## Big Ideas Math: Modeling Real Life

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Title ISBN Edition Publisher Year
BIG IDEAS MATH: MODELING REAL LIFE GRADE 8 STUDENT EDITION 9781635989052 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 8 TEACHER EDITION 9781635989076 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 8 STUDENT JOURNAL 9781642081695 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 8 ASSESSMENT BOOK 9781642081701 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 8 RESOURCES BY CHAPTER 9781642081718 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES 6 TO 8 9781642083057 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES DAY AT THE BEACH 9781635989007 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 1 STUDENT EDITION SET 9781635989069 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 1 TEACHER EDITION SET 9781635989083 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 1 ASSESSMENT BOOK 9781635989632 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 1 RESOURCES BY CHAPTER SET 9781635989663 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 1 INSTRUCTIONALRESOURCES 9781635989670 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE SKILLS REVIEW HANDBOOK 9781642080155 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES COOLEST ROCKIN DAY EVER 9781635988987 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE K STUDENT EDITION SET 9781635989021 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE K TEACHER EDITION SET 9781635989045 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE K ASSESSMENT BOOK 9781635989311 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE K RESOURCES BY CHAPTER SET 9781635989342 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE K INSTRUCTIONALRESOURCES 9781635989359 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE SKILLS REVIEW HANDBOOK 9781642080155 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 6 STUDENT EDITION 9781635988970 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 6 TEACHER EDITION 9781635988994 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 6 STUDENT JOURNAL 9781642080810 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 6 ASSESSMENT BOOK 9781642080827 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 6 RESOURCES BY CHAPTER 9781642080834 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES 6 TO 8 9781642083057 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 7 STUDENT EDITION 9781635989014 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 7 TEACHER EDITION 9781635989038 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 7 STUDENT JOURNAL 9781642081251 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 7 ASSESSMENT BOOK 9781642081268 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 7 RESOURCES BY CHAPTER 9781642081275 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES 6 TO 8 9781642083057 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 4 STUDENT EDITION SET 9781635989137 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 4 TEACHER EDITION SET 9781635989144 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES SKATE PARK ADVENTURE 9781635989212 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 4 ASSESSMENT BOOK 9781642080353 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 4 RESOURCES BY CHAPTER SET 9781642080384 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 4 INSTRUCTIONALRESOURCES 9781642080391 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019
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
BIG IDEAS MATH: MODELING REAL LIFE GRADE 3 STUDENT EDITION SET 9781635989113 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 3 TEACHER EDITION SET 9781635989120 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES NIGHT IN MADRID 9781635989205 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 3 ASSESSMENT BOOK 9781642080094 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 3 RESOURCES BY CHAPTER SET 9781642080124 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 3 INSTRUCTIONALRESOURCES 9781642080131 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE SKILLS REVIEW HANDBOOK 9781642080155 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 2 STUDENT EDITION SET 9781635989090 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 2 TEACHER EDITION SET 9781635989106 BIG IDEAS LEARNING, LLC 2019
MATH MUSICALS NEWTON AND DESCARTES FOUR LEGGED FUN 9781635989199 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 2 ASSESSMENT BOOK 9781635989861 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE GRADE 2 INSTRUCTIONALRESOURCES 9781635989908 BIG IDEAS LEARNING, LLC 2019
BIG IDEAS MATH: MODELING REAL LIFE SKILLS REVIEW HANDBOOK 9781642080155 BIG IDEAS LEARNING, LLC 2019
RICH MATH TASKS GRADES K TO 5 9781642083040 BIG IDEAS LEARNING, LLC 2019
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### Overall Summary

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 partially meet the expectations for alignment. The instructional materials meet expectations for Gateway 1, focus and coherence. The materials are coherent and consistent with the Standards and focus on the major work of the grade. The instructional materials partially meet the expectations for Gateway 2, rigor and practice-content connections. Although the materials give appropriate attention to procedural skill and fluency, the materials partially meet expectations for rigor. 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.

###### Alignment
Partially Meets Expectations
Not Rated

### Focus & Coherence

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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' | indicatorName}}
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.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 meet expectations for assessing grade-level content.

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

• Chapter 1, Test A, Assessment Book, Item 7, “You want to play as many games as possible with 18 tokens. Each game costs 3 tokens. Which model can you use to find how many games you can play?” Students determine which of 3 models represent $$18\div3$$. (3.OA.2)
• Chapter 3, Test A, Assessment Book, Items 1-6, “Find the product. [9 x 3, 4 x 5, 6 x 6, 10 x 7, 8 x 4, 7 x 9]”. (3.OA.7)
• Chapter 7, Test A, Assessment Book, Items 1-4, “1. Round 54 to the nearest 10; 2. Round 770 to the nearest hundred; 3. Round 44 to the nearest ten; 4. Round 550 to the nearest hundred.” (3.NBT.1)
• Chapter 9, Test A, Assessment Book, Item 11, “Find 8 x 50. How many hundreds are in the product? How many tens?” (3.NBT.3)

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.

Examples of assessment items that assess above grade-level content include:

• Chapter 2, Test B, Assessment Book, Item 12, “Tell whether the number 15 is a multiple of 2, 5, or both.” (4.OA.4)
• Chapter 3, Test A, Assessment Book, Item 9, “Which are not multiples of 9? 18, 24, 71, 81, 27, 35”. (4.OA.4)

#### Criterion 1.2: Coherence

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.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Big Ideas Math: Modeling  Real Life Grade 3 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 examined: 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 10.5 out of 15 chapters, which is approximately 70% 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 83 out of 98 lessons, which is approximately 85% of the instructional time.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 111 out of 158 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 1.3: Coherence

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 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.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 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 7, Lesson 5, connects the supporting work of understanding place value to perform multi-digit arithmetic (3.NBT.2) with the major work of solving two-step word problems (3.OA.8). In the Think and Grow section, Problems 20 and 21, students add two 3-digit numbers and then subtract in order to find "about how many more" in a two-step word problem.
• Chapter 10, Lesson 2, connects the supporting work of partitioning shapes with equal areas (3.G.2) to the major work of understanding a fraction 1/b as the quantity formed by one part when the whole is partitioned into b equal parts (3.NF.1). For example, Problem 14 states, “You paint a plate that has 4 equal parts. You paint two parts orange and one part red. You paint the rest of the plate yellow. What fraction of the plate is yellow?”
• Chapter 14, Lesson 6, connects the supporting work of making a line plot using measurement data from measuring lengths (3.MD.4) with the major work of representing a fraction on a number line (3.NF.2). In the Think and Grow section, students are provided a two-inch ruler compared to a number line with the fractions labeled 0/2 through 4/2 to show the correspondence between the number line and a ruler. Students "Measure the length of each line to the nearest half inch. Then record each length on the line plot." Students are provided four different length lines and are asked to fill in the missing numbers on the line plot, then mark the correct length on the line plot.
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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 158 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 3 is divided into 15 Chapters. The 158 instructional days include the following:

• 98 days of Lessons
• 15 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.
• 30 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 4, 8, 12, and 15.
• 15 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' | indicatorName}}
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.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 meet expectations for being consistent with the progressions in the Standards. The Grade 3 materials develop according to the grade-by-grade progressions with content from prior and future grades clearly identified and related to grade-level work. Materials give students extensive work with grade-level problems and the materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

• 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.
• Each chapter contains a chapter overview with a “Through the Grades” chart. The chart shows the chapter learning skills with the progression from Grade 2 through Grade 4.  For example, in Chapter 6, the “Through the Grades” identifies the Grade 2 skill: “Find the total number of squares in a rectangle;” the Grade 3 skill: “Use addition and multiplication to find the area of a shape;” and the Grade 4 skill: “Use area and perimeter formulas to solve word problems.”  The manual does not give specific references to standards.
• 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 (pages T-1C and T-1D): “This chapter develops an understanding of multiplication and division through multiple representations: equal groups, equal-sized groups, number lines, skip counting, and writing equations. This understanding builds the foundation for future use with multi-digit whole numbers, integers, fractions, and decimals. Students begin to build connections between prior knowledge of repeated addition and subtraction to see how this knowledge can be applied to a new concept. This interconnectedness of mathematics is important for understanding the progression of numbers and operations, rather than compartmentalizing mathematics as a set of non-related topics.”
• “Multiply and divide within 100” (3.OA.C) is developed across several chapters. For example, in Chapter 1, the first four lessons develop an understanding of multiplication. These lessons include identifying equal groups, writing a repeated addition equation for equal groups, using a number line to skip count, identifying the number of rows and columns in an array, writing a multiplication equation for an array, and using arrays to show the Commutative Property of Multiplication. The final three lessons develop an understanding of division. These lessons include using division to find the size of equal groups, writing a division equation, using division to find the number of equal groups, using a number line to skip count backward, and writing repeated subtraction equations and a division equation. Chapter 2 includes multiplying by 2, 5, and 10, using properties to multiply by 0 or 2, using the Distributive Property to multiply, and using the problem-solving plan to solve word problems involving multiplication. In Chapter 3, the first six lessons address multiplying by 3, 4, 6, 7, 8, and 9, respectively. Each lesson uses models, develops fact fluency, and includes practice in finding products. Lesson 7 addresses multiplication strategies for multiplying two factors. Lesson 8 introduces the Associative Property of multiplication and multiplying three factors to find a product. The last lesson in the chapter focuses on solving problems involving multiplication. Additional lessons in Chapters 4, 5, 6, 12, 14, and 15 continue work with this standard.

The instructional materials give all students extensive work with grade-level problems. For example:

• Each lesson has “Explore and Grow” that provides students a hands-on approach. For example, in Chapter 8, Lesson 1, students “use the addition table to write all of the addition equations that have a sum of 13.”
• Each lesson has “Think and Grow” that offers teacher-guided instruction. For example, in Chapter 3, Lesson 1, students use an array model and the Distributive Property to multiply by 3.
• Each lesson has “Show and Grow” that presents students with 2-5 problems and helps teachers to formatively assess student understanding. For example, Chapter 4, Lesson 1 includes 4 problems involving division and arrays.
• Each lesson has “Apply and Grow” which provides students independent practice. For example, Chapter 5, Lesson 2 includes 17 problems for students to solve independently involving multiplication and division facts.
• Each lesson has “Think and Grow: Modeling Real Life” that brings problem solving and real life situations together for students to apply their learning. For example, Chapter 6, Lesson 3 states “Your rectangular animal poster is 4 feet long and 1 foot wide. Which poster has a greater area, your animal poster or your space poster?” (Space poster and its dimensions are shown on the student page.)
• Each lesson has “Connect and Extend Learning” that includes homework and practice problems as well as Cross-Curricular Connections. For example, Chapter 11, Lesson 7 contains a cross-curricular connection for Language Arts, and 11 Homework and Practice Problems.

Each chapter includes a “Progressions Through The Grades” chart that makes explicit connections to the prior knowledge in relation to the content in the chapter. However, there is not explicit guidance by lesson connecting prior knowledge to the content of the lesson, although connections can be made. For example:

• Chapter 4, Division Facts and Strategies, builds on students' learning of multiplication strategies (arrays) and division in Chapter 1 as well as learning from previous grades (fact families, place value) to use strategies to divide. The mathematics include interpreting whole-number quotients of whole numbers (3.OA.2), using multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (3.OA.3), understanding division as an unknown-factor problem (3.OA.4), fluently multiplying and dividing within 100 (3.OA.7), and applying properties of operations as strategies to multiply and divide (3.OA.5).
• In Chapter 6, Relate Area to Multiplication, students build an understanding of area (3.MD.5), measure area by counting unit squares (3.MD.6), and relate area to the operations of multiplication and addition (3.MD.6).
• In Chapter 13, Classify Two-Dimensional Shapes, students build on previous learning of shapes and attributes to identify, classify, and draw shapes. The mathematics of this chapter focuses on identifying shapes by name and attributes, comparing shapes using their attributes, and identifying examples and non-examples of quadrilaterals (3.G.A.1). This grade-level work is the foundation for future work with points, lines, and angles.
##### Indicator {{'1f' | indicatorName}}
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.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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 where the connections are natural and important.

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

• In Chapter 1, Lesson 1, the Learning Target “Use Equal Groups to Multiply” is shaped by 3.OA.B, Understand properties of multiplication and the relationship between multiplication and division.
• In Chapter 6, Lesson 3, the Learning Target “Use multiplication to find the area of a rectangle” is shaped by 3.MD.C, Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
• In Chapter 10, Lesson 3, the Learning Target “Identify and write a fraction” is shaped by 3.NF.A, Develop understanding of fractions as numbers.
• In Chapter 12, Lesson 8, the Learning Target “Measure masses in grams and kilograms” is shaped by 3.MD.A, Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

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

• Chapter 6, Lesson 3, connects understanding concepts of area (3.MD.C) with representing and solving problems involving multiplication and division (3.OA.A) by having students multiply to find the area of rectangles. For example, Problem 8 states, “A city street parking spot has an area of 72 square feet. The parking spot is 9 feet long. How wide is the parking spot?”
• Chapter 5, Lesson 3, connects representing and solving problems involving multiplication and division (3.OA.A) with multiplying and dividing within 100 (3.OA.C). For example, Think and Grow, Problem 11, “You make favor bags for a birthday party. Complete the table to find how many of each item you need for the given numbers of bags.”

### Rigor & Mathematical Practices

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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.

##### Gateway 2
Partially Meets Expectations

#### Criterion 2.1: Rigor

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.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 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' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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 an Explore and Grow and a Think and Grow section, where students develop conceptual understanding of key mathematical concepts through teacher-led activities. The Explore and Grow section contains one to three problems where students model math and then discuss their understanding through guided questions from the teacher. The Think and Grow section reinforces and extends the learning of the Explore and Grow section. For example:

• In Chapter 1, Lesson 3, Explore and Grow, teachers direct students to “Put 24 counters into equal rows. Draw your model.” “Put 24 counters into a different number of rows. Draw your model.” “Compare your models. How are the models the same? How are they different?” This example builds conceptual understanding under the cluster heading, “Represent and solve problems involving multiplication and division” and specifically the standards 3.OA.1 and 3.OA.3. In the Think and Grow section, students model an array with 2 rows and 7 columns and build both a repeated addition equation (7 + 7 = 14) and a multiplication equation (2 x 7 = 14).
• In Chapter 8, Lesson 7, Explore and Grow, students use a hundred chart and a number line for students to subtract. Students “Color to find 79 - 47. Then model your jumps on the number line.”...“How can finding 79-47 help you find 379-47?” Throughout the lesson, students use the number line to model addition and subtraction. This example builds conceptual understanding for 3.NBT.A “Use place value understanding and properties of operations to perform multi-digit arithmetic.” In the Think and Grow section, students learn and model “count back” and “count on” strategies prior to moving to independent work for the lesson.

While there are some opportunities for students to demonstrate conceptual understanding independently, the instructional materials do not always provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. Within the Apply and Grow and Homework and Practice sections, students have limited opportunities to independently demonstrate conceptual understanding. For example:

• Chapter 2, Lesson 1, Explore and Grow, students “Model 3 x 2 using equal groups.” They answer: “How can you use the model to find 4 x 2?” Throughout the Think and Grow and Apply and Grow sections, students are given representations and tools to show both repeated addition and the math facts. In the Homework and Practice section, students have limited opportunities to use arrays, models, and repeated addition to demonstrate conceptual understanding of multiplication independently. In Problems 3 through 13 students “Find the Product.”
• Chapter 4, Lesson 3, “Divide by 2, 5, or 10", Explore and Grow, students “Use the number line to model 10 ÷ 2” and answer ‘In your number line model, does 2 represent the number of equal groups or the size of the groups? Explain.’” Students have no additional opportunities to show their conceptual understanding in this lesson.
• Chapter 11, Lesson 7, “Compare Fractions", Explore and Grow, students “Use a strategy to find the greater fraction.” Students are given the fractions “2/3” and “2/8”. Students are directed to “Use a different strategy to check your answer. Tell your partner which strategy you prefer. Explain.” In the Think and Grow section, students are provided fraction strips to compare two fractions during the teacher directed activity. As students transition to the independent work in the Apply and Grow section, they are asked to complete many problems with the directions to “Compare,” with examples such as “1/4 ____ 2/4." Scaffolding is available in the Laurie’s Notes section, however, students are not required to demonstrate conceptual understanding during their independent work. The Homework and Practice problems provide limited opportunity for students to demonstrate conceptual understanding using fraction strips (3.NF.3d).
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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 3 including addition/subtraction within 1000 (3.NBT.2) and multiplication/division within 100 (3.OA.7). For example:

• In Chapter 2, Lesson 2, Multiply by 5, students use a number line to skip count and find the products of a multiplication fact with a factor of 5. Throughout the lesson, students have many opportunities to practice their products of math facts with a factor of 5. For example, Problem 1, “Complete the model and the equation (___ jumps of 5, ___ x ___ = ___).” Problem 16, “10 = 2 x ___”. Problem 20, “You recycle 9 bottles and receive 5¢ for each bottle. You spend 25¢ on a pack of gum. How many cents do you have left?” and Problem 11, "5 x ___= 20” (3.OA.7).
• Chapter 5, Lesson 3, Complete Multiplication Tables, students fill in various multiplication tables for six multiplication facts (3.OA.7).
• Chapter 8, Lesson 5, Add Three-Digit Numbers, students use a three-step procedure to solve addition of three-digit numbers. "Step 1: Estimate. Round each addend to the nearest ten… Step 2: Find the sum. Add the ones, then the tens, then the hundreds. Step 3: Check.” (3.NBT.2)
• Chapter 8, Lesson 10, Relate Addition and Subtraction, students connect addition and subtraction by using inverse operations to check answers. Students have multiple opportunities to practice addition and subtraction within 1000 both with procedural problems and word problems (3.NBT.2).

In addition to the Student Print Edition, Big Ideas Math: Modeling Real Life Grade 3 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 “Three in a Row - Multiplication” allows students to practice multiplication fluency. “Product Lineup” allows students to practice division facts. Additionally, the Dynamic Student Edition includes videos that explain procedures and can be accessed through the QR Code in the Student Edition.

##### Indicator {{'2c' | indicatorName}}
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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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. For example:

• In Chapter 3, Lesson 8, Think and Grow, students solve the problem, “There are 26 students in your class. Your teacher brings in 4 boxes of muffins. Each box has 4 packages with 2 muffins in each package. Are there enough muffins for the class?” In the Teacher Notes, teachers are given guiding questions: “How could we draw a picture of this situation? Which container is the largest, the box or the package? How many boxes should we draw? How many packages do you see? What is inside one of the packages? How can we adjust our equation to show we have 4 full boxes? Where would you place grouping symbols? Why?...Complete the multiplication using your choice of grouping. Decide if there are enough muffins for each of the students to have one. Compare your answer with your partner and discuss how you solved it.”
• In Chapter 9, Lesson 4, Explore and Grow, students solve, “A box of 8 burritos costs $9. How much does it cost a group of friends to buy 40 burritos?” The Teacher Notes include guiding questions and directions: “Point to What do you know? and read the first statement. Demonstrate how to return to the problem, reading it again to find the information and complete the statements. Do the same for What do you need to find? ‘Now we are ready to make a plan.’ Show how to use the information in the Understand the Problem to complete the How will you solve? ‘Why does the plan write a division equation to find b? What other equations might a student use?’ The 40 burritos are boxed in equal-sized groups of 8. Division can be used to find the number of groups...As you work through Steps 1 and 2 with students, ask ‘What does b represent? What does c represent? How is the value for b used to find c? What if we get an answer of$10, does this seem reasonable?...What about 1 million dollars?”

The materials present opportunities for student to independently demonstrate routine application of mathematics; however, there are few opportunities for students to independently demonstrate application of grade-level mathematics in non-routine settings. Examples of routine applications include:

• In Chapter 6, Lesson 3, Show and Grow, Problem 11: “A sign has an area of 18 square feet. The sign is 6 feet long. How wide is the sign?” This is a routine application problem requiring students to find a missing factor.
• In Chapter 4 Lesson 5, Think and Grow: Modeling Real Life,  “There are 42 students in gym class. The teacher divides the students into 7 teams. How many more students would be on each team if the teacher divides the students into 6 teams?” This is an example of a routine application as students need to revise the problem to represent a different divisor.
##### Indicator {{'2d' | indicatorName}}
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.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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 11, Lesson 4, Explore and Grow, students engage in conceptual understanding as they solve “Color each fraction. Circle the greater fraction. Explain to your partner how you can compare fractions with the same denominator.” Two examples with 2 equally partitioned parts are provided.
• Chapter 3, Lesson 4, Apply and Grow: Practice, students engage with procedural skill and fluency as they solve 11 multiplication problems.
• Chapter 2, Lesson 5, Question 9, Show and Grow, students engage with application as they solve, “A joke book has 20 pages. There are 5 jokes on each page. You read 16 jokes. How many jokes do you have left to read?”

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 3, Lesson 4, Dig In, Explore and Grow and Think and Grow sections, students demonstrate conceptual understanding through the use of number lines and models for multiplying by 7s. In Apply and Grow Practice, students engage with conceptual knowledge (using arrays), as well as procedural skills and fluency. During the Think and Grow: Modeling Real Life, and Show and Grow, students engage with application. In Homework and Practice, students engage in conceptual understanding, procedure skill, and fluency.
• In Chapter 7, Lesson 3, during the Dig In and Explore and Grow sections, students engage in conceptual understanding using a hundreds chart and number line. The Think and Grow, Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice sections focus on procedural understanding.
• In Chapter 10, Lesson 3, students focus on conceptual understanding as they determine how many parts in a whole (denominator) and how many of the parts are shaded (numerator). However, within the context of story problems, students are introduced to the key words used to determine how many parts in a whole, thus proceduralizing the concepts. During Review & Refresh, students complete two problems that involve fact families involving multiplication and division.
• In Chapter 11, Lesson 7, conceptual understanding of equivalent fractions is addressed in the Dig In and Explore and Grow sections with students using fraction strips to explore comparing fractions. In the Think and Grow section, the focus shifts to procedural understanding by providing students with a process to compare fractions. In the Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice sections, the mathematics is predominantly procedural (3.NF.3.d).

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 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' | indicatorName}}
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Math Grade 3 meet expectations for identifying the Mathematical Practices (MPs) and using them to enrich the Mathematical Practices.

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 in the Dig In, Explore and Grow, Think and Grow, and Think and Grow: Modeling Real Life sections. For example:

• Chapter 1, Lesson 1, Explore and Grow, MP7 - Teachers are instructed to ask students, “What is the same in both of your models? What is different? Why? Tell your partner.”
• Chapter 3, Lesson 9, Dig In, MP3 - Students have been introduced to a problem solving planning tool in a previous lesson. In this lesson they need to convince their partner that they should use the their problem solving plan. Teachers say, “One of you will try to convince your partner that they should use the plan. The other partner will listen and ask questions. Pretend your partner has never used the problem-solving plan. You may need to explain the parts of the plan. Your partner might ask questions. At the end of 3 minutes I will call time and you will switch roles.”
• Chapter 10, Lesson 1, Think and Grow, MP8 - Students explore equal parts in different shapes. Teachers ask, “‘What do you think will happen if we lay the parts of the circle on top of each other?  Why?’ Confirm by laying parts over each other to see that the smaller portions do not cover a larger piece completely. Shade the pieces different colors to emphasize differences on the overlay.”
• Chapter 11, Lesson 7, Dig In, MP2 - Using a fraction strip divided into 8ths with 3/8ths folded under, teachers ask, “‘How much is missing to get to 1?’ Listen to their responses and reasoning. Reveal the 3/8 to confirm. Repeat the activity several times with different denominators and missing parts. ‘Knowing how much is missing to reach one whole can be a useful strategy for deciding if one fraction is greater than another.’”

The MPs are identified in the digital Student Dashboard under Student Resources, Standards for Mathematical Practice. This link takes you to the same information found in the Teacher Edition. In the Student Edition, the MPs are identified in the Explore and Grow, Apply and Grow: Practice, and Homework and Practice Sections. For example:

• Chapter 11, Lesson 7, Explore and Grow, students use two different strategies to find the larger fraction. “MP Construct Arguments” - labels the following question: “Tell your partner which strategy you prefer. Explain.” (MP3 - assumed)
• Chapter 2, Lesson 1, Apply and Grow: Practice, students are provided with two models. One shows two groups of four and the other provides four groups of two. “MP Structure” labels the following question: “How are the models similar? How are they different?” (MP7 - assumed)
• Chapter 6, Lesson 4, Homework and Practice, “MP Structure” is identified in a question where students are given two equations and asked to “Draw a rectangle for the expression.” (MP7 - assumed)

MP5 is under-identified. MP5 is identified explicitly in two lessons.

##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. The materials do not attend to the full meaning of three or more Mathematical Practices.

The instructional materials do not present opportunities for students to engage in MP4: Model with mathematics, MP5: Use appropriate tools strategically, MP7: Look for and make use of structure, and MP8: Look for and express regularity in repeated reasoning.

MP4: The instructional materials present few opportunities for students to model with mathematics. Throughout the materials, models are provided for students. For example:

• Chapter 9, Lesson 1, Laurie’s Notes, Dig In, “We can model the multiples of 20 by covering the numbers you skipped. As you and your partner count by 20s again, place a counter over the numbers that you skip. When you finish, only the multiples of 20 should be showing.” Students do not need to model with mathematics, and are given a number line for skip counting.
• Chapter 7, Lesson 1, Laurie’s Notes, Dig In, “Model two- and three- digit numbers with base ten blocks. Have students record the number in one of the various forms: standard, expanded, or word. Each time, discuss the following: ‘Explain how you know your answer is correct. What digit is in the tens (hundreds) place? What is its value? How do the blocks show this? How does the form show this? What if I add a rod? What if I add a flat, how does the standard (expanded, word) form of the number change?’”

MP5: While the Dynamic Student Edition includes tools for students, the instructional materials present few opportunities for students to choose their own tool, therefore, the full meaning of MP5 is not being attended to.  MP5 is only identified a total of two times throughout the instructional materials. Big Ideas Math: Modeling Real Life Grade 3 presents limited opportunities for students to choose tools strategically, as the materials indicate what tools should be used. For example:

• Chapter 8, Lesson 10, Laurie’s Notes, Explore and Grow, “Point to an anchor chart with a number line. ‘What will undo a jump of 10?’ Jump back 10. Use a collection of base ten blocks. ‘What will undo subtracting a rod?’ Adding a rod point to a hundred chart. ‘What will undo jumping down two rows?’ Jumping up two rows.” In this example, base-ten blocks are the tools provided for student use.
• Chapter 7, Lesson 5, Laurie’s Notes, Dig In, “Allow time to discuss in small groups and decide how they might estimate. Some may want to try comparing heights of counters in each container, counting around the edges, or employing other useful tools. Provide access to string, rulers, balance scales, etc. Make it fun for them to try to get a close estimate without just blindly guessing.” In this example, students have a choice of tools; however, it was the only example in the series.

MP6: The instructional materials do not support students to attend to precision. In most instances, teachers attend to precision for students. For example:

• Chapter 8, Lesson 5, Laurie’s Notes, Show and Grow, students add 236 + 378. The Teacher Edition identifies MP6 with the following teaching notes: “Work through each step. ‘6 + 8 is 14. That is 4 ones and 1 group of ten. 1 + 3 + 7 is 11 and this is the tens place value so we have 11 tens. That is 1 ten and 1 group of one hundred. 1 + 2 + 3 is 6 and this is the hundreds place value. The sum is 614.’” In this example, the teacher is the one attending to precision, not the student.
• Chapter 11, Lesson 6, Think and Grow: Modeling Real Life, students are given a recipe for Vegetable Soup. The teaching notes identifies MP6 and provides teachers with the question, “Why could we not compare 1/4 to 3/8 to decide whether there is more corn or more Creole seasoning in the recipe?” In this example, the teacher is the one attending to precision, not the student.
• Chapter 6, Lesson 2, Laurie’s Notes, Dig In, “‘What size do you think a square that covers 1 square inch would be?' -show with your fingers”. Draw a square on the board, with a measuring stick, and label the inside as area = 1 square inch and the edges as 1 inch. Relate a bench mark for 1 inch. Repeat for 1 centimeter.” In this example, the teacher is the one attending to precision, not the student.

MP7: The instructional materials often label content MP7 Structure, but the teaching notes and problems do not attend to the full meaning of the MP.  For example:

• Chapter 1, Lesson 1, Laurie’s Notes, Explore and Grow, students put 24 counters into different equal-sized groups. The teaching notes identify MP7, “What is the same in both of your models? What is different? Why? Tell your partner.” Students do not need to identify and make use of structure to answer these questions.
• Chapter 12, Lesson 7, Laurie’s Notes, Think and Grow, “Review that 1,000 grams equals 1 kilogram. Yesterday students learned that 1,000 milliliters equals a liter.” Students do not look for or make use of structure.
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 partially meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples of where students engage in the full intent of MP3 include the following:

• Chapter 15, Lesson 2, You be the Teacher section is not identified with a MP; however, students need to construct an argument: “Descartes says that a square will always have a greater perimeter than a triangle because it has more sides. Is he correct? Explain.” The explanation requires the use of the properties of quadrilaterals.
• Chapter 7, Lesson 3 Homework and Practice, You be the Teacher does not identify a MP; however, students construct a viable argument: “Descartes says that a number rounded to the nearest ten can be greater than the same number rounded to the nearest hundred. Is Descartes correct? Explain?”
• Chapter 7, Lesson 5, students estimate the differences “173-63” and “263-197”. The bottom of the page is marked “MP Construct Arguments”, as students “Compare your answers to your partner’s answers. Explain why they are the same or why they are different.”
• Student Edition, Chapter 5, Lesson 3, Explore and Grow, students complete a multiplication table. MP Critique Reasoning is noted: “Describe how you completed the table. Compare your method to your partner’s method. How are they the same? How are they different?”

The Student Edition labels Standards of Mathematical Practices with “MP Construct Arguments”, however, these noted activities do not always indicate that the students are constructing arguments or analyzing arguments of others. For example:

• In Chapter 11, Lesson 4, Explore and Grow, students “Explain to your partner how you can compare fractions with the same denominator.” Students do not need to construct an argument.
• Chapter 4, Lesson 5, Explore and Grow, students “Complete the statements and the models: 42 6 and 42 7." Students answer, “Without solving, which quotient is greater? Explain how you know.” The students had already solved it, and the model that is created for them shows the answer. There is no thinking, analyzing or arguing that occur.
• In Chapter 4, Lesson 8, Explore and Grow, students solve 36 ÷ 4, “What other strategies can you use to solve? Explain the strategy to your partner.” In this example, students explain a strategy, they do not need to construct an argument.
##### Indicator {{'2g.ii' | indicatorName}}
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.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 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.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. For example:

• Chapter 8, Lesson 2, Think and Grow: Adding on a Number Line, students find “245 + 38”. The teacher is guided with the following question, “Could we start at 38 and count on 245? Would you? Explain.”
• Chapter 13, Lesson 4, Think and Grow: Drawing Quadrilaterals, students “draw a quadrilateral that has four right angles and name the quadrilateral.” The teacher is directed to poll the class for the results “rectangle or square.” “Explain to your partner why square is a more specific name than the rectangle.” This is a missed opportunity for the teacher to ask the students to provide a different name for their quadrilateral and argue which name best describes the quadrilateral, rather than telling the student that a “square is more specific."
• Chapter 14, Lesson 1, Explore and Grow, students read and interpret a picture graph. MP3 is identified in the teaching guide, “Explain to your partner how you found the total.” The materials do not assist teachers in having students construct viable arguments and analyze the arguments of others.

There are occasions where the materials do assist teachers to engage students to construct and/or analyze an argument. For example:

• Chapter 3, Lesson 9, Think and Grow: Using the Problem-Solving Plan, teacher guidance includes: “How do we know we should multiply the 8 and 3 to find the number of feathers used?” The materials encourage the teacher to “prompt justifications with questions: ‘Why not 30 x 3? Why subtract the product from 30?”
• Chapter 10, Lesson 2, Think and Grow: Modeling Real Life, teachers are guided to have students look at flags from different countries, and based on their understanding of fractions, teachers ask: “How can you argue that there is only one flag in Exercise 13 that represents a unit fraction for the amount of red? Present your argument to your partner. Answer any questions your partner asks about your choice.”
• Chapter 13, Lesson 3, Dig In, Circle Time, teachers create a rectangle on a geoboard and ask: “How do you know it is a rectangle?” The teacher is prompted to “ask students to write how they know and show their partner. Do their reasons agree?” Based on the teacher’s observations they are then asked to “solicit reasons from students”.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 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 1, Laurie’s Overview states, “The new precise mathematical terms introduced are: Commutative Property of Multiplication, factors, product, multiplication, division, multiplication symbol, division symbol.”
• Each chapter contains Vocabulary Cards for students and a vocabulary activity to introduce and reinforce the terms. For example, the Chapter 4 vocabulary cards include the terms: dividend, divisor, fact family, and quotient.  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 11, Lesson 4, Think and Grow, teachers are directed to review the use of the signs > and <.  The inequality 3>2 can also be written 2<3.
• “MP Precision” is labeled in the student book and highlights the precise use of numbers, symbols, and terminology. For example, in Chapter 4, Lesson 1, Homework and Practice, students are asked to “Label the parts of a division problem using quotient, dividend, and divisor.” In Chapter 10, Lesson 5, Explore and Grow, students are asked to “Complete the fractions on the number line. Plot 3/2 on the number line. What do you notice? Explain.”

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

### Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
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.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
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.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
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.
##### Indicator {{'3h' | indicatorName}}
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.
##### Indicator {{'3i' | indicatorName}}
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.
##### Indicator {{'3j' | indicatorName}}
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).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
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).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
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.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
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.
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.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

### Summary of Alignment & Usability for Big Ideas Math: Modeling Real Life | Math

#### Math K-2

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grades K-2 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence. The instructional materials partially meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials were not reviewed for Gateway 3, instructional supports and usability indicators.

##### Kindergarten
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated

#### Math 3-5

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grades 3-5 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations in Grades 3 and 5 and partially meet expectations in Grade 4 for Gateway 1, focus and coherence. The instructional materials partially meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials were not reviewed for Gateway 3, instructional supports and usability indicators.

###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated

#### Math 6-8

The instructional materials reviewed for Big Ideas Math: Modeling Real Life, Grades 6-8 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence. The instructional materials partially meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials were not reviewed for Gateway 3, instructional supports and usability indicators.

###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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