## Alignment: Overall Summary

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for alignment. The materials spend the majority of the time on the major work of the grade, and the assessments are focused on grade-level standards. Content is aligned to the standards and progresses coherently across the grades and within each grade. The lessons include conceptual understanding, fluency and procedures, and application. There is a balance of these aspects for rigor. The Standards for Mathematical Practice (MPs) are used to enrich the learning.

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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
17
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
30
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 The Utah Middle School Math Project Grade 7 meet the expectation for being focused on and coherent with the Common Core State Standards in Mathematics. The Unit Assessments do not assess above grade-level topics, and the instructional materials devote over 65 percent of class time to major work. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and will foster coherence between the grades. The materials explicitly relate grade-level concepts to prior knowledge from earlier grades, and the materials foster coherence through connections at a single grade, where appropriate and required by 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials did not include any assessment questions that were above grade-level.

### 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 The Utah Middle School Math Project Grade 7 meet the expectations for focus within assessment. Overall, the instructional material does not assess content from future grades within the assessment sections of each unit.

There are multiple Self-Assessments within each unit. Each assessment includes a scoring rubric that helps students articulate their understanding of key concepts being assessed. All assessments have answer keys provided in the Teacher Workbook.

• Chapter 2 Section 2.3- Students demonstrate their knowledge of 7.NS.2 by applying and extending previous understandings of multiplication and division of fractions to multiply and divide rational numbers. Question 2c on the Self-Assessment states: “Estimate each product or quotient. Then find the actual product or quotient of -89(0.5).”
• Chapter 6 Section 6.3- Students solve word problems leading to linear inequalities demonstrating their knowledge of 7.EE.4b. Question 3b on the Self-Assessment states: “Write an inequality to represent each of the following word problems. Solve each problem. Explain your solution in context. 'Jeremy is two years older than Rachel. The sum of the ages of Jeremy and Rachel is less than 46. How old could Jeremy be?'”

### 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for having students and teachers using the materials as designed, devoting the large majority of class time to the major work of the grade. Overall, the materials devote approximately 82 percent of class time to major work.

### 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 Grade 7 meet expectations for focus by spending a majority of class time on the major clusters of the grade including all clusters in 7.RP, 7.NS, and 7.EE. To determine this, three perspectives were evaluated: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of weeks devoted to major work. Of the three perspectives, the number of lessons is most representative and was used to determine the score for this indicator.

Overall, the materials spend approximately 82 percent of instructional time on the major clusters of the grade. The Grade 7 materials have 8 chapters that contain 139 lessons, which accounts for a total of 31 weeks of class time including Anchor Problems and Self-Assessments.

• Grade 7 instruction is divided into eight chapters. More than half of Chapter 1 addresses 7.NS. Chapter 2 addresses 7.NS. Chapter 3 addresses 7.EE. Chapter 4 addresses 7.RP. More than half of Chapter 6 addresses 7.EE. Therefore, approximately 4.5 out of 8 chapters (56 percent) focus exclusively on the major work of the grade.
• Grade 7 instruction consists of 139 lessons. Approximately 114 lessons out of 139 (82 percent) focus on the major work of the grade level, which includes supporting work that connects to the major work of the grade.
• Grade 7 instruction is divided into 31 weeks. Approximately nineteen out of 31 weeks (61 percent) focus exclusively on the major work 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for being coherent and consistent with the standards. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior or future grades is clearly identified, and the materials explicitly relate grade-level concepts to prior knowledge from earlier grades. The objectives for the materials are shaped by the CCSSM cluster headings, and they also incorporate natural connections that will prepare a student for upcoming grades.

### 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 The Utah Middle School Math Project Grade 7 meet the expectation for the supporting content-enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the lessons that focus on supporting content also engage students in major work where natural and appropriate.

The following examples demonstrate where the supporting work enhances understanding of the major work of Grade 7.

• Chapter 5: Sections 5.2b, 5.2c, and 5.4b work with 7.G.1, and 7.G.6 supports 7.RP.2 by having students create and solve ratios and proportions to find similar figures. For example, in the overview teachers are told that the central idea of Section 5.2 is scale and its relationship to ratio and proportion. The standard for ratio and proportion are not listed. Ratio language is used in the Activities and Homework problems.
• Chapter 6: Section 6.1 supports 7.EE.4 and 7.NS.1 by having students find angle pairs which involves working with rational numbers and creating/solving equations.
• Chapter 7: Activities 7.1a and 7.1b support 7.NS.1 by having students compare populations which involves working with rational numbers.
• Chapter 7: Sections 7.1 and 7.2 include problems that are related to ratio and proportions (7.RP.2) while working with statistics. For example, Chapter 7, Class Activity 7.2b, Teacher Workbook, page 7WB7 – 43, students use the ratio of colors of jellybeans for a statistical experiment.
• Chapter 8: Activity 8.1c supports 7.EE.4 by having students create and solve equations in real-life mathematical problems based on composite area.

### 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

The instructional materials reviewed for Grade 7 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The instructional materials are designed to take approximately 155 days. According to the publisher, completing the work would take a total of 31 weeks. That includes days for Anchor Problems, Class Activities, Homework, and Spiral Review. According to the Preface, “Each lesson covers classroom activity and homework for a 50-minute class. Sometimes the demands of the material exceed this limitation; when we recognize this, we say so; but some teachers may see different time constraints, and we defer to the teacher to decide how much time to devote to a lesson, how much of it is essential to the demands of the relevant standard. What is important are the proportions dedicated to the various divisions, so that it all fits into a year’s work. Within a lesson, the activities for the students are graduated, so that, in working the problems, students can arrive at an understanding of a concept or procedure. In most cases there is an abundance of problems, providing the teacher with an opportunity to adapt to specific needs.” The number of weeks was converted to days for this review. Each chapter has built-in days for Self Assessments. Overall, the amount of content that is designated for this grade level is viable for one school year.

### 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 materials reviewed for The Utah Middle School Math Project Grade 7 meet expectations for consistency with the progressions in the Standards. In general, materials develop according to the grade-by-grade progressions in the Standards and provide extensive work with grade-level problems. Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior and future grade levels is identified in Connections to Content at the beginning of each student and teacher workbook chapter. Chapter overviews/summaries, as well as section overviews, include a written explanations of what students will be doing throughout the chapter. Summaries explain what students will learn and how they will use this knowledge in future learning.

• Chapter 1 explains that “throughout the chapter, students are provided with opportunities to review fractions, decimals and percents.” (page 7WB1 - 2)
• Chapter 2: “The development of rational numbers in 7th grade is a progression in the development of the real number system that continues through 8th grade. In high school students will move to extending their understanding of number into the complex number system.” (pages 7WB2 – 3)
• Chapter 4: “The chapter begins by reviewing ideas from 6th grade as well as 7th grade chapters 1-3 and transitioning students to algebraic representations. Student will rely on knowledge developed in previous chapters and grades in finding unit rates, proportional constants, comparing rates and situations in multiple forms, writing expressions and equations, and analyzing tables and graphs.“ (page 7WB4 – 2)
• Chapter 6: “Work on inequalities in this chapter builds on Grade 6 understandings where students were introduced to inequalities represented on a number line. The goal in Grade 7 is to move to solving simple one-step inequalities, representing ideas symbolically rather than with models.” (page 7WB6 - 2)
• Chapter 8: “In 8th grade, students will continue working with volume, formalizing algorithms for volume of cylinders and adding methods for finding the volume of cones and spheres.” (page 7WB8 – 3)

Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections between concepts are addressed in the Connections to Content, chapter overviews/summaries, and Math Textbook. Examples of these explicit connections include:

• Chapter 4, Class Activity 4.1a: “Equivalent Ratios, Fractions, and Percents (Review from 6th grade): They should know a ratio expresses a numerical relation between two quantities. Students studied ratios extensively in 6th grade.” (p. 7WB4 – 14)
• Chapter 8, Connections to Content: “Towards the end of this section students review the use of nets (a concept from 6th grade) to find surface area of prisms and cylinders and then to differentiate this measure from volume, which they will also find.” (page 7WB8 – 2)

### 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

In the teacher's workbook, the CCSSM are identified on the introduction page of each chapter. Each chapter correlates to a Grade 7 domain, with sections within the chapter focusing on standards within the domain. There is a section titled, “Concepts and Skills to Master," which identifies specific learning objectives for each section in the teacher, parent, and student workbooks.

• “Investigate chance processes, develop/use probability models, as well as the work within the section,” a learning objective from Chapter 1 Section 1.1, reflects Cluster 7.SP.C (Investigate chance processes and develop, use, and evaluate probability models).
• In Chapter 3, students are engaged in activities aligned to Cluster 7.EE.A (Use properties of operations to generate equivalent expressions). In Section 3.1a (page 7WB3-7 - 12), the first Activity, “Naming Properties of Arithmetic,” has an objective to “recognize properties of arithmetic and use them in justifying work when manipulating expressions.” Students are engaged in using the identified properties and identifying pairs of equivalent expressions. In Anchor Problem 3.0 (page 7WB3 - 6), a teacher’s note reflects the cluster heading: “A big idea you’re after right now is that one can write equivalent expressions in a number of ways and that different ways shed light on different thinking.”

The materials include problems and activities that serve to connect two or more clusters in a domain where connections are natural and important.

• The Chapter 3 Overview connects 6.EE.1 and 6.EE.2 through this statement: “By the end of this section (3.1) students should be proficient at simplifying expressions and justifying their work with properties of arithmetic. Section 3.2 uses the skills developed in the previous section to solve equations…Section 3.3 ends the chapter with application contexts.” (pages 7WB3 - 2 and 7WB3 - 3)

The materials include problems and activities that serve to connect two more domains in a grade where connections are natural and important.

• Chapter 3 Section 3.1 and 3.2 connects 7.NS.A and 7.EE.A as students transfer integer properties to algebraic expressions. Students use the Distributive Property of Multiplication and Division over Addition and Subtraction to write equivalent algebraic expressions and to develop an understanding of combining coefficients of like terms and calculating the product of two numbers. (pages 7WB3 – 6 and 7WB3 - 93 through 7WB3 - 109)
• In Chapter 4, Class Activities 4.3d and 4.3e 7.RP.A, 7.NS.A and 7.EE.B are connected as students write equations and compute to solve percent problems. (pages 7WB4 - 173 through 7WB4 - 181)

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for rigor and mathematical practices. The materials meet the expectations for rigor as they balance and help students develop conceptual understanding and procedural skill and fluency. The materials meet the expectations for mathematical practices as they identify and use each of the MPs and support the Standards' emphasis on mathematical reasoning.

### 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance in all three aspects of rigor.

### 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 reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Each chapter starts with an Anchor problem which poses a mathematical situation that students will learn to solve. Many of these are conceptual in nature. For example, Chapter 3 Anchor Problem 3.0 engages students in the understanding that there are different ways to write equivalent expressions and that the different ways shed light on ways of thinking about the problem. The Teacher’s Notes for that problem emphasize developing understanding.

Many Class Activity problems involve hands-on activities or models. In Chapter 3, students use the properties of operations to generate equivalent expressions. This chapter gives students practice with algebra tiles to build a conceptual understanding of equivalent expressions. In Chapter 3 Class Activity 3.1d, students learn how to use algebra tiles to build a representation of factoring. Later in Class Activity 3.1h, students are shown two ways to factor. Method 1 encourages the use of a model, and in Method 2 students use the greatest common factor.

The teacher notes for each lesson describe the purpose of the lesson and how to guide students to develop their conceptual understanding. The notes include prompts and questions during instruction that lead to conceptual understanding.

Chapters 1 and 2 address 7.NS.A.

• The Chapter 1 Section 1.2 Overview states: “The concept of equivalent fractions naturally leads students to the issues of ordering and estimation. Students will represent order of fractions on the real number line.” Students understand where rational numbers are placed on a number line and use models to solve multi-step problems.
• The Chapter 2 Section 2.1 Overview summarizes the use of hands-on manipulatives and number lines so that students can eventually “reason through addition and subtraction of integers without a model.” Students develop a conceptual understanding of negative numbers and additive inverse by adding integers on a number line, using chips to model addition problems, and using the number line to model subtraction problems.

Chapters 3 and 6 address 7.EE.A.

• In Chapter 3 Class Activity 3.1a and Homework, students determine if two expressions are equivalent and justify their conclusions, consolidating their understanding of the properties of operations.
• In Chapter 3 Class Activity 3.1c and Homework, students use algebra tiles to rewrite algebraic expressions.
• Students demonstrate conceptual understanding to solve Chapter 6 Class Activity 6.2c Problem 1: “Matt, Rosa, and Kathy are cousins. If you combine their ages, they would be 40 yrs. old. Matt is one-third of Rosa's age. Kathy is five years older than Rosa. How old are they? Show several ways to solve the problem. Be able to explain how you came to your answer.”

### 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
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, when the intention is that procedural skill and fluency be developed, the materials offer opportunities for their development.

There are examples and repetition in practice in each lesson and homework. Spiral Reviews are found in each chapter that set an expectation of procedural skill and fluency. For example, the Chapter 2 Spiral Review (page 7WB3 - 24) addresses a number of computational standards from previous grades as well as 7.NS.A. Question 5 asks students to solve 5 × (−9).

The following standards are addressed within the course:

• 7.NS.A: Section 2.1 and 2.3 give students practice adding and subtracting rational numbers. Students begin to describe situations in which opposite quantities combine to make 0, and as teachers introduce the properties of arithmetic, students use these properties to add and subtract fluently. Students practice multiplying and dividing rational numbers. Extra Practice sections are also provided.
• 7.EE.1: In Chapter 3, students begin the concept of generating equivalent expressions through the use of concrete models. Students use the commutative property as well as the distributive property to generate an equivalent expression. Students continue procedural practice with solving equations. By the end of Chapter 3, students are expected to be fluent with the properties of operations.
• 7.EE.4: Students move from translating contexts to numeric expressions in Chapter 3 Class Activity 3.1b and Homework to translating contexts to algebraic expressions in Class Activity 3.1c Homework and Additional Practice. In Section 3.2 students build procedural skill and fluency by modeling two-step equations and by using their knowledge of properties. Class Activities 3.2a-c give students practice using models (algebra tiles) to solve two-step equations with and without rational numbers. Class Activities 3.2d and 3.2.e provide opportunities to continue working on this skill to gain fluency.

### 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
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectation that teachers and students spend sufficient time working with engaging applications of mathematics, without losing focus on the major work of the grade. Overall, the materials have opportunities for students to apply mathematical knowledge and/or skills in a real world context.

Throughout the materials students engage in application problems in Class Activity and Anchor Problems. These problems are contextual, and some include multiple representations and steps. Students are asked to present their solutions in ways that demonstrate their understanding of the mathematics in the context.

• Chapter 3 Class Activity 3.3a (7WB3 - 119) includes contextual problems. For example, “Today is Rosa’s 12th birthday. She has a savings account with $515 in it, but her goal is to save$10,000 by the time she turns 18. How much money should she add to her savings account each month to reach her goal of $10,000 between now and her 18th birthday?” Students draw a model, write an equation that represents the model, solve the equation, and answer the question in a full sentence. • Chapter 4’s Anchor Problem, “Tasting Lemonade,” is a multi-step, real-world, contextual problem that develops analysis of proportional relationships (7.RP.A). It emphasizes solving the problem using a variety of strategies. Students are presented with the context that “you want to sell lemonade in a park” and have five different recipes to choose from, consisting of different concentrate and water ratios. The following problems develop students’ understanding on how the different ratios would affect the flavor of the lemonade, and the Teacher Notes that follow provide a variety of solution strategies to share with students to help them develop flexibility in their application of mathematics. • “Which one would be the most 'lemony'?" • “Which would use 10 cups of water?” • “How much would you need to make 50 cups of each recipe?” • Chapter 4 Class Activity 4.3c has a variety of multi-step and contextual problems. For example, Question 1 reads as follows: “Ginger and her brother Cal have red and green planting buckets in the ratio of 3:1. a. If there are 5 green buckets, how many red buckets are there? b. Ginger and Cal bought more buckets because they have more to plant. They purchased the buckets in the same red:green ratio of 3:1. If they now have 28 buckets total, how many red and green buckets do they have? c. How are the problems different?” In Grade 7, some specific standards that include application are 7.NS.3 and 7.EE.3. Examples of problems that address these standards include: • On page 7WB1 – 55, students are asked to solve problems involving investment rates, target heart rates, and the cost of dinner with tax and tip. (7.NS.3) “Rico's resting heart rate is 50 beats per minute. His target exercise rate is 350% of his resting rate. What is his target rate?” Students use a model and write a number sentence to solve the multi-step problem. • In Chapter 2 Lesson 2.3a Problem 25 students use a number line to model situations, answer questions using their knowledge of the number line, write an addition equation, and explain their thinking. (7WB2 - 20) (7.EE.3) • In Chapter 6 Section 6.2 students work in two “different directions.” In some sections, students are given a context and asked to find relationships and solutions while in other sections students are given relationships and asked to write contexts. • “Write a context that models the following equation. 2L + 2(3L) = 990.” (7WB6 - 66) (7.EE.3) • “Martha divides$94 amongst her four friends. Leon gets twice as much money as Kokyangwuti. Jill gets five more dollars than Leon. Isaac gets ten less dollars than Kokyangwuti. How much money does each friend get?” (7WB6 - 67) (7.EE.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
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separated. Every chapter includes all three aspects of rigor. In some lessons the aspects of rigor are addressed separately, and in some lessons multiple aspects of rigor are addressed. Overall, the three aspects of rigor are balanced in this program.

There are lessons where the aspects of rigor are not combined.

• In Homework 4.3b students practice their procedural skill in solving proportions.
• Spiral Reviews throughout the materials provide opportunities for students to reinforce their procedural skills and fluencies from previous standards and lessons.

There are multiple lessons where two or all three of the aspects are interwoven.

• Class Activity 2.1a (page 7WB2 - 7) begins with exploring additive inverses in contexts. For example, “A hydrogen atom has one proton and one electron.” Students demonstrate their understanding by creating a model/picture, writing the net result in words, and answering how many zero pairs exist in the context.
• In Class Activity 2.2c students make connections between multiplication and division of integers. Students solve division problems and also solve contextual problems. At the end of this lesson/homework there is an extra practice section for students to gain fluency with integer operations as well as more contextual problems with integers.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectations for practice–content connections. The materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialized language of mathematics. The instructional materials also support the Standards' emphasis on mathematical reasoning.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade.

The Standards for Mathematical Practices are identified in both the Teacher and Student Workbooks in most lessons. The MPs are explained in the beginning of the chapter and are identified using an icon within the lessons where they occur.

Overall, the materials clearly identify the MPs and incorporate them into the lessons. All of the MPs are represented and attended to multiple times throughout the year, and MPs are used to enrich the content and are not taught as a separate lesson.

• Chapter 1 Class Activity 1.1c Question 5 asks students to "look for and express regularity in repeated reasoning" as students determine patterns emerging in the previous examples of probability (MP8).
• The Chapter 2 Anchor Problem presents a number line with 0, 1, and variables (a) and (b). Students are asked: “Which of the following numbers is negative? Choose all that apply. Explain your reasoning.” Students reason abstractly and quantitatively (MP2) as well as construct viable arguments (MP3).
• Chapter 4 Class Activity 4.1f asks students to "attend to precision" as they find the unit rate in word problems and compare two quantities (MP6). For example, “Frosted Flakes has 11 grams sugar per ounce and Raisin Bran 13 grams per 1.4 ounces. Which cereal has more sugar per ounce?

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 partially meet the expectations for attending to the full meaning of each Mathematical Practice Standard. The MPs are most frequently identified in Teacher Notes where they are aligned to a particular practice activity or question. Many times the note is guidance on what the teacher does or says rather than engaging students in the practice.

The intent of the MPs is often not met since teachers engage in the MPs as they demonstrate to students how to solve the problems.

• Many problems marked MP1 do not ensure that students have to make sense of problems and persevere in solving them. For example, Chapter 2 Class Activity 2.1 directs students to “use the idea of 'zero pairs' to complete the worksheet.” Students are not making sense of problems but answering problems based on how the teacher models the problem.
• MP4 is identified throughout the program; however, it is rarely identified in situations where students are modeling a mathematical problem and making choices about that process. In many situations, it is labeled when directions are provided for how the teacher models. For example, in Chapter 3 Class Activity 3.1i students are given a number line as the model.
• Where MP5 is labeled, the materials suggest a specific tool for students to use which does not lead students to develop the full intent of MP.5. For example, in Chapter 4 Class Activity 4.2b students are told to use the graph and table to model the context.

### 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
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectation for prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards.

In many cases, students are asked to construct arguments and justify their thinking.

• Throughout the materials students are asked to justify their thinking. For example, Chapter 4 Homework 4.2b Question 3b asks, “Which solution is saltier, Solution A or Solution B? Justify your answer with at least two pieces of evidence.”
• There are instances where students are asked to make conjectures. For example, in Chapter 1 Class Activity 1.1a Question 7 students are asked to “make a conjecture about how many GREEN tiles are in your bag if the bag contains 12 total tiles.”
• Students are asked to engage in Error Analysis in some of the lessons. For example, in Chapter 4 Class Activity 4.1b Question 6 students must identify the error in the table of values that is represented. In the given solution the error was in adding 2 to each value in column A to get Column B rather than multiplying by 3/2 in Column A.

### 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 meet the expectation of 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. Many of the directions for MP3 are the same as those found written in the Student Workbook. Guidance is given on how to assist students in expressing arguments.

A few examples of guidance provided for teachers include:

• In Chapter 6 Homework 6.1a Questions 11-15 the Teacher Notes state: “Note: constructing an argument to disprove a statement only requires one counterexample, while constructing an argument to 'prove' something is more involved. In other words, one affirmative example does not prove a statement. In 7th grade attention to precision in making statements is an important first step towards building arguments. So, for #14, press students to explain why the statement is true; look for statements that build on understanding of supplementary angles and transitivity.”
• In Chapter 4 Class Activity 4.1b the students are given: “The values in the table below represent the lengths of corresponding sides of two similar figures. The side lengths are proportional to one another. Darcy filled in the remaining values in the table and has made a mistake. Find her mistake and fix it by filling in the correct values in the table on the right. Then provide an explanation as to what she did wrong.” The Teacher Note says: ”This problem allows students to critique Darcy’s reasoning and then make their own conjectures about the proportional constant.”
• There are some prompts for the teachers in the form of questions to ask or problems to present. For example, in Chapter 1 Class Activity 1.1b the students roll dice to simulate a horse race. Students determine a specific answer about which horse won most often and why. The Teacher Notes clarify the question and prompt the teacher to ask follow up questions: “Have students justify their arguments. Ask them for evidence to support their claims. Do you think that this game is fair? Why or why not?”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for attending to the specialized language of mathematics. Overall, the materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols. When students are introduced to new mathematical vocabulary, it is explained, and teachers are encouraged to tell students to use the new terms.

• Each chapter in the workbook begins with a vocabulary list of words used in the chapter that includes words from previous learning as well as new terms.
• Throughout the chapter, these terms are used in context during Class Activities, Homework, and Self-Assessments.
• Vocabulary is bold in the context of the lesson.
• Vocabulary is presented throughout the Textbook: Mathematical Foundations along with accurate definitions. For example on 7MF2 - 17, “A golden rectangle is a rectangle that is not a square, but has this property: if we remove the square of whose side is the length of the smaller side of the rectangle, the remaining rectangle is a smaller version of the original.”
• Students are encouraged to use vocabulary appropriately. For example, Class Activity 1.1c Question 2f asks: “Have you been computing theoretical or experimental probability? Explain.” Class Activity 3.2a, between questions #10 and #11 asks: “What do the terms evaluate and solve mean? What is the difference between an equation and an expression?”
• At times the Teacher Notes give suggestions for using vocabulary in a lesson. For example, in Chapter 1 Class Activity 1.1a, students are learning about experimental probability, and the Teacher notes recommend, “Discuss again as a group. Compare their thinking now with their thinking before the experiment. Formalize the definition.”.
• The terminology that is used in the course is consistent with the terms in the standards.

Although it is not included in the CCSSM, the word simplify is used throughout the instructional materials. For example, in Chapter 3 Class Activity 3.1e, between Questions 8 and 9: “Your friend is struggling to understand what it means when the directions say, 'simplify the expression.' What can you tell your friend to help him? Teacher Note: Answers will vary. Discuss 'simplify' vs. 'evaluate' vs. 'solve' and 'expression' vs. 'equation.' Also discuss why we simplify—when does it help and when is it easier to not simplify? You might refer back to Activity 2 above."

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials for The Utah Middle School Math Project Grade 7 meet the expectations for use and design. Materials are well-designed, and lessons are intentionally sequenced. Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter. Students produce a variety of types of answers including both verbal and written answers. Manipulatives are used in the instructional materials as mathematical representations and to build conceptual understanding.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

The chapters begin with a non-routine problem that introduces new concepts and is labeled as an Anchor Problem. The chapters are subsequently sectioned into Class Activities, Homework, Spiral Reviews, and Assessments.

Generally, each Class Activity has problems to solve together as a class with instructor guidance. Occasionally, they are intended to review previous grades' concepts in order to connect them to seventh grade concepts. Most often, the Class Activities are for the students to apply what they have already learned.

The mathematics taught in each Class Activity is reinforced by an accompanying Homework component.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials for Grade 7 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter.

Within each chapter, concept development is sequential. During Class Activities, the teacher introduces new concepts or builds upon prior knowledge. Students work individually or as a whole class when engaged in the Class Activities. The Homework component reinforces the mathematical concepts taught during the previous Class Activity. Spiral Reviews are used to provide continued practice of newly learned mathematical concepts throughout the year.

The progression of lessons taught is intentional and assists students in building their mathematical understanding and skill. Students begin with activities to build conceptual understanding and procedural skill, and progress to applying the mathematics with more complex problems and procedures.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet the expectation for the variety in what students are asked to produce.

Throughout the Class Activities, students are asked to produce answers and solutions, discuss ideas, make conjectures, explain solutions and justify reasoning, make sketches and diagrams, and use appropriate models. These aspects are found individually within problems as well as in combination with others, such as provide an explanation of a solution and include a diagram.

• Chapter 3 Class Activity 3.1b: Models are used to represent the quantities and relationships stated in contextual problems. Students examine the models and write numeric expressions that represent the quantities and relationships represented by the models as well as explain why the various correct representations are equivalent. In subsequent tasks students determine and explain which expressions are equivalent, write contexts for expressions, and explain how they determined if various expressions adequately represent given contexts. The final problems provide opportunity for application.
• Chapter 3 Class Activity 3.1c: Students transition from writing numeric expressions to algebraic expressions using the same types of tasks and problem formats as those presented in 3.1b. The materials provide additional practice for students to draw models, define variables, and write expressions that model given situations.

### Indicator 3d

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

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

Colored tiles are used when students work with probability. In Class Activity 1.1a, students are learning the difference between experimental and theoretical probability with the activity, “How Many Green Tiles Are In Your Bag?” Students draw several tiles out of a bag and record the color each time. By using the tiles, students are able to make conjectures, as well as compare theoretical and experimental probability.

The Anchor Problem in chapter 7, “The Teacher Always Wins,” uses teacher-created colored number cubes to create data through a game between the students and the teacher. Students use the data collected from the game to analyze the probability of winning when using different colored cubes.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet the expectation that the visual design is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

• The student materials are clear and consistent between activities within a grade level as well as across grade levels.
• Each Class Activity and Homework is clearly labeled and provides consistent numbering for each investigation and problem set with both a lesson number and page number.
• The examples shown in the Textbook: Mathematical Foundation are consistently labeled and numbered within each section.

### Criterion 3f - 3l

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

The instructional materials for The Utah Middle School Math Project Grade 7 meet the expectations for supporting teachers’ learning and understanding of the standards. The instructional materials provide questions that support teachers in delivering quality instruction. The teacher’s edition is easy to use and consistently organized and annotated. The teacher’s edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.

### Indicator 3f

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

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

• Anchor Problem 4.0 focuses on making sense of quantities given and understanding their relationship to each other as students connect prior learning from 6th grade on determining the unit rate. The teacher notes guide the students’ mathematical development by prompting the teacher to, “Consider having students share out different strategies so that students can consider and respond to the strategies and arguments of others.”
• Class Activities are the guided lessons where a teacher facilitates students through conceptual, procedural, and application work. In Class Activity 4.2c, “Equations of Proportional Relationships,” the teacher notes state, “Students should see that in order to get the output, we multiply the input by the constant of proportionality. It will be more difficult for them to connect the unit rate to the equation, so you may wish to help them transform the equation to the one shown above.”

### 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.
2/2
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Indicator Rating Details

The materials for Grade 7 meet expectations for containing a Teacher Workbook that has ample and useful annotations and includes 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.

• The Teacher Workbook offers suggestions and annotations, labeled in red, on how to present the content.
• Chapter 8 Class Activity 8.1a: Suggestions are listed as to the ideas that should be discussed as students engage in the activity. The suggestions include, “Are all squares rectangles? Are all rectangles squares?” and “Relationship between perimeter and area: Discuss similarities and differences in how each is found.”
• There are suggestions occasionally placed as to common student mistakes and misconceptions that teachers could expect. In Chapter 3 Class Activity 3.2a, “Model and Solve Equations,” the teacher notes read, “It will be very helpful to change the problem to x + (−1) = 6 and continue this structure throughout. In this way we are always adding the additive identity. As problems become more complex, students often become confused with problems like 5x – 7 = −3; students will not know if they should add 7 or −7 or if they should subtract 7 or −7. Attend to precision.
• Scaffolding is provided as, "remind students that...” or “probe students to think..."
• A small number of links are embedded to assist in presenting the material. However, geometry software and graphing calculators are mentioned for students use.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet expectations for containing a Teacher Workbook that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

• Mathematical Foundations, written for each chapter, is a resource for teachers to understand the mathematics of the chapter and for teachers to expand their understanding of the mathematical concepts.
• Each Mathematical Foundations includes problems, explanations of problems, examples, and connections to CCSSM.
• The Teacher Workbook provides clear, step-by-step solutions.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet expectations for containing a teacher edition (in print or clearly distinguished and accessible as such 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 chapter contains an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior chapters and/or grades is explicitly called out in this section. The Prior Knowledge section for Chapter 8 states, “During their study of geometry in 6th grade, students should have learned that the height and base of an object are always perpendicular to each other. They will build on this understanding as they apply their knowledge of area and volume to real life contexts and as they explore cross sections and plane sections.”
• The teacher edition connects the learning from previous grade levels and explains how standards build on one another throughout the program. The chapter overview for Chapter 4 states, “Students will use proportions as a basis for understanding scaling. In 8th grade, proportions form the basis for understanding the concept of constant rate of change (slope). Also in 8th grade students will finalize their understanding of linear relationships and linear functions; proportional relationships studied in this chapter are a subset of these relationships.”

### 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
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Indicator Rating Details

The instructional materials for Grade 7 meet expectations for providing a list of lessons in the teacher edition (in print or clearly distinguished/accessible as such in digital materials), cross-referencing the standards covered, and providing a pacing guide on the estimated instructional time for each chapter.

• The materials provide an overview for each chapter that specifies the standards addressed in each chapter.
• Each chapter contains a Table of Contents that organizes the lessons into topics but does not state which lesson(s) align to each standard.
• Each chapter overview identifies the number of weeks for instruction.

### 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
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Indicator Rating Details

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

The parent manual for each chapter is available in PDF and Word files that can be downloaded. The manual contains general course information, questioning suggestions, keys for student success, content explanations, examples, and practice problems with answers aligned by topic and chapter.

### Indicator 3l

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

The instructional materials for Grade 7 do not contain explanations of the instructional approaches of the program and identification of the research-based strategies within the teaching materials.

There are no connections to research-based strategies within the lessons. There are chapter overviews and connections to content listed at the beginning of each chapter; however, these do not explain the program’s instructional approaches. They list what the students will be learning through the chapter.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
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Criterion Rating Details

The instructional materials for The Utah Middle School Math Project Grade 7 partially meet expectations for providing teachers resources and tools to collect ongoing data about student progress. There are no assessments that purposely identify prior knowledge within and across grade levels. There are some suggestions in the teacher materials that identify common misconceptions and errors, but there are no specific strategies to address these when they arise. Opportunities for ongoing review, practice, and feedback occur in various forms. Standards are identified that align to the section, and there is mapping of Standards to items for the Self-Assessments. There are opportunities for students to monitor their own progress.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
1/2
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Indicator Rating Details

The instructional materials for Grade 7 partially meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

While no explicit method for assessing students’ prior knowledge is used, there are some ways that the materials lead to gathering this information.

The teacher notes give suggestions on how to proceed with instruction when students may or may not have demonstrated mastery of a topic, however, there is no guidance on how to gather the information needed to determine mastery.

The Section 4.1 overview page (7WB4 - 13) is labeled at the bottom with an icon that reads, “Formative Assessment: Many lessons in this section are review from 6th grade. This is a good time to check for prior knowledge and assess skill deficits. Reducing the number of problems and/or combining lessons may be appropriate; however be sure that all skills/concepts are adequately covered in the selection of problems.”

There is an explanation for the meaning of the icon on the previous page (7WB4 - 5). It states, “This icon is used throughout the chapter offering suggestions on how to differentiate instruction. To learn more about the suggested strategies, see the supplemental document titled Differentiated Instruction.” This icon is found only in Chapter 4 of the Teacher Workbook materials.

### Indicator 3n

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

The instructional materials for Grade 7 partially meet expectations for identifying and addressing common student errors and misconceptions. Materials provide occasional suggestions for teachers to identify and address common student errors and misconceptions. Student misconceptions are often identified for the teachers, however, instructional plans to address these misconceptions are not detailed. The suggestions to address misconceptions consist of phrases such as, “Remind the students…, Discuss with students…, Point out that….”

Chapter 3, Class Activity 3.1d, Simplifying Algebraic Expressions with Models: “Attention will have to be paid to: a–(–b)=a+b and a–b=a+(–b). For example, #1 can be expressed as x – 2 or x + (–2); take time to discuss this.”

Chapter 5, Class Activity 5.1b, Building Triangles Given Three Measurements: “This (#1-3) is often difficult for students. It would be best to allow students to try them first alone (1-3 minutes) then confirm answers with another student before discussing as a class.”

### Indicator 3o

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

The instructional materials for Grade 7 meet expectations for providing opportunities for ongoing review and practice for students in learning both concepts and skills.

Over the course of each chapter, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support within the Class Activities to independent problem solving within the Homework. The Anchor Problems at the beginning of each chapter incorporate review and practice of previously taught standards.

• Chapter 1, Class Activity 1.3a, Teacher Note: “As you go through this lesson, repeatedly ask the students how much of the whole/original is left. This will help them transition to finding the percent change.”
• Anchor Problems engage students in both previously-taught standards as well as standards that are to be covered in the chapter. The Anchor Problems often guide the teacher to return to the problem while working through the concepts in the chapter. Anchor Problem 2.0: Operations on the Number Line, reads, “Ask students to justify their conjectures with viable arguments. Then give student groups the opportunity to communicate their reasoning. Return to this activity as you work through the chapter and ask students to reevaluate their conjectures.”
• Mathematical concepts are reinforced by an accompanying Homework component for each Class Activity that is designed for individual practice.
• The materials provide frequent opportunities for ongoing review and practice in the Spiral Review component located within the Homework. The Spiral Review consists of five questions from standards covered both from within the chapter and from previous chapters.
• Opportunities are provided for ongoing practice as extra lessons in a chapter. Chapter 6, Section 6.2e has a lesson labeled, “Extra Practice: Write and Solve Equations.” This lesson is treated separately as it does not contain the accompanying Homework lesson that do the Class Activities.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

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

The instructional materials for Grade 7 partially meet expectations for offering summative Self-Assessments for the students denoting which standards are being emphasized.

• Each standard that is being emphasized is noted within the “Concepts and Skills to be Mastered” at the beginning of each section.
• There are no summative assessments provided within the instructional materials. The assessments for this program consist solely of each section's Self-Assessment.
• Self-Assessments are developed to assess particular standards, and the scoring guidelines specifically use the wording of these standards.

### 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.
1/2
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Indicator Rating Details

The instructional materials for Grade 7 partially meet expectations for assessments including scoring guidelines that provide sufficient guidance to teachers in interpreting student performance but do not include suggestions for follow-up.

• Each Self-Assessment includes a scoring guideline, as well as worked-out solutions for correct responses.
• The scoring guidelines are easy to understand and interpret.
• Self-Assessment scoring guides are provided, but follow-up suggestions based on scoring criteria are not provided.

### Indicator 3q

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

The instructional materials for Grade 7 encourage students to monitor their own progress.

There is a Self-Assessment for students at the end of every section within each chapter. The directions to students are: “Consider the following skills/concepts. Rate your comfort level with each skill/concept by checking the box that best describes your progress in mastering each skill/concept. Corresponding sample problems, referenced in brackets, can be found on the following page.”

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
8/12
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Criterion Rating Details

The instructional materials for The Utah Middle School Math Project Grade 7 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. Activities provide students with multiple entry points and a variety of solution strategies and representations. However, the materials provide few strategies for ELL students, special populations, or to challenge advanced students to deepen their understanding of the mathematics.

### Indicator 3r

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

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

The sequencing and scaffolding are built into lesson development so that teachers pose problems as they progress through more rigorous processes or skills, however, if students need additional support, the guidance is not explicit.

The scaffolding guidance for Chapter 6, Class Activity 6.2a, “Write and Solve Equations for Word Problems 1,” reads, “You may want to model one or two of the problems below for students. Divide students into groups of 2 to 4. Give each group select problems for which to write a context. Have groups do selected problems and present their context to the class. Remaining problems should be homework. If you feel your class does not need practice drawing models, simply have them write the equation.” There are no strategies provided for students who may still need additional support.

Advanced students have “Honor” class extensions that involve more rigorous topics from later grades that can be used at teacher discretion, such as Class Activity 3.2a, Model and Solve Equations. The teacher notes state, “Discuss that the expression 2x + 1 was set equal to three different numbers, resulting in different values of the unknown x. Extension: Can you set 2x + 1 equal to any number? Will it always have a solution?” A question about the answer always having a solution leads into a discussion about no solutions or infinite solutions, which is an 8th grade standard.

### Indicator 3s

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

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

The Teacher Workbook includes limited notes providing strategies to help teachers sequence or scaffold lessons. The notes are concise, such as, "ask students" or "remind students of a definition."

Chapter 5, Class Activity 5.1a, “Triangles and Labels - What’s Possible and Why?” has a teacher note that reads, “In elementary school, students learned these terms. Remind students that triangles are classified by angle measure and/or side length. Also, recall that all equilateral triangles are isosceles.”

Chapter 3, Class Activity 3.1f, “Vocabulary for Simplifying Expressions” provides teachers with a more specific option to incorporate a Frayer Model into the lesson. The teacher note states, “You may want to create a Frayer model for the vocabulary terms. Above are 'examples' of the terms; ask students to provide non-examples of terms as well.”

### Indicator 3t

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

The instructional materials for Grade 7 meet expectations for frequently embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Tasks allow students to use multiple entry points and to solve problems using a variety of strategies, paths, and/or models. For example, the Anchor Problem for Chapter 6 involves negative and positive numbers on a number line. Students determine what equations are positive or negative, given the information on the number line. This problem requires students to make their own assumptions and simplifications.

Teachers are asked to model various solution strategies and to lead students through finding a solution path.

### 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
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Indicator Rating Details

The instructional materials for Grade 7 partially meet expectations for suggesting options for 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). Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners. The notes in the Teacher Workbook use suggestions like, "give students time to analyze..." or "remind students of a definition." The suggestions are not specific to the content being taught.

### Indicator 3v

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

The instructional materials for Grade 7 partially meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

• Extension problems are placed sporadically throughout the materials, however, it is unclear if extension problems are optional for the entire class, scaffolded for the class, or explicitly for students who need advanced mathematics. Chapter 7, Optional Class Activity 7.1f, “Free Throws or Monty Hall” (page 7WB7 - 34), the teacher notes state, “Discuss results as a class. Extension: How do your chances change, if you foul a person with a 50% free throw percentage? OR if your best three-point shooter has a 50% success rate. Which is better?”
• There are Optional Class Activities that do not include guidance around who would complete the activities or how a teacher would determine if it is appropriate to use. For example, Chapter 7, Optional Class Activity 7.1f, “Free Throws or Monty Hall” (page 7WB7 - 34). The directions do suggest having students only complete one of the two activities. This is followed with an Optional Homework Project: Mickey Match.

### Indicator 3w

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

The instructional materials for Grade 7 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

• No examples of bias was found.
• Pictures, names, and situations present a variety of ethnicities and interests. In Chapter 1, Class Activity 1.2e, a variety of ethnicities and interests are present throughout many multi-step problems. The examples include, “Juan earned money for creating a webpage for a local business. He used 1/2 of the money he earned for new shoes and 2/3 of the rest for music. He has \$20 left. How much money did he earn for his work?” “Mila rode in a bike tour across Utah. On one particular day, 40% of her ride was uphill. Of the rest of her ride, 1/3 was downhill and 2/3 was flat. If the flat portion of her ride was 36 miles, how far did she ride that day?” and “Marco’s football team was 20 yards from the goal when they got possession of the football. At the end of one play, they got halfway to the goal. After the second play, they made half that distance closer to the goal. After the third play, they got half the remaining distance. How far were they from the goal line before the fourth play?”

### Indicator 3x

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

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

• Some Class Activities and Anchor Problems are intended for cooperative learning groups, though there are no recommendations for forming groups or mention of why students work within a certain group size.

### Indicator 3y

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

The instructional materials for 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.

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

The instructional materials for The Utah Middle School Math Project Grade 7 provide limited support for the effective use of technology to enhance student learning. The materials are available for download online using Microsoft Word which would allow access from multiple operating systems. The suggested (optional) technology is intended to be used for students developing an understanding of the mathematical content. The technology provides limited opportunities to personalize instruction, and suggestions for customization are not provided. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.

### 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

The instructional materials for Grade 7 do not generally integrate technology, such as interactive tools or virtual manipulatives. Technology suggestions occur in conjunction with Geometry standards. There are directions for the students in Chapter 5, Class Activity 5.1b: "Building Triangles Given Three Measurements," that read, “Materials: GeoGebra and 5.2 GeoGebra files.” In Homework 5.1c, it says in the Teacher Notes, “Encourage students to use GeoGebra or a protractor and ruler.”

### 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
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Indicator Rating Details

The instructional materials for Grade 7 are available for download online using Microsoft Word which would allow access from multiple operating systems. There are no web-based portions in the core materials.

### Indicator 3ab

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

The instructional materials reviewed for Grade 7 are all paper and pencil based. The suggested (optional) technology is intended to be used for students developing an understanding of the mathematical content.

### 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
+
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 are not easily customizable for individual learners or users. Suggestions and methods of customization are not provided.

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
+
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 do not include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Report Published Date: 08/30/2017

Report Edition: 2017

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

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.

## Educator-Led Review Teams

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.

• 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.

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