## Alignment: Overall Summary

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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 8 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 8 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 8 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 4 Section 4.1- Students demonstrate their knowledge of 8.EE.8 by graphing or solving simultaneous, linear equations by substitution or elimination. Question 3 on the Self-Assessment states: “One equation in a system of linear equations is ???? = −2???? + 4. a. Write a second equation for the system so that the system has only one solution.”
• Chapter 5 Section 5.3- Students demonstrate their knowledge of 8.F.5 by analyzing and then describing a graph. Question 1 Concept 3 on the Self-Assessment states: “Below are two graphs that look the same. Note that the first graph shows the distance of a car from home as a function of time and the second graph shows the speed of a different car as a function of time. Describe what someone who observes the car’s movement would see in each case.”
• Chapter 8 Section 8.2- Students demonstrate their knowledge of 8.EE.4 by subtracting, adding, multiplying, and dividing numbers in scientific notation and then converting the answer to standard form. Question 2a on the Self-Assessment states: “Change the numbers below into scientific notation. 3,450,000,000.” Question 2c states: “Change the number given below into standard form. 6.03 x 108.”

### 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 8 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 80 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 8 meet the expectation for focus by spending a majority of class time on the major clusters of the grade including all clusters in 8.EE, 8.F, 8.GA, and 8.G.b. 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 80 percent of instructional time on the major clusters of the grade. The Grade 8 materials have 10 chapters that contain 164 lessons, which accounts for a total 33 weeks of class time including Anchor Problems and Self-Assessments.

• Grade 8 instruction is divided into 10 chapters. Approximately 8 out of 10 chapters (80 percent) focus exclusively on the major clusters of Grade 8, while the other 2 chapters focus primarily on supporting work that does not often support major work.
• Grade 8 instruction consists of 139 lessons. Approximately 131 out of 164 lessons (80 percent) focus on the major clusters of the grade.
• Grade 8 instruction is divided into 33 weeks. Approximately 24.5 out of 33 weeks (74 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 8 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 8 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 8.

• Chapter 6: Section 6.1 focuses on fitting a straight line to the scatter plot. Students then write a prediction function for the line of best fit and explain the meaning of the slope and y-intercept of the function in context. This work uses 8.SP.A to support 8.F.A and 8.F.B.
• Chapter 6: Section 6.2a and 6.2b uses 8.SP.A to support 8.EE through the use of trend lines and finding the line of best fit.
• Chapter 7: In Activity 7.1a 8.NS.A supports 8.G.B. Through creating squares of different areas, the idea of the Pythagorean Theorem emerges as the sides of a right triangle form three squares and the two sides of a right triangle place together equals the longest side square.
• Chapter 7: Activity 7.2a uses 8.NS.A to support 8.EE through students creating and solving expressions and equations based on powers and roots.
• Chapter 7: Section 7.3 8.NS.A is used to support major work as it focuses on rational and irrational numbers. Under Concepts and Skills to be Mastered, it lists, “Know that the square root of a non-perfect square is an irrational number,” which is a part of 8.EE.2.
• Chapter 10: This chapter links geometry with both number system and expressions and equations, 7.EE.4, as students write and solve Pythagorean Theorem equations where solutions are approximated.

### 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 8 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 165 days. According to the publisher, completing the work would take a total of 33 weeks. (There is some discrepancy in the material regarding Chapter 3. The Chapter overview states that the Chapter is designed for 4 weeks, but the title of the Chapter folder indicates 3 weeks.) Completing the work includes days for Anchor Problems, Class Activities, and Homework. 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 8 meet the criteria 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 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: The Section 1.1 Overview explains that Section 1.1 “involves a review of algebraic expressions.” The teacher notes emphasize this further, telling teachers that the first section is 7th grade material and to work through it faster with an honors class or assign it as homework. (page 8WB1 - 8)
• Chapter 2: “Students begin this chapter by reviewing proportional relationships from 6th and 7th grade, recognizing, representing, and comparing proportional relationships. In 8th grade, a shift takes place as students move from proportional linear relationships, a special case of linear relationships, to the study of linear relationships in general.” (page 8WB2 – 2)
• Chapter 3: “In Chapter 5 students will solidify the concept of function, construct functions to model linear relationships between two quantities, and interpret key features of a linear function. This work will provide students with the foundational understanding and skills needed to work with other types of functions in future courses.” (page 8WB3 - 2)
• Chapter 5: “This chapter builds an understanding of what a function is and gives students the opportunity to interpret functions represented in different ways, identify the key features of functions, and construct functions for quantities that are linearly related. This work is fundamental to future coursework where students will apply these concepts, skills, and understandings to additional families of functions.” (page 8WB5 – 2)

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 1, Math Textbook: “The first three chapters of grade 8 form a unit that completes the discussion of linear equations started in 6th grade and their solution by graphical and algebraic techniques.” (page 8MF1 - 1)
• Chapter 6, Class Activity 6.1a: “Problems 1 and 2 provide students with an opportunity to connect what they have learned in 6th/7th grade with what they will learn in 8th grade. Problem 1 is a review of 6th and 7th grade content where students learned to display and analyze univariate data. Students have learned…In 8th grade, students connect this learning with bivariate data.” (page 8WB6 - 10)

### 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 8 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 8 domain, with sections within the chapter focused 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.

• The Chapter 4 Overview reflects 8.EE.C (Analyze and solve linear equations and pairs of simultaneous linear equations) as students work with and “discuss intuitive, graphical, and algebraic methods of solving simultaneous linear equations; that is, finding all pairs (if any) of numbers (x, y) that are solutions of both equations.” (page 8WB4 - 2)
• In Chapter 5 Cluster 8.F.A students work with functions (define, evaluate, and compare functions). In Section 5.2 Explore Linear and Nonlinear Functions, students distinguish between linear and nonlinear functions given a context, table, graph, or equation. In Section 5.3 Model and Analyze Functional Relationships, the objective is to analyze functional relationships between two quantities given different representations.

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

• Chapter 3 Section 3.1 Classroom Activity 3.1f problems 1-6 include content from both 8.F.A and 8.F.B as students review the slope-intercept form of a linear equation and then use their understanding to model relationships between quantities. (page 8WB3 – 49)
• Chapter 5 Section 5.3 Classroom Activity 5.3a connects 8.F.A and 8.F.B. Students construct functions to model linear relationships while they are comparing properties of functions that are represented in different ways. (page 8WB5 - 76)

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

• Chapter 2 Section 2.3d-g connects 8.EE.5 and 8.F.A as students determine the rate of change from graphs. Students compare the rates of graphs, compare the steepness of several lines on the same graph, and relate the steepness of the lines to their rates of change. (pages 8WB2 - 84, 8WB2 - 85 & 8WB2 - 126)
• Chapter 8 Section 8.3 connects 8.EE.A and 8.G.C as students use square root and cube root symbols and evaluate square roots and cube roots while solving problems involving the volume of cylinders, cones, and spheres. (page 8WB8 - 72)

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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 8 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 8 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Each chapter/section starts with an Anchor Problem which poses a mathematical situation that students will learn to solve. Many of these are conceptual in nature and also provide explicit connections to prior knowledge. For example, Chapter 3 Anchor Problem 3.0: Solutions to a Linear Equation specifically refer to prior learning from Chapter 1 involving writing and solving linear equations with one variable. Students then move on to more complex linear equations as the activity guides them toward problems with infinite solutions and plotting ordered pairs on the coordinate plane. The Teacher Notes say, “Project the grid on the board and ask students to come up and plot an ordered pair that is a solution to the equation. They will soon see that the ordered pairs follow a pattern. Some students may even come up with solutions that include fractions. If not, ask them if there are solutions that fall between integer ordered pairs. Begin filling in all of these solutions as well. Soon a line will start to appear because all of the fractional solutions will start to 'merge' together.” The Teacher Notes emphasize developing understanding.

Many Class Activity problems involve hands-on activities or models. In Chapter 10 Homework 10.2a students use grid paper to draw squares adjacent to the given triangle sides showing a proof of the Pythagorean theorem.

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

Chapter 2 addresses 8.EE.B as students make the connection between proportional relationships, lines, and linear equations. Students explain, generalize, and connect ideas using supporting evidence; make and justify conjectures; compare information within or across data sets; and generalize patterns. Chapter 2 builds conceptual development as students make the connection between proportional relationships, lines and linear equations.

• The Section 2.1 Concepts and Skills to Master lists conceptual objectives for the students.
• "Graph and write equations for a proportional relationship and identify the proportional constant or unit rate given a table, graph, equation, or context."
• "Compare proportional relationships represented in different ways."
• Throughout Chapter 2 Class Activities and Homework, students are asked to identify correspondences between contexts, tables, graphs, and equations. Students explain, generalize, and connect ideas using supporting evidence (Question 10a, page 8WB2 - 13 and Question 2e-f, page 8WB2 - 46); compare information within or across data sets (Question 7, page 8WB2 - 19), and generalize patterns (2.2a Class Activity & Homework).
• A Teacher Note provides the following directive and explanation to assist teachers in engaging students in the conceptual understanding of the work: “Please refer to the Mathematical Textbook for Chapter 2, as this will help the teacher understand why it is important to approach Standard 8.EE.6 from the perspective that the slope is the same between any two distinct points on a line because of dilations. Transformational geometry is integrated with slope by understanding that a dilation produces figures with proportional parts. Right triangles that are formed from any two distinct points on a line are dilations of one another. Since they are dilations of one another they have corresponding parts that are proportional and parallel. This is why the rise/run ratio is the same from any of these triangles and thus the slope is the same between any two distinct points.” (page 8WB2 - 85)

Chapter 9 addresses 8.G.A.: Lessons develop conceptual understanding of translations, reflections, rotations, dilations, their properties, as well as their roles in determining if/when two figures are congruent, and if/when they are similar. Students examine preimages and images, use patty paper to perform reflections and rotations, use tables to record coordinates of images and preimages, describe transformations, draw figures congruent and/or similar to ones shown, and write coordinate rules for transformations shown. Properties of translations, reflections, rotations, and dilations are experimentally verified and compared/contrasted.

### 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 8 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.

• 8.EE.7: In Lessons 1.1a, 1.2a, 1.2b, and 1.2d students have opportunities to develop procedural skill and fluency in solving linear equations. Students work with rational numbers throughout. In the Homework students are tasked with problems that promote fluency, including being able to identify common mistakes (pages 8WB1 - 35 and 36). Throughout Chapter 1 and in other chapters in the grade (Chapters 3, 4, and 6), students are solving linear equations in one variable that includes rational coefficients. This leads them to fluency by the end of the year.
• 8.G.9: In the student content in Chapter 8, students are introduced to volume in a conceptual way, as they are asked to describe what volume is and its importance. Attention is given to 8.G.9 in Section 8.3. In Lessons 8.3b, 8.3c, and 8.3d, students find the volume of spheres, cones, and cylinders using the correct formulas. Students derive the equations for the volume of cones, cylinders, and spheres and practice problems related to them in Section 8.3. In Class Activity 8.3b Questions 7-12 and Homework Questions 1-6, students find the volume and/or missing measurement of each cylinder. In Class Activity 8.3c Questions 7-12 and Homework Questions 1-6, students find the volume and/or missing measurement of each cone. In Class Activity 8.3d8 - 13 and Homework 1-6 students are given the directions to find the volume and/or missing measurement of each sphere.

Note that there are no spiral reviews in Grade 8 to provide additional procedural skill and fluency practice.

### 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 8 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 multiple opportunities for application.

The materials incorporate Anchor Problems at the beginning of each chapter which provide students multi-step questions where they solve problems by using a variety of paths.

• In Anchor Problem 1.0 students use their own assumptions to model several situations mathematically. Students are directed to “(c)onsider the following situations. Then answer the questions below. Include any pictures, models, or equations you used to solve the problem and clearly explain the strategy you used.” For example, students explore the following situation: “Two students, Theo and Lance, each have some chocolates. They know that they have the same number of chocolates. Theo has four full bags of chocolates and five loose chocolates. Lance has two full bags of chocolates and twenty-nine loose chocolates. Determine the number of chocolates in a bag. Determine the number of chocolates each child has.” (page 8WB1 - 7)
• Chapter 4’s Anchor Problem, “Chickens and Pigs,” has multiple ways to solve (trial and error, a table, pictures or symbolic representations, and equations and graphs). There is flexibility for students in this contextual problem to apply their mathematical understanding. “A farmer saw some chickens and pigs in a field. He counted 30 heads and 84 legs. Determine exactly how many chickens and pigs he saw. There are many different ways to solve this problem, and several strategies have been listed below. Solve the problem in as many different ways as you can and show your strategies below.“ (page 8WB4 – 6)

In Grade 8, a specific standard and cluster that include application are 8.EE.8c and 8.F.B. Examples of problems that address these standards include:

• Chapter 4 "Who will win the race?" Class Activity and Homework is a multi-step problem leading to two linear equations in two variables that encourage students to use their own methods of problem solving so that there are multiple paths of entry. (8.EE.8c)
• In Chapter 4 Section 4.2 students solve simultaneous linear equations that have one, no, or infinitely many solutions using algebraic methods. For example, Homework 4.2e Question 4 asks the following: “Sarah has $400 in her savings account, and she has to pay$15 each month to her parents for her cellphone. Darius has $50, and he saves$20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have?” (8.EE.8c)
• In Chapter 2 students calculate the cost for attending the state fair and riding various rides given the costs for the fair and each ride. Students determine the total number of rides that can be be purchased, given a specific amount, and create a table and graph to represent the situation. (8.F.B)
• Chapter 5 Section 5.3 includes real-world contexts such as a height vs. time function, pennies earned per day, and the half-life of Carbon-14. (8.F.B)

### 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 8 meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separate. 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.

• Homework 3.1a provides a variety of problems for students to practice their procedural skill of writing equations in slope-intercept form.
• In Class Activity 9.1a students develop their conceptual understanding of translations by answering a variety of questions designed to illicit similarities and differences between the properties of translations.

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

• In Class Activity 4.2c (page 8WB4 - 44) students are first asked to solve, in any way they choose, a couple of contextual problems that can be modeled and solved using systems of linear equations. For example, “Carter and Sani each have the same number of marbles. Sani’s little sister comes in and takes some of Carter’s marbles and gives them to Sani. After she has done this, Sani has 18 marbles and Carter has 10 marbles. How many marbles did each of the boys start with? How many marbles did Sani’s sister take from Carter and give to Sani?” Students then determine the values of "shape-addends" that form two shape equation systems designed to match the contextual problems. This work is followed by more shape equation systems for students to represent algebraically and to solve using the elimination method. Students apply their understanding of the elimination method and develop procedural skills as they solve several systems of linear equations. In the final task students create a context for a given system, solve the system, and write the solution in a complete sentence.
• In Class Activity 1.1c students use models to solve linear equations by combining like terms. Students develop an understanding of like terms through the models leading to development of procedural skill. By the end of the lesson, students are asked to solve equations and verify their solutions.

### 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 8 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 8 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 listed in the beginning of the chapter and are also 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 3 Homework 3.1g Questions 1-4 ask students to "reason quantitatively" as they write equations from graphs of linear representations and then tell the story that relates to the equation (MP2). For example, “The graph below shows a trip taken by a car where x is time (in hours) the car has driven and y is the distance (in miles) from Salt Lake City. Label the axes of the graph. Use your graph and equation to tell the story of this trip taken by the car.”
• Chapter 4 Class Activity 4.2c highlights MP1 as students make sense of problems. The problem states: “Ariana and Emily are both standing in line at Papa Joe’s Pizza. Ariana orders 4 large cheese pizzas and 1 order of breadsticks. Her total before tax is $34.46. Emily orders 2 large cheese pizzas and 1 order of breadsticks. Her total before tax is$18.48. Determine the cost of 1 large cheese pizza and 1 order of breadsticks. Explain the method you used for solving this problem..” The Teacher Note also emphasizes that “there are a variety of ways to solve this problem” and gives examples of methods which reinforce the goal of students making sense and persevering in solving the problem as students can solve the problem many different ways.
• Chapter 5 Class Activity 5.1b, “The Function Machine,” asks students to “attend to precision” by figuring out the rule from a table of values. Students rely upon accurately calculating the values to figure out the rules (MP6).

### 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 8 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, in Chapter 4 Class Activity 4.2b and Homework, problems are heavily scaffolded and centered around using systems of equations. This does not give students an opportunity to engage in making sense of the problem or persevering in solving them.
• 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 6 Class Activity 6.1a: “In 10-13 above the adjacent angle pairs are also examples of supplementary angles. Are adjacent angles always supplementary? Why or why not?” The Teacher Notes add: “No, have students draw a counterexample.” “Also, begin to talk about simple equations. For example, #12 can be written as: B + 123 = 180 or 180 – 123 = B. In other words, you’re beginning to discuss modeling with mathematics.”
• 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 MP5. For example, in Chapter 3 Class Activity 3.1c students are told to graph each equation by hand and then use a graphing calculator to check their line.

### Indicator 2g

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

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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 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, in Class Activity 1.2c Questions 9-13 students are asked to “plot each fraction on the number line. Fill in the blank with &lt; , &gt; or = . How do you know your answer is correct? Justify your answer.”
• There are instances where students are asked to make conjectures. For example, in Chapter 5 Class Activity 5.1a Questions 1-3 the directions state: “Make a conjecture (an educated guess) about what kind of relationship makes a function and what disqualifies a relation from being a function.”
• Students are asked to engage in Error Analysis in some of the lessons. For example, in Chapter 10 Homework 10.2c Question 15 students identify the error in using the Pythagorean Theorem Formula to calculate the leg between hypotenuse and other leg. In the given solution, the error was in subtracting, instead of adding the area of the squares before finding the square root.

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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:

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Grade 8 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Grade 8 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 3aa - 3z

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

The instructional materials for The Utah Middle School Math Project Grade 8 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 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Grade 8 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Grade 8 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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.).
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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.).

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Grade 8 do not generally integrate technology, such as interactive tools or virtual manipulatives. Technology suggestions occur in conjunction with Proportional Relationship and Geometry standards.

In Chapter 2, Class Activity 2.3j, “Use Dilations and Proportionality to Derive the Equation y = mx + b” includes a Teacher Note at the end of the activity that reads, “Interactive lesson similar to the ones in derivations in this activity can be found at: http://learnzillion.com/lessons/1472-derive-ymx-using-similar-triangles http://learnzillion.com/lessons/1473-derive-ymxb-using-similar-triangles”

In Chapter 3, teachers are encouraged to allow students to use on-line graphing calculators to check their work with graphs.

In Chapter 9, the Teacher’s Notes explain that the chapter was written so that they could use pencil and paper, but that they could “choose” to use Geometer’s Sketchpad or GeoGebra.

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Report Published Date: 2020/09/03

Report Edition: 2019

## Math K-8 Review Tool

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

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

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

A University of Utah Partnership Project for 6th, 7th, and 8th Grade Math

http://utahmiddleschoolmath.org/

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

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

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

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

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

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

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

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

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

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