## Big Ideas Math: Modeling Real Life

##### v1
###### Usability
Our Review Process

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 4 partially meet the expectations for alignment. The instructional materials partially 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.

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

### Focus & Coherence

The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 partially 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. However, students and teachers using the materials as designed would not devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

##### Gateway 1
Partially 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 4 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain an assessment item that assesses above grade-level content, but this 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 4 meet expectations for assessing grade-level content. One above grade-level assessment item is present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. 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 3, “Compare. 502,956 and 482,956”. (4.NBT.2)
• Chapter 2, Test B, Assessment Book, Item 5, “67,542 + 89,227 = ______”. (4.NBT.4)
• Chapter 3, Test A, Assessment Book, Item 8, “Write the multiplication equation represented by the expression. (2,000 x 7) + (80 x 7) + (6 x 7)”. (4.NBT.5)
• Chapter 5, Test A, Assessment Book, Item 7, “Each table at a banquet seats 8 people. There are 456 people at the banquet. How many tables are there?” (4.NBT.6)
• Chapter 10, Test B, Assessment Book, Item 6, “0.2 + 0.7 = _____”. (4.NF.5

#### 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 4 do not 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 56% 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 4 do not 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 9 out of 14 chapters, which is approximately 64% 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 66 out of 108, which is approximately 61% of the instructional time.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 84 out of 150 days or 56%.

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 56% 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 4 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, but the materials do not explicitly connect prior knowledge to lesson content.

##### 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 4 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 3, connects the supporting work of factors and multiples (4.OA.4) with the major work of understanding equivalent fractions (4.NF.1). In the Think and Grow section, students find an equivalent fraction for 8/12 using division. Students list the factors of 8 and 12 and circle the factors they have in common and list them. Students divide 8/12 by the common factor 2 in order to create an equivalent fraction. Students also find equivalent fractions, for example Problem 3, “ 4/10 = ▢/5.”
• Chapter 11, Lesson 6, connects the supporting work of making a line plot with a data set (4.MD.4) with the major work of understanding fraction equivalence and ordering (4.NF.A). For example, Think and Grow section, Problem 1, “You survey 10 people about the amount of water each person drinks in 1 day. Make a line plot to display the data. Which amount of water consumed is the most common?” Students are given a table “Amount of Water (gallon)” with 10 fractions and a line plot that is partially created.
• Chapter 12, Lesson 2, connects the supporting work of applying the area and perimeter formulas for rectangles in real world and mathematical problems (4.MD.3) with using the four operations to solve problems (4.OA.1). For example, Homework & Practice, Problem 8, “An interior designer says that a rug under a dining room table should be 4 feet longer and 4 feet wider than the table. What is the area of a rug a customer should buy for under the table?” [The table is 6 ft. by 3 ft.]
##### 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 4 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 150 days. The 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 4 is divided into 14 Chapters. The 150 instructional days include the following:

• 94 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' | 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 4 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 grade-level standards because off-grade level content is present, and they do not explicitly connect prior knowledge to lesson content.

• 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 3 through Grade 5.
• 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 One “Place Value Concepts” (pages T-1C and T-1D): “This chapter begins with a review of the place value ideas developed in Grade 3... Students will read and represent numbers with precision, becoming comfortable moving between representations.” Additionally, “A major strand in Grade 4 is developing depth of conceptual place value understanding. This chapter focuses on place value relationships, concept of numbers, and then rounding. These ideas will form a basis for ideas to come; properties of operations and fluency of multi-digit arithmetic.”
• Cluster 4.NF.C “Understand decimal notation for fractions, and compare decimal fractions" is developed across the grade level. For example, prerequisite work on understanding fractions (4.NF.A, 4.NF.B) is the focus of Chapter 7 (Understand Fraction and Equivalence and Comparison), Chapter 8 (Add and Subtract Fractions), and Chapter 9 (Multiply Whole Numbers and Fractions). In Chapter 10 - Relate Fractions and Decimals - the focus is on understanding decimal notation for fractions and comparing decimal fractions. Lessons 1 and 2 build an understanding of tenths and hundredths. Lesson 3 focuses on writing tenths and hundredths in both fractions and decimals. Lesson 4 focuses on comparing decimals to the hundredths place. Lesson 5 explores using equivalent fractions to add decimal fractions and decimals. Lesson 6 brings in money and focuses on writing amounts of money in different ways (dollar sign and decimal, fractions or mixed numbers). The last lesson in the Chapter, Lesson 7, asks students to add, subtract, multiply, and divide amounts of money.

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 4, 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 4, Lessons 6-8 extend beyond Grade 4 (4.NBT.5) when the standard algorithm for multiplication is used, including regrouping (5.NBT.5). For example, in Lesson 8, students are provided an example problem: “A store receives a shipment of 5 boxes of pretzels. Each box is 50 centimeters high and has 24 bags of pretzels. How many ounces of pretzels does the store receive in the shipment?” Step 1 of the problem is written as a standard algorithm. Additionally, there are two regrouping boxes for students to put the regrouped tens. This example serves as a model to students for the remainder of the lesson. In the Dynamic Classroom, these problems are modeled using only the standard algorithm.
• Chapter 5, Lessons 6-8 extend beyond Grade 4 content when students use the standard algorithm for division (6.NS.2). For example, in Lesson 7, the example problem “Find 3,129 ÷ 4=______.” The examples use the standard algorithm and then students engage in six practice problems. In this chapter, 3 of the 9 lessons focus on the standard algorithm, which takes away the focus on the grade-level standards.
• In Chapter 9, Lesson 4, students multiply a whole number by a mixed number, extending beyond the Grade 4 standard, 4.NF.4 (“Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.”)  Example problems include: “2 x 1 1/2 + ______”; “2 x 3 5/6 = ___”; “4 x 3 6/10 = ___”.

Each chapter includes “The Progressions Through The Grades” table 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 2, Add and Subtract Multi-Digit Numbers, (4.NBT.3, 4.NBT.4, 4.OA.3) builds on the Grade 3 work of “Fluently add and subtract within 1,000 (3.NBT.2)” and “Use all operations to solve two-step word problems (3.OA.8).” In Grade 4, students “Round multi-digit numbers to a given place” (in Lesson 1, students round to estimate sums and differences), “Fluently add and subtract multi-digit numbers...” and ”Use comparative relational thinking to determine whether an addition or subtraction equations is true or false.” (In Lesson 6, students use number sense to tell whether an addition equation is true or false, and in Lesson 7, they use number sense to tell whether a subtraction equation is true or false.)
• Chapter 6, Factors, Multiples and Patterns, (4.OA.4) builds on the Grade 3 work of “Fluently multiply and divide within 100. Use multiplication facts to divide. Use properties of addition and multiplication to explain addition and multiplication patterns.” (In Lesson 1, students use models to find factor pairs; in Lesson 2, they use division to find factor pairs; in Lesson 3, they use their understanding of the relationship between factors and multiples.)
##### 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 4 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 6, Lesson 5, the Learning Target “Create and describe number patterns” is shaped by 4.OA.C, Generate and analyze patterns.
• In Chapter 14, Lesson 5, the Learning Target “Classify quadrilaterals” is shaped by 4.G.A, Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
• In Chapter 6, Lesson 1, the Learning Target “Use models to find factor pairs” is shaped by 4.OA.B, Gain familiarity with factors and multiples.
• In Chapter 8, Lesson 7, the Learning Target “Add mixed numbers with like denominators” is shaped by 4.NF.B, Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

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

• Chapter 16, Lesson 5, connects 4.OA.B with 4.OA.C when students solve problems using multiples and patterns. For example, Think and Grow: Modeling Real Life, Problem 17, “The pattern of animals on a Chinese calendar repeats every 12 years. The year 2000 was the year of the dragon. How many times will the year of the dragon occur between 2001 and 2100?
• Chapter 2, Lesson 1 connects 4.NBT.A with 4.NBT.B when students estimate numbers and add. For example, Think and Grow: Modeling Real Life, Problem 16, “Mount Saint Helens is a volcano that is 8,363 feet tall. Mount Fuji is a volcano that is 4,025 feet taller than Mount Saint Helens. About how tall is Mount Fuji?”

### Rigor & Mathematical Practices

The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 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 4 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 4 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 Think and Grow section 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 4, Lesson 1, “Multiply by Tens” addresses standard 4.NBT.6, “Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and or the relationship between multiplication and division.” In the Explore and Grow section, students are asked to “Model each product. Draw a model. [2 x 3, 2 x 30, 2 x 300, 2 x 3,000]” and further asked, “What pattern do you notice in the products? How can the pattern help you find 20 x 30?” In the Think and Grow section, students explore using place value and properties to multiply two-digit numbers. The teaching notes suggest the use of base-ten blocks for students to build the product.
• Chapter 7, Lesson 3, “Generate Equivalent Fractions by Dividing” addresses 4.NF.1, “Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.” In the Explore and Grow section, students “Shade the second model in each pair to show an equivalent fraction. Then write the fraction.” Students “Describe the relationship between each pair of numerators and each pair of denominators. How can you use division to write equivalent fractions? Explain. Then use your method to find a fraction that is equivalent to 610.” In the Think and Grow section, students extend this understanding to build from the concrete to abstract. The teacher introduces the term “common factor” as a way to find an equivalent fraction through division. In the Teacher’s Guide, “Supporting Learners,” teachers are directed to “Provide grid paper and a multiplication table. Have students draw the fraction first.” This is a way to support students who need a concrete model to demonstrate their conceptual understanding.
• Chapter 10, Lesson 2, “Understand Hundredths” addresses 4.NF.6, “Use decimal notation for fractions with denominators of 10 and 100.” In Explore and Grow, students work on “How many pennies have a total value of one dollar? Draw a model. One penny is what fraction of one dollar? Write your answer in words and as a fraction.” In addition, they answer “How is one tenth related to one hundredth? How do you think you can write 1/100 in a place value chart?” In the Think and Grow section, students shade a model and use a place value chart to demonstrate their understanding of hundredths.

The instructional materials provide limited opportunities for students to demonstrate conceptual understanding independently throughout the grade-level. The Apply and Grow, and Homework and Practice sections do not engage students in conceptual understanding. For example:

• Chapter 3, Lesson 6, Apply and Grow, Problem 14, students independently write a multiplication equation shown by an area model. In the Homework and Practice sections, no opportunities are evident for students to demonstrate their conceptual understanding independently.
• Chapter 5, Lesson 1, “Divide Tens, Hundreds, and Thousands” addresses 4.NBT.6. In the Apply and Grow and Homework and Practice sections, no opportunities are evident for students to demonstrate their conceptual understanding independently.
• Chapter 11, Lesson 7, Apply and Grow, students are given problems with the directions, “Find the equivalent amount of time.” Problem 7, “3 wk = ____”. In the Homework and Practice section students have similar conversion problems, but no opportunities to demonstrate their conceptual understanding independently.
##### 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 4 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 4 including 4.NBT.4, Fluently add and subtract multi-digit whole numbers using the standard algorithm". For example:

• Chapter 2, Lesson 2, Add Multi-Digit Numbers, students use a step-by-step breakdown for adding multi-digit numbers within 1,000,000. For example, “307,478 + 95,061.” Students use place value to line up the addends, and “add the ones, then the tens, and then the hundreds. Regroup if necessary.” Then they add the thousands, one place value at time and regroup. Students use this strategy during the Apply and Grow and Homework and Practice sections, where they have multiple opportunities to practice adding multi-digit numbers (4.NBT.4).
• Chapter 2, Lesson 3, Subtract Multi-Digit Numbers, students use place value to line up the numbers and subtract each place value beginning with the ones, regrouping as necessary. Students are provided multiple opportunities to practice the procedural skill in Think and Grow, Apply and Grow, and Homework and Practice sections. For example, Homework and Practice problems include procedure practice such as “9,127 - 6,753” (4.NBT.4).
• Chapter 5, Lesson 1, Divide Tens, Hundreds, and Thousands, students divide a multiple of ten, one hundred, or one thousand by a one-digit number, applying their understanding of place value and division facts. In Think and Grow, procedural understanding is developed. For example, Problem 1, “Find 2,400 ÷ 6”. Students are directed to think about the fact “24 ÷ 6”. Then students are encouraged to think of 5,600 as “56 hundreds ÷ 8” which is equal to “7 hundreds” or “700”. Students answer additional questions using this procedure. For example, Problem 13, “2400 ÷ 6 = ____”; Apply and Grow, Problem 24, “There are 240 students visiting a fair. They are divided equally among 8 barns. How many students are in each barn?”; Homework and Practice, Problem 3, “Find each quotient. 12 ÷ 2=___, 120 ÷ 2=___, 1200 ÷ 2=___,” and Problem 14, “50 ÷ ___=10” (4.NBT.4).

In addition to the Student Print Edition, Big Ideas Math: Modeling Real Life Grade 4 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 “Race to the Moon” allows students to practice subtracting multi-digit numbers. “Multiplication Quest” allows students to practice multiplying one-digit numbers. 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 4 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:

• In Chapter 3, Lesson 2, Think and Grow: Modeling Real Life, “An aquarium has 7 bottlenose dolphins. Each dolphin eats 60 pounds of fish each day. The aquarium has 510 pounds of fish. Does the aquarium have enough fish to feed the dolphins? Step 1: How many pounds of fish do all of the dolphins eat? 7 x 60 = ____. All the dolphins eat ____ pounds of fish. Step 2: Compare the number of pounds of fish all of the dolphins eat to the number of pounds of fish the aquarium has. The aquarium ____ have enough fish to feed the dolphins.”

The materials present opportunities for students to independently demonstrate routine application of mathematics. Examples of routine and non-routine applications include:

• Chapter 9, Lesson 1, Think and Grow: Modeling Real Life, “A piece of rope is 8/5 meters long. You cut the rope into 1/5 meter long pieces. How many pieces do you cut?”
• Chapter 5, Performance Task, “The students in fourth grade go on a field trip to a planetarium.”
• “1) The teachers have $760 to buy all of the tickets for the teachers and students. They receive less than$6 in change. a. Each ticket costs $6. How many tickets do the teachers buy? b. Exactly how much money is left over? c. There are 6 groups on the field trip. Each group has 1 teacher. There are equal number of students in each group. How many students are in each group? d. Two groups can be in the planetarium for each show. The planetarium has 7 rows of seats with 8 seats in each row. How many seats are empty during each show? • 2) The groups will be at the planetarium from 11:00 A.M. until 2:30 P.M. During that time, they will rotate through 7 events: the planetarium show, 5 activities, and lunch. The planetarium show lasts 45 minutes. Each activity lasts 22 minutes. Students have 5 minutes between each event. How long does each group have to eat lunch?” This is a non-routine application." • Chapter 10 Performance Task, “You have a recipe to make one loaf of homemade whole wheat bread. You want to make 8 loaves of bread.” • “1) You need between 6.5 cups and 7 cups of whole wheat flour for one loaf of bread. a. So far, you measure 3 1/4 cups of flour for one loaf. What is the least amount of cups you need to add? b. There are about 4 cups of flour in 1 pound. How many 5-pound bags of whole wheat flour should you buy to make all of the bread? c. You use a$10 bill to buy enough bags of whole wheat flour for 8 loaves. What is your change? [there is a picture of a bag of flour at 2.60] • 2) You need to add 2 1/4 cups of warm water for one loaf of bread. The temperature of the water should be about 110°F. a. How many cups of water do you need for all of the bread? b. You find the temperatures of 3 different samples of water. Which sample of water should you use. Explain [Table provided].” Students need to reason and apply the skills of the chapter independently. This is a non-routine application." • Chapter 6, Lesson 5, Think and Grow: Modeling Real Life, Problem 19, “You start with 128 pictures on your tablet. You take 6 pictures and delete 3 pictures each day. How many pictures do you have on your tablet after 6 days.” (4.OA.3) • Chapter 2, Lesson 4, Problem 16, “Students at a school want to recycle a total of 50,000 cans and bottles. So far, the students recycled 40,118 cans and 9,862 bottles. Did the students reach their goal? If not, how many more cans and bottles need to be recycled?” (4.NBT.4) ##### 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 4 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 1, Lesson 3, Dig In, in the Explore and Grow and Think and Grow sections, students demonstrate conceptual understanding through the use of a place value chart in order to compare multi-digit numbers. The mathematics becomes procedural as they compare numbers by looking at place value both in isolation and within the context of story problems. • In Chapter 4, Lesson 5, Divide by 6 or 7, students use multiple strategies to multiply and divide by 6 or 7. In the Apply and Grow and Homework and Practice sections, students have multiple opportunities to develop fluency with questions that ask students to “Find the Quotient”, reinforcing division facts for 6 and 7. • In Chapter 6, Lesson 3, Think and Grow: Modeling Real Life, “You need 96 balloons for a school dance. Balloons come in packs of 4, packs of 6, and packs of 9. Which packs could you buy so you have no leftover balloons?” Teachers ask “What do we need to find out?”, “How do we decide if 96 is a multiple of 4?”, and “We don’t know the divisibility rule for 4 so let’s divide 96 by 4, 4 is a multiple of 96. This means if packages of 4 are purchased there will be no leftover balloons.” 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: • Chapter 3, Lesson 7, addresses both conceptual understanding and procedural skill and fluency. During Dig In, students use base-ten blocks to build 4 groups of 17. In the Explore and Grow and Think and Grow sections, students demonstrate conceptual and procedural understanding as they explore multiplication. In the Apply and Grow, Think and Grow: Modeling Real Life, and Homework & Practice sections, students engage in procedural understanding and fluency. • In Chapter 9, Lesson 3, the Dig In section explores conceptual understanding as students use the fraction templates to model fractions. In the Explore and Grow section, students use models to multiply whole numbers by fractions. In the Think and Grow section, students have one last conceptual model for multiplying a whole number by a fraction. In the remaining sections, procedural skill and fluency are addressed as they multiply whole numbers by fractions with limited opportunities to demonstrate conceptual understanding independently. • In Chapter 11, Lesson 7, in the Dig In and Explore and Grow sections of the lesson, students explore time as they review the number of seconds in a minute, minutes in an hour and hours in a day and how to convert between units. In the Think and Grow, Apply and Grow, Think and Grow: Modeling Real Life, and Homework and Practice sections, students are given conversion tables and use procedural understanding and fluency to convert measures of time. #### 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 4 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 Grade 4 meet expectations for identifying the Mathematical Practices (MPs) and using them to enrich the Mathematical Practices. The MPs are identified in both the Teaching 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 14, Lesson 1, Line Symmetry - (MP4) Dig In, “Line Symmetry” is marked with MP4 - Model with Mathematics. Teacher asks students, “How many diagonals does each quadrilateral have? Fold across one diagonal in each of these shapes. Keep the quadrilateral folded, don’t unfold it.” The teacher is then instructed to have students discuss what they notice about the folded quadrilaterals and provide them with some possible conversations that may occur. • Chapter 8, Lesson 4, Use Models to Subtract Fractions (MP4), students are asked to create and use a model to find 9/12 - 5/12. The teacher is directed, “Ask several volunteers to share their models. You will likely see many number line diagrams. Students may recall how to show subtraction with an area model by crossing out the subtrahend.” 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, Units of Time - Explore and Grow, MP - Structure is identified in the Student Edition with the following question, “You know the amount of time in minutes. Without using a clock or a stopwatch, how can you find the amount of time in seconds?” The teaching notes identify the MP and the teacher is directed to ask, “When you know an amount of time in minutes, how can you find the amount of time in seconds?” (MP7 - assumed) • Chapter 2, Lesson 2, Add Multi-Digit Numbers - Explore and Grow: MP - Reasoning is identified in the Student Edition. Students are given several addition problems and asked to determine which problems show a correct way to find the answer, focusing on the vertical alignment of the digits with in the number. Students are asked the question, “Why do you need to use place value when adding? Explain.” There are no teaching notes for this question to support teacher facilitation of the MP. (MP2 - assumed) • Chapter 3, Lesson 1, Homework and Practice, MP - Precision is identified in a question where students are asked to “Compare the door’s height to the desk’s height using multiplication and addition.” This item does not meet the full intent of MP6. While students do use symbols to create a comparison between the height of the door (8 ft) and the height of the desk (2 ft), they are not communicating this to others. The teaching notes do not identify this specific MP. (MP6 - assumed) MP5 and MP8 are under-identified. ##### 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 4 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 MP1: Make Sense of Problems and Persevere in Solving Them, MP4: Model with mathematics, MP5: Use appropriate tools strategically, and MP8: Look for and express regularity in repeated reasoning. MP1: The instructional materials present few opportunities for students to make sense of problems and persevere in solving them. For example: • Chapter 3, Lesson 1, Laurie’s Notes, Think and Grow: Modeling Real Life, “Circulate as students discuss the model and then solve the problem. Students should recognize that there are 5 parts total for the amount of liquid. Knowing that the 5 parts represent 10 tablespoons of liquid helps them reason that each part must be 2 teaspoons.” Students are not given the opportunity to make sense and persevere independently as the problem is scaffolded. • Chapter 10, Lesson 6, Laurie’s Notes, Think and Grow: Modeling Real Life, “‘How can the two money amounts be compared?’ Write the fraction of a dollar (Newton’s money) as a decimal dollar amount or write the price tag as a fraction of a dollar.” Students compare 85/100 and0.99.

MP4: The instructional materials present few opportunities for students to model with mathematics. For example:

• Chapter 3, Lesson 10, Laurie’s Notes, Think and Grow, students solve, “A coach buys 6 cases of sports drinks and spends $60. Each case has 28 bottles. A team drinks 85 bottles at a tournament. How many bottles are left?” Laurie’s Notes state, “A tape diagram helps us to visualize the 6 cases of sports drinks. The letter k represents the unknown product, the number of bottles in 6 cases. If we find out what k equals, will we be able to find out n, the number of bottles left?” Students do not model to solve this problem and the tools are provided for them. • Chapter 5, Lesson 4, Laurie’s Notes, Think and Grow: Use Partial Quotients to Divide, students use an area model and partial quotients to find 235 ÷ 5. Laurie’s Notes state, “The area model shows how we reasoned through the problem. We don’t know the missing factor. Why? It is not a division fact we know, so we estimate. We use a fact we do know, 5 x 20, we subtract and the difference is 135. We can subtract another 5 x 20. We continue to subtract multiples until the remainder is less than the divisor.” Students do not need to model with mathematics. 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 four times throughout the instructional materials and only in two chapters. Big Ideas Math: Modeling Real Life Grade 4 presents limited opportunities for students to choose tools strategically, as the materials indicate what tools should be used. For example: • Chapter 8, Lesson 6, Laurie’s Notes, Dig In, students hold a rope and stand at points 0, 1, 2, and 3, with each whole segment divided into two equal parts. Teachers are directed to “Ask a volunteer to locate the fraction 1/2 and explain how they know they are correct. Label the location 1/2 with a sticky note. ‘Now I want to divide the length between 1 and 2, and between 2 and 3 into two equal parts.’ Clip two sticky notes at 1 1/2 and 2 1/2 but label them A and B. ‘Tell your partner what names we should write for these two locations.’ Elicit responses from students.” Students do not select tools strategically. The activity is fully guided by the teacher. • Chapter 5, Lesson 6, Laurie’s Notes, Dig In, students use “base 10 blocks to find a quotient where regrouping of 1 ten and 10 ones is needed. The figures show the stages of thinking that connect to the written record. The first figure shows three groups of ten with 1 ten and 2 ones left to be divided. Then 1 ten is regrouped as 10 ones plus 2 more ones for a total of 12 ones. Then 12 ones can be divided evenly into the three groups. The quotient is 4. It is important for students to manipulate the base ten blocks and explain aloud how they are using the blocks to find 42÷3. Have students write on their whiteboards to show how partial quotients can be used to solve 42 ÷ 3.” Students do not choose tools strategically as they are given a tool. ##### 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 4 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 4, Lesson 2, Explore and Grow, identifies “MP Constructing Arguments”. Students are asked: “Which estimated product do you think will be closer to the product of 29 and 37? Explain your reasoning.” By comparing the estimates and using mathematical justification, students are constructing arguments. • Chapter 10, Lesson 6, Apply and Grow: Practice, You Be the Teacher, Exercise 12 does not identify MP3; however, students have an opportunity to analyze the arguments of others: “Your friend has three$1 bills and 2 pennies. Your friend writes ‘I have $3.2’ Is your friend correct? Explain.” Students use mathematics to analyze the reasoning of others and construct arguments to explain the mathematics correctly. • Chapter 4, Lesson 3, Homework and Practice, You Be the Teacher, Exercise 7 does not identify MP3, but states: “Your friend finds 12 x 42. Is your friend correct? Explain.” The problem includes an area model and an equation. Students need to analyze their friends argument and use a mathematical argument to support their analysis. 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: • Chapter 8, Lesson 7, Explore and Grow, MP Construct Arguments is noted in the Student Edition. Students answer: “How can you use the whole number parts and fractional parts to add mixed numbers with like denominators? Explain why your method makes sense.” • Chapter 4, Lesson 8, Explore and Grow, MP Construct Arguments is noted in the Student Edition. Students use information about a ferry that can transport 64 cars each time it leaves the port. Students “Make a plan to find how many cars the ferry can transport in 1 week.” • Chapter 11, Lesson 6, Explore and Grow, MP Construct Arguments is noted in the Student Edition. Students create a line plot showing the length of each student’s hand length and are asked: “What conclusions can you make from the line plot?” ##### 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 4 partially meet expectations that the instructional materials assist teachers in engaging students in constructing viable arguments and analyzing 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 3, Lesson 8, Think and Grow: Modeling Real Life, teachers are prompted to ask, “Can you answer Exercise 19 by subtracting$152 - $144 =$8 first, then multiplying by 8? Explain.” In this example, the materials do not provide teachers with questions that elicit viable arguments or analyze the arguments of others.
• Chapter 6, Lesson 6, Think and Grow: Create Shape Patterns, supports the teacher to use a four shape pattern that is repeated twice. Teachers, “Solicit explanations as to how they can find the 42nd shape. Ask other students to critique each other’s reasoning.” The materials do not provide guidance for the teacher to model the conversation, or include additional probing questions to support students to analyze the reasoning of others.
• Chapter 13, Lesson 6, Explore and Grow, teachers ask, “‘Who can explain how they can tell by looking whether an angle is greater or less than 90 degrees?' Students can recall their mental image of a 90 degree angle. By comparing the given angle to their mental image, they can explain how the angle compares to a right angle.” The materials do not support the teacher to engage students in constructing an argument.

There are examples where the materials do assist teachers in having students develop an argument. For example:

• Chapter 10, Lesson 7, Think and Grow, students are asked to solve four money problems, each requiring a different operation. The materials provide guidance for teachers: “Focus on one example at a time. Ask a volunteer from a group to (a) explain their strategy for solving and (b) why it make sense. The focus is on the process not the answer.” The materials support teachers to engage students in constructing an argument. “Ask volunteers from other groups to critique the reasoning offered. Did they give a valid reason for the strategy they used? Again, focus on the process not the answer. How they carried out the strategy may vary.” The materials provide support support for teachers to engage students to critique the reasoning of others.
• Chapter 3, Lesson 4, Dig In, students use the distributive property to multiply tiles to create arrays. The teacher prompts, “If each partner is given a certain number of tiles to make a rectangle with no dimension equal to 1, will there always be just one rectangle when you combine the tiles?” Teachers engage students to construct an argument based on multiplication and the distributive property.
• Chapter 8, Lesson 1, Explore and Grow, students add fractions using models. The teacher asks the students questions to explain why you add the numerator and not the denominator. For example, “You did not add the denominators to get 16. Can you explain why?”
##### 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 4 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 7, Laurie’s Overview states, “Vocabulary terms equivalent and equivalent fractions are introduced and explored in the first three lessons. Models used to develop understanding of equivalent fractions are fraction strips, area models, and number lines. In all three models, students need to be able to see the whole.”
• Each chapter contains Vocabulary Cards for students and a vocabulary activity to introduce and reinforce the terms.  For example, the Chapter 5 vocabulary cards include the terms partial quotients and remainder. 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 13, Lesson 3, Homework and Practice, teachers are provided the following note: “Proficient students are generally able to understand how a given quadrilateral can have two different names. They need to attend to this possibility at all times. Sometimes a proficient student will forget and only select the most obvious category.” In Chapter 10, Lesson 1, Think and Grow, the following is noted, “The decimal point is read as and, not point. Read 2.8 as ‘two and eight tenths.’”
• “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, Apply and Grow, students are asked to “Match each fraction with an equivalent expression.” In Chapter 3, Lesson 1, Homework and Practice, student are given the height of a door and desk and asked to “Compare the door’s height to the desk’s height using multiplication and addition.” Students are asked to be precise in their description, such as “the door is 4 times as tall as the desk” and “The door is 6 feet taller than the desk.”

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

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

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### Overall Summary

###### Alignment
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###### Usability
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