## Alignment: Overall Summary

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and the materials connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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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
38
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 Math Expressions Grade 5 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

### Criterion 1a

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

### 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.
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 5 meet expectations that they assess grade-level content.

The assessments are aligned to grade-level standards and do not assess content from future grades.  The Grade 5 Assessment Guide includes a Beginning of Year Test, Middle of Year Test, End of Year Test, and tests for each Unit. Each Unit Test includes multiple choice, multiple-select, short answer, constructed response, and a separate performance task assessment.  The materials include a form A and form B assessment for each unit.

Digitally available assessments are PARCC and Smarter Balanced aligned practice tests. Each digital platform includes a variety of practice tests. Digital assessments assess grade-level content.

Examples of on-grade level assessment items include:

• Unit 1, Form B, Item 16, “It takes Juan's family 3 3/4 hours to drive to his grandparents’ house. That is 1 7/10 hours longer than it takes them to drive to his aunt’s house. How long does it take Juan’s family to drive to his aunt’s house?” (5.NF.1)
• Unit 4, Form B, Item 10, “Find the products: $$47\times10^1, 47\times10^2, 47\times10^3$$” (5.NBT.1, 5.NBT.2)
• Unit 7, Form A, Item 5, “Select the expression that represents dividing 6 by n and then subtracting 8. Mark all that apply.” (5.OA.2)
• Grade 5, Middle of Year Test, Item 18, “Latasha planted a fern tree in her yard that measured 1/3 meter tall. When she measured the tree a month later, it was 3/4 meter tall. How much did Latasha’s tree grow?” (5.NF.2)
• Grade 5, End of Year Test, Item 23, “A rectangular garden has a width of 2 2/3 yards. The length of the garden is 2 yards. What is its area?” (5.NF.4b.)
• Grade 5, PARCC Test Prep: Standard 5.NF.B.5a Practice Test, Item 5, “Stuart rode his bicycle 6 3/5 miles on Friday. On Saturday he rode 1 1/3 times as far as he rode on Friday. On Sunday he rode 5/6 times as far as he rode on Friday. Which statements are correct? Mark all that apply.” (5.NF.5a)

### 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.
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

### Indicator 1b

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 8, which is approximately 75%.
• The number of Big Ideas, CCSSM clusters, devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 20 , which is approximately 75%.
• The number of lessons devoted to major work (including assessments and supporting work connected to the major work) is approximately 101 out of 111, which is approximately 91%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each unit.  As a result, approximately 91% of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

### Indicator 1c

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of connections between supporting work and major work include the following:

• In Unit 1, Lesson 10, students answer questions based on a given line plot (5.MD.B) supporting their work with operations on fractions (5.NF.A). The Student Activity Book includes an application problem, “Every week, Mr. Park asks for about 1 pound of potato salad at the deli. The line plot shows the actual weight of the salad the deli worker has given him for the past several weeks. What is the difference between the greatest and least width shown on this graph?”
• In Unit 3, Lesson 13, students answer questions from given line plots (5.MD.B) supporting their work with operations on fractions (5.NF.A). “Six students slept 8 1/2 hours. What total number of hours do these six values represent?” “Hala can ride her bike 7 1/2 miles in an hour. How far will she ride in 2/3 hours? How far will she ride in 1/3 of an hour?” “Mr. Dayton uses 8 cups of flour to make three identical loaves of bread. How much flour is in each loaf?”
• In Unit 8, Lesson 9, addresses supporting standard 5.MD.A, convert like measurements within a unit system, to support standard 5.NBT.A, understand the place value system. Students convert metric units using multiplication and division including decimals. Students complete real world problems requiring students to use metric conversions to determine the answer. Student Activity Book problem 14, “Erin’s water bottle holds 665 milliliters. Dylan is carrying two water bottles. Each one holds 0.35 liters. Who is carrying more water? How much more?”

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 150 days. The Pacing Guide can be found on page I18 in the Teacher Edition. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.

• The program is designed with eight units and 95 lessons. Most lessons require one day.
• The Pacing Guide notes 18 lessons that could take two days, but this is not noted in the Day at a Glance for each lesson.
• All Units designate two days for Unit Assessments.
• The instructional materials consist of 20 days of Quick Quizzes and Strategy/Fluency Checks which are listed in the Pacing Guide.
• Unit 1 designates one day for the Prerequisite Skills Inventory Test.

Teachers start each lesson with a 5-minute Quick Practice and each lesson is comprised of several activities with estimated time ranging from a total of 55-65 minutes per lesson. Math Activity Centers are tailored for all levels of achievement across readiness and learning styles. They can be completed within the lesson or after, however, the time required for the activity is unstated.

### 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.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations for the materials being consistent with the progressions in the Standards. Content from prior and future grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

The materials clearly identify content from prior and future grades and connect concepts to grade level work. Each unit includes a Unit Overview providing a Learning Progression. The Learning Progression explains connections between the standards of the prior grade, current grade, and future grade. Additionally, each unit contains a Math Background Section. This section contains in depth information for the teacher articulating the learning progressions and the progression of the content between lessons.  For example:

• Unit 1, the Learning Progress chart makes connections between Grade 4, Grade 5, and Grade 6 within Number and Operations-Fractions and Number System as they relate to addition and subtraction with fractions. “In Grade 4, students represented fractions as sums of unit fractions, composed and decomposed fractions and mixed numbers, and used bar models to represent equivalent fractions and find sums and differences. In Grade 5, students will use number lines to represent equivalent fractions, express fractions with unlike denominators in terms of the same unit fraction so they can be added or subtracted, use bar models to visualize a sum or difference, use equations and models to solve real world problems, and use estimation to determine whether answers are reasonable. In Grade 6, students will use number lines to represent rational numbers.”
• Unit 4, the Math Background quotes from the Learning Progressions for Numbers and Operations in Base Ten as it relates to place value. “Place Value and Shift Patterns - Students extend their understanding of the base-ten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. New at Grade 5 is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left.”

The instructional materials provide extensive work with grade-level problems. Students work with grade-level problems in each lesson. Within each lesson, students practice grade level problems within Quick Practice, Student Activity Book pages, Homework, and Remembering activities. During modeled and guided instruction, students are given opportunities to engage in the grade level work by doing various examples with teacher and peer support. The independent practice in the Student Activity Book aligns with the lesson and provides students the opportunity to work with grade level problems using models to extend concepts and skills. For example:

• Unit 2, Lesson 4 , students add and subtract decimals which leads to the standard algorithm. Students continue their work with decimals by relating decimals to metric lengths in Problem 14, “Tori had fabric that was 6.2 meters long. She used some and now has 1.45 meters. How much did she use?” (5.NBT.7)
• Unit 5, Lesson 1, students recall what they remember about division with whole numbers to activate prior knowledge. The Math Talk in this lesson includes students dividing with whole numbers and with decimals to hundredths. Students use estimation to check reasonableness of answers, and consider the contexts of real world division problems to determine the best way to handle remainders. In the Student Activity Book, Lesson 1, students compare three different methods for dividing. In the following lessons, students continue to work with division including remainders, division with two digit divisors, and dividing by numbers with decimals. (5.NBT.6)

Each lesson contains Math Center Activities, as well as Homework and Remembering (spiral reviews) pages which provide additional practice with grade-level problems.  For example:

• Unit 3, Lesson 1, Homework, students practice multiplying by unit fractions and writing comparison statements.
• Unit 4, Lesson 2, Remembering, students use inequality symbols to compare fractions with unlike denominators, multiply fractions by whole numbers, and solve multiplication problems involving multiples of ten.

### 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.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Each unit is structured by specific domains and big ideas. Learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

• Unit 2, Big Idea 1, “Read and Write Whole Numbers and Decimals” is shaped by 5.NBT.A, “Understand the place value system.” Lesson objectives in this section include, “Students learn about decimals as equal divisions of a whole. Students expand their understanding of decimals to thousandths. Students compare decimal numbers through thousandths.”
• Unit 7, Lesson 1, lesson objective states, “Students will learn to read and write numerical expressions.” This is shaped by cluster 5.OA.A, “Write and interpret numerical expressions.”

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. For example:

• Unit 1, Lesson 10, cluster 5.MD.A connects to cluster 5.NF.A, when students solve problems involving addition and subtraction of mixed numbers with unlike denominators using data from a line plot.
• Unit 3, Lesson 7, cluster 5.OA.A, 5.NF.A, and 5.NF.B, are connected when students relate operations with fractions to operations with whole numbers as they engage in problems involving operations with fractions and evaluating expressions with parentheses. Teachers use the following example with students, 2/5 x (4/7 x 1/2) = (2/5 x 4/7) x 1/2.
• Unit 7, Lesson 4, 5.OA connects to 5.NF, when students generate and extend numerical patterns, identify relationships of corresponding terms, and use expressions to support their analysis of numerical patterns. In the Student Activity Book, Problem 1, “Write two expressions for the next term (the sixth term) in the pattern 3, 5, 7, 9, 11…”

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

### 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.
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to developing students’ conceptual understanding and procedural skill and fluency. The instructional materials also do not always treat the aspects of rigor separately or together.

### 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.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials identify Five Core Structures: Helping Community, Building Concepts, Math Talk, Quick Practice, and Student Leaders as the five crucial components that are the organizational structures of the program. “Building Concepts in the classroom experiences in which students use objects, drawings, conceptual language, and real-world situations - all of which help students build mathematical ideas that make sense to them.”

The instructional materials present opportunities for students to develop conceptual understanding. For example:

• Unit 3, Lesson 4, students use diagrams and number lines to represent multiplication by a unit fraction. In the teaching notes, “Making Connections. The fraction-bar model has number-line-diagram labels to connect these two length models, fraction bars and number line diagrams.” Students add units of 1/4 to find 2/4, 3/4, etc., in both the diagram and on the number line.
• Unit 6, Lesson 7, Model a fraction problem. “Trey spent 3/4 of an hour doing homework. Kylie spent 1/2 hour. How much less time did Kylie spend doing homework than Try?” Teachers are given the following guidance, “Be sure students understand that comparison bars can be used to model and solve additive problems involving, whole numbers, decimals, or fractions.”

The instructional materials include opportunities in the Student Activity Book for students to independently demonstrate conceptual understanding. For example:

• Unit 3, Lesson 1, Solve Comparison Problems, Problem 19, “Fred has 24 model cars. Scott has 1/6 as many. How many models cars does Scott have?" Students need to understand the whole - 24 cars - and that 1/6 represents 24/6 as the number of cars that Scott has.
• Unit 6, Lesson 2, Reasonable Answers, Problem 6, “Suppose you were asked to multiply the numbers at the right (2,500 x 0.6). Without actually multiplying, give a reason why an answer of 15,000 is not reasonable.”
• Unit 7, Lesson 4, students explore patterns and relationships. Problem 6a, “Write the first five terms of two different patterns.” Problem 6b, “If possible, describe two different relationships that the corresponding terms of your patterns share.”

### 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.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials provide regular opportunities for students to attend to the standard 5.NBT.5, fluently multiply multi-digit whole numbers using the standard algorithm.

The instructional materials develop procedural skill and fluency throughout the grade-level. Each lesson includes a “Quick Practice” described as “routines [that] focus on vitally important skills and concepts that can be practiced in a whole-class activity with immediate feedback”. Quick Practice can be found at the beginning of every unit on the pages beginning with the letters QP. Student materials and instructions are also found in the Teacher Resource Book on pages beginning with Q. Examples include:

• Unit 1, Teacher Resource Book, Find a Common Denominator: Denominators Have No Common Factors, “Student Leader 1 points to the problem and asks: How can we do this? The class responds: Find a common denominator. Student Leader 1: How? Class: The denominators have no common factors. We can multiply the numerator and denominator of each fraction by the other denominator.”
• Unit 7, Teacher Resource Book, "The Student Leader uses a similar routine for each expression in the problem set. Class responses for the order of operations will vary for the different expressions in the set.” For example, $$(20-10)\div2$$.

The instructional materials provide opportunities for student to independently demonstrate procedural skill and fluency throughout the grade-level. These include: Path to Fluency Practice, and Fluency Checks. For example:

• Unit 2, Lesson 4, students build computational fluency with addition and subtraction of decimals. For example: 0.9 + 0.06; 0.47 + 0.25. (5.NBT.7)
• Unit 4, Lesson 4, Pathway to Fluency, students practice multiplying multi-digit numbers using any method. Problem types include: multiplying two-digit by one-digit numbers, three-digit by one-digit numbers, and two-digit by two-digit numbers. Students are also presented opportunities to determine the error in a completed problem using the standard algorithm.
• Fluency Checks are provided throughout the materials. For example, fluency standard 5.NBT.5 is assessed in Fluency Check for Unit 4, Lesson 12, with 15 multiplication questions.

In addition, Homework and Remembering activity pages found at the end of each lesson provide additional practice to build procedural skill and fluency.

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 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.

Students engage with application problems in many lessons for the standards that address application in solving real-word problems. In Unit 2, Lesson 4, Student Activity Book, students solve contextual problems involving measurement with metric lengths. “Matt is competing in the long jump event. His first jump was 3.56m. So far, the longest jump in the event is 4.02m. How much farther than his first jump must Matt jump to be in first place?” Students are applying mathematics with metric conversions and decimal place value within the context of a real-world situation.

Each lesson includes an Anytime Problem listed in the lesson at a glance, and Anytime Problems include both routine and non-routine application problems. For example, Unit 5, Lesson 6, Anytime Problem, “To ride his bike to school, Emilio rides 2 blocks west, 5 blocks north, and then 3 blocks west. To get home, he rides 5 blocks south, and then he rides east. How many blocks does he ride east to get back home?”

The instructional materials present opportunities for students to engage routine applications of grade-level mathematics. Examples include:

• Unit 1, Lesson 12, Student Activity Book, students write equations to solve word problems involving addition and subtraction of mixed numbers. “Ariel ran 6 1/4 miles on Saturday. This is 1 3/4 miles more than Harry ran. How far did Harry run? Why is the answer reasonable?”
• Unit 3, Lesson 3, Student Activity Book, students apply their understanding of fractions to model multiplication with fractions. “Farmer Smith has 4 acres of land. She plows 1/3 of her land. Divide and shade the drawing at the right to show the part of the land she plows.” In Item 2, students “Express 1/3 x 4 as a sum of unit fractions. 1/3 x 4 =___.”
• Unit 6, Lesson 2, Teacher Edition, the teacher presents the following problem: “A pastry chef divided a 1/2 pound block of cream cheese into 4 identical pieces. What was the weight of each piece?” Students are asked, “In this problem, what is the total amount of cream cheese? We don’t know the weight of each of the 4 pieces. But we do know that if we multiply the weight of one piece by 4, the result should be 1/2, the total amount of cream cheese in pounds. What situation equation represents this problem?”
• Unit 6, Lesson 10, Student Activity Book, Question 2, students apply mathematics to solve a multi-step story problem involving multiplication, addition, and subtraction. “Sasha earns $8 per hour working at her grandparents’ farm. During July she worked 39 1/2 hours at the farm and earned$47 babysitting. How much more money does Sasha need (d) to buy a gadget that costs $399?” Remembering pages at the end of each lesson are designed for Spiral Review anytime after the lesson occurs. One feature of the Remembering problems are those titled Stretch Your Thinking, which often present opportunities for students to engage with non-routine problems. For example: • Unit 3, Lesson 11, Remembering, Stretch Your Thinking, Exercise 19, “Harrison is playing a board game that has a path of 100 spaces. After his first turn, he is 1/5 of the way along the spaces. On the second term, he moves 1/4 fewer spaces than he moved on his first turn. On his third turn, he moves 1 1/4 times as many spaces than he moved on his first turn. What space is he on after three turns?” • Unit 6, Lesson 1, Remembering, Stretch Your Thinking, Exercise 16, “Garrett wants to buy a soccer ball, a pair of shorts, and a pair of soccer shoes. The ball costs$12.55, the shorts cost $22.98, and the shoes cost$54.35. Garrett has 85.00. How much more money does Garrett need? Write an equation to solve the problem.” • Unit 8, Lesson 9, Remembering, Stretch Your Thinking, Exercise 6, “Shannon pours four different liquid ingredients into a bowl. The sum of the liquid ingredients is 8.53 liters. Two of her measurements are in liters and two of her measurements are in millimeters. Give an examples of possible measurements for Shannon’s four liquids.” ### Indicator 2d Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. 2/2 + - Indicator Rating Details The instructional materials for Math Expressions Grade 5 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 represented in the materials. For example: • Each lesson has a 5-minute Quick Practice providing practice with skills that should be mastered throughout the year. • There are Performance Tasks throughout the series, where students use conceptual understanding to perform a mathematical task. For example, Unit 4, “How Much Does it Cost: Jon is a travel agent. This week he is planning tours for groups of 6, 8, 20, and 40 people. The table shows the cost of each tour, per person. Problem 1: A group of 6 people wants to take either the Caribbean cruise or the U.S. train tour. How much more money would it cost to take the Caribbean cruise?” • Fluency Checks are included throughout the series, where students practice procedural skills and fluency. Unit 4, Fluency Check 1, students solve 15 multiplication problems involving multi-digit by single digit, and two-digit by two-digit. For example, Problem 9, “3,070 x 7.” (Problems are presented vertically.) • Application problems are embedded into practice in the Student Activity book. For example, Unit 6, Lesson 2, Problem 1, “How many individual pieces of cheese, each weighing 1/4 lb. can be cut from a block of cheese weighing 5 pounds?” Examples where student engage in multiple aspects of rigor: • Unit 2, Lesson 4, students write equations and solve routine word problems involving given measurements. Problem 14, “Tori had fabric that was 6.2 meters long. She used some and now has 1.45 meters. How much did she use?” Problem 17, “Sarita has some ribbon. After she used 23.8 cm of it, she had 50 cm left. How much ribbon did Sarita start with?” • Unit 6, Lesson 2, Activity 1, students write equations for multiplication and division situations. For example, “In a school gymnasium, 375 students have gathered for an assembly. The students are seated in 15 equal rows. How many students are seated in each row?” and “A pastry chef divided a 1/2 pound block of cream cheese into 4 identical pieces. What was the weight of each piece?” ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 8/10 + - Criterion Rating Details The instructional materials reviewed for Math Expressions Grade 5 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and use accurate mathematical terminology. The instructional materials also partially support teachers and students in students constructing viable arguments and analyzing the arguments of others. ### Indicator 2e The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Math Expressions Grade 5 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. Mathematical Practice Standards are clearly identified in a variety of places throughout the materials. For example: • The Mathematical Practices are identified in both volumes of the Teacher’s Edition. Within the introduction, on page I13 in the section titled The Problem Solving Process, the publisher groups the Mathematical Practices into four categories according to how students will use the practices in the problem solving process. Mathematical Practices are also identified within each lesson. • Each time a Mathematical Practice is referenced it is listed in red with a brief description of the practice. • At the beginning of each Unit is a section devoted to the Mathematical Practices titled "Using the Common Core Standards for Mathematical Practices". Within this section, each Mathematical Practice is defined in detail. In addition, an example from the Unit is provided for each practice. For example, in Unit 6, page MB25-U6 illustrates how MP2 is used in Lesson 6-1 and Lesson 6-3. • The Mathematical Practices align and connect with the content of daily lessons, rather than being included as stand-alone topics. Examples of Mathematical Practices that are identified, and enrich the mathematical content include: • Unit 2, Lesson 3, MP5, Use Appropriate Tools | MathBoard. Students use their MathBoards to develop an understanding of hundredths and tenths related to a whole. • Unit 4, Lesson 2, MP7, Look for Structure | Identify Relationships. Teachers write multiplication problems on the board and have students give the answers quickly (5x1, 5x2, 5x3, etc.). Students will be reminded that every other answer ends in zero because it is a multiple of 10. • Unit 6, Lesson 4, MP8, Use Repeated Reasoning | Generalize. Students use rounding to assess the reasonableness of answers in a variety of story problems. Groups are asked to share their explanations with the class. Students demonstrate other ways those same strategies can be used to decide reasonableness. • Unit 8, Lesson 9, MP1 Make Sense of Problems is identified. Student Activity Book, Problems 13-17, students solve multistep problems that require one or more metric unit conversions. Teachers are instructed to remind students that in order to perform addition or subtraction on numbers with units, the units must be the same. Students may choose to convert to different units. It should be noted that while the Mathematical Practices are clearly identified in the teacher materials, they appear to be over identified. Many lessons have multiple Mathematical Practices listed. ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 1/2 + - Indicator Rating Details The instructional materials reviewed for Math Expressions Grade 5 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of Mathematical Practice 5. Mathematical Practice 5: The instructional materials do not meet the full meaning of MP5 as tools are chosen for students, and there are few opportunities for students to choose tools strategically. For example: • Unit 5, Lesson 6 identifies MP4 and MP5 Model with Mathematics/Use Appropriate Tools | Play Money. “Organize the students into groups of three and distribute the play money.” Students do not choose the tool (play money). • Unit 8, Lesson 14 identifies MP5. Students are given a set of quadrilateral cards to use to complete a math activity. The materials identify the cards as a tool, however, the cards are the activity. Students do not need to use a tool to engage in the activity. • Unit 8, Lesson 16 identifies MP5 Use Appropriate Tools | Math Boards. “Groups should draw two large overlapping ovals on their MathBoards.” Students do not select a tool to strategically complete a math task. ### 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 + - Indicator Rating Details The instructional materials reviewed for Math Expressions Grade 5 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Math Expressions includes a Focus on Mathematical Practices lesson as the last lesson within each unit. Activity 3 of each of these lessons prompts students to determine whether a mathematical statement is true or false or to establish an arguable position surrounding a mathematical statement. These activities provide students opportunities to construct an argument and critique the reasoning of others. Student volunteers ask questions of other students to verify or correct their reasoning. Examples of Focus on Mathematical Practices lessons include, but are not limited to: • Unit 1, Lesson 13, students determine a position for the following statement: “If you add two fractions less than 12, the sum will always be less than 12.” Students establish an arguable position in writing and include examples or counterexamples. Volunteers share their positions and explanations with the class. The class asks the volunteers questions and verifies or corrects reasoning errors. • Unit 6, Lesson 11, students determine a position for the following statement: “The Commutative Property can be applied to subtraction, so the following equation is true: 5.55 - 3.25 = 3.25 - 5.55.” Students establish an arguable position in writing and include examples or counterexamples. Volunteers share their positions and explanations with the class. The class asks the volunteers questions and verifies or corrects reasoning errors. • Unit 7, Lesson 7, students determine a position on the following statement: “The expression 5 + 3(4 ÷ 2) − 1 simplifies to 15.” Students establish an arguable position in writing and include examples or counterexamples. Volunteers share their positions and explanations with the class. The class asks the volunteers questions and verifies or corrects reasoning errors. Puzzled Penguin problems are found throughout the materials and provide students an opportunity to correct errors in the penguin’s work. These tasks focus on error analysis, and many of the errors presented are procedural. Examples of Puzzled Penguin problems include: • Unit 3, Lesson 5, Puzzled Penguin problem, students find a calculation error in a perimeter problem. • Unit 5, Lesson 8, Puzzled Penguin problem, students identify the error the penguin made in a division problem. • Unit 7, Lesson 5, Puzzled Penguin problem, students determine whether the coordinates of a point are accurate. In addition, Remembering pages at the end of each lesson often present opportunities for students to construct arguments and/or critique the reasoning of others. For example: • Unit 3, Lesson 14, Remembering, Stretch Your Thinking, Exercise 10, “If you start with 1 and repeatedly multiply by 1/2 will you reach 0? Explain why or why not.” • Unit 4, Lesson 10, Remembering, Stretch Your Thinking, Exercise 15, “Taylor estimated the music departments would raise1,100 by selling tickets to a performance next week. Each ticket will be \$12,75. About how many tickets does the music department need to sell for Taylor’s estimate to be reasonable?”
• Unit 6, Lesson 4, Remembering, Stretch Your Thinking, Exercise 8, “Kaley has 2 3/8 yards of fabric. She cuts and uses 1 1/16 yards from the fabric. She estimates that less than one yard of fabric is left over. Is her estimate reasonable? Explain.”

### Indicator 2g.ii

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

The instructional materials reviewed for Math Expressions Grade 5 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Overall, the teacher materials provide students multiple opportunities to construct viable arguments, however there are missed opportunities to support teachers in engaging students in analyzing the arguments of others throughout the materials.

Throughout the Teacher Edition, MP3 is identified with explanations and guidance for teachers, either in reference to specific parts of the lesson, or in specific activities such as Math Talks. However, this guidance often supports teachers to engage students in explaining their methods, instead of constructing arguments or critiquing reasoning. For example:

• Unit 5, Lesson 5, Math Talk in Action, Problem 15, “One quart is equal to 32 ounces. How many quarts are equal to 6,672 ounces?” Teacher prompts are used to engage students in explaining, with sample responses provided. “Nishay, explain how you reasoned about Problem 15.”  “And, what do you get when you divide?” Problem 18, “Ayala has 655 computer files she wants to put on a thumb drive. If she can fit 18 files on each thumb drive, how many thumb drives will she need?” “Jamison, tell us what you did for Problem 18.” “What did you do with the remainder?” These prompts do not support teachers to engage in MP3.
• Unit 2, Lesson 4, Math Talk, teachers use the prompt, “Describe how you added these decimals,” to lead a discussion allowing students to construct arguments supporting how they add decimal numbers. Students do not need to construct an argument, they need to describe what they did.

Examples of materials assisting teachers to engage students in constructing viable arguments:

• Unit 4, Lesson 4, Puzzled Penguin, teachers are given guidance on how to present the problem, and a detailed explanation of the Puzzled Penguin’s error in a multiplication problem. Students are asked if he is correct, if not, students determine what did he do wrong and how they can show he is wrong without actually doing the problem. Support is provided to teachers with a further explanation of Puzzled Penguin’s error.
• Unit 8, Lesson 17 has the teacher sketch an aerial view of the roof of a building that is U shaped and let students assume that all of the dimensions of the building are known. Teachers then ask if subtraction could be used to find its volume. Students are asked to establish an arguable position by writing or stating sentences that support a specific point of view.

There are instances where MP3 is identified in A Day at a Glance for a lesson, but there is no guidance for teachers on how to engage students to construct arguments or analyze the arguments of others.

### Indicator 2g.iii

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations that materials use accurate mathematical terminology.

• New vocabulary is introduced at the beginning of a Lesson or Activity.
• The Teacher Edition provides instruction for teachers on how to develop the vocabulary, with guidance for teachers to discuss and use of the vocabulary.
• The student materials include Unit Vocabulary Cards that students can cut out and use in school or at home to review vocabulary terms.
• The Student Activity resource contains activities that students can do with the vocabulary cards; however, the teacher materials do not provide guidance as to when students should engage in these activities to support learning the vocabulary.
• There is an eGlossary providing audio, graphics, and animations in both English and Spanish of the vocabulary needed in the lessons.
• Study POP! is an interactive digital charades app that includes Math Expressions vocabulary to help students practice and develop mathematical vocabulary. Study POP! is listed at the beginning of many lessons, but is not referenced during the lesson.

Examples of how vocabulary is incorporated within lessons include:

• Unit 3, Lesson 12, lists dividend, divisor, and quotient as vocabulary at the beginning of the lesson. The terms are reviewed in the Student Activity Book in Activity 2, but are not used anywhere else in the lesson or Student Activity Book directions.
• Unit 6, Lesson 4, lists benchmark as vocabulary at the beginning of the lesson. The term is used in the title and directions for Activity 2. At the beginning of the Activity there is a teacher-led whole group discussion introducing the use of benchmark fractions. The teacher prompts provide very few opportunities to make meaning of benchmark numbers; therefore, students only have a limited opportunity to make sense of the new vocabulary.
• Unit 8, Lesson 3, lists perimeter, area, square centimeter, and square unit as new vocabulary. The Teacher’s Edition suggestions include a discussion on perimeter and area. The teacher asks students what they remember about perimeter and area. Five specific points are listed for teachers to elicit from students through discussion. In this teacher-led discussion, once students have made the five points listed in the Teacher’s Edition, the discussion concludes. This type of discussion does not ensure all students have a full understanding or memory of area and perimeter. In addition, the terms square centimeter and square unit are not written anywhere within the Student Activity pages for this lesson, with the exception of the word square unit being included in the the definition of area at the beginning of the student page.

In addition, there are instances where teachers are told to look for precise use of words, facts, and symbols. For example:

• Unit 1, Lesson 13, “MP6 - Attend to Precision: The sentences must include precise mathematical terms and any examples or counterexamples must include precise facts and symbols.” Students must use precise mathematical language to develop an argument of true or false regarding the following statement: “If you add two fractions less than 1/2, the sum will always be less than 1/2.”
• Unit 5, Lesson 11, “MP6 - Attend to Precision: The sentences must include precise mathematical words, and any examples or counterexamples must include precise facts and symbols.” Students must decide whether the inequality statement, $$20\div0.95>20$$, is true or false and develop an argument that supports their position.

## 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
+
-
Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

### Indicator 3a

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials distinguish between problems and exercises.

Materials provide the opportunity for students to learn new mathematics through problem solving activities. In a typical lesson, Activity 1 and Activity 2 develop the new math content of the lesson. Lessons are outlined according to an Inquiry Lesson Path based on four phases: Phase 1 Guided Introduction, Phase 2 Learning Unfolds, Phase 3 Knead Knowledge (practice stage), and Phase 4 Maintaining and Integrating Fluency. Students build mastery through practice problems/exercises. In a typical lesson, during Activity 2 and Activity 3, students complete problems in the Student Activity Book which provide practice with the math content. The purpose of each Activity within a unit is explained in the “Teaching the Lesson Section” found on the first page of each lesson.

Examples include but are not limited to:

• In Unit 3, Lesson 2, Teaching the Lesson Section, Activity 1, Extend Unit Fraction Multiplication, is stated as important because “Through the use of number lines, students will expand their understandings of the connection between multiplying by a unit fraction and multiplying by a non-unit fraction.” Activity 2, Multiplication with Fractions Practice Metric, is stated as important because “This multiplication practice with unit and non-unit fractions will use skills developed in the previous activity to help students understand the relationships in multiplicative comparison problems.”
• In the Student Activity Book, Unit 8, Lesson 4, Activity 2, students count cubes to find the volume of a rectangular prism: “Find the number of cubes and the volume.” A picture of a prism is shown that is 5 cubes in length, 4 cubes in width, and 3 cubes in height. In Activity 3, students compare measurement of volume with standard and improvised units. Teachers prompt students to build a rectangular prism using their math books, describe the volume of the prism, and try to build another prism the same size with a different set of books.

### Indicator 3b

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide tasks in an intentional sequence.

The design of the assignments follows a natural progression, leading to full understanding and mastery of new mathematics. Lessons follow a consistent pattern of two or three activities per lesson. Activity 1 usually focuses on the new learning. This learning is reinforced in Activity 2, and then students practice the new learning by completing Student Activity Book pages during Activity 3. Activity 3 either reinforces the new skill, or it reviews previously learned content.

Examples include but are not limited to:

• In Unit 2, Lesson 5, students discuss various strategies for making a new ten when adding. Next, students practice adding decimals and whole numbers and finally adding money.
• In Unit 4, Lesson 4, students multiply 2-digit numbers using the Place Value Rows Method (area models). Then students transition to multiplying using the Short Cut Method (traditional algorithm).
• In Unit 5, Lesson 4, students explore different situations and discuss what the remainder means. Then students solve two-digit division problems and interpret the remainders.

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
+
-
Indicator Rating Details

The instructional materials for Math Expressions Grade 4 meet expectations that materials provide varied opportunities for students to present their mathematical knowledge.

Examples of how students produce answers and solutions include but are not limited to:

• Using fraction bars to solve problems
• Using Arrays and Area Models to solve multiplication problems
• Using drawings to make sense of mathematics
• Using bar diagrams to solve division problems
• Using Place Value Charts to compare whole numbers and decimals
• Providing thinking explanations as they answer Check for Understanding questions in the Student Activity Book
• Completing fluency checks and practice in the Student Activity Book
• Critiquing the Reasoning of others by asking “good thinker questions” and using “good justifications”
• Practicing “good explanations”
• Identifying the error and correcting it (Puzzled Penguin)
• Solving problems and exercises in the Student Activity Book

### Indicator 3d

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide virtual and physical manipulatives that are faithful representations of the mathematical objects they represent and are connected to the written material.

Students use a variety of manipulatives including MathBoards, Secret Code Cards, base-ten blocks, Square Inch Tiles, fraction bars, number lines, coordinate grids, Math Mountains, and Math Mountain Cards. Most of the manipulatives are available virtually in the itools found in ThinkCentral. Manipulatives are often connected to written methods when appropriate.

Examples include but are not limited to:

• Unit 1, Lesson 1, students use MathBoard Fraction Bars to use unit fractions to build equivalent fractions.
• Unit 2, Lesson 2, students use Secret Code Cards to model whole numbers and decimals and write the numbers in standard, expanded, and word form.
• Unit 7, Lesson 5 students use coordinate grids to name the ordered pair for a point’s location and to place a point on the grid.

### 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
+
-
Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the mathematics.

Student Activity Book pages include many exercises per page, but they follow a consistent layout and do not feel cluttered because there are no extra and unnecessary pictures on the pages. Additionally, students are provided ample space to show their work. When needed, models, which are consistent with the materials used in the lesson, are included on the pages. For example, on Student Activity Book page 295, a coordinate grid is shown, and students use it to name ordered pairs for points on the plane.

In the Teacher Guide, lessons follow a consistent layout, moving from one activity to another. Each Activity includes a large blue box that highlights the mathematical content and practice standards, the focus of the lesson, and materials needed. Parts of the lesson, such as MathTalk, are clearly labeled. For example, in Unit 2, Lesson 8, a MathTalk in Action box shows examples of how students might share their methods for estimating sums.

The digital interactive game, Poggles, includes simple, appealing characters that do not distract students as they practice addition and subtraction. Poggles are small squarish characters with animated faces whose appearance can be changed by adding hair and hats to the Poggle squares.

### Criterion 3f - 3l

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Examples of teacher support include but are not limited to:

• Questions for teachers to pose are consistently included in the lesson narrative. They are italicized, making them easily visible.
• MathTalk in Action boxes include questions for the teacher to ask and potential student responses. For example, in Unit 1, Lesson 5, the teacher is guided to ask the questions: “Rashida, will you explain your work? How did you change 8/3 to a mixed number? What did you do next?”
• Teacher Notes are also provided at the bottom of the lesson pages and include questions to deepen students understanding of the mathematics. For example, in Unit 4, Lesson 1, Inquiry Notes state, “As you discuss the generalizations outlined in the three bulleted points use questions such as ‘How do you determine what number to use as the exponent when you write a number as a power of ten? When multiplying by a whole number by a power of ten, how is the exponent related to the number of zeros in the product? When you multiply a whole number by a power of ten, what does the exponent of the power of ten tell you?’”

### 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 for Math Expressions Grade 5 meet expectations that 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. Materials also, when necessary provide teacher guidance for the use of embedded technology to support and enhance student learning.

Ample guidance is provided in the Teacher Guide for planning. The Pacing Guide provides guidance for each unit. Charts show the Learning Progression for the Content Standards Across Grades for the standards addressed in the Unit. A Planning Chart for each Unit that includes Math Activity Center Resources, Big Idea Resources, and Lesson Resources is provided. The Planning Chart also includes the standards addressed in each lesson, the digital and print resources for each lesson, and the assessments for the Unit. A table of the Standards for Mathematical Practice and the lessons where each is embedded is included. Also, a Table of the Math Content Standards and the lessons where they are taught is provided. Finally, a list of Assessment, Review, and Intervention Resources for the Unit is provided.

Examples include but are not limited to:

• Each lesson includes guidance on the focus of each Activity and why it is important. For example, in Unit 2, Lesson 6, Activity 1, Ungroup With Zeros, is stated as important because “By providing several methods to subtract when ungrouping with zeros, students can choose a method that makes the most sense for them and use it to solve subtraction problems with decimals.”
• Each Activity includes an explanation of what the teacher should do or say and includes possible correct responses to questions posed by the teacher.
• Formative Assessment and Check for Understanding questions are highlighted in the Teacher Guide.
• Math Practices are highlighted in the lesson narratives.
• A list of questions that can be used to build a Math Talk community is included at the beginning of each Unit.
• Notes at the bottom of each page of the lesson narrative give useful suggestions for implementing the lesson, asking questions, acquiring vocabulary, and building concepts. For example, in Unit 3, Lesson 1, the Teaching Notes for Language and Vocabulary states, “Some students may not equate the word ‘of’ with multiplication. To help them, focus on the ‘groups of’ language below the pictures for Exercises 3 and 4. For example, say and write: 3 groups of 6 = 3 * 6 = 18. Give students a chance to say and write other ‘groups of’ phrases in the same way.”
• Digital Resources for each lesson are highlighted on the first page of the lesson, and itools, which include virtual manipulatives, are shown in the lesson narrative when it may be beneficial to use them. For example, in Unit 6, Lesson 4, a picture of itools Number Lines are shown because they may be used in the lesson.

### 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 for Math Expressions Grade 5 meet expectations that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

Notes are provided at the bottom of each lesson narrative in the Teacher Edition to deepen teacher understanding of the mathematics and to improve instruction. Math Background Notes provide information about the math topic to deepen teacher’s understanding. Watch For! Notes provide information about potential misconceptions and things to watch for as students complete the lesson. What to Expect from Students notes provide information about how students might engage with the math and why the math is important. Building Concepts notes provide explanations of the math and how students learn.

Examples include but are not limited to:

• Path to Fluency Charts are provided.
• Chart of the Addition/Subtraction and Multiplication/Division problem types is provided.
• Table of the Major Work and Major Clusters of the Grade is provided.
• Table of the Common Core State Standards for Mathematical Content is provided.
• Table of the Common Core State Standards for Mathematical Practice with an explanation for each Mathematical Practice is provided.
• The Putting Research into Practice section at the beginning of each unit provides research about best practices in teaching children mathematics.
• The Math Background section, prior to each unit, includes sections that deepen teacher knowledge of the math in the unit. Examples include Learning Path in the Common Core Standards, Help Students Avoid Common Errors, Effective Practice Routines, Relate Mathematics to the Real World, and Focus on Mathematical Practices.
• The Math Background section, prior to each unit, provides excerpts from the Progressions for the Common Core State Standards.
• The Mathematical Practices section, prior to each unit, provides information on how students will engage with the Practice Standards throughout the unit.
• A Teacher Glossary is provided.

### 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 for Math Expressions Grade 5 meet expectations that materials contain a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

A Path to Fluency: Kindergarten through Grade 6 Chart is provided and highlights the fluency requirements of each grade level, activities that target fluency, and interventions for Grades 3, 4, 5, and 6. Also, a Major Work and Major Clusters of the Grade Chart for Grades K-6 is provided. Finally, for each unit, a Learning Progressions for the Common Core State Standards Chart for the domains addressed in the unit, which includes the current, prior, and next grade level standards is provided.

### 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 for Math Expressions Grade 5 provide a list of lessons in the teacher's edition, cross-referencing the standards addressed and providing an estimated instructional time for each lesson, chapter, and unit.

Math Expressions does not include chapters, but rather units which are divided by Big Ideas, which are further divided into lessons. The Pacing Guide provides estimated instructional time for lessons and units. This Pacing Guide provides an estimated number of days for each unit, including lessons that may take two days and the number of days for assessments and quizzes. It should be noted that Lessons identified as taking two days in the Pacing Guide are not identified in the lesson narratives, nor is a breaking point indicated.

Examples include but are not limited to:

• The Table of Contents provided in the introduction to the materials includes standards for all units’ Big Ideas.
• The Chart of the Common Core State Standards for Mathematical Content provided identifies the lessons in which each standard will be addressed.
• The Chart of the Common Core State Standards for Mathematical Practice provided identifies the lessons in which each Mathematical Practice will be addressed.
• A Planning Chart is provided in the Overview for each unit that includes the standards that are addressed in each lesson.
• Charts of the Math Content Standards and Math Practice Standards are provided in the Overview for each unit. These charts include a list of each standard and the lessons where they are addressed.
• The Content and Practice Standards are identified on the first page of each lesson. The standards are also listed for each Activity within a lesson.

### 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 for Math Expressions Grade 5 contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Letters for each unit are found in the Student Activity Book. These letters explain content, manipulatives students may use, and an explanation of terminology that may be unfamiliar to parents. Most units include between 1-3 Family Letters. Spanish versions of the letters are also included in the Student Activity Book.

### 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 for Math Expressions Grade 5 meet contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher Edition contains explanations of the program’s instructional approaches and research-based strategies. An Inquiry Learning Path describes the four phases of the Math Expressions classroom: Guided Introduction, Learning Unfolds, Knead Knowledge, and Maintaining and Integrating Fluency. The Putting Research into Practice pages at the beginning of each Unit explain best practices related to the content of the Unit. Excerpts from the Progressions for the Common Core State Standards are included in the Math Background section of each Unit. Research Notes are sometimes included in the Teaching Notes at the bottom of the lesson narrative in the Teacher Edition. For example, the Teaching Notes in Unit 4, Lesson 3, Activity 2, What to Expect from Students After this lesson state, “Students may choose to use any multiplication method including traditional methods they may already know. Some students may be confused about what to multiply by what. These students tend to prefer the Place Value Sections Method because this method organizes the various factors in a clear way.”

### Criterion 3m - 3q

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

### Indicator 3m

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

Examples include but are not limited to:

• The Assessment Guide contains a Prerequisite Skills Inventory Test, organized by Domains, and a corresponding Prerequisite Skills Inventory Test Correlation document. The correlation aligns each question with a description of the prerequisite skill addressed, as well as the DoK level of the question. This correlation document is formatted as a table so each student’s performance by question/skill can be recorded. The Prerequisite Skills Inventory Test is designed to be administered at the beginning of the school year.
• When a student completes practice opportunities and tests in the Personal Math Trainer, all of the performance data and adaptive learning information follows each student to the next grade.
• Quick Practice activities at the beginning of each lesson are designed to “provide opportunities for students to call to mind their prior understanding of a topic that has already been discussed in class or to begin to build a prerequisite skill for a topic that is to come later” (Teacher Edition page I4).
• Quick Quizzes and Fluency Checks are embedded within the units to check understanding of Big Ideas prior to moving on to the next Big Idea instruction, and to monitor progress toward computational fluency. For example, Fluency Check 1 assesses multi-digit multiplication (5.NBT.5).
• Students take three progress monitoring assessments to assess grade level skills and concepts students have learned. The Beginning of Year test assesses concepts they will learn throughout the year, the Middle of Year Test shows progress made in the first half of the year, and the End of Year Test measures growth throughout the school year.

### Indicator 3n

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide support for teachers to identify and address common student errors and misconceptions.

Examples include but are not limited to:

• Common student errors are identified for each Unit Review/Test question along with a direction on how to help students. For example, on the Unit 2 Review/Test, if a student misses Questions 5, 8, or 9, the common error identified states, “Student does not read or write the expanded form correctly.” Teachers are directed to “First, decompose the number using the total value of each digit. Then, ask students to factor each value such as 90 = 9 x 10. Finally, show them how to use addition to group the factors.”
• The Math Background section of each Unit provides a narrative called “Help Students Avoid Common Errors”.
• Puzzled Penguin activities highlight typical student mistakes and misconceptions by challenging students to find the Puzzled Penguin’s mistake and correct it. Teachers are provided questions in order to lead classroom conversations through a MathTalk format that revolve around the mistake and its correction, helping students understand the mathematics.
• Watch For! are teaching notes periodically found in each unit. These notes alert teachers to common misconceptions they should be on the lookout for. For example, in Unit 3, Lesson 3, the Watch For! note states, “Some students may benefit from a brief review of how to multiply a unit fraction by a whole number.”

### 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 for Math Expressions Grade 5 meet expectations that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include but are not limited to:

• Homework and Remembering pages provide a review of recently taught topics as well as a spiral review throughout the year. The Personal Math Trainer online platform allows students to complete homework tasks for each lesson, receive instant feedback, and  step-by-step guidance if needed.
• Unit Review/Test and Performance Tasks for each unit are found in the Student Activity Book. The author states, You can use this Unit Review/Test as an end-of-unit review to determine if children have mastered the content of the unit.  You can assess children’s knowledge with one of the forms of the Unit 1 Test in the Assessment Guide.” Teachers are provided with a Data-Driven Decision Making Table which suggests specific reteaching activities for students who incorrectly answer the correlated questions, as well as suggestions for which Standards Quiz to assign in the Personal Math Trainer which provides a personalized intervention for the student. The Performance Task includes a detailed scoring rubric which can be used to provide feedback to students.
• The Personal Math Trainer can be used for homework practice, fluency practice, standards practice, unit pre-tests with instant feedback, and step-by-step guidance when needed. Everything a student completes in the platform helps to improve the adaptive workflow (powered by Knewton Adaptivity) for the student throughout the year.
• The Knewton Adaptivity, Homework with Daily Intervention and Enrichment can be used in multiple ways in the classroom. A 5-minute Warm-Up provides students with personalized review prior to the assignment. On-level and advanced students may receive less or no warm-up, as determined by Knewton. After the warm-up, the HMH pre-built assignment is given to students. A 10-minute personalized enrichment is provided for students who demonstrate mastery (95% or higher) on the assignment.  Enrichment shows students proximate, forward-looking concepts based on the assignment content.
• Other Formative Assessment opportunities include: daily Check Understanding tasks on select Student Activity Book pages, daily observation with anecdotal notes, observations during Math Talk conversations, and analyzing student work samples and student responses in the Student Activity Book. Portfolio suggestions are also provided at the end of each unit.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
Narrative Evidence Only

### Indicator 3p.i

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

The materials reviewed for Math Expressions Grade 5 meet the expectation for offering ongoing assessments that clearly denote which standards are being emphasized.

Examples include but are not limited to:

• Every unit includes two versions of a Unit Assessment, Form A and Form B, found in the Assessment Guide. Both assessments provide PARCC and Smarter Balance question formats and a Standards Correlation Document which can be used to collect student performance data. This document also aligns each question to a DoK Level and Standard(s).
• Each unit contains a Performance Assessment which can be found in the Assessment Guide. The standards are clearly noted for the assessment as a whole, and not by specific question.
• There are three Benchmark Assessments (Beginning of the Year Inventory, Middle of the Year Inventory and End of Year Assessment) found in the Assessment Guide. Standards for these assessments are clearly noted on the Correlation Document and DoK Levels are noted.

### 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.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Examples include but are not limited to:

• Scoring Guides are provided for each Unit Performance Assessment found in the Assessment Guide. Each question is assigned a point value and a rubric is provided to determine Performance Levels 0-3 based on the number of points earned. Additionally, each Performance Level is further defined on a task-specific basis and indicates specifics about student understanding to assist teachers in interpreting student work. Sample student work for each Performance Level is also provided in the Assessment Guide.
• Answer keys for the Unit Assessments, Form A and Form B, are located in the back of the Assessment Guide. However, no guidance or suggestions for follow-up instruction are included in the Assessment Guide.
• The online Personal Math Trainer can be utilized to administer Beginning, Middle and End of Year Tests, Unit Assessments, and Fluency Checks. The data from these assessments is collected and analyzed, and a Personal Study Plan is prescribed through Adaptive Workflow settings (through Knewton Adaptivity) based on the data and the mastery threshold percentage established for the assessment. The primary use is for end of the unit assessments, or to provide targeted students with occasional review, intervention, and re-assessment opportunities. Students must complete an initial assignment (test). Students who do not demonstrate mastery receive a Personal Study Plan, consisting of a personalized review and intervention assignment lasting 15 minutes. After completing the Personal Study Plan, the initial assignment is given again, but numbers in the assessment are changed.

### Indicator 3q

Materials encourage students to monitor their own progress.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 do not encourage students to monitor their own progress and do not provide direction for teachers to encourage students to monitor their progress.

### Criterion 3r - 3y

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

The instructional materials reviewed for Math Expressions Grade 5 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

### Indicator 3r

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Teachers guide students through an inquiry path to become mathematically proficient. The four stages of the path to learning are guided introduction, learning unfolds, knead knowledge through practice, and maintain fluency. As stated by the publisher, “Within the curriculum, a series of learning progressions reflect research on students’ natural learning stages when mastering concepts such as computation and problem-solving strategies. These learning stages informed the order of concepts, the sequence of units, and the positioning of topics in Math Expressions.”

Examples include but are not limited to:

• Unit 1, Lesson 4, students find strategies for comparing fractions. Prompts are given for EL students at three different levels: emerging, expanding, bridging. A teaching note is included to help teachers diagnose if students are at an Emerging, Expanding, or Bridging level. Teachers are instructed, “Write common denominator on the board. Write 7/9 and 5/6 on the board. A common denominator for a pair of fractions is a number that each denominator divides into evenly.” Emerging: “18 is divisible by both denominators 9 and 6. Write 7/9 = 14/18 and 5/6 = 15/18 on the board. 18 is a common denominator for 7/9 and 5/6. Have students repeat.” Expanding: “ Write 7/9 = 14/18 and 5/6 = 15/18 on the board. Why is 18 the common denominator?” Bridging: “What is a common denominator?”
• In Unit 5, Lesson 6, the Universal Access/Extra Help teaching note instructs teachers, “Some students may need to use play money to act out these problems. Pair them with a Helping Partner so they can talk through the problem together.”
• In Unit 3, Lesson 5, students are using multiplication strategies. The Universal Access/Special Needs teacher note states, “If a student has difficulty maintaining focus, stand near the student as you speak to the class. Give the student the opportunity to get involved with the activity by asking the student to write examples on the board or repeat a description in his or her own words.”

### Indicator 3s

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Examples include but are not limited to:

• An explanation of differentiated instruction is provided in the Teacher Edition.
• A list of intervention resources is provided for each unit in the Unit Overview Assessment.
• Math Activity Centers resources for on-level, challenge, and intervention are provided for each unit’s lessons.
• Teaching notes for English Learners are provided for emerging, expanding, and bridging students and are provided for each unit’s lessons.
• Some lessons have Differentiated Instruction notes provided for universal access/extra help.

### Indicator 3t

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

MathTalks provide “an inquiry environment that encourages constructive discussion of problem-solving methods through well-defined classroom activity structures. . . comprises four components: questioning, explaining math thinking, contributing math ideas, and taking responsibility for learning” (Teacher Edition page I3). Initially, teachers model MathTalks and then students run the MathTalk. For example, in Unit 4, Lesson 4, MathTalk, Best Practices states, “You must direct student math talk for it to be productive. Over time, as students become more skilled at discussing their thinking and talking directly with one another, you will fade into the background more. But you will always monitor, clarify, extend, and ultimately make the decisions about how to direct math conversation so that it is productive for your students.”

### 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).
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 meet expectations that 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.

Examples include but are not limited to:

• Scaffolding of vocabulary is provided. For example, in Unit 4, Lesson 6, the word twice is explained for EL students. Teachers are instructed to “Write ‘twice’ on the board. Twice means 2 times as many. Write x 2 on the board. Have one volunteer draw between 1 and 5 circles. Ask another volunteer draw twice as many.”
• Extra support is provided for EL students. For example, in Unit 6, Lesson 4, students use rounding to find estimates. The teacher prompt states, “Write ‘benchmark’ on the board. A benchmark is a number we use to compare. On the board, draw and label a number line from 0 to 1 by eighths. Draw a dot at 3/8, and then highlight 0, 1/2, and 1. Explain that the highlights are benchmarks - numbers we use to compare.”
• Each unit lesson contains a Math Activity Center with activities and resources for students who are on-level and those needing challenge and intervention.
• Teaching notes included in some lessons provide specific guidance for teachers to support students who are emerging, expanding, and bridging language acquisition.

### Indicator 3v

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Examples include but are not limited to:

• Math Lessons contain Differentiated Instruction Math Activity Centers. Challenge Resources specify which Activity Card will challenge advanced students.
• The online Personal Math Trainer provides personalized enrichment with learning supports.
• Challenge worksheets for each lesson are available in print and digitally and are noted on the Differentiated Instruction page for each lesson.
• Math Readers, books in the Math Activity Center, place math content in the context of stories and support higher levels of critical thinking.

### Indicator 3w

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

The instructional materials for Math Expressions Grade 5 meet expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

Examples include but are not limited to:

• Puzzled Penguin appears throughout the unit to provide opportunities to help students avoid common errors. These errors are presented as letters to students. Students teach Puzzled Penguin the correct way and explain why the penguin is wrong.

### Indicator 3x

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

The instructional materials for Math Expressions Grade 5 provide opportunities for teachers to use a variety of grouping strategies.

Examples include but are not limited to:

• Math Activity Centers are provided at the conclusion of each lesson and students can be grouped individually, in pairs, or in groups to complete the Activity Cards. For example, in Unit 3, Lesson 1, Intervention Activity card 3-1, students work with number cards 2, 4, 8, 16, and 32. Each person turns over one card then they make a comparison statement using the word times
• Math Writing Prompts are part of the Math Activity Centers and provide opportunities for students to work individually, in pairs, or in groups. For example, in Unit 7, Lesson 2, the Challenge Math Writing Prompt states, “Write two numerical expressions with the same numbers and operations, but with different values. Explain how to find the value of each expression.”
• MathTalks provide various grouping structures. During Solve and Discuss, 4-5 students go to the board and solve the problem while the rest of the class is solving independently or as part of a small group consisting of 2-3 students. During Scenarios, a group of students act out a particular mathematical situation for other students to see.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 sometimes encourage teachers to draw upon home language and culture to facilitate learning.

Family Letters for each unit are found in the Student Activity Book. Spanish versions of these letters are also included in the Student Activity Book. However, instructional materials do not encourage teachers to draw upon home language and culture to facilitate learning. English Learner notes in the Teacher Edition do not reference Spanish vocabulary 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
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 5: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides 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
+
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 are web-based and compatible with multiple internet browsers. In addition, materials are platform neutral and allow the use of tablets and mobile devices.

Web-based instructional materials for both teachers and students can be accessed using multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, both students and teachers can use multiple devices to access instructional materials (desktop computer, tablet, iPad, Smartboard, laptop, or cellphone). Students with disabilities can use mobile devices, assistive technology, or PCs to access materials. For example, non-readers have the option to have the entire text in an audio format. Additionally, the materials are platform-neutral for a variety of operating systems.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 provide opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Online assessments are available. Teachers have the ability to create their own assessments or customize those provided by the program. A variety of assessment types are provided: multi-step, fill in the blank, multiple-choice, or teacher-created questions. For example, teachers giving the computer adaptive test may edit the format and/or values of the text causing the corresponding complexity of the lesson to change accordingly.

The Personal Math Trainer is an online adaptive assessment and learning system of mathematical understanding and procedural skill/fluency. Teachers can identify question types, assignment type, or standard tested. Once students have completed the task or assessment, various charts and graphs can be generated based on standards to inform instruction. Reports are available for individual students and the entire class.

### 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
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

Teachers can manipulate the Personal Math Trainer to create learning experiences for students targeting their needs. Additionally, teachers can create lesson materials that are specific to the learning targets for specific unit lessons. For example, in Unit 3, Lesson 2, students can use the digital Number Lines to multiply a unit fraction by a non-unit fraction.

The instructional materials for Math Expressions Grade 5 can be easily customized for local use.

Digital materials include adaptive technological innovations for teachers to personalize learning for students. Digital materials can be differentiated based on individual student’s needs. For example, when using the Personal Math Trainer, teachers can add or modify existing tasks to a student’s personalized learning path. Additionally, adaptive technology allows teachers to provide two flexible differentiated styles (Daily Intervention and Enrichment or Personal Study Plan) for students.

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
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 do not include reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Materials do not provide opportunities for students and teachers to participate in discussion groups using technology.

### 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
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Indicator Rating Details

The instructional materials for Math Expressions Grade 5 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Examples include but are not limited to:

• The Student Activity eBook provides audio, ability to submit answers online, a drawing tool for math drawings, guided practice to help students solve problems, and virtual manipulatives.
• The Personal Math Trainer is an online adaptive assessment and personalized learning system for students. It analyzes student activity to determine strengths, weaknesses, learning style preferences, and pace. It provides a personalized learning path for students and generates reports for teachers to inform instruction.
• The online Math Activity Center provides online differentiated instruction opportunities for practice, reteach, and challenge. Teachers can assign RTI assignments to students who struggle on Big Idea Quick Quizzes. Fluency Builders develop students’ basic facts and automaticity.
• OSMO is an interactive gaming system for iPads to build students’ fluency and problem-solving skills. It offers physical manipulatives and provides immediate feedback.
abc123

Report Published Date: 2019/09/04

Report Edition: 2018

Title ISBN Edition Publisher Year
CCSS Homework and Remembering BLM Grade 5 9781328703606 Houghton Mifflin Harcourt 2018
CCSS Assessment Guide BLM Grade 5 9781328703675 Houghton Mifflin Harcourt 2018
Teacher Resource Book Grade 5 9781328703743 Houghton Mifflin Harcourt 2018
CCSS Teacher Edition Collection Grade 5 9781328741455 Houghton Mifflin Harcourt 2018
CCSS Softcover Consumable Student Activity Book Collection w/Mathboards Grade 5 9781328764287 Houghton Mifflin Harcourt 2018

## 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

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.