## Alignment: Overall Summary

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 partially meet the expectations for alignment. 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 partially meet the expectations for Gateway 2, rigor and practice-content connections. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet expectations for practice-content connections. The materials identify the practices and attend to the specialized language of mathematics, however, they do not attend to the full intent of the practice standards.

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## Gateway 1:

### Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
11
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
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

### Criterion 1a

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.

### Indicator 1a

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet expectations for assessing grade-level content. Probability, statistical distribution, similarity, transformation, and congruence do not appear in the assessments.

Examples of assessment items aligned to grade-level standards include:

• Chapter 1, Test A, Assessment Book, Item 6, “Round 4.822 to the nearest hundredth.” (5.NBT.4)
• Chapter 2, Test B, Assessment Book, Item 4, “Evaluate [17 + (15 x 20)] - 58.” (5.OA.2)
• Chapter 3, Test A, Assessment Book, Item 3, “Evaluate 22.16 - 8.5 + 46.83 = ______”. (5.NBT.7)
• Course Benchmark 1, Assessment Book, Item 4, “Round 2.369 to the nearest tenth.” (5.NBT.4)
• Chapter 9, Test B, Assessment Book, Item 4, “Find the area of the rectangle. Write your answer in simplest form.” [The dimension of the rectangle is 7/9 by 1/4.] (5.NF.4b)

Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. In the Dynamic Classroom, assessments can be downloaded as an editable document. Examples of assessment items that assess above grade-level content include:

• Assessment Book, Chapter 3, Test A, Item 13; and Test B, Item 13, “Order the expressions from least to greatest.” Two of the expressions include fractions with a denominator of 1,000 (“510/1,000 + 46/1,000 and 689/1,000-136-1,000”), a third expression includes decimals to the thousandths (“1.79 - 1.26”), and the fourth includes adding and subtracting decimals to the thousandths (“2.186 - (1.6 + 0.034”). The fourth expression is aligned to 6.NS.3.

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 70% of the time is spent on the major work of the grade.

### Indicator 1b

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet expectations for spending a majority of instructional time on major work of the grade.

To determine the focus on major work, three perspectives were evaluated: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of days devoted to major work.

• The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10 out of 14, which is approximately 71% of the instructional time.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 82 out of 93, which is approximately 88% of the instructional time.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 104 out of 149 days or 70%.

A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons. As a result, approximately 70% of the instructional materials focus on the major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, the materials do not meet the full intent of the standards because off-grade level content is present.

### Indicator 1c

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

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

• Chapter 4, Lesson 3, connects the supporting work of writing and interpreting numerical expressions (5.OA.1) with the major work of fluently multiplying multi-digit whole numbers (5.NBT.5). For example, Think and Grow: Modeling Real Life states, “A Cuvier’s beaked whale can dive 1,324 feet deeper than 4 times the depth a beluga whale can dive (2,123 feet). How deep can a Cuvier’s beaked whale dive? Write and solve an equation to find the depth.”
• Chapter 7, Lesson 9, connects the supporting work of writing and interpreting numerical expressions (5.OA.2) with the major work of performing operations with multi-digit whole numbers with decimals to hundredths (5.NBT.7). For example, Think and Grow: Problem Solving: Decimal Operations states, “You spend $67.45 on the video game controller, the gaming headset, and 3 video games. The video games each cost the same amount. How much does each video game cost?” Students are given a scaffolded “Plan” including writing an equation to solve the problem. • Chapter 11, Lesson 6, connects the supporting work of representing and interpreting data (5.MD.2) with the major work of multiplying fractions (5.NF.4). For example, Think and Grow: Make Line Plots, students multiply fractions in order to create fractions with the same denominator (eighths) and place the fractions on a line plot that has been divided into eighths. ### Indicator 1d The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. 2/2 + - Indicator Rating Details The instructional materials for Big Ideas Math: Modeling Real Life 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 149 days. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide is found on pages xl and xli in the Teacher’s Guide (Volumes 1 and 2). Grade 5 is divided into 14 Chapters. The 149 instructional days include the following: • 93 days of Lessons • 14 days of Lesson Opener Activities - Each Chapter begins with a chapter opener. • 28 days for “Connect and Grow” Activities - Two days per chapter are dedicated to these activities which include a performance task and chapter practice on one day and centers on the other day. The STEAM performance tasks are designated to be administered the same day as the cumulative practice following chapters 3, 7, 11, and 14. • 14 days for Chapter Assessments - Each chapter has a final chapter assessment. Three days are set aside for Benchmark Assessments to be used formatively, however the series does not identify when these should be administered. ### 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. 1/2 + - Indicator Rating Details The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 partially meet expectations for the materials being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade level and provide all students with extensive work on grade-level problems. The materials make connections to content in future grades, but they do not meet the full depth of the standards because off-grade level content is present. The Grade 5 materials develop according to the grade-by-grade progressions with content from prior or future grades clearly identified and related to grade-level work. • The Teacher Edition contains a “Progressions Through the Grades” section (pages xxxiv-xxxv). This contains the vertical progressions and identifies the domain and chapters in which they are found in each grade level. However, the progression ends at Grade 5, so the progression for Grade 6 is not noted. • Each chapter contains a chapter overview with a “Through the Grades” chart. The chart shows the chapter learning skills with the Progression from Grade 4 through Grade 6. • In each chapter, there is a written summarization (Laurie’s Overview/Preparing to Teach) about prior teaching that informs teachers of the conceptual progression of the upcoming chapter/lesson. For example, in Laurie’s Overview for Chapter 1 “Place Value Concepts” (pages T-1C and T-1D): “The first two sections of this chapter begin with a review of the place value ideas for multi-digit whole numbers... Understanding tenths and hundredths was developed in Grade 4 using manipulatives and relating to fraction equivalents... A major strand in Grade 5 is expanding students’ understanding of operations of the base ten system to decimals through thousandths.” • Cluster 5.NBT.B “Perform operations with multi-digit whole numbers and with decimals to hundredths” is developed in the following chapters: In Chapter 3, Add and Subtract Decimals, Lessons 1-7, students use rounding or compatible numbers to estimate sums and differences in decimals (Lesson 1), use models to add or subtract decimals (Lesson 2), add decimals and check whether the sum is reasonable (Lesson 3), subtract decimals and check answers (Lesson 4), use addition and subtraction to evaluate expressions involving decimals (Lesson 5), use mental math to add or subtract decimals (Lesson 6), and solve multi-step word problems involving money (Lesson 7). In Chapter 4, Lessons 3-5, students multiply multi-digit numbers by one-digit numbers (Lesson 3), multiply multi-digit numbers by two-digit numbers (Lesson 4), and multiply multi-digit whole numbers (Lesson 5). Students continue to work with 5.NBT.B in multiple lessons within Chapters 5, 6, 7, 10, 11, and 13. The instructional materials do not always attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. In Big Ideas Math: Modeling Real Life Grade 5, there are multiple examples where the content extends beyond the grade-level standards, which takes away from the focus of the grade-level mathematics. For example: • Chapter 3, Add and Subtract Decimals, Lessons 3-7 includes the mathematics of adding and subtracting decimals using the standard algorithm (6.NS.3). For example, in Lesson 3, “Find the sum, check whether your answers are reasonable." Problem 1: “1.3 + 7.5”; Problem 2: “601.58 + 82.31”; Problem 3: “19.73 + 7.16”; Problem 4: “84.6 + 44.7.” Four of the seven lessons in this chapter require the standard algorithm and do not use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. • Chapter 5, Multiply Decimals, Lesson 8 uses the standard algorithm to multiply decimals. (6.NS.3) The standard algorithm is demonstrated extensively throughout the lesson, and most multiplication problems have the directions, “Find the Product.” For example, Problem 10: “46.5 x 0.73=______”; Problem 11: “14.8 x 9.3 = _______”; Problem 12: “1.54 x 2.6 =_____.” In the Dynamic Classroom for the above problems, students can select a “?” and see how the problem is solved. In all of these examples, the video demonstrates solving the problems using the standard algorithm. • In Chapter 6, Divide Whole Numbers, Lessons 4 and Lessons 7 - 9, students divide whole numbers using the standard algorithm for division of up to four-digit dividends and two-digit divisors (6.NS.2). For example, Lesson 7 (Homework and Practice) includes the following: Problem 1 "21⟌735"; Problem 2: "64⟌802"; and Problem 3: "40⟌901”. The example problem is solved using the standard algorithm. Four of the nine lessons in the chapter require the use of the standard algorithm and do not use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Prior knowledge from earlier grades is explicitly related to grade-level concepts. For example: • Chapter 2, Numerical Expressions, (5.OA.1, 5.OA.2) builds on Grade 4 work in using all four operations to solve multi-step word problems and using variable to represent unknown numbers (4.OA.3). For example, Lesson 3, “Newton has$20. He spends $4 on lunch and$13 at the store. Write an expression to represent the situation.”
• Chapter 5, Multiplying Whole Numbers, (5.NBT.2, 5.NBT.5) builds on Grade 4 work of fluently adding and subtracting multi-digit numbers (4.NBT.4), and using properties and strategies to multiply up to a four-digit number by a one digit number and two two-digit numbers (4.NBT.5). For example, Lesson 3, “You build the card tower shown. Each row is 0.08 meter tall. Your friend’s card tower is 0.3 meter tall. Whose tower is taller? Because your card tower has 4 rows, multiply by 0.08 to find the height of your tower. Use a model. Shade 4 groups of 0.08. Compare the height of your tower to the height of your friend’s tower. So, ________ tower is taller.” A 10 x 10 grid is provided in the problem for students.
• Chapter 8, Add and Subtract Fractions, (5.NF.1, 5.NF.2) builds on the Grade 4 work of comparing two fractions with different numerators and denominators (4.NF.2), and adding and subtracting mixed numbers with like denominators (4.NF.3.C). For example, Lesson 4, Problem 13: “The George Washington Bridge links Manhattan, NY, to Fort Lee, NJ. The part of the bridge in New Jersey is about 1/2 mile long. The part in New York is about 2/5 mile long. About how long is the George Washington Bridge?"

### 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 Big Ideas Math: Modeling Real Life Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when the connections are natural and important.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• In Chapter 5, Lesson 3, the Learning Target “Use models to multiply decimals and whole numbers” is shaped by 5.NBT.B, Perform operations with multi-digit whole numbers and with decimals to hundredths.
• In Chapter 13, Lesson 3, the Learning Target “Use a formula to find volumes of rectangular prisms” is shaped by 5.MD.C, Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
• In Chapter 11, Lesson 6, the Learning Target “Make line plots and use them to solve problems” is shaped by 5.MD.B, Represent and interpret data.
• In Chapter 12, Lesson 2, the Learning Target “Relate Points and find distances in a coordinate plane” are shaped by 5.G.A, Graph points on the coordinate plane to solve real-world and mathematical problems.

Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:

• Chapter 13, Lesson 3 connects 5.MD.C and 5.NBT.B when students need to understand volume and perform operations with multi-digit whole numbers. For example, Homework & Practice, Problem 8, “A sandbox is a rectangular prism. The area of the base is 3,600 square inches. The height is 11 inches. You add 38,000 cubic inches of sand to the box. Do you fill the sandbox to the top? Explain.”
• Chapter 12, Lesson 7, connects 5.G.A with 5.OA.B when students graph relationships on a coordinate plane and analyze these relationships. For example, Think and Grow: Modeling Real Life states, “Some friends plan to go to a trampoline park for 2 hours. They want to go to the park that costs less money. Which park should they choose? What is the cost for each person? Graph the relationship between time and cost at both parks.”

## Rigor & Mathematical Practices

#### Partially Meets Expectations

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Gateway Two Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 partially meet the expectations for rigor and mathematical practices. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet the expectations for practice-content connections, they identify the Standards for Mathematical Practices, and attend to the specialized language of mathematics, but do not attend to the full intent of each practice standard.

### 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.
5/8
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Criterion Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 partially meet the expectations for rigor and balance. The instructional materials give appropriate attention to procedural skill and fluency, but lack opportunities for students to independently demonstrate conceptual understanding and application. The materials also partially address the three aspects of rigor with balance, treating them separately but never 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 Big Ideas Math: Modeling Real Life Grade 5 partially meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The instructional materials do not always provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level.

Each lesson begins with Explore and Grow and Think and Grow sections where students develop conceptual understanding of key mathematical concepts through teacher-led activities. Explore and Grow contains one to three problems where students model math and discuss their understanding through guided questions from the teacher. Think and Grow reinforces and extends the learning of the Explore and Grow section. For example:

• Chapter 1, Lesson 5, “Place Value with Decimals”, in Explore and Grow students “Model the number (3.33). Draw your model. Then write the value of each digit.” Students “Compare the value of the ones digit to the value of the tenths and the hundredths digit. Explain why you can use base ten blocks to model ones, tenths, hundredths.” In the “Think and Grow” section, a place value chart is used as students write numbers to the thousandths. (5.NBT.1)
• Chapter 6, Lesson 1, “Relate Multiplication and Division”, during teacher-led Explore and Grow and Think and Grow sections, students use area models to multiply and divide to develop understanding. For example, in Explore and Grow students “Use the area models to find 6 x 19 and 114 ÷ 6.” They are provided the question, “How do you think you can use multiplication to solve a division problem?” (5.NBT.B)
• Chapter 8, Lesson 6, “Add Mixed Numbers”, in the Explore and Grow and Think and Grow sections, students use models to add mixed numbers. For example, in the Explore and Grow section, students are asked to “Use a model to find the sum of 1 ¾ + 2 ⅛”. They are asked to discuss “How can you add mixed numbers with unlike denominators without using a model? Explain why your method makes sense.” (5.NF.A)

The instructional materials provide limited opportunities for students to demonstrate conceptual understanding independently throughout the grade-level. Within the Apply and Grow and Homework and Practice sections, students have limited opportunities to independently demonstrate conceptual understanding.

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials attend to the CCSSM fluency standards for Grade 5 including 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm". For example:

• Chapter 4, Lesson 4, Multiply by Two-Digit Numbers, Explore and Grow, students “Use the area model and partial products to find 28 x 13.” In Think and Grow, steps are introduced to “Find 312 x 82.” The steps modeled are: “Step 1: Multiply 312 by 2 ones, or 2. Regroup as necessary. Step 2: Multiply 312 by 8 tens, or 80. Regroup as necessary. Step 3: Add the partial products.” These steps are the traditional algorithm of multiplication. In the Show and Grow, Problem 3, “5,046 x 91 =____” [Written vertically]. In Apply and Grow, Problem 9, “9,513 x 67 = ____” [Written horizontally]. In Think and Grow, Problem 12, “A store sells 15 drones. How much money does the store collect?”

Students have multiple opportunities to use procedural skills. For example:

• Chapter 3, Lesson 4, Subtract Decimal, Explore and Grow, students begin by modeling “Find the difference. 427-156=____”. The remainder of the lesson provides multiple opportunities for students to practice the procedures for subtracting decimals. For example, Think and Grow, Problem 3, “24.75 - 9.10 =___” [Vertical Problem]. Apply and Grow, Problem 7, “856.02 - 48.12 =____” [Horizontal Problem]. Think and Grow, Problem 14, “An athlete’s fitness tracker reads 2.69 miles at noon. The figure shows the athlete’s fitness tracker before going to sleep that night. How many miles were recorded after noon?”
• Chapter 9, Lesson 5, Multiply Fractions, Explore and Grow, students “Use models to help you complete the table. What do you notice about each expression and its product?” The students are given four expressions “1/2 x 1/5; 3/4 x 1/2; 1/2 x 1/2 ; 2/3 x 2/3.” Students “Explain how to multiply two fractions without using a model.” During Think and Grow, the procedure for multiplying fractions is explained and modeled. For example, “Find 1/2 x 3/2. Multiply the numerators and multiply the denominators.” Students practice this procedure in problems throughout the lesson. For example, Think and Grow, Problem 1, “Multiply. 1/2 x 4/3=____” [Horizontal]. Apply and Grow, Problem 11, “(7/6 - 5/6) x 2/3=_____.” Think and Grow, Problem 16, “At a zoo, 3/5 of the animals are mammals. Of the mammals, 5/12 are primates. What fraction of the animals at the zoo are not primates?”(5.NF.4a, 5.NF.6).

In addition to the Student Print Edition, Big Ideas Math: Modeling Real Life Grade 5 has a technology package called Dynamic Classroom. The Dynamic Student Edition includes a game library where students can practice fluency and procedures. For example, the game “Decimal Dots” allows students to practice adding and subtracting decimals. “Mixed Number Subtract and Add” allows students to practice adding and subtracting mixed numbers. Additionally, the Dynamic Student Edition includes videos that explain procedures and can be accessed through QR Code in the Student Edition.

• Chapter 3, Lesson 3, Add Decimals, in the Apply and Grow and Homework and Practice sections, students have no opportunities to demonstrate conceptual understanding. In the Apply and Grow section, students are given 13 problems to solve that demonstrate procedural understanding. For example, Problem 10, “49.87 + 32.53 = ____”.  Homework and Practice include additional procedural and application problems, but none that require students to independently demonstrate their conceptual understanding (5.NBT.7).
• Chapter 4, Lesson 5, Multiply Multi-Digit Whole Numbers, in the Apply and Grow and Homework and Practice sections, students have no opportunities to demonstrate conceptual understanding. In the Apply and Grow section, students answer eleven questions that stress procedural understanding. For example, Problem 8, “1,907 x 218 = ____”. Homework and Practice includes additional procedural and application problems, but none that require students to independently demonstrate their conceptual understanding (5.NBT.5).
• Chapter 7, Lesson 1, Division Patterns with Decimals, in the Apply and Grow and Homework and Practice sections, students have no opportunities to demonstrate conceptual understanding. In the Apply and Grow section, students answer questions such as Problem 5, “2.9 ÷ 0.01 = ____” and Problem 7, “95.8 ÷ k = 958”. In the Homework and Practice section, students solve additional procedural and application problems, but does not include additional problems allowing them to show their conceptual understanding (5.NBT.2, 5.NBT.7).

### 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 Big Ideas Math: Modeling Real Life Grade 5 partially meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The series includes limited opportunities for students to independently engage in the application of routine and non-routine problems due to the heavily scaffolded tasks.

The instructional materials present opportunities for students to engage in application of grade-level mathematics; however, the problems are scaffolded through teacher led questions. During the Dig In, Explore and Grow, and Think and Grow sections of lessons, teachers are provided with explicit guidance to support students to engage with applications of mathematical content, and/or students are given steps to solve the problem. For example:

• Chapter 7, Lesson 9, Think and Grow: Modeling Real Life, “Descartes spends $16.40 on the game app, an e-book, and 5 songs. The e-book costs 4 times as much as the game app. The songs each cost the same amount. How much does each song cost?” Students have the following scaffolded questions: “What do you know? What do you need to find? How will you solve? Step 1: Multiply the cost of the app by 4 to find the cost of the ebook. Step 2: Write and solve an equation to find the cost of each song.” • Chapter 3, Lesson 2, Think and Grow: Modeling Real Life. Students find “How much longer is the duration of the wooden roller-coaster ride than the duration of the steel roller-coaster ride?” (Wooden Roller Coaster 4.25 minutes, Steel Roller Coaster 1.50 minutes). Students “Find the difference of the duration” with the expression 4.25-1.50 given. In the Teacher’s Guide, teachers guide students with the following prompts: “Tell your partner what the problem means. What are you trying to find out? What should our plan be to determine the difference in the roller coaster ride lengths?” and “We subtract the hundredths first. Are there any hundredths to subtract? Next we subtract tenths. What do we need to do?” The materials present opportunities for students to independently demonstrate routine and non-routine application of mathematics. Examples include: • In Chapter 6, Lesson 8, Think and Grow: Modeling Real Life, “The Great Barrier Reef is 2,300 kilometers long. A marine biologist studies the entire reef. He can explore no more than 75 kilometers of the reef each week. How many kilometers of the reef does the biologist explore the last week?” “Divide the total length by the length he can explore each week to find how many weeks he explores the reef.” • Chapter 5 Performance Task, includes three non-routine tasks: • 1.) “You have a corn root sample and a corn stem sample on microscope slides. When you view the samples through a microscope, the magnification number tells you how many times larger the image will be than the actual size. You see only a portion of the enlarged image. a. The corn root sample is 0.6 millimeters wide. You magnify the image by 400. What is the width of the magnified corn root image? b. You magnify the corn root sample by 1,200. How much wider is the image when magnified by 1,200 than by 400? c. You have a sample of a corn stem. The corn stem sample is 9.6 times wider than the corn root sample. What is the width of the corn stem sample? • 2.) An ear of corn has about 16 rows of kernels. Each row has about 50 kernels of corn. a. About 0.2 of the kernels are white and the rest are yellow. How many kernels are yellow? b. Each ear of corn has about 0.25 pound of kernels. How many pounds of kernels are in a dozen ears of corn? • 3.) You measure the growth of a corn stalk. The corn stalk grows about 1.75 inches each day. About how many inches does the plant grow in 1 month? Justify your answer.” • Chapter 9, Performance Task, students demonstrate their understanding of multiplying fractions. “You see a rock formation at a national park. The formation has layers that formed millions of years ago when particles settled in water and became rock. You make a model of the rock formation using 3/16 inch foam sheets. a. The three types of sedimentary rocks are limestone, sandstone, and shale. Use the number of foam sheets to find the height of each sedimentary rock layer. [Foam sheet diagram and table for students to fill in is included.] b. What is the combined height of the sedimentary rock layers? c. Will you use more foam sheets for the granite layers or the shale layers? Explain. d. The height of the topsoil layer is 1 1/4 times the height of the sandstone layer. How many foam sheets do you use in the topsoil layer? e. On your model, 1 inch represents 40 feet. What is the actual height of the rock formation? f. Why do you think the rock formation has layers?” • Chapter 5, Lesson 3, Show and Grow, Exercise 10: “You have 1 meter of ribbon. Do you have enough ribbon to border the outside of the square picture frame?” (a picture frame with one side length is given-0.33m) Students apply their knowledge of perimeter, geometry (knowing that a square has equivalent sides) and adding decimals to determine this answer. This question does not give a model for the students to use, so students need to apply their knowledge of models to solve (MAFS.5.NBT.2.7). ### 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. 1/2 + - Indicator Rating Details The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Students engage with each aspect of rigor independently. For example: • In Chapter 3, Lesson 3, Adding Decimals, the Dig In and Explore and Grow sections present students with limited opportunities to demonstrate conceptual understanding of addition of decimals. The remaining sections of the lesson (Think and Grow, Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice) focus on procedural understanding and fluency in addition of decimals. • In Chapter 3, Lesson 4, “Show and Grow and Apply and Grow: Practice” students use procedural skills and fluency as they practice subtracting decimals (12 problems). • Chapter 6, Lesson 8, Think and Grow: Modeling Real Life, Exercise 14, “A recreation director prepares the course of a 3-mile race by posting a motivational sign every 85 yards along the course. How many signs does the director use? Explain.” The instructional materials present opportunities for students to engage in multiple aspects of rigor within a lesson, however, these are often treated separately. For example: • In Chapter 6, Lesson 4, Divide by One-Digit Numbers, students have the opportunity to work with conceptual understanding during the Dig In and Explore and Grow sections as they use an area model to divide. The remaining sections of the lesson (Think and Grow, Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice) focus on procedural understanding and fluency in division. • In Chapter 11, Lesson 4, Weight in Customary Units, students develop an understanding of the customary units of weight including ounce, pound, and ton. In the Explore and Grow section, students use a number line labeled in pounds and tons, and convert between units. In the Think and Grow section, all aspects of rigor are noted as students use an area model to model converting between units of measure and procedures to convert between measures in customary units. In the remaining sections (Apply and Grow, Think and Grow: Modeling Real Life, Homework & Practice) there is an emphasis on converting between units through the use of a table with ounces, pounds, and tons. • In Chapter 4, Lesson 5, teachers begin the lesson by looking at strategies for finding the product of 400 x 80 in the Dig In and Explore and Grow. The remaining sections of the lesson (Think and Grow, Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice) focus on procedural understanding and fluency in multiplication. There are limited opportunities for students to demonstrate conceptual understanding in the lesson. ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 6/10 + - Criterion Rating Details The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 partially meet the expectations for practice-content connections. The materials identify the practice standards and explicitly attend to the specialized language of mathematics. However, the materials do not attend to the full meaning of each practice standard. ### 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 Big Ideas Math: Modeling Real Life Grade 5 meet expectations for identifying the Mathematical Practices (MPs) and using them to enrich the Mathematical Practices. The MPs are identified in both the Teacher Edition and Student Edition and the practices are connected to the mathematical content. The Standards for Mathematical Practice (MP) are identified in the digital Teacher's Edition on page vi. The guidance for teachers includes the title of the MP, how each MP helps students, where in the materials the MP can be found, and how it correlated to the student materials using capitalized terms. For example, MP2 states, "Reason abstractly and quantitatively. • "Visual problem-solving models help students create a coherent representation of the problem. • Explore and Grows allow students to investigate concepts to understand the REASONING behind the rules. • Exercises encourage students to apply NUMBER SENSE and explain and justify their REASONING." The MPs are explicitly identified in Laurie’s Notes in each lesson, and are connected to grade-level problems within the lesson. For example: • Chapter 10, Lesson 5, Problem Solving: Fraction Division (MP1) - In “Think and Grow: Modeling Real Life” students are given the problem, “A sponsor donates$0.10 to a charity for every 1/4 kilometer of the triathlon an athlete completes. The athlete completes the entire triathlon. How much money does the sponsor donate? Think: What do you know? What do you need to find? How will you solve?” The teacher is directed to ask students, “Describe your process for solving to your partner.”
• Chapter 7, Lesson 1, Division Patterns with Decimals (MP2) - In the “Dig In” section, students are engaged in a “Divide Around” activity where students divided by a power of 10.  MP2 is noted in the teaching notes with the following script for teachers, “The dividend (center circle) was the same for five problems. The divisor (along the curved arrow) was a power of 10. What did you notice about the quotient (outer circle) as the power of 10 decreased?”

### Indicator 2g.iii

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet expectations that materials use precise and accurate terminology and definitions when describing mathematics and the materials support students to use precise mathematical language. For example:

• In the beginning of each chapter is “Laurie’s Overview.” In this section, the mathematics of the chapter is described. For example, Chapter 9, Laurie’s Overview states, “No new vocabulary is introduced in this chapter.  Students continue to use the terms improper and proper fraction, mixed number, simplest form, and unit fractions.”
• Each chapter contains Vocabulary Cards for students and a vocabulary activity to introduce and reinforce the terms. For example, the Chapter 1 vocabulary cards include: base, exponent, period, power, thousandth, and thousandths place. The reverse side of each card gives a definition and an example.
• Teachers are provided explicit instructions in utilizing accurate mathematical terminology. For example, in Chapter 6, Lesson 2, Think and Grow, teachers are provided the following note: “When you model and say, 120 tens divided by 4 tens is 30, students often ask why the quotient is not 30 tens. Isn’t tens divided by tens equal to tens? In this example, there are 30 groups of 4 tens in 120 tens. In the first example, there are 7 groups of 9 hundred in 63 hundreds.” Chapter 9, Lesson 6, Dig In, identifies MP6 in the Teacher Edition. It directs teachers to ask students: “How is 1 square foot different from 1 foot? Can you and your partner show me what 1 square foot looks like?” In this example, the teacher guides students into understanding the mathematical language associated with linear and area measurements.
• “MP Precision” is labeled in the student book and highlights the precise use of numbers, symbols, and terminology. For example, in Chapter 8, Lesson 2, Homework & Practice, identifies MP Precision in the student work. Students are asked, “Your friend says 5/8 + 7/12 is about 2. Find a closer estimate. Explain why your estimate is closer”. This opportunity allows students to work with a mathematical expression and use mathematical language to explain their reasoning. Chapter 11, Lesson 8, Explore and Grow, identifies MP Precision in the student work. Students answer, “Which bag of fruit is heavier? Explain.” This exercise allows students to work with their understanding of ounces and pounds.

Overall, the materials accurately use numbers, symbols, graphs, and tables. Students are encouraged throughout the materials to use accurate mathematical terminology. The teaching guide reinforces the use of precise and accurate terminology.

## Usability

#### Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

### 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.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### 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.
N/A

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

### 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.
N/A

### 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.
N/A

### 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.
N/A

### 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).
N/A

### 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.
N/A

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### 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.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

### 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).
N/A

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

### Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

### 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.
N/A

### 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.
N/A

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

### 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.
N/A

### Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
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## Additional Publication Details

Report Published Date: 12/05/2019

Report Edition: 2019

Title ISBN Edition Publisher Year
BIG IDEAS MATH: MODELING REAL LIFE GRADE 5 STUDENT EDITION SET 9781635989151 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 5 TEACHER EDITION SET 9781635989168 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES PET CENTER ADVENTURE 9781635989229 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE SKILLS REVIEW HANDBOOK 9781642080155 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 5 ASSESSMENT BOOK 9781642080582 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 5 RESOURCES BY CHAPTER SET 9781642080612 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 5 INSTRUCTIONALRESOURCES 9781642080629 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019

## About Publishers Responses

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

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

## Educator-Led Review Teams

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

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

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

## Rubric Design

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

## Advancing Through Gateways

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
• Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

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

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

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

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

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

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

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

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

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

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

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