major work of 7.SP.6-8. Students apply properties of operations to calculate probabilities with numbers in fraction, decimal and percent form, converting between forms as appropriate.
• In Module 6, Lessons 20-27: 7.G.6 supports the major work of 7.EE.3-4. Students solve real-world area and volume problems using numerical and algebraic expressions and equations.

### 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
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Indicator Rating Details

Instructional materials for Eureka Grade 7 meet expectations that the amount of content designated for one grade-level is viable for one year. As designed, the instructional materials can be completed in 180 days. The suggested amount of time and expectations of the materials for teachers and students are viable for one school year as written and would not require significant modifications.

The instructional materials consist of six modules. Instruction and assessment days are included in the following count:

• Module 1: 30 days
• Module 2: 30 days
• Module 3: 35 days
• Module 4: 25 days
• Module 5: 25 days
• Module 6: 35 days

All lessons are paced to be 45 minutes in length. Information on how to customize lessons is included in the Preparing To Teach a Lesson section.

### 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.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 7 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials give all students extensive work with grade-level problems and identify as well as explicitly connect grade-level work to prior or future grades.

Each module starts with a summary of what concepts will be taught within that module. This summary explains how the lessons support the progression of Grade 7 standards by explicitly stating connections to prior or future grades. For example:

• Module 5, Statistics and Probability: “In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. The concept of probability provides a foundation for the thinking required to make inferential reasoning that is developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data collected from random samples.”

Each module has a “Module Standards” section that contains tabs named “Focus Grade-Level Standards” and “Foundational Standards.” The Focus Grade-Level Standards tab contains Grade 7 standards that are covered within the module. The Foundational Standards tab contains prior grade-level standards as well as grade-level standards that are the foundational skills needed for the lessons within the module. Foundational standards from Grade 6 or from previous Grade 7 work are included for each module. An example from Module 1 is:

• Geometry 6.G.1 | 6.G.3
• Ratios and Proportional Relationships 6.RP.1 | 6.RP.2 | 6.RP.3 | 6.RP.3.a |6.RP.3.b | 6.RP.3.c | 6.RP.3.d
• Solve real-world and mathematical problems involving area, surface area and volume 6.G.1 | 6.G.3
• Understand ratio concepts and use ratio reasoning to solve problems 6.RP.1 | 6.RP.2 | 6.RP.3 | 6.RP.3.a | 6.RP.3.b | 6.RP.3.c | 6.RP.3.d

The instructional materials for Eureka Grade 7 materials do not contain content from future grade levels. In places where the content might be confused with that of a future grade, explanations are provided, such as the one found in the Topic Overview of Module 6, Topic B (page 56): “In Lessons 9–10, students explore the conditions that determine a unique triangle. Note that the discussion regarding the conditions that determine a unique triangle is distinct from the discussion regarding whether two figures are congruent, which requires a study of rigid motions (Grade 8, Module 2). However, the study of what constitutes uniqueness is inextricably linked to the notion of identical figures.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Most lessons contain a “Problem Set” which includes questions and word problems that focus on the standards of the lesson. In Module 4, Lesson 4, Problem Set Question 2 states, “An item that was selling for $72.00 is reduced to$60.00. Find the percent decrease in price. Round your answer to the nearest tenth.” Students use proportional relationships to solve multi-step ratio and percent problems (7.RP.3).

Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 1, Lesson 5, Exit Ticket Question 1 states, “The following table gives the number of people picking strawberries in a field and the corresponding number of hours that those people worked picking strawberries. Graph the ordered pairs from the table. Does the graph represent two quantities that are proportional to each other? Explain why or why not.” Students identify proportional relationships in various situations such as in tables and graphs (7.RP.2a).

### 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
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Indicator Rating Details

The instructional materials for Eureka Grade 7 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. For example:

• In Module 1, Topic A: “Proportional Relationships” is visibly shaped by 7.RP.A, “Analyze proportional relationships and use them to solve real-world and mathematical problems.”
• In Module 3, Topic B: “Solve Problems using Expression, Equations, and Inequalities” is visibly shaped by 7.EE.B, “Solve real-life and mathematical problems using numerical and algebraic expressions and equations.”

Materials include problems and activities that 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. For example:

• In Module 1, Lesson 8: 7.RP.A connects to 7.EE. Students use their knowledge of constant of proportionality to write equations.
• In Module 1, Lesson 16: 7.RP.A connects to 7.G.A. Students use understanding of ratios to complete scale drawings.
• In Module 1, Lesson 18: 7.RP.2b connects to 7.G.1 as students apply their understanding of proportional relationships to “find the relationship between the lengths in the scale drawing of a shopping mall and the corresponding actual lengths, and use this relationship to calculate the width of the actual mall entrances” to determine if backdrop panels measuring 10 feet by 10 feet will fit through the entrance.
• In Module 3, Lesson 6, Exercise 1: 7.NS.1 connects to 7.EE.1 as students use knowledge of operations with rational numbers to collect like terms with rational-number coefficients.
• In Module 3, Lesson 10: 7.G.A connects to 7.EE. Students use knowledge of angles to write equations to solve for future angles.
• In Module 4, Topic B: 7.RP.3 connects to 7.EE.3 as students create algebraic representations and apply their understanding of percent to interpret and solve multi-step word problems related to markups or markdowns, simple interest, sales tax, commissions, fees and percent error.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials for Eureka Grade 7 meet the expectation for rigor and mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and they also attend to the balance among the three aspects. The instructional materials identify the mathematical practices and use them to enrich mathematics content within and throughout the grade level, emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, and 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.
8/8
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Criterion Rating Details

The instructional materials for Eureka Grade 7 meet the expectation for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications, and do not always treat the three aspects of rigor together or separately.

### 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
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Indicator Rating Details

The instructional materials for Eureka Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade level. For example:

• In Module 2, Lesson 2, students develop conceptual understanding of rational numbers by representing integers on a number line with arrows and use the length of the arrows to understand absolute value. The number line is used to model addition and subtraction with integers to help develop the concept visually. (7.NS.1)
• In Module 3, Lesson 4, students develop conceptual understanding by using area models to learn how to write expressions. The area model shows how products are written as sums which the students will use to solve real-life situations. (7.EE.2)
• Module 3, Lesson 17, Example 2, students develop conceptual understanding as they use the formula for the area of the circle to solve, "A sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet, What is the area of the circular region covered by the sprinkler? Express your answer to the nearest foot. Draw a diagram to assist you in solving the problem. What does the distance of 12 feet reporesent in this problem?"(7.G.4)

The materials provide opportunities for students to demonstrate conceptual understanding independently throughout the grade level. For example:

• In Module 2, Lesson 2, students independently demonstrate a conceptual understanding of integer addition as they complete the Exit Ticket. The students determine if the arrows on a number line correctly represent an expression involving the addition of three integers, draw a correct number line model and write a real-world situation that would represent the sum. (7.NS.1)
• In Module 3, Lesson 6, students independently demonstrate a conceptual understanding of equivalent expressions as they write two different expressions that represent the new cost of a shirt and a pair of pants, and explain the different information each one shows. Example Problem 2 states, “At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half. Write two different expressions that represent the new cost of the items, using s for the cost of each shirt and p for the cost of a pair of pants. Explain the different information each one shows.” (7.EE.2) ### 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 for Eureka Grade 7 meet expectations that they attend to those standards that set an expectation of procedural skill. The instructional materials develop procedural skill throughout the grade level. For example: • In Module 2, Lessons 1-11, students develop procedural skill with integer operations. Students develop procedural skill of integer operations through a card game, number-line models, and real-world contexts. (7.NS.1-2) • In Module 2, Lessons 22-23, students develop procedural skill with expressions and equations when translating word problems into algebraic equations. Students solve equations of the form p + q = r and p(x+q)=r, where p, q, and r are specific rational numbers. (7.EE.1, 7.EE.4a) • In Module 3, Lessons 8-9, students develop procedural skill with writing sequences of equations underneath each other, linked together by if-then moves and/or properties of operations. (7.EE.1, 7.EE.4a). The instructional materials provide opportunities to demonstrate procedural skill independentlythroughout the grade level. For example: • In Module 2, Lessons 15-16, students independently demonstrate procedural skill when determining the product of integers within a “Sprint” activity. Problem 31 states, “11 x -33” (7.NS) • In Module 3, Lesson 2, students independently demonstrate procedural skill when writing equations in standard form within a “Sprint” activity. (7.EE.1) ### 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 2/2 + - Indicator Rating Details The instructional materials for Eureka Grade 7 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level. For example: • In Module 1, Lesson 14, students engage in grade-level mathematics by solving multi-step problems including fractional markdowns, markups, commissions, and fees. Classwork Example 2 states, “A used car salesperson receives a commision of 1/12 of the sales price of the car for each car he sells. What would the sales commission be on a car that sold for$21,999?” (7.RP.3)
• In Module 3, Lesson 9, students engage in grade-level mathematics by using addition, subtraction, multiplication, and substitution properties of equality to solve word problems.. Exit Ticket states, “Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. If after 3 hours, Brand A scooter traveled 24 miles at its top speed, at what rate did Brand B scooter travel at its top speed if it traveled the same distance? Write an equation to determine the solution. Identify the if-then moves used in your solution.” (7.EE.B)
• In Module 4, Lesson 12 students engage in grade-level mathematics by creating scale drawings of given drawings. Problem Set Question 3 states, “The accompanying diagram shows that the length of a pencil from its eraser to its tip is 7 units and that the eraser is 1.5 units wide. The picture was placed on a photocopy machine and reduced to 66 2/3%. Find the new size of the pencil, and sketch a drawing. Write numerical equations to find the new dimensions..” (7.G.1, 7.RP.A)

The instructional materials provide opportunities for students to demonstrate independently the use of mathematics flexibly in a variety of contexts. For example:

• In Module 1, Lesson 17, students independently demonstrate the use of mathematics by using a table or an equation to create a scale drawing of a rectangular swimming pool. The Exit Ticket states, “A rectangular pool in your friend’s yard is 150 ft. × 400 ft. Create a scale drawing with a scale factor of 1/600. Use a table or an equation to show how you computed the scale drawing lengths.” (7.G.1)
• In Module 3, Lesson 13, students independently demonstrate the use of mathematics by using inequalities to solve word problems. The Exit Ticket states, “Shaggy earned $7.55 per hour plus an additional$100 in tips waiting tables on Saturday. He earned at least 160 in all. Write an inequality and find the minimum number of hours, to the nearest hour, that Shaggy worked on Saturday.” (7.EE.4) • In Module 4, Lesson 16, students independently demonstrate the use of mathematics by writing and using algebraic expressions and equations to solve percent word problems. Problem Set Question 3 states, “During lunch hour at a local restaurant, 90% of customers order a meat entrée and 10% order a vegetarian entrée. Of the customers who order a meat entrée, 80% order a drink. Of the customers who order a vegetarian entrée, 40% order a drink. What is the percent of customers who order a drink with their entrée?” (7.RP.3) ### 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. 2/2 + - Indicator Rating Details The instructional materials for Eureka Grade 7 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Conceptual understanding is addressed in Classwork. During this time, the teacher guides students through a new concept or an extension of the previous day’s learning. Students practice solving procedural problems in problem sets. The materials provide engaging applications of grade-level concepts throughout each lesson. The program balances all three aspects of rigor in every lesson. All three aspects of rigor are present independently throughout the program materials. For example: • In Module 1, Lesson 18, students engage in the application of mathematics when finding actual lengths and areas from scale drawings. Problem Set 4 Question states, “A model of a skyscraper is made so that 1 inch represents 75 feet. What is the height of the actual building if the height of the model is 18 ⅗ inches?” (7.G.1) • In Module 4, Lesson 1, students practice the procedural skill of converting from one form of a number to another (decimal, percent, fraction) as they play the “I have, who has?” game. In Exercise 1 cards, one of the cards states, “I have the equivalent value, 0.11. Who has the card equivalent to 350 percent?” (7.EE.3) • In Module 6, Lesson 5, students develop conceptual understanding of the structure of a triangle, noticing the conditions that determine a unique triangle, more than one triangle, or no triangle. Classwork Example 2 states, “Two identical triangles are shown below. Give a triangle correspondence that matches equal sides and equal angles.” (7.G.2) Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example: • In Module 4, Lesson 3, students practice procedural skill when solving word problems involving percent more and percent less than a quantity. Exit Ticket Question 1 states, “Solve each problem below using at least two different approaches. Jenny’s great-grandmother is 90 years old. Jenny is 12 years old. What percent of Jenny’s great-grandmother’s age is Jenny’s age?” (7.RP.3) • In Module 6, Lesson 21, students develop conceptual understanding of area and practice procedural skill when using the distributive property on expressions. Class work Example 2 states, “Bobby draws a square that is 10 units by 10 units. He increases the length by x units and the width by 2 units. Draw a diagram that models this scenario. Assume the area of the large rectangle is 156 units squared. Find the value of x.” (7.G.6) ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 8/10 + - Criterion Rating Details The instructional materials for Eureka Grade 7 partially meet the expectation for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. Overall, the materials identify the mathematical practices and use them to enrich mathematics content within and throughout the grade level, emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, and 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 Eureka Grade 7 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. All of the eight MPs are identified within the grade-level materials. The Standards for Mathematical Practice are identified at the beginning of each module under the Module Standards. The tab named “Highlighted Standards for Mathematical Practice” lists all of the MPs that are focused on in the module. Each MP is linked to the definition of the practice as well as in which lessons throughout the series that practice can be found. Each Module Overview contains a section titled, “Focus Standard for Mathematical Practice." Every practice that is identified in the module has a written explanation with specific examples of how each practice is being used to enrich the content of the module. For example: • In Module 5, the explanation for MP 4 states, “Model with mathematics. Students use probability models to describe outcomes of chance experiments. They evaluate probability models by calculating the theoretical probabilities of chance events and by comparing these probabilities to observed relative frequencies.” Each lesson specifically identifies where MPs are located, usually within the margins of the teacher edition. ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 1/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. Examples of where the instructional materials attend to each of the MPs include: • In Module 1, Lesson 7, MP 1 is identified in the teacher edition and attends to the full meaning of the practice where students make sense of problems by organizing data in order to find the constant of proportionality. “Encourage students to make a chart to organize the data from the problem, and then explicitly model finding the constant of proportionality. Students have already found unit rate in earlier lessons but have not identified it as the constant of proportionality.” • In Module 2, Lesson 20, MP 2 is identified in the teacher edition and attends to the full meaning of the practice where students use quantitative reasoning to find the beginning balance of a given transaction log. • In Module 3, Lesson 1, MP 8 is identified in the teacher edition and attends to the full meaning of the practice where students discuss how different forms of the same expression relate to each other. “Discuss the variations of the expressions in part (b) and whether those variations are equivalent. This discussion helps students understand what it means to combine like terms; some students have added their number of triangles together and number of quadrilaterals together, while others simply doubled their own number of triangles and quadrilaterals since the envelopes contain the same number. This discussion further shows how these different forms of the same expression relate to each other. Students then complete part (c). Next, discuss any variations (or possible variations) of the expression in part (c), and discuss whether those variations are equivalent. Are there as many variations in part (c), or did students use multiplication to consolidate the terms in their expressions? If the latter occurred, discuss students’ reasoning.” There are a few instances where the materials do not attend to the full meaning of one or two MPs. For example: • In Module 5, Lesson 6, MP 5 is identified in the teacher edition where students solve probability problems. “After developing the tree diagram, pose the questions to students one at a time. Allow for more than one student to offer an answer for each question, encouraging a brief (two-minute) discussion.” This is an example of not attending to the full practice as students are given a tree diagram to use to solve the probability problem. Students do not choose the appropriate tool to solve the problem. ### Indicator 2g Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: 0/0 ### 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. 2/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Student materials consistently prompt students to construct viable arguments and analyze the arguments of others. • In Module 3, Lesson 1, students construct viable arguments and analyze the arguments of others when determining if a fictional student’s statement and justification are correct. Example 3f states, “Alexander says that 3x + 4y is equivalent to (3)(4) + xy because of any order, any grouping. Is he correct? Why or why not?” • In Module 5, Lesson 12, students construct viable arguments and analyze the arguments of others when estimating probabilities. Students determine if their results agree with a fictional students results and explain their decision. Exercise 3 states, “Collect data for Sylvia. Carry out the experiment of shaking a cup that contains four balls, two black and two white, observing, and recording whether the pattern is opposite or adjacent. Repeat this process 20 times. Then, combine the data with those collected by your classmates. Do your results agree with Philippe’s equally likely model, or do they indicate that Sylvia had the right idea? Explain.” • In Module 5, Lesson 14, students construct viable arguments and analyze the arguments of others when creating random sequencing. Exercise 2 states, “Working with a partner, toss a coin 20 times, and write down the sequence of heads and tails you get. Compare your results with your classmates. How are your results from actually tossing the coin different from the sequences you and your classmates wrote down? Toni claimed she could make up a set of numbers that would be random. What would you say to her?” • In Module 6, Lesson 25, students construct viable arguments and analyze the arguments of others when finding the volume of rectangular prisms. Exercise 2 states, “Two aquariums are shaped like right rectangular prisms. The ratio of the dimensions of the larger aquarium to the dimension of the smaller aquarium is 3:2. Addie says the larger aquarium holds 50% more water than the smaller aquarium. Berry says that the larger aquarium holds 150% more water. Cathy says that that larger aquarium hold over 200% more water. Are any of the girls correct? Explain your reasoning.” ### 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. 1/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. The teacher material frequently provides quality questions the teacher can pose to students to elicit their reasoning, however, guidance for the teachers to assist students in critiquing the reasoning of others is significantly less. Teacher materials sometimes assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. • In Module 3, Lesson 1, teachers are prompted to encourage students to substitute positive and rational numbers in given expressions to justify their argument. “Encourage students to substitute a variety of positive and negative rational numbers for x and y because in order for the expressions to be equivalent, the expressions must evaluate to equal numbers for every substitution of numbers into all the letters in both expressions. What can be concluded as a result of part (f)? We found that we can use any order, any grouping of terms in a sum, or of factors in a product. Why? Can we use any order, any grouping when subtracting expressions? Explain.” • In Module 5, Lesson 16, teachers are prompted to have students share their thinking about a given data set and the posibility of it being a random sample. “Sallee argued that the set (20, 24, 27, 32, 35, 40, 45, 50, 120, 500) could not possibly be a random sample of ten numbers from 1 to 500 because the set had too many small numbers. Do you agree or disagree with Sallee? Explain your thinking. Why is it important to choose a random sample when you are collecting data?” • In Module 6, Lesson 23, teachers are prompted to facilitate a student discussion with a partner to determine if the surface area of two given figures are the same. “Have students predict in writing or in discussion with a partner whether or not the sum of the two surface areas in part (b) will be the same as the surface area in part (a). How did you determine the surface area of the shape on the left?” However, there are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. • In Module 5, Lesson 13, teachers are prompted to have students answer questions involving data collection. There are no directives or suggestions for facilitating student thinking and the prompt reads more as the directions to the exercise. “Be sure students answer the questions as if they had no other source available; they could not go to the Internet and ask for the average home cost, for example. They would have to figure out how to get enough information to estimate an average cost. Pose questions from this exercise one at a time, and allow for multiple responses. While discussing the answers, point out the difference between a population and a sample and how that might be related to each part of this exercise. A population is the entire set of objects (e.g., people, animals, and plants) from which data might be collected. A sample is a subset of the population. Consider organizing a table similar to the following for selected parts of this exercise as students discuss their answers.” An opportunity for students to analyze the arguments of others is not suggested. ### Indicator 2g.iii Materials explicitly attend to the specialized language of mathematics. 2/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 meet expectations for explicitly attending to the specialized language of mathematics. In each module, the instructional materials provide new or recently introduced mathematical terms that will be used throughout the module. The mathematical terms that are the focus of the module are highlighted for students throughout the lessons and are reiterated at the end of most lessons. Each mathematical term that is introduced has an explanation, and some terms are supported with an example. The terminology that is used in the modules is consistent with the terms in the standards. The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams and symbols. For example: • In Module 1, Lesson 3, the materials prompt students to respond to the questions, “Is the pay proportional to the hours worked? How do you know?” A sample response is included and states, “Yes, the pay is proportional to the hours worked because every ratio of the amount of pay to the number of hours worked is the same. The ratio is 8:1, and every measure of hours worked multiplied by 8 will result in the corresponding measure of pay.” • In Module 4, Lesson 2, the materials guide teachers through the teaching process of finding a part when given the percent of the whole. Example 1 states, “Is 30 the whole unit or part of the whole? What percentage of Ty’s class does the quantity 30 students represent? Solve the problem first using a tape diagram.” The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them. For example: • In the Module 1 Overview, a description of proportional relationships is provided: “A proportional relationships is a correspondence between two types of quantities such that the measures of quantities of the first type are proportional to the measures of the quantities of the second type. Note that proportional relationships and ratio relationships describe the same set of ordered pairs but in two different ways.” • In Module 1, Lesson 2, the mathematical term proportional is introduced. The Student Outcomes section provides a definition for the constant of proportionality and a description for proportional. “Students understand that two quantities are proportional to each other when there exists a constant (number) such that each measure in the first quantity multiplied by this constant gives the corresponding measure in the second quantity.” • In Module 3, Lesson 1, the mathematical term expression in standard form is introduced. The teacher edition calls attention to an important note regarding the term standard form: “Important: An expression in standard form is the equivalent of what is traditionally referred to as a simplified expression. This curriculum does not utilize the term simplify when writing equivalent expressions, but rather asks students to put an expression in standard form or expand the expression and combine like terms. However, students must know that the term simplify will be seen outside of this curriculum and that the term is directing them to write an expression in standard form.” ### Gateway Three ## Usability #### Partially Meets Expectations ### Criterion 3a - 3e Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing. 8/8 + - Criterion Rating Details The instructional materials for Eureka Grade 7 meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent. ### 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. 2/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 meet the expectation that the underlying design of the materials distinguishes between lesson problems and student exercises for each lesson. It is clear when the students are solving problems to learn and when they are applying their skills to build mastery. Each lesson follows a sequence that is facilitated by the teacher and may include components such as Opening Exercise, Examples, Challenges, Discussion and Closing. Exercises are included in each lesson to be completed by students within the class period either individually or with a partner. These Exercises generally reinforce and/or extend the new mathematical concepts explored in a lesson. Students build mastery when they apply what they have learned to solve problems in the Problem Set component of a lesson. The Problem Set problems typically mirror the types of problems introduced in the Exercises. Most lessons include an Exit Ticket at the end of a lesson. The Exit Ticket is aligned to problems in the Exercises and Problem Sets a majority of the time. ### Indicator 3b Design of assignments is not haphazard: exercises are given in intentional sequences. 2/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 meet the expectation for not being haphazard; exercises are given in intentional sequences. Module sequences follow the progressions outlined in the CCSSM Standards to support students’ conceptual and skill development. Lessons within modules are intentionally sequenced so students develop understanding leading to content mastery. The overall structure of a lesson provides students with problems and activities that are sequenced from concrete to abstract thinking. ### 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. 2/2 + - Indicator Rating Details The instructional materials reviewed for Eureka Grade 7 meet the expectation for having variety in what students are asked to produce. The instructional materials prompt students to produce mathematical models and explanations of their reasoning when finding solutions to various problems. For example, in Module 4, Lesson 4, Problem Set 6, students determine if a fictional student makes a correct statement and justifies their reasoning. “Henry is considering purchasing a mountain bike. He likes two bikes: One costs500, and the other costs \$600. He tells his dad that the bike that is more expensive is 20 percent more than the cost of the other bike. Is he correct? Justify your answer.”

Students produce solutions, construct viable arguments, and critique the reasoning of others within all components of the instructional materials including group and partner discussions. Students use mathematical models such as number lines, double number lines, tape diagrams, graphs and tables. The materials consistently call for students to use the language and intent of the standards when producing solutions.

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet the expectation for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of manipulatives and integrates hands-on activities that allow the use of physical manipulatives. For example:

• Manipulatives are consistently aligned to the expectations and concepts in the standards. The majority of manipulatives used are geometry tools. In Module 6 Lesson 6, students use a compass when drawing geometric shapes.

Examples of manipulatives for Grade 7 include:

• Integer Cards deck
• Compasses
• Protractors
• Rulers
• Centimeter Cubes
• Set Squares

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
+
-
Indicator Rating Details

The visual design in Eureka Grade 7 is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The instructional materials follow a consistent visual format. The teacher materials coincide with the student materials when both consistently label the modules, topics and lessons. Within each module, lessons with similar or related content are grouped into topics.

The print and visuals on the materials are clear without any distracting visuals or an overabundance of text features. Lesson materials for students have distinct consistent headings such as Classwork or Problem Set to distinguish group work from individual work. A framed Lesson Summary is often included at the end of the lesson to emphasize important concepts to students.

Student practice problem pages frequently include enough space for students to write their answers and demonstrate their thinking. Exit Tickets provide clearly labeled models as well as space to solve the given problem. There are no distracting or extraneous pictures, captions or "facts" within lessons.

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 7 partially meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials contain full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge and explain the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains an opening narrative for the teacher. Included in this narrative is a section labeled Student Outcomes, and often included is a section labeled Lesson Notes. The Student Outcomes section lists the objectives of the lesson, and the Lesson Notes section gives teachers a mathematical summary of the concept being presented, examples of the concept, as well as suggestions to help students make connections between concepts. The Classwork section provides questions for discussion and guiding questions designed to increase classroom discourse and ensure understanding of the concepts. For example:

• In Module 4, Lesson 6, a Closing question states, “Describe how you can mentally determine the whole given that 15 is 30 percent of a number.”

However, the materials do not include instructions or guidance for how to adjust a lesson or the questions that a teacher asks to guide instruction based on the needs of students.

There is not sufficient guidance on how to group students or structure questions that can support all students in accessing the material.

### 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectations for containing a teacher 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 also include teacher guidance on the use of embedded technology to support and enhance student learning.

Some lessons include a Lesson Notes section which provides useful suggestions on how to present content and/or explanations as to why a particular model is used. Most lessons have pictures or other graphics with annotations, demonstrating the concepts for the teacher.

Often, the scaffolding provided is to "remind students." There are limited suggestions for how to modify lessons, questions and/or problem sets for students who already understand or struggle with the content of the given lesson.

Beyond an occasional link to a video, there are no suggestions for teachers on the use of technology, including a calculator, and therefore no guidance on how to use such technology.

Answer keys are included for all of the Problem Sets, Exit Tickets, Homework, and Tests, including written annotations to show how student work should look.

### 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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet expectations for the teacher edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

The module Overview provides information about the mathematical connections of concepts being taught. Previous and future grade levels are also referenced to show the progression of the mathematics over time. Important vocabulary is included along with definitions and examples of the terms.

Lesson narratives provide specific information as well as examples about the mathematical content within the lesson and are presented in adult language. These narratives contextualize the mathematics of the lesson to build teacher understanding, as well as guidance on what to expect from students and important vocabulary.

The teacher edition provides each step of the solution to the problems posed to students.

### 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.
2/2
+
-
Indicator Rating Details

The materials do contain a teacher edition (in print or clearly distinguished or accessible 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 12.

• Each module has an overview section at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics, Kindergarten through Grade 12.
• Knowledge required from prior modules and/or grades is explicitly called out in this section.

### 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).
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 provide a list of concepts in the teacher edition that cross-references the standards addressed and provides an estimated instructional time for each unit and lesson.

The materials provide a module overview that specifies the grade-level standards addressed in each module. The standards are listed in the Focus Standards section of the overview. An estimated number of instructional days is given for each module to be completed.

Each section within a lesson is labeled with an estimated number of minutes that it should take to complete.

### 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.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

There are resources online that inform parents about the mathematics of the program as well as give suggestions for how they can help support their child.

The online parent resources are divided into several categories. The Parent Support section allows parents to create an account to gain access to resources. Parent Tip Sheets are free to parents and include suggested strategies, vocabulary, and tips to support learning at home. Parents can learn more about the spiral bound books that can be purchased that provide step-by-step explanations of homework problems in the Homework Helpers section. The Grade Roadmaps section explains grade-level math concepts and gives suggestions on facilitating learning outside of the classroom.

There is also a section where parents can download card games to help build fluency in math.

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 contain some explanations of the instructional approaches of the program. Some modules contain Methods of Instructional Delivery. When this section is available, it provides teachers with information on how to prepare to teach the lesson, strategies utilized throughout the lesson, and the benefits of the strategies. There is additional information about the instructional approaches in A Story of Ratios Curriculum Overview. Lastly, the opening letter from Executive Director Lynne Munson addresses some of the research and philosophy behind the instructional materials.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
4/10
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 7 do not meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide ongoing review and practice with feedback. The instructional materials do not provide strategies for gathering information about students’ prior knowledge, partially provide strategies for identifying and addressing common student errors and misconceptions, partially have assessments with standards clearly denoted, and do not include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 do not meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

There are no strategies or assessments that are specifically for the purpose of assessing prior knowledge.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions.

The teacher edition often identifies common student errors and/or misconceptions within the lesson, although strategies to address the errors and/or misconceptions are not provided.

Teachers can address errors and misconceptions by facilitating mathematical conversations between students. Teachers are provided with a list of possible discussion questions for most lessons.

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure consisting of an opening exercise, discussion, exercises, closing, exit ticket, and problem sets provides students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently with partners and in groups where review, practice, and feedback are embedded into the instructional routine.

The Opening Exercise section of a lesson provides ongoing review and practice of previously taught concepts. The Problem Set problems for each lesson activity reinforce skills and enable students to engage with the content and receive timely feedback. In addition, discussion questions in the Discussion section provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

The summative assessments contain rubrics to provide feedback to the teacher and student on a student’s progress towards mastery.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation for assessments clearly denoting which standards are being emphasized.

The summative assessments which include the Mid-Module and End-of-Module Assessment meet the expectations by clearly denoting the standards being emphasized; however, the formative assessments such as Exit Tickets do not.

The Mid-Module and End-of-Module Assessments align each item to specific standard(s). Each of these assessments include a Progression Toward Mastery rubric that lists specific standards being assessed and describes how mastery is determined.

### 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.
0/2
+
-
Indicator Rating Details

Formative assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.

• Each Mid-Module and End-of-Module assessment includes a rubric as well as worked-out solutions for correct responses.
• There are no strategies or suggestions for follow-up provided. There are no rubrics or scoring guidelines for any formative assessment tasks (nor are any items or tasks identified as formative assessment opportunities).

### Indicator 3q

Materials encourage students to monitor their own progress.
0/0
+
-
Indicator Rating Details

The instructional materials for Eureka Grade 7 do not include opportunities for students to monitor their own progress.

There are no evident strategies or opportunities for students to monitor their own progress. Objectives or outcomes for each lesson and/or assignment are not provided to students in any of the student material.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
7/12
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 7 do not meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide a balanced portrayal of various demographic and personal characteristics, but the instructional materials partially provide: strategies to help teachers sequence or scaffold lessons; strategies for meeting the needs of a range of learners; tasks with multiple entry points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for advanced students to investigate mathematics content at greater depth.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The modules and topics within each module are sequenced according to the CCSSM "Progressions of Learning." A description of the module sequence and layout is provided.

In the module and topic overviews, the structure of how the lessons build and develop a concept is discussed in narrative form. Lessons are sequenced to build from conceptual understanding, using representations ranging from concrete and pictorial to the more abstract.

There is little guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure: Opening Exercise, Examples, Challenges, Discussion, and Closing all include guidance for the teacher on the mathematics of the lesson, possible misconceptions, and specific strategies to address the needs of a range of learners.

There are limited marginal notes that provide strategies in the teacher materials. The suggested strategies are vague such as "use questioning strategies" or "remind students of a definition" and do not offer strategies that will impact the outcome of a lesson/problem.

The differentiation list online mirrors the strategies in the teacher materials; however, it does not offer additional clarification or suggestions.

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Although most of the tasks allow students to utilize multiple entry points and to solve problems using a variety of strategies, paths and/or models, the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.

At times, teachers are prompted to lead students through a particular task rather than provide students with an opportunity to create a solution path on their own. Students are not always encouraged to produce a variety of solution strategies. For example:

• In Module 1, Lesson 8, Example 1, students are presented with a situation about miles driven and the amount of gas used, and they are asked to determine if the mom will run out of gas. Instead of presenting the data and the question, the problem provides the data and a set of questions that guide students through finding the constant of proportionality; students then write an equation and use that equation to determine if the driver has enough gas to get to her destination. Since determining the constant was part of a previous lesson, students could have been directed to simply solve the problem-does the mom have enough gas to get to her destination-using more than one method. With multiple entry points and suggestions for sharing student work, the lesson could have been designed to encourage a variety of solution strategies and ended with the strategy that was the focus of the lesson. (Note: the last step of this problem does provide choice in using either an algebraic strategy or a numerical strategy, but only that one step provides that choice.)

### 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).
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation that the materials include support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

There are limited marginal notes that provide strategies in the teacher materials. The suggested strategies are vague, such as "use questioning strategies" or "remind students of a definition," and do not offer strategies that will impact the outcome of a lesson/problem.

The differentiation list online mirrors the strategies in the teacher materials; however, it does not offer additional clarifications or suggestions for English Language Learners and other special populations.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

There are limited marginal notes in the teachers edition that provide strategies for advanced students. The Notes on Multiple Means of Engagement give teachers suggestions about meeting the needs of advanced students.

“Challenge” problems are occasionally included; however, it is difficult to determine if those problems were optional for the entire class, to be scaffolded for the class, or explicitly for students who needed advanced mathematics.

The curriculum specifies that not all pieces within a section of a lesson must be used, so advanced students could be asked to tackle problems or sections a teacher does not use for all students. Overall, the materials provide minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. The names chosen in the lessons represent a variety of cultural groups.

The application problems include real-world situations that would appeal to a variety of cultural and gender groups.

There is a balanced approach to the use of gender identification.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 provide limited opportunities for teachers to use a variety of grouping strategies.

Notes within the lessons provide teachers a variety of options for whole group, small group, partner, or individual work. Although suggestions are made, there is often no mention of the reason that a student should work within a specific group size. The groups do not have explicitly-stated assigned roles or expectations to help teachers enhance the involvement of every student.

There are opportunities for different groupings, however the fundamental models are Modeling with Interactive Questioning, Guided Practice, and Independent Practice.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 7 do not encourage teachers to draw upon home language and culture to facilitate learning.

There is no evidence of teachers needing to draw upon home language and culture to facilitate learning.

### Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
+
-
Criterion Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this criterion.

### 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.
0/0
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### 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.
0/0
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### 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.
0/0
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### Indicator 3ad

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.).
0/0
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

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## Additional Publication Details

Report Published Date: 08/27/2018

Report Edition: 2015

## About Publishers Responses

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Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

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Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

## Advancing Through Gateways

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. 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).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, 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.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric 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.

Eureka Math K-8 (2015) was previously reviewed by EdReports. This is a re-review of the 2015 program due to added digital/online components.

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.

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.

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