## Alignment: Overall Summary

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 meet expectations for alignment to the CCSSM. The materials meet expectations for Gateway 1: focus and coherence by assessing grade-level content, spending the large majority of instructional time on major work of the grade, being coherent with the progressions of the standards, and making meaningful connections between supporting and major work of the grade. The materials are viable for one school year and present all students with opportunities to engage in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials meet expectations for Gateway 2: rigor and the Mathematical Practices as they develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications, and do not always treat the three aspects of rigor together or separately. The materials partially attend to practice-content connections by attending to the full meaning of most of the mathematical practices. The materials do not attend to the full meaning of MP4 and MP5, and they do not assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## Gateway 3:

### Usability

0
22
31
38
29
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 6 meet expectations for focus and coherence. The materials do not assess topics before the grade level in which they should be introduced, spend at approximately 71% of class time on the major work of the grade, and are coherent and consistent with the Standards.

### Criterion 1a

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

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 meet expectations for assessing grade-level content. The materials do not assess topics before the grade level in which the topic should be introduced.

### Indicator 1a

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

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 meet expectations for assessing grade-level content. The assessments are aligned to grade-level standards.

There are multiple summative Self-Assessments within each unit that include a scoring rubric to help students identify their understanding of the concepts being assessed. All Self-Assessments have answer keys provided in the Teacher Workbook. Examples include:

• In Chapter 2, 2.2f, Problem 1 states, “How much chocolate will each person get if 3 people share $$\frac{1}{2}$$ a pound of chocolate equally? Complete the following to answer this question. $$\frac{1}{2}÷3=$$ ____ because ____ $$× 3 =\frac{1}{2}$$.” (6.NS.1)
• In Chapter 3, 3.1j, Problem 2 states, “Construct a number line to show the location of the integers from -8 to 8. Explain how you used ideas about symmetry and opposites to construct your number line.” (6.NS.6)
• In Chapter 4, 4.2f, Problem 2 states, “Find and interpret the mean, median, and mode for each set of data below. Then determine which measure of center best represents the data. Be sure to justify your answer. Number of sit ups: 78, 86, 86, 96, 90, 71, 110, 102, 92, 80, 106, 100.” (6.SP.2)
• In Chapter 6, 6.2i, Problem 5 states, “Write the expression 6x + 42 as the product of two factors.” (6.EE.3)

There are no Self-Assessments for Chapter 0: Fluency and Chapter 5: Geometry.

### 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 6 meet expectations for students and teachers, using the materials as designed, devoting the majority of class time to the major work of the grade. The materials spend approximately 71% of class time on the major work of the grade.

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Grade 6 meet expectations for spending a majority of class time on the major clusters of the grade. The instructional materials contain chapters which identify the total number of weeks for instruction. Within each chapter are sections consisting of multiple Class Activities (lessons). While the materials do not specify the total number of days, some Class Activities include a statement that they may take multiple days. There are 105 Class Activities in Grade 6.

• The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 4 out of 7 chapters, which is approximately 57%.
• The number of Class Activities devoted to major work of the grade (including assessments and supporting work connected to the major work) is 75 out of 105 Class Activities, which is approximately 71%.
• The number of weeks devoted to major work of the grade (including assessments and supporting work connected to the major work) is 18 out of 28, which is approximately 64%.

Class Activities are the best representation of the amount of class time spent on major work of the grade, and supporting work connected to major work of the grade as it includes all lessons. Thus, approximately 71% of instructional time is spent on 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 6 meet expectations for being coherent and consistent with the Standards. The materials connect supporting content to enhance focus and coherence, are consistent with the progressions of the standards, foster connections at a single grade where appropriate, and include extensive work with grade-level problems to meet the full intent of grade-level standards.

### Indicator 1c

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

The instructional materials reviewed for Utah Middle School Math Grade 6 meet expectations for 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.

Examples of supporting content connected to the major work of the grade include:

• In Chapter 0.2e, the Class Activity connects supporting cluster 6.NS.B to major cluster 6.EE.A, as students use the GCF and the Distributive Property to find equivalent expressions. In Question 5 students, “Use the distributive property to find all the equivalent expressions for each sum given. Circle the expressions that contain a factor that is the GCF of the two addends in the original sum. Check and see if this expression follows the same principle as the expressions with the GCF from the numbers 1 and 2 above, a. 45 + 60, b. 42 + 70, c. 20 + 60.”
• In Chapter 1.1c, Homework connects supporting cluster 6.NS.B to major cluster 6.RP.A, as students use ratio reasoning to solve problems. In Question 1, students determine “The ratio of sugar to flour used in a sugar cookie recipe is 1 cup sugar to 2 cups flour. Determine the amount of each ingredient needed to double, triple, quadruple, and half the recipe.”
• In Chapter 2.2d, Homework connects supporting cluster 6.NS.B to major cluster 6.NS.A, as  students divide fractions by fractions using the ability to fluently find common multiples. In Question 1, students determine “How many halves fit into three-fourths?”
• In Chapter 5.1b, Class Activity connects supporting cluster 6.G.A to major cluster 6.EE.A, as students use a formula to find the area of parallelograms. In Question 4, students “Describe in words and write a formula to find the area of any parallelogram.”

### 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 Utah Middle School Math Grade 6 meet expectations that the amount of content designated for one grade-level is viable for one school year.

According to the publisher, each chapter has a designated amount of time spent in weeks. There is no guidance from the publisher on the suggested length of daily work including Class Activities, Homework, Self-Assessment, and Anchor Problems.

The guidance for length of daily work is generalized in the overall time for the length of the unit. According to the Mathematical Foundations for Chapter 0, it is intended to “be inserted into the natural flow of the course where appropriate.” Since the publisher did not indicate a number of weeks for Chapter 0, the review team allocated two weeks for Chapter 0. Therefore, the following units are assigned the following number of weeks:

• Chapter 0: 2 weeks
• Chapter 1: 4 weeks
• Chapter 2: 5 weeks
• Chapter 3: 4 weeks
• Chapter 4: 6 weeks
• Chapter 5: 3 weeks
• Chapter 6: 4 weeks

The total number of 28 weeks in the materials would be equivalent to an average of 140 days (28 weeks x 5 days/week) of instruction including assessments.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Grade 6 meet expectations for being consistent with the progressions in the Standards.

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. Content from prior and future grade levels is identified in the Connections to Content section found at the beginning of each chapter. Examples include:

• In Chapter 2, Chapter Overview, Connections to Content, Future Knowledge states, “In Chapter 6 of this text, students will learn how to write and solve equations to represent the different types of percent problems studied in this chapter. In 7th grade, students will continue to focus on proportional relationships, learning how to set up and solve a proportion to solve percent problems, including problems involving discounts, interest, taxes, tips, and percent increase and decrease.”
• In Chapter 3, Chapter Overview, Connections to Content, Future Knowledge states, “In Grade 7, students will learn to operate with positive and negative rational numbers. In Grade 8, the number system is expanded to include irrational numbers. Students come to understand that irrational numbers are points on the real number line even though they cannot be represented with an exact decimal value.”
• In Chapter 6, Chapter Overview, Connections to Content, Future Knowledge states, “In 7th grade, students will encounter expressions with positive and negative rational numbers. As coursework progresses, students will write expressions to model different types of functions such as exponential and quadratic functions. Being able to examine numeric expressions and identify abstract patterns is an important part of being able to write explicit rules to model a function. In later grades, students will see more complex equations.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Examples include:

• In Chapter 2, 2.2d Homework, Questions 1-8, students solve word problems involving division of fractions. Students are instructed to “Create a model of your choice to answer the questions below. Then, write a number sentence to represent the problem.” Question 1 states, “How many halves fit into three-fourths?” (6.NS.1)
• In Chapter 4, 4.1a Homework, Questions 1-6, students determine if a question is a statistical question. The materials state, “Yesterday, Ruth and Carl invited 10 friends to go out to lunch. The questions below came up during the meal. Decide whether or not each question is a statistical question, and justify your decision.” Question 1 states, How much does each person’s meal cost?” Question 3 states, “Would Carl rather have burgers or pizza?” (6.SP.1)
• In Chapter 5, 5.1a Class Activity, students solve 14 questions as they find the area of figures in square units. Question 7 states, “Gloria is painting a feature wall in her bedroom. The dimensions of the wall measure 14 feet by 11 feet. The gallon of paint she purchased will cover 400 square feet. Does she have enough paint to do two coats on the wall? Justify your answer.” Students also complete a Homework activity with an additional 9 questions. For example, Question 6 states, “How many 4-inch square tiles are needed to cover a table that measures 24 inches by 40 inches? Draw and label if needed.” (6.G.1)
• In Chapter 6, 6.1c, Class Activity 3 contains questions for students to write algebraic expressions for each phrase. Activity Three states,  a.“The sum of a number $$n$$ and twenty. b. The sum of twenty and a number $$n$$. c. Four less than a number $$c$$.” (6.EE.2)

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of explicit language from the Teacher Edition Workbook for teachers to use include:

• In Chapter 2, Chapter Overview, Connections to Content, Prior Knowledge states, “In this chapter students draw on their work with ratio from Chapter 1 as they explore the meaning of percent – a part to whole ratio with a whole equal to 100. They express parts of a whole using fraction, decimal, and percent notation. To do this, they construct models learned previously (area models, including hundred grids, tape diagrams, double number lines, tables, etc.). Students know how to express a fraction as a decimal by creating an equivalent fraction with a denominator of 10 or 100 (4.NF). Students will rely on their ability to operate fluently with rational numbers (5.NF and 6.NS). Students use understanding of a rational number, $$\frac{a}{b}$$, as both a groups of $$\frac{1}{b}$$ (3.NF and 4.NF) and $$a÷b$$ (5.NF). Students have also used models to divide whole numbers by unit fractions and unit fractions by whole numbers (5.NF). They will build on this knowledge to divide fractions by fractions.”
• In Chapter 5, Chapter Overview, Connections to Content, Prior Knowledge states, “In previous grades students have investigated writing and solving simple equations. Working with area and volume provides a context for developing and using these equations. Students have also classified triangles and quadrilaterals and have developed an understanding of their properties and relationships. They have also learned how to graph points in the coordinate plane. In 3rd grade they recognize area as an attribute of plane figures and investigate concepts of area measurement. In 4th grade they apply area formulas to real-world and mathematical problems. Volume is studied in 5th grade where students learn to recognize it as an attribute of solid figures and investigate concepts of volume measurement.”
• In Chapter 6, Chapter Overview, Connections to Content, Prior Knowledge states, “In previous grades, students worked with the properties of operations with whole numbers, fractions, and decimals. In 5th grade, students learned how to use whole number exponents to represent powers of ten. Students have been writing numerical expressions throughout their elementary course work. Additionally, students have been writing and solving equations, representing the unknown with question marks, boxes, and letters.”

### 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 Utah Middle School Math Project Grade 6 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The instructional materials include learning objectives that are visibly shaped by CCSSM cluster headings. Examples of chapter and section headings shaped by cluster headings include:

• In Chapter 1, Section 1.1: Representing Ratios and Section 1.2: Rates, Graphs, and Equations are visibly shaped by cluster 6.RP.A, understand ratio concepts and use ratio reasoning to solve problems.
• In Chapter 2, Section 2.2: Division of Fractions is visibly shaped by cluster 6.NS.A, apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• In Chapter 3, Section 3.1: The Symmetry of the Number Line, Section 3.2: Absolute Value and Ordering, and Section 3.3: Negative Numbers in the Real World are visibly shaped by cluster 6.NS.C, apply and extend previous understandings of numbers to the system of rational numbers.
• In Chapter 6, Section 6.2: Writing, Simplifying, and Evaluating Algebraic Expressions and Section 6.3: Equations and Inequalities in One Variable are visibly shaped by cluster 6.EE.B, reason about and solve one-variable equations and inequalities.

Examples of problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important include:

• In Chapter 1, Homework 1.2g connects major cluster 6.RP.A to major cluster 6.EE.B as students write equations to represent proportional relationships. Question 2 states, “Jack and Carol both submitted drawings for the cover of the yearbook. The student body voted on whose drawing will be on the cover. For every vote Jack receives, Carol receives three. a. Complete the table to show the relationship between votes for Jack, votes for Carol, and total votes. b. Write an equation that shows the relationship between votes for Jack, j, and votes for Carol, c. c. Write an equation that shows the relationship between votes for Jack, j, and total votes, t.”
• In Chapter 2, Homework 2.2d connects major cluster 6.EE.B to major cluster 6.NS.A as students write and solve equations using rational numbers requiring a fraction divided by a fraction. Question 6 states, “Lisa has $$\frac{3}{4}$$ of a cup of sugar; it’s $$\frac{1}{2}$$ of what she needs. How much sugar does she need?”
• In Chapter 4, Class Activity 4.2d connects supporting cluster 6.SP.B to supporting cluster 6.NS.B as students perform operations with decimals to find measures of central tendency. Question 11a states, “Find the mean, median, and mode for each set of data. Round your answer to the nearest hundredth. 13.22, 11.05, 10.77, 15.04, 12.3, 12.89, 14.7, 16.3, 13.9.”
• In Chapter 5, Class Activity 5.1d connects supporting cluster 6.G.A to supporting cluster 6.NS.B as students use decimal calculations to find the area of trapezoids. Question 5c states, “Find the area of each trapezoid.” A trapezoid is shown with bases of 8.5 units and 11.5 units and a height of 7 units.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 meet expectations for rigor and the mathematical practices. The materials attend to each of the three aspects of rigor individually and also attend to balance among the three aspects. The materials emphasize mathematical reasoning and partially attend to practice-content connections by attending to the full meaning of most of the mathematical practices. The materials do not attend to the full meaning of MP4 and MP5, and they do not assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 meet expectations for reflecting the balances in the Standards and helping students to meet the Standards’ rigorous expectations. The materials help students develop and demonstrate conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications. The materials do not always treat the three aspects of rigor together or separately.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include Anchor Problems, Class Activities, and Homework that develop conceptual understanding throughout the grade-level. There is one Anchor Problem at the beginning of each chapter. The Class Activities are question sets for teachers to guide student discussion and learning. The Homework questions are assigned as independent work for students. Examples that elicit conceptual understanding include:

• In Chapter 2, 2.2a Class Activity introduces students to the concept of dividing fractions using models and equations (6.NS.1). Class Activity 4 states, “You have $$\frac{1}{2}$$ of a pizza left over from dinner last night. You invite two friends over and the 3 of you share the leftover pizza. What portion of a whole pizza will you each be getting? Solve using a model and an equation.”
• In Chapter 3, 3.0 Anchor Problem states, “Create a model to represent the elevations of the locations shown in the table. You may need to create another number line to zoom in on the elevations of Badwater Basin, Furnace Creek, Beatty Junction, and Stovepipe Wells. Students can think of it as magnifying that portion of the graph to better distinguish the points.” (6.NS.6)
• In Chapter 5, 5.4a Class Activity introduces drawing nets to help students calculate the surface area of three-dimensional figures (6.G.4). Question 2 states, “Draw a net for the “Family Size” cereal box shown. Try to draw the net differently than you do for the cereal box described in number 1 [previous question]. Be sure to label all the dimensions.”
• In Chapter 6.1a, Class Activity, students generate as many expressions as they can to represent different scenarios, then simplify the expressions to determine whether they “work” or “don’t work,” (6.EE.3). Question 2 states, “Carmen has 420 tickets to spend at the prize counter at an arcade. She buys 3 packs of Nerds that cost 50 tickets each. How many tickets does Carmen have left?” Students complete a table with the headings Expression, Simplified Form, Does It Work, and Ideas.

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. In the Homework assignments, students complete conceptual problems independently that are similar to the conceptual exercises done with teacher guidance and support in the Anchor Problems and Class Activities. This independent practice reinforces their conceptual understanding. Examples where students independently demonstrate conceptual understanding include:

• In Chapter 1, 1.1a Homework, Question 2, students “Write three different ratio statements about the picture below. Use words like ‘to’, ‘per’, ‘for every’, ‘each’, and ‘ratio’. Consider the relationship between birds and branches and also the relationship between birds and body parts of a bird. For example, ‘Each bird has two wings.’” (6.RP.1)
• In Chapter 2, 2.2c Homework, students “solve each problem using the model of your choice.” Question 3 states, “Sasha has 18 yards of string for her kite; it’s one and half times what she needs. How much string does she need?” (6.NS.1)
• In Chapter 3, 3.2a Homework, Question 1, students “Use the number line below to answer the questions. a. Is the value of A positive or negative? b. Is the distance from zero to A positive or negative? Explain.” (Students use a number line with 0 in the middle. A is located to the left of 0.) (6.NS.7c)
• In Chapter 6, 6.3h Homework, students “1) Write an inequality to represent the situation. 2) Create a number line diagram to represent the situation. 3) Give two values that make the inequality true. Make sure your values make sense in the problem.” Question 1 states, “A minimum of three people need to show up for a workout class for the instructor to hold class.” Question 2 states, “A maximum of 45 people can be in the school library at one time.” (6.EE.8)

### 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 Utah Middle School Math Project Grade 6 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level. Chapter 0 is specifically dedicated to fluency in Grade 6. The Section 0.1 Overview states, “This section specifically addresses a student’s ability to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.” In the Section 0.2 Overview, the first Class Activity focuses on, “divisibility rules...being able to draw upon them makes working with factors and multiples much easier for students, especially when dealing with larger numbers.” The Section 0.3 Overview states, “students build upon their knowledge of operations with multi-digit whole numbers and extend similar reasoning to multi-digit decimals.”

Examples of procedural skill and fluency developed throughout the grade-level include:

• In Chapter 0, 0.1b Class Activity, Part 3, Questions 1-8, students “Estimate each quotient. Then use the standard algorithm to find the exact quotient. 1. $$14\lceil322$$, 2. $$12\lceil5484$$, 3. $$115\lceil8625$$, 4. $$205\lceil21115$$, 5. $$20\lceil361$$, 6. $$41\lceil4970$$, 7. $$352\lceil6890$$, 8. $$6\lceil108.75$$.” (6.NS.2)
• In Chapter 0, 0.3d Class Activity, Question 7 states, “$$13.6 + 901.15$$.” (6.NS.3)
• In Chapter 6, 6.1c Class Activity, Activity 2, Question J states, “Equivalent or Not? $$4n + 2n$$ and $$(4 + 2)n$$.” (6.EE.A)
• In Chapter 6, 6.2a Class Activity, Part I, Activity 4 states, “Simplify the expression. If the expression is already simplified, write ‘already simplified’. There are 26 expressions for students to simplify. For example, Question h states, “$$3(7x)-10x$$.” (6.EE.A)

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level. Examples include:

• In Chapter 0, 0.1b Homework, Questions 5-14, students “Estimate each quotient. Then use the standard algorithm to find the exact quotient. Express remainders as decimals. 5. $$\frac{78}{6}$$, 6. $$\frac{352}{16}$$, 7. $$\frac{540}{18}$$, 8. $$\frac{49815}{405}$$, 9. $$\frac{578}{32}$$, 10. $$\frac{4635}{45}$$, 11. $$\frac{6996}{212}$$, 12. $$\frac{1018}{72}$$, 13. $$\frac{326}{8}$$, 14. $$\frac{40613601}{4263}$$.” (6.NS.2)
• In Chapter 0, 0.2e Homework, students “Use the distributive property and the GCF to write an equivalent expression for each given sum. In Question 5, “$$16 + 36$$.” (6.EE.A)
• In Chapter 1, Spiral Review, Question 2, students answer, “What is $$108 ÷ 8$$?” (6.NS.2)
• In Chapter 3, Spiral Review, Question 3, students “Write an equation to show the relationship between number of pies p and cups of cherries c.” (6.EE.A)
• In Chapter 4, Spiral Review, Question 1a, students calculate, “$$25 ÷ 4$$.” (6.NS.2)
• In Chapter 6, 6.1c Homework, students “Write an algebraic expression for each phrase. A number j increased by four.” (6.EE.A)

### 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 Utah Middle School Math Project Grade 6 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level. Both routine and non-routine applications are found in the Anchor Problems and Class Activities for students. Routine applications are also found in the Homework questions for students.

The materials provide multiple opportunities for students to engage in routine applications of mathematics. Examples include:

• In Chapter 3, 3.3b Class Activity, Activity 7 states, “In February of 2011, Nowata, Oklahoma experienced a 110-degree rise in temperature over a 7-day period. On February 10, 2011, the low temperature was -31℉, the coldest temperature ever recorded in Oklahoma. On February 17, 2011, the temperature at one point during the day was 110 degrees hotter than the temperature on February 10, 2011. What was the high temperature on February 17, 2011 in Nowata, Oklahoma?” (6.NS.5)
• In Chapter 5, 5.2c Class Activity, Question 2 states, “A coordinate grid represents the map of a city. Each square on the grid represents one city block. a. Heather’s apartment is at the point (5, 7). She walks 4 blocks south, then 8 blocks west, then 4 blocks north, and then finally 8 blocks east back to her apartment. How many blocks did she walk total? Describe the shape of her path. Mark and label her apartment and highlight her walk.” (6.G.3)

The materials provide multiple opportunities for students to engage in non-routine applications of mathematics. Examples include:

• In Chapter 1, the Anchor Problem states, “Two gears are connected as shown in the picture below. The smaller gear has 8 teeth and the larger gear has 12 teeth. a. Find a way to determine the number of revolutions the small gear makes based on the number of revolutions the large gear makes. Organize your results. a. If the smaller gear makes 24 revolutions, how many revolutions will the larger gear make? b. If the larger gear makes 20 revolutions, how many revolutions will the smaller gear make? c. If the smaller gear makes 24 revolutions, how many revolutions will the larger gear make? d. If the larger gear makes 1 full revolution, how many revolutions does the smaller gear make? e. If the smaller gear makes 1 full revolution, how many revolutions does the larger gear make? f. Create four different representations of the relationship between the number of revolutions the large gear makes and the number of revolutions the small gear makes. Make up a question that can be answered using each representation.” (6.RP.3)
• In Chapter 6, Alternative Anchor Problem, Part 1 states, “The side length of a square is unknown. Write an expression for the perimeter of the square. Write an expression for the area of the square. Write an expression to show the perimeter of 3 copies of the square. Assume the squares are not touching. Write an expression to show the area of 3 copies of the square. The side length of the square from above is tripled. Write an expression for the new perimeter of the square. Compare the perimeter of the new square to the perimeter of the original square. Write an expression for the new area of the square. Compare the area of the new square to the area of the original square.”

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

• In Chapter 0, 0.3d Homework, Question 20 states, “Seth wants to buy a new skateboard that costs $167. He has$88 in the bank. a. If he earns $7.25 an hour pulling weeds, how many hours will Seth have to work to earn the rest of the money needed to buy the skateboard?” (6.NS.3) • In Chapter 1, 1.1e Homework, Question 1 states, “Students in Mrs. Benson’s gym class are voting on whether the next sport they learn how to play should be basketball or soccer. The tape model shows the results of the survey. a. If there are 35 students in Mrs. Benson’s gym class, how many voted for soccer? Solve this problem using at least two different methods. Explain the methods you used and how they are related.” (6.RP.3) • In Chapter 5, 5.4b Homework, Question 7 states, “Carly and Nadia are painting their bike ramp. They have one quart of paint which will cover 100 ft2. Do they have enough paint to do the two coats? Justify your answer.” (6.G.4). • In Chapter 6, 6.3j Homework, Question 1 states, “Iya sells friendship bracelets for$4. Write and solve an inequality to represent the number of bracelets Iya needs to sell to make at least $150?” (6.EE.8) ### Indicator 2d Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently in the materials, and multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples of where the materials attend to conceptual understanding, procedural skill and fluency, and application independently include: • Conceptual Understanding: In Chapter 4, 4.2c Class Activity, Question 1 states, “Carly’s teacher says that the center of this data is the balance point. Discuss with a neighbor what you think she means by this. Then draw a triangle under the dot plot where you think the balance point is.” (6.SP.3) • Procedural Skills and Fluency: In Chapter 6, Spiral Review, Question 1, students “Write an algebraic expression for each phrase. a. Twice the sum of a number n and 5. b. The sum of twice a number n and 5. c. The sum of twice a number n and ten.” (6.EE.A) • Application: In Chapter 2, 2.2d Class Activity, Activity 4, students apply their knowledge of division of fractions to real-world situations. Students “create a model of your choice to answer this question. Then, write a number sentence to represent the problem.” Question c states, “Josephine has run 7.5 miles, which is $$\frac{2}{5}$$ of her training distance for the day. How far was she planning on running today?” (6.RP.3) Examples where two or three of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials include: • In Chapter 0, 0.3b Class Activity connects all three aspects of rigor. In Part 1, Question 4, students engage in conceptual understanding as they “Assume the side length of the large square is 0.1. What is the area of the large square? What is the side length of a small square? What is the area of the small square?” In Part 3, Question 4, students solve real-world problems using procedural skills, “You work part time at a bookstore and get paid$12.05 per hour. In the entire month of March you worked 78.25 hours. How much money did you make in March?”
• In Chapter 4, 4.3d Class Activity, students engage in conceptual understanding of box plots and data, use procedures to find the Interquartile Range, and apply their understanding and skills to determine how the data best fits the discussion. Question 1 states, “The three box plots below represent the test scores for three different classes. Examine each plot and then discuss the questions that follow. a. What is the same about these box plots and what is different? b. Find the IQR for each plot and use it to compare the variability of each set of class scores. c. Make an argument for each class that supports the claim that this class performed the best on the test.” (6.SP.3-5)
• In Chapter 5, 5.3a Class Activity, Question 10 connects conceptual understanding and procedural skills as students “make a prediction about which rectangular prism below has the greatest volume, which one has the smallest volume? Find the volume of each prism to check your predictions.” (6.G.2)

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 partially meet expectations for practice-content connections. The materials attend to the full meaning of most of the mathematical practices. The materials do not attend to the full meaning of MP4 and MP5, and they do not assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

### 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 Utah Middle School Math Project Grade 6 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade-level.

Examples of the Standards for Mathematical Practice (MPs) being clearly identified in two ways include:

• At the beginning of each chapter, there is a section labeled “Standards of Mathematical Practice.” This section provides an explanation about how the MPs are applied specifically in the chapter, and includes an example problem the students will see later in the materials.
• In the Anchor Problems and Class Activities, the MPs are identified by icons that match the MPs at the beginning of the chapter.

Examples of the MPs being used to enrich the mathematical content:

• MP1: In Chapter 4, Standards for Mathematical Practice states, “The example problem given shows how students must make sense of practical problems and turn them into statistical investigations. They must make sense of what statistical arguments can be made about the data. They must determine what statistical measures might be used to support their arguments and how to go about finding them. Throughout the solving process, students must stop and evaluate their progress.”
• MP2: In Chapter 2, 2.2c Class Activity, Activity 1a states, “Eli has 8 pints of ice cream. It’s $$\frac{2}{3}$$ of what he needs. How much does he need? Draw a model of your choice to answer this question. Then, write a number sentence to represent the problem.” Students decontextualize a fraction model to quantitatively reason with fractions.
• MP4: In Chapter 0, 0.3a Class Activity states, “Marta has created the model below. She claims that this model can be used to represent the sum of 24 and 38. 1. If Marta’s claim is true, what is the value of the small square? 2. What is the value of a rod (long rectangle)? 3. Find the sum of 24 and 38 using the addition algorithm and discuss how this relates to the model above.” Students create a model that represents the sum of numbers and could be used to solve other problems.
• MP5: In Chapter 1, Standards for Mathematical Practice states, “Throughout this chapter, students are exposed to a variety of tools that can be used to represent ratio relations and solve real world problems. These tools include concrete manipulatives such as tiles and chips, pictures, tape diagrams, tables, graphs, and equations. The chapter starts with more concrete tools then progresses into tools that are more abstract. For example, students start by modeling ratio relations with chips and tiles (concrete), then pictures (pictorial), and then tape diagrams (abstract). They understand that these all show the same relationship but more abstract representations can be more efficient and flexible for solving problems. They make connections between the different tools. For example, they consider patterns in tables and on graphs. They understand that an equation shows the explicit relationship between two variables given in a table.”
• MP6: In Chapter 4, 4.1b Class Activity states, “When creating data displays it is so important to attend to the precision of labeling your model so that all the information that the model presents is clearly understood.” Question 7 states, “Marta records the high temperatures for each day she goes swimming in the month of August. She has recorded her data on the dot plot below. a. Marta did not label her dot plot with units or a title. Determine the appropriate units for this data and how the data was collected. Then give the dot plot an appropriate title.”
• MP7: In Chapter 3, 3.2a Class Activity, Activity 8 states, “This problem requires students to make sense of the structure of the ordered pairs. Devise a strategy for finding the distance between two points without graphing. Then, find the distance between the two points. a. (3,157) and (3, 84).”
• MP8: In Chapter 6, 6.1d Class Activity, Question c states, “Marin has 50 tickets to spend on rides at a carnival. Each ride takes 6 tickets. Write different expressions to represent the number of tickets Marin has left based on the number of rides she goes on.”

### 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 Utah Middle School Math Project Grade 6 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of two MPs.

Examples of the materials attending to the full meaning of the MPs include

• MP1: In Chapter 5, 5.3d Class Activity, Question 4 states, “Gloria is planning on pouring a set of concrete cement steps on the side of her front porch. She has drawn out a diagram of the steps below where the “rise” and “run” of each step is equal. a. Determine the total amount of cement she will need for the steps. Assume that angles that appear to be right angles are right angles. Students use the understanding that you need to subdivide the steps into composite figures that you can find the volume of as an entry point for solving this problem. The total volume is the sum of the composite volumes. This explanation acts as a ‘road map’ for solving the problem, rather than just jumping right into making calculations that they do not understand.”
• MP2: In Chapter 5, 5.1b Class Activity, Question 4 states, “Describe in words and write a formula about how to find the area of any parallelogram. Throughout this chapter students generalize methods for finding area and volume of polygons and 3D objects into formulas. As students develop these formulas they decontextulize as they move from finding the area or volume of one specific shape or object to finding the area or volume any of these given shapes or objects.”
• MP6: In Chapter 6, 6.3a Class Activity, students “Evaluate the expressions when $$r=12$$, $$s=2$$, and $$t=5$$. $$4t^2 + 3t^2$$. $$5r - s^3 + 2$$. $$\frac{(t - s)}{r}$$. When evaluating expressions with exponents there are many details for students to consider. In the first expression, what is the operation between the 4 and $$t^2$$? Do I multiply $$t$$ by 4 and then square the result or do I square $$t$$ first and then multiply the result by 4? What does it mean to square a number? Am I following the order of operations? Do I know and understand the different grouping symbols? Am I computing correctly, particularly when fractions and decimals are involved?”
• MP7: In Chapter 4, 4.2b Class Activity, students analyze, “The most recent test scores for Mr. Petrov’s science class are shown in the table. Make a dot plot of the data. Be sure to label your number line and give it a title. b. How many students are in Mr. Petrov’s science class? c. Which test score was earned by the largest number of students? d. Describe any peaks, clusters, or gaps in the data by marking them on the plot. e. What is the overall shape of the data? Justify your answer. f. Mr. Petrov asks, ‘What is the most typical score for this test?’ Use the distribution of data to answer this question. Students use structure when analyzing the shape of a data distribution. While identifying peaks, clusters, gaps, skewness, symmetry, and outliers students infer more knowledge about the characteristics of the data. While looking at shape is not numerical structure it is graphical structure and being able to identify what that structure infers about the data is imperative in its analysis.”
• MP8: In Chapter 4, 4.2e Class Activity, Question 5, students determine “What does the shape of the data distribution tell you about which measure of center to use to summarize the data?” Additional prompting for teachers includes, “After students have analyzed the shape and center of a series of data distributions they begin to understand through repeated reasoning that generally if the shape of the data is fairly symmetrical then the mean is a good measure of center. If the shape of the data is skewed or there are significant outliers, then a good measure of center is the median. Similarly, it is through repeatedly analyzing the shape, center, and spread of several data distributions that they begin to understand how to interpret data, make meaningful conclusions, and answer statistical questions.”

The materials do not attend to the full meaning of MP4 and MP5. Examples include:

• MP4: In Chapter 1, 1.2a Class Activity, Activity 1 states, “Harmony runs 6 miles per hour. How far can Harmony run in 1 hour? 2 hours? 3 hours? 4 hours? Organize your results in the table below.” Additional information for teachers includes, “A model that is commonly used to represent ratios where the units of measure are different is a double number line diagram. We can use the model below to represent the problem about Harmony.” Students do not engage with the full intent of MP4 as the models (tables, number lines) are provided.
• MP4: In Chapter 6, 6.2b Class Activity, Question b states, “the following are area models that can be used to represent the number 50. Under each area model, fill in the blanks to write an expression for the area model shown. 5(__) = 50, 5(__+__) = 50, 5(__) +5 (__) = 50, 15 + 35 = 50.” Students do not engage with the full intent of MP4 as they fill in the blanks of an expression for a picture of an area model instead of applying the mathematics they know.
• MP5: In Chapter 4, 4.2c Class Activity, Question 1 states, “Carly wants to know how long her friends can do a handstand. She asks two of her friends to do a handstand. One friend can do a handstand for 9 seconds, her other friends can only do a handstand for 1 second. She records their times on the dot plot below. 1. Carly’s teacher says that the center of this data is the balance point. Discuss with a neighbor what you think she means by this. Then draw a triangle under the dot plot where you think the balance point is.” Students do not choose and use tools strategically as the tools and strategies are provided.
• MP5: In Chapter 5, 5.4a Class Activity, Question 5 states, “Draw a line to match each solid with its net.” Additional information provided for teachers in the Mathematical Practice Standards section includes, “You can explore nets with online interactive manipulatives as you investigate the problem above. Online tools for viewing 3D objects and their nets can really help students that have difficulty visualizing how an object and its net are related. These tools bring this relationship to life as students can see how the faces, edges, vertices, etc correspond to each other between a 3D object and its net.” Students do not choose and use tools strategically as the tools and strategies are provided.

### Indicator 2g

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

### 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 Utah Middle School Math Project Grade 6 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples from the Student Edition Workbook for prompting students to construct viable arguments include:

• In Chapter 0, 0.3b Class Activity, Question 2 states, “Dallin has begun to do the following multiplication problem. His work is shown below; he does not know where to place the decimal point in the product. Correctly place the decimal point for him and justify your answer.”
• In Chapter 3, 3.1b Homework, Question 5a states, “The number line below shows the location of 2.5. Explain a method for representing −2.5 on the number line.”
• In Chapter 4, 4.3d Class Activity, Question 1c states, “The three box plots below represent the test scores for three different classes. Examine each plot and then discuss the questions that follow. Make an argument for each class that supports the claim that this class performed the best of the test.”

Examples from the materials for prompting students to analyze the arguments of others include:

• In Student Edition Workbook, Chapter 0, Mathematical Practice Standards, MP3, students solve, “Roxy’s cashier has made some calculations for some of the purchases at the candy store and has made some mistakes, his work is shown below. For problems 5, 6, and 7 go through each transaction and determine the mistake, explain how to perform the calculation correctly and fix the mistake.” Additional information for students includes, “Throughout this appendix, you will find several problems that take on the form of ‘Find, Fix, and Justify.’” For these problems students analyze another student’s work and must identify mistakes in the work. They make arguments as to why something is wrong by pointing out explicit errors observed. Once they fix the mistake they must justify why their reasoning is correct.
• In Student Edition Workbook, Chapter 3, 3.1d Class Activity, Activity 3, Problem 20 states, “Will said, ‘The opposite of the opposite of a number is sometimes positive.’ Is Will’s statement true or false? Explain.”
• In Chapter 5, 5.3c Class Activity, Question 8, “Olivia claims that where s is the side length of a cube is the formula you should use to find the volume of a cube. Harrison claims that the correct formula is where l is the length, w is the width, and h is the height of the cube. a. Who is correct? Why or why not.”

There are a few instances where the MP3 icon is noted in the instructional materials, but students do not engage in MP3 in those questions. Examples include:

• In Chapter 3, 3.1i Class Activity, Activity 1d states, “Write three true statements based on the diagram. For example, ‘All team sports are sports.’”
• In Chapter 6, 6.2a Class Activity, Activity 7a states, “Explain what each word means. Use examples and non-examples to support your ideas. Term, Constant, Coefficient, Like Terms

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
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Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Examples include:

• In Chapter 4, 4.2d Class Activity, Question 10 states, “As students critique the reasoning of others in the problem below, they must identify the mistakes of others. The mistakes represent common misconceptions that students may have when finding the median.”
• In Chapter 6, 6.1a Class Activity states, “Encourage students to consider the arguments of their classmates and ask clarifying questions if they think an expression is incorrect or they think the expression given does not correspond to the way the student thought about the problem. Students will see that correct expressions simplify to the same value while incorrect expressions do not simplify to correct value. Once students have given the different expressions they came up with, put up any expressions from the teacher manual key that students did not come up with (some are incorrect and highlight common errors) and ask students if they think the expressions are correct. Then, simplify the expressions to verify.”

Examples of the materials not assisting teachers in engaging students with constructing viable arguments and analyzing the arguments of others include:

• In Chapter 1, 1.1a Class Activity, Question 14 states, “Sophia’s teacher asked her to create a pattern using only circles and squares so that the ratio of circles to total shapes is 2:5. Sophia created the following pattern. b. Is Sophia’s pattern correct? Justify your answer.” The teacher guidance includes, “Sophia’s pattern is not correct. Sophia created a pattern in which the ratio of circles to squares is 2:5 (or the ratio of circles to total shapes is 2:7).” The teacher guidance provides the correct answer and information about student errors, but it does not assist teachers in engaging students to construct or analyze arguments.
• In Chapter 3, 3.1b Class Activity, teachers “remind students to always start at 0 and work their way out.” Question 1 statess, “Mrs. Henderson asked her students to create a number line to represent the integers from −6 to 6. The work of five different students is shown below. Circle the names of the students who created a correct number line. For the number lines that are incorrect, explain the error.” Additional guidance for the teacher includes, “Emma’s number line represents a common error. Students graph 1 – 6, working from left to right. Then, they graph −1 to −6, also working from left to right. Remind students to always start at 0 and work their way out.” While the teacher guidance does provide reminders and information about student errors, it does not assist teachers in engaging students to construct or analyze arguments.
• In Chapter 3, 3.2b Class Activity, Question 39 states, “Ms. Tucker tells her class that a and b are rational numbers and $$a<b$$. Describe what would have to be true about the values of $$a$$ and $$b$$ for the following statements to be true. Justify your answers.” The teacher guidance includes, “it may help students to have a number line available to work through this problem.” This does not assist teachers in engaging students in MP3.
• In Chapter 5, 5.1d Class Activity, Question 12 states, “Of the polygons shown, which have equal areas? Explain how you know.” The teacher guidance includes, “As students work, teachers should be on the lookout for alternate approaches. Students could be asked to share their approach with the class, or different approaches could be highlighted in something like a gallery walk.” This does not assist teachers in engaging students in MP3.

### 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 Utah Middle School Math Project Grade 6 meet expectations for explicitly attending to the specialized language of mathematics.

Examples of the materials providing explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols include:

• At the beginning of each chapter, in the Student and Teacher Edition Workbooks, there is a list of academic vocabulary for the chapter.
• In the Mathematical Foundations book, accurate mathematical language is explained to assist teachers in the presentation of materials.
• In Chapter 3, Section Overview 3.3, Negative Numbers in the Real World states, “The first lesson is focused on the vocabulary associated with positive and negative quantities.” Concepts and Skills to Master are listed for teachers. The first concept includes “use and interpret academic vocabulary used to describe situations with positive and negative quantities.”
• In Chapter 6, 6.1c Class Activity, Activity 3, students “write an algebraic expression for each phrase.” In the Teacher’s Edition, additional guidance for the teacher states, “Students will likely need a review of the following vocabulary: sum, difference, product, and quotient. Have students underline key words. When a phrase starts out as ‘the sum of’, ‘the difference of’, ‘the product of’, or ‘quotient of’ students should look for the word and – it helps to identify the different parts of the expression - the addends (addition), the minuend and subtrahend (subtraction), the factors (multiplication) and the dividend and divisor (division).”

Examples of the materials using precise and accurate terminology and definitions when describing mathematics, and support students in using them, include:

• In Chapter 1, 1.2g Class Activity, Activity 2 states, “Marcus is training for an ultra-marathon where he will be running 100 miles. He can run 7 miles per hour. a. Complete the table below to show the relationship between time and distance for Marcus.” The Teacher’s Edition includes, “when appropriate, introduce the vocabulary dependent variable and independent variable. The decision as to which quantity is the dependent variable and which quantity is the independent variable is usually interchangeable and is driven by the question being asked.”
• In Chapter 3 Academic Vocabulary includes, “number line, whole number, positive number, negative number, integer, rational number, line symmetry, opposites, scale, quadrant, origin, x-axis, y-axis, absolute value, greater than, less than, deposit, withdrawal, debit, credit, ascend, descend, profit, loss.”
• In Chapter 5, 5.4b Class Activity, Question 3, students “explain in your own words what surface area is and how to find the surface area of a three-dimensional object.”
• In Chapter 6, 6.0a Class Activity, Frayer charts/models are provided so students can create a reference for each property (Commutative Property, Associative Property, Additive Identity Property of Zero, Multiplicative Identity Property of One and Distributive Property). The materials state, “At the start of the chapter, fill out the chart with the definition in words and symbols and any examples and notes that would be helpful at the time. Then, refer to the reference sheet and continue to add examples and notes when you come across a problem in the chapter that relies on one of the properties.”

## 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 reviewed for The Utah Middle School Math Project Grade 6 meet expectations for being well designed and taking into account effective lesson structure and pacing. The materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations 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 for the chapter. The chapters are sectioned into Class Activities, Homework, Spiral Reviews, and Self Assessments.

Typically, each Class Activity has problems that teachers guide students through as a class. Occasionally, problems are intended to review previous grades’ concepts in order to connect them to Grade 6 concepts. Most often, Class Activities are for the students to apply new learning. The mathematical concepts in each Class Activity are reinforced by accompanying Homework components.

### 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 reviewed for Utah Middle School Math Project Grade 6 meet expectations that the design of the 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 concepts learned throughout the year.

The progression of lessons is intentional and assists students in building their mathematical understandings and skills. 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 reviewed for Utah Middle School Math Project Grade 6 meet expectations for having a variety in what students are asked to produce.

Throughout the Class Activities, students 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 providing an explanation of a solution and including a diagram. Examples include:

• In Chapter 2, 2.1d Class Activity, students produce a variety of work in relation to fractions, decimals and percents. Question 1 states, “$$\frac{3}{5}$$ of the 6th grade class at a certain school own a cell phone. a. Make a tape diagram to represent this situation. b. What percent of the students own a cell phone? c. What percent of the students do not own a cell phone? d. What is the ratio of students who own a cell phone to the ratio of students who do not own a cell phone? e. If there are seventy-five 6th graders at this school, how many own a cell phone?”
• In Chapter 3, 3.1a Homework, Problems 1-3, students make a model (number line), explain their method, and provide answers. The materials state, “In the space below, construct a number line showing the integers from −5 to 5. Explain the process you used to create your number line. What steps did you take? What tools did you use? How many points are 3 units away from 0 on your number line? Explain.”

### 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 reviewed for Utah Middle School Math Project Grade 6 meet expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models.

Although the use of manipulatives is limited, teachers are given general guidance, other options, and explanations on how to connect the manipulatives to written methods. Examples include:

• In Chapter 1, 1.0 Anchor Problem, Connected Gears, Question c. states, “If the smaller gear makes 24 revolutions, how many revolutions will the larger gear make? If the smaller gear makes 24 revolutions, the larger gear will make 16 revolutions.” The teacher notes state, “Again, students can use a variety of strategies including manipulatives, tape diagrams, partial tables, and numeric methods.”
• In Chapter 6, 6.2e Class Activity, Activity 3 states, “Prior to doing this lesson, you may want to introduce students to the algebra tiles if you plan to use them in the lesson. Depending on your students, you may choose not to use the physical tiles and move right into having students draw pictures and models to represent the problems.”
• In Chapter 5, students “can explore nets with online interactive manipulatives as you investigate the problem above.” Additional guidance for teachers includes, “online tools for viewing 3D objects and their nets can really help students that have difficulty visualizing how an object and its net are related.” Using physical 3D shapes and nets, in addition to viewing them on a 2D platform, could assist students in visualizing nets and 3D objects.

### Indicator 3e

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 include a visual design that is not distracting or chaotic and supports students in engaging thoughtfully with the subject. Examples include:

• The student materials are clear and consistent between activities within the grade level.
• Each Anchor Problem, Class Activity, Spiral Review, Self Assessment, and Homework are clearly labeled and provide consistent numbering for each problem set with a chapter and page number.
• The examples shown in the Mathematical Foundations book 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 reviewed for The Utah Middle School Math Project Grade 6 meet expectations for supporting teacher learning and understanding of the Standards. The materials contain: support for planning and providing learning experiences with quality questions; ample and useful notations and suggestions on how to present the content; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development. Examples include:

• In Chapter 1, 1.0 Anchor Problem, students investigate ratios and determine that the quantities in a ratio are connected. The teacher notes guide the students’ mathematical development by prompting the teacher in a variety of ways. For example, “You may want to show students animations of gears to make sure they know how gears work. Ask questions such as, ‘If the smaller gear is rotating clockwise, which direction will the larger gear rotate?’ ‘If you turn the larger gear one full rotation, does the smaller gear make one revolution, more than one revolution, or less than one revolution?’”
• Class Activities are the guided parts of lessons where a teacher facilitates students’ work. In Chapter 6, 6.3j Class Activity, teachers guide students in their understanding of inequalities. For example: “In this lesson, students are making sense of problems, asking the following questions: What are the constraints in the given situation? When I solve for the inequality, what answers make sense in the context? For example, in problem 2 below, it does not make sense to order part of a pizza based on the way the problem is set up. In #10, students need to think realistically about the degree of precision someone will use when cutting fabric or paper.”

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for containing a Teacher Edition Workbook that has useful annotations and includes suggestions on how to present the content in the student edition. Where applicable, materials include teacher guidance to support and enhance student learning. The Teacher Edition Workbook offers suggestions and annotations, labeled in red, on how to present the content. Examples include:

• In Chapter 2, 2.1f Class Activity states, “This lesson is intended to introduce students to three different types of percent problems: 1) Find a percent given a part and the whole; 2) Find a part of a quantity given a percent and the whole; 3) Find the whole given a part and a percent. Students have already practiced changing a fraction to a percent in the previous lessons (e.g., Express $$\frac{15}{20}$$ as a percent). These types of problems are included again here so that students can compare the different types of percent problems.”
• In Chapter 5, 5.1a Class Activity, guidance is included to help students graph regular and irregular shapes on graph paper and use graphs to determine the area. The materials state, “Encourage students to share their reasoning and different methods for finding the area with each other. As students try to find the area of each figure, they must recognize that they can decompose different parts of the figure in order to recompose them into whole square units that they can count. As they do this they must step back and shift their perspective of how to view a square unit of area.”

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for containing a Teacher Edition 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. Examples include:

• Each chapter resource list contains a Mathematical Foundations book, a resource to help teachers understand the mathematics of the chapter and to expand their understanding of the mathematical concepts.
• Each Mathematical Foundation book includes problems, explanations of problems, examples, and connections to prior and future work, and CCSSM alignment.
• The Teacher Edition Workbook provides clear, step-by-step solutions to problems.

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for containing a digital Teacher Edition Workbook that explains the mathematics in the context of the overall mathematics curriculum throughout the grades. Each chapter contains a Connections to Content section where teachers gain an understanding of the mathematical content in the lessons as well as where the content fits in the scope of mathematics from Kindergarten to Grade 12. Knowledge required from prior chapters and/or grade is explicitly identified in this section. Examples include:

• In Chapter 5, Prior Knowledge states, “In 3rd grade they recognize area as an attribute of plane figures and investigate concepts of area measurement. In 4th grade they apply area formulas to real-world and mathematical problems. Volume is studied in 5th grade where students learn to recognize it as an attribute of solid figures and investigate concepts of volume measurement. This prior work with area and volume help them to develop competencies in shape composition and decomposition and form a foundation for understanding the formulas for area and volume and the coordinate plane.”
• The Teacher Edition Workbook connects the learning in Grade 6 to future grade levels and explains how standards build on one another throughout the program. For example, in Chapter 2, Connections to Content states, “In Grade 7, students move from concentrating on analysis of data to production of data. They understand that good statistical answers depend on a well-developed plan for collecting data. They investigate random sampling, and in turn, concepts related to probability. In 8th grade, students extend their knowledge of shape, center, and spread to the analysis of bivariate data, (collection of counts with 2 variables or characteristics) as related to their work with linear functions.”

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 provide 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. Examples include:

• 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 identify which lesson(s) align to specific standards.
• Each Chapter Overview identifies the number of weeks for instruction for the entire chapter.

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 contain strategies for informing parents or caregivers about the mathematics program and give suggestions for how they can help support 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 do not contain explanations for 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. The list contains information the students learn throughout the chapter.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
5/10
+
-
Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project do not meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The materials do not provide strategies to gather information on students’ prior knowledge opportunities, partially provide opportunities for addressing common student errors and misconceptions, and partially offer summative Self-Assessments for students and rubrics and guidance for teachers to interpret student performance and suggestions for follow-up. The materials do provide opportunities for ongoing review and practice for students and encourage students to track their own progress.

### Indicator 3m

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 do not meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

There are no explicit methods or strategies for assessing students’ prior knowledge. The materials mention prior knowledge that should be known throughout the activities. However, there is no guidance nor strategies provided on how to gather the information about students’ prior knowledge within and across grade levels. Examples include:

• In Chapter 0, 0.1a Class Activity states, “This task gives students the opportunity to review what they know about operations with multi-digit numbers. It also allows the teacher to assess their students' understanding of how the algorithms for these operations work. In 4th and 5th grade students performed operations with multi-digit whole numbers and with decimals to hundredths. They used strategies based on place value, the properties of operations, and/or the relationship between inverse operations to find sums, differences, products, and quotients.”
• In Chapter 1, Chapter Overview states, “In this chapter, students build on their understanding of multiplication and division from earlier grades. Models such as arrays and area models and an understanding of the distributive property, concepts from 3.OA, are helpful tools for finding equivalent ratios. Students will rely on their fraction sense and operations with fractions, 5.NF, to determine and iterate unit rates. In 5.G, students graphed points in the first quadrant which will help them to plot equivalent ratios.”
• In Chapter 4, Chapter Overview states, “In this chapter, students build on their knowledge and experience in data analysis developed in previous grades.” The explanation continues, “as students continue to expand their knowledge in data analysis, they begin to characterize data distributions by measures of shape, center, and spread.”

### Indicator 3n

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 partially meet expectations for identifying and addressing common student errors and misconceptions. Student misconceptions are identified for the teachers in the Find, Fix, and Justify problems; 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…” Examples include:

• In Chapter 4, 4.1b Class Activity, Find, Fix, and Justify, Question 12 states, “Penelope thinks that each dot represents one yellow flower and the quantity on the number line is the number of vases. The correct statement is that 4 vases have 13 yellow flowers. On the plot, each dot represents the number of vases and each quantity on the number line is the number of flowers.”
• In Chapter 5, 5.1a Class Activity, Find, Fix, and Justify, Question 9 states, “Antonia has overlapped the two rectangles within the figure. If she multiplies 10 by 22, then she will need to subtract 10 feet from 25 feet to get the length of the other rectangle. The correct calculation is: $$10×22 + 15×15 = 220 + 225 = 445$$. Antonia will need 445 square feet of grass sod.”

### Indicator 3o

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 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. Examples include:

• Anchor Problems engage students in standards that are to be taught in the chapter. The Anchor Problems often guide the teacher to return to the problem while working through the concepts in the chapter. In Chapter 4, Anchor Problem 4.0 states, “This anchor problem should be revisited throughout the chapter as students gain more knowledge of how to analyze and interpret the shape, center, and spread of a data distribution.”
• 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 located with the Homework. The Spiral Review consists of problems from standards covered both from within the chapter and from previous chapters. For example, in Chapter 4, Spiral Review includes review questions on the following concepts: multiplying, adding, and subtracting decimals, measurement conversions and finding volume. Examples include: “1. $$5 × 3.21$$, 6. $$5 + 0.682 - .03$$, 11. 54 inches = ____ ft, 13. Find the volume of a rectangular prism that has a length of 7 inches, a width of 5 inches, and a height of 9 inches.”

### Indicator 3p

Materials offer ongoing formative and summative assessments:
Narrative Evidence Only

### Indicator 3p.i

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 partially meet expectations for offering summative Self-Assessments for the students denoting which standards are being emphasized. Examples include:

• Each standard that is emphasized is noted within the “Concept 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
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 partially meet expectations for assessments including scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. Examples include:

• 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Utah Middle School Math Project Grade 6 encourage students to monitor their own progress.

There is a Self-Assessment for students at the end of every section within each chapter. Student directions include, “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
+
-
Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 6 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The materials provide strategies to help teachers sequence and scaffold lessons, offer tasks with multiple entry points, and provide a balanced portrayal of various demographic and personal characteristics. The materials include partial guidance in meeting the needs of a range of learners, including advanced learners, and limited guidance for using a variety of grouping strategies. The materials do not offer supports and accommodations for English Language Learners and special populations or encourage teachers to draw upon students’ home language and culture to facilitate learning.

### Indicator 3r

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 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. Examples include:

• In Chapter 1, Section 1 Overview provides assistance for teachers, “As students progress, their pictures often become more abstract. For example, a student may draw 5 circles (of the same size) to represent the three cups of flour and two cups of sugar. Another way to illustrate a ratio is to draw a tape diagram. A tape diagram is simply a rectangle composed of smaller, equal-sized pieces to represent each of the smaller parts of the ratio. For the ratio of 3 cups of flour to 2 cups of sugar, a tape diagram would look like Figure 1.”
• In Chapter 2, 2.1b Class Activity, teacher guidance includes, “Refer to the Anchor Problem Part 1 to help students to make sense of what they are being asked to do. If they are trying to express a part as a decimal, the whole is equal to 1. If they are trying to express the part as a percent, the whole is 100. Once they have identified the value of each box, they can use repeated reasoning to determine the value of the shaded portion of the grid.”
• In Chapter 4, 4.4b Class Activity, Question 4, students determine “what possible arguments could Roman give to his principal that on average at least 40 candy bars are sold from the vending machine each day?” Guidance for teachers includes, “assess how much guidance your students might need to answer the question above. You can provide them with a series of discussion questions to scaffold their thinking. Possible discussion questions are below.” Questions include specific direction for students to determine answers from the histogram.

### Indicator 3s

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners. The Teacher Edition Workbook provides teachers with limited strategies for meeting the needs of a range of learners. Examples include:

• In Chapter 3, 3.1e Class Activity, “In this lesson, students rely on several of the ideas studied so far in the chapter including the structure of the number line and different ways of scaling number lines. In the first few problems, students are determining the value of opposites. Finding the positive value first is usually the easiest way to approach these problems. As the problems progress, this scaffolding is taken away.”
• In Chapter 6, 6.3g Homework, “These problems become more challenging toward the end. Differentiate as needed for your students.”

### Indicator 3t

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for frequently embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. Class Activities and Homework provide tasks that include multiple entry points that can be solved using a variety of strategies or representations. Examples include:

• In Chapter 5, 5.1a Class Activity, “As students try to find the area of each figure, they must recognize that they can decompose different parts of the figure in order to recompose them into whole square units that they can count. As they do this they must step back and shift their perspective of how to view a square unit of area.”
• In Chapter 6, 6.0 Anchor Problem, “A local charity has a benefit to raise money. You are on the planning committee and have been tasked to determine the number of tickets that must be sold for the charity to raise at least \$5,000 after all expenses have been covered.” The materials also list different information students will need while working on the problem. Students work with decimals, fractions, expressions, equations and inequalities. Because this problem involves so many components, there are multiple entry-points for a student to make sense and solve the problem.

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 do not meet expectations for suggesting 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). The materials do not suggest support, accommodations, or modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

### Indicator 3v

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 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. Examples include:

• In Chapter 5, 5.4b Class Activity, Challenge Extension states, “What is the surface area of a hexagonal pyramid with the same dimensions of the shade, if the perpendicular distance from the edge of the base hexagon to its center is 6.93 in?”
• In Chapter 6, 6.3j Class Activity, Question 2b states, “In an accelerated math class, you may wish to explore compound inequalities. This situation would be described by the following compound inequality: $$0 ≤ p ≤ 7.5$$where p is a whole number.”

### Indicator 3w

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 meet expectations for providing a balanced portrayal of various demographic and personal characteristics, and no examples of bias were found. Examples include:

• Pictures, names and situations present a variety of ethnicities and interests. In Chapter 2, 2.2a Class Activity, Question 4 states, “Eduardo is painting a mural depicting the beauty of the four seasons in his neighborhood. He wants to divide the spring portion ($$\frac{1}{4}$$ of the mural) into 4 equal parts showing graduation activities, planting of gardens, melting of snow, and children playing outside. What portion of the mural will depict graduation activities?”
• In Chapter 5, 5.1a Class Activity, Problem 9, Antonia is wearing a head wrap.

### Indicator 3x

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

The instructional materials reviewed for Utah Middle School Math Project Grade 6 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 reviewed for Utah Middle School Math Project Grade 6 do not encourage teachers to draw upon home language and culture to facilitate learning. There is no evidence of teachers drawing 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 reviewed for The Utah Middle School Math Project Grade 6 do not integrate technology and are paper-and-pencil based with no web-based portions, but materials are available to download using multiple internet browsers, and there is suggested optional technology for developing students’ understanding of mathematical content. The materials do not include opportunities to personalize learning for students or opportunities for teachers and/or students to collaborate with each other.

### 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 reviewed for Utah Middle School Math Project Grade 6 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 reviewed for Utah Middle School Math Project Grade 6 are entirely 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 Utah Middle School Math Project Grade 6 are not easily customizable for individual learners or users. Suggestions and methods of customizations 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 Utah Middle School Math Project Grade 6 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 reviewed for Utah Middle School Math Project Grade 6 do not generally integrate technology, such as interactive tools or virtual manipulatives. Technology suggestions occur in conjunction with Geometry standards. Directions in the Teacher Edition Workbook include:

• In Chapter 5, 5.1d Class Activity states, “There are many online interactive tools that show how to find the area of any trapezoid. Consider using the following resources in your class.”
• In Chapter 5, 5.4a Class Activity states, “You can explore nets with online interactive manipulatives as you investigate the problems below. Some online interactives can be found at the links provided.
abc123

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.

## Math K-8

K‑8 Evidence Guide K‑8 Review 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.