## Alignment: Overall Summary

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet the expectations for alignment. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials partially meet the expectations for Gateway 2, rigor and practice-content connections. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet expectations for practice-content connections. The materials identify the practices and attend to the specialized language of mathematics, however, they do not attend to the full intent of the practice standards.

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## Gateway 3:

### Usability

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

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

### Criterion 1a

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.

### Indicator 1a

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet the expectations for assessing the grade-level content and if applicable, content from earlier grades.

There are no above grade level assessment items for Grade 7. Examples of assessment items which assess grade-level standards include:

• Chapter 1, Quiz 2, Item 9, students use a vertical number line that shows elevations of a submarine after certain events to determine the distance the submarine rises after diving and the original elevation of the submarine. (7.NS.1.c)
• Chapter 3, Test A, Item 13, students factor a linear expression in order to determine the length of a square patio that has a perimeter of 16x + 12 feet. (7.EE.1)
• Chapter 3, Performance Task, Item 1, students write and simplify expressions from information provided in a diagram and a table. They describe and explain what they notice about the two expressions. (7.EE.1-2)
• Chapter 5, Test A, Item 6, students find the density of a substance in grams per millimeter by examining a graph. (7.RP.2.d)
• Course Benchmark 2, Item 30, students find the actual perimeter and area of a square using information about the scale drawing of a square. (7.G.1)
• Chapter 8, Alternative Assessment, Item 1, students are given the scenario about finding out how the residents in their town feel about opening a new gas station. Students describe how to conduct a survey so that the sample is biased, and unbiased survey of 200 people. They project how many residents out of 6200 will support the gas station if 80 out of 200 supported it. (7.SP.1-2)

### Criterion 1b

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 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 78% of the time is spent on the major work of the grade.

### Indicator 1b

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet expectations for spending a majority of instructional time on major work of the grade. This includes all the clusters in 7.RP.A, 7.NS.A, and 7.EE.A, B.

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

• There are 10 chapters, of which 7.4 address major work of the grade, or approximately 74%
• There are 152 lessons, of which 119 focus on the major work of the grade, or approximately 78%
• There are 152 instructional days, of which 119 focus on the major work of the grade, or approximately 78%

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 78% of the instructional materials focus on the major work of the grade.

### Criterion 1c - 1f

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, above grade-level content is present and not identified.

### Indicator 1c

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The supporting domain Statistics and Probability enhances focus and coherence to major standard/clusters of the grade, especially domains 7.NS and 7.RP. For example:

• In Chapter 5, Section 5.2, Solve Problems Involving Scale Drawings of Geometric figures (7.G.1) is connected to the major work of analyzing proportional relationships (7.RP.A). Students write and solve a proportion using the scale and ratios of the lengths of a drawing.
• In Chapter 7, Section 7.1, 7.SP.5 is connected to 7.RP.A as students work with probability as the ratio of desired outcomes to possible outcomes, and examine the probability between 0 and 1 including 0 and 1 of an event.  Relative frequency is also defined as a ratio. For example, in Problem 4, students describe the likelihood of each event when making three-point shots or missing the shots.
• In Chapter 7, Section 7.3,  Compound Events, connects 7.G.8a with 7.RP.3 when students determine probability by computation of rational numbers, and representing answers as fractions and percents. For example, Problem 4 expresses the probability as 1/6 or 16 2/3%.
• In Chapter 7, Section 7.3, Probability of Compound Events, 7.SP.8 is connected to the major work of solving real-world problems with rational numbers involving the four operations, 7.NS.3. Students solve simple and compound probabilities using rational numbers in various forms.
• Chapter 8, Section 8.1, Example 3 utilizes proportions to solve a problem to make projections for modeling real world problems. After randomly surveying 75 students, students use the results to estimate the number of students from the total population of 1200. Cluster 7.SP.A supports 7.RP.3.
• In Chapter 8, Section 8.2, Self-Assessment, Problem 4, students apply and extend previous understandings of operations with fractions (7.NS.A) to draw inferences about a population (7.SP.A). Students find the means of three samples of the number of hours music students practice each week, and use the means to make one estimate for the mean number of practice hours. The calculations result in a rational number that, when converted to a decimal, results in a repeating decimal, which they make sense of in order to answer the question about the number of hours music students practice each week (7.NS.2).
• Chapter 9, Section 9.5, Problem Solving with Angles, 7.G.5 is connected to the major work of solving word problems leading to equations, 7.EE.4.a as students write and solve equations to find the missing angle using properties of supplementary, complementary, adjacent, and vertical angles.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 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 152 days.

The pacing shown in the Teacher Edition includes a total of 152 days.  This is comprised of:

• 122 days of lessons (62 lessons),
• 20 days for assessment (one day for review, one day for assessment), and
• 10 days for “Connecting Concepts”, which is described as lessons to help prepare for high-stakes testing by learning problem-solving strategies.

The print resources do not contain a pacing guide for individual lessons. The pacing guide allows three days for this section. Additional time may be spent utilizing additional resources not included in the pacing guide: Problem-Based Learning Investigations, Rich Math Tasks, and the Skills Review Handbook. In addition, there are two quizzes per chapter located in the Assessment Book which indicates where quizzes should be given. The Resources by Chapter materials also include reteaching, enrichment, and extensions.  In the online lesson plans, it is designated that lessons take between 45-60 minutes. The day to day lesson breakdown is also noted in the teacher online resources.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet expectations for the materials being consistent with the progressions in the Standards.

The materials concentrate on the mathematics of the grade, and are consistent with the progressions in the Standards. The publisher recommends using four resources together for a full explanation of the progression of skill and knowledge acquisition from previous grades to current grade to future grades. These resources include: “Laurie’s Notes”, “Chapter Overview”, “Progressions”, and “Learning Targets and Success Criteria”. For example:

• Laurie’s Notes, “Preparing to Teach” describe connections between content from prior grades and lessons to the current learning. For example, in Chapter 4, Section 4, “Students should know how to graph numbers on a number line and how to solve one-variable inequalities using whole numbers. In the exploration, students will be translating inequalities from verbal statements to graphical representations and symbolic sentences.”
• Chapter Overviews describe connections between content from prior and future grades to the current learning, and the progression of learning that will occur. For example, Chapter 5, “Laurie’s Notes: Chapter Overview”, “The study of ratios and proportions in this chapter builds upon and connects to prior work with rates and ratios in the previous course.” This supports Standard 6.RP. In Sections 5.1 and 5.2, students decide whether two quantities are in a proportional relationship using ratio tables. This supports Standard 7.RP.2.a and uses unit rates involving rational numbers. During Sections 5.3, 5.4, and 5.5, students write, solve, and graph proportions. This supports Standard 7.RP.2.a-7.RP.3, “Graphing proportional relationships enables students to see the connection between the constant of proportionality and equivalent ratios”, but the term “Slope”, Standards 8.EE.5-6, is not included. In Section 5.6, students work with scale drawings, which supports Standard 7.G.1.
• Each chapter’s Progressions page contains two charts. “Through the Grades”, lists the relevant portions of standards from prior and future grades (grades 6 and 8) that connect to the grade 7 standards addressed in that chapter. For example, Chapter 4, Sections 4.1-4.2, students use algebra tiles to review the process of solving one-step equations. This is identified as revisiting work from a prior grade-level in the “Chapter Exploration and supports grade-level work in section 4.3 of solving equations of the form px + q =r and p(x + q) =r.  This supports Standard 7.EE.4a.

Each lesson presents opportunities for students to work with grade-level problems. However, “Scaffolding Instruction” notes suggest assignments for students at different levels of proficiency (emergent, proficient, advanced). These levels are not defined, nor is there any tool used to determine which students fall into which level. In the Concepts, Skills and Problem Solving section at the end of each lesson problems are assigned based on these proficiencies, therefore, not all students have opportunities to engage with the full intent of grade-level standards. For example:

• In the Teacher Edition, Chapter 6, Section 6.5, the assignments for proficient and advanced students includes a reasoning task in which students determine the price of a drone that is discounted 40%, and then discounted an additional 60% a month later. This reasoning task is omitted from the assignments for emerging students.
• In the Teacher Edition, Chapter 9, Section 9.2, the assignments for advanced students include a critical thinking task in which students determine how increasing the radius of a circle impacts the area of the circle. This critical thinking task is omitted from the assignments for emerging and proficient students.
• Each section within a chapter includes problems where the publisher states, “students encounter varying “Depth of Knowledge” levels, reaching higher cognitive demand and promoting student discourse”. In Chapter 8, Section 8.1, students examine a sample of a population for validity. This supports Standard 7.SP.1 and use a random sample to draw inferences about a population which supports Standard 7.SP.2.
• In “Exploration 1” students “make conclusions about the favorite extracurricular activities of students at their school” by first identifying the population and samples of the population, (DOK Level 1) and then by evaluating the differences between two samples and evaluating their conclusions for validity and explain their thinking, (DOK Level 3).
• Problem 2 students compare two samples to determine which sample is unbiased, (DOK Level 2).
• In Chapter 4, Section 4.6, students roll two different colored dice with negative and positive numbers on each cube. When the students roll a pair of dice, they write an inequality to represent them. Then they roll one die and multiply each side of the inequality to represent them. They are then asked if the original inequality is still true. Finally, they are asked to make conjectures about how to solve an inequality of the form ax <b for x when a>0 and when a<0. These conjectures will help to develop the key idea(s) for the section which is to write and solve inequalities using multiplication and division. This supports standard 7.EE.4.b.
• In Chapter 6, students use a percent model to justify their answers, instead of assessing the reasonableness of answers using mental computation and estimation strategies.  Mental computation and estimation are strategies specifically called for in standard 7.EE.3.

Materials explicitly relate grade-level concepts to prior knowledge from earlier grades. At the beginning of each section in Laurie’s Notes, there is a heading marked “Preparing to Teach”, which includes a brief explanation of how work in prior courses relates to the work involved in that lesson. In some cases it outlines what happened in prior courses, but is not specific to which grade or course this happens. For example:

• In Chapter 1, Section 1.1, it states that in prior courses students were introduced to integers, absolute value, and number lines. For example, “It is important that students review these foundational skills because they are necessary for adding and subtracting rational numbers.”  In Chapter 1, Section 1.1, students review the concept of absolute value (6.NS.7). This leads into Section 1.2 where students begin adding integers (7.NS.1.b).
• In Chapter 3, Section 3.3 states that students have used the distributive property in previous courses. It adds, “They will extend their understanding to include algebraic expressions involving rational numbers. This property is very important to algebraic work in future courses”.  In Chapter 3, Section 3.3, Exploration 1, students build upon their experience with the distributive property to include rational numbers. In Example 1, students apply the distributive property to simplify expressions.
• In Chapter 5, Section 5.2, the Preparing to Teach notes, explain the connection between students’ prior work with ratios (describing ratio relationships, completing tables), (6.RP.A), and the content in Section 5.2, stating, “In this lesson, they will extend their work with ratios to include fractions, making connections to their recent work with fractions.” In Section 5.1, students complete ratio tables, and write and interpret ratios, but now with fractions, forming a bridge to upcoming work of finding and using unit rates involving rational numbers (7.RP.1).
• In Chapter 6, Section 6.1, Preparing to Teach, notes state students “should know how to solve simple percent problems, and how to use ratio tables, Standard 6.RP.3.” The remainder of Chapter 6, “will build upon this understanding to write and solve percent proportions.”  (7.RP.3)
• In the Resources by Chapter book, each chapter has a few questions that are named as “Prerequisite Skills Practice”. The intent is for practice from prior knowledge. There is no mention of previous grade knowledge or previous lesson knowledge.

### Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Chapter headings indicate the learning targets for each section and are outlined at the beginning of each chapter in the Teacher Edition. Each chapter also begins with a table that identifies the standard that is taught in each section with an indication if the lesson is preparing students, if it completes the learning or if students are learning or extending learning. For example:

• In Chapter 5, Algebraic Expressions and Properties, 6.EE, Apply and extend previous understandings of arithmetic to algebraic expressions is directly related to the Chapter 5 learning goals of, “Evaluate algebraic expressions given values of their variables (Section 5.1), Write algebraic expressions and solve problems involving algebraic expressions (Section 5.2), Identify equivalent expressions and apply properties to generate equivalent expressions (Section 5.3), Identify equivalent expressions and apply properties to generate equivalent expressions (Section 5.4), and Factor numerical and algebraic expressions (Section 5.5).

Materials consistently include problems and activities that connect two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important. Multiple examples of tasks connecting standards within and across clusters and domains are present. These connections build deeper understanding of grade-level concepts and the natural connections which exist in mathematics. For example:

• In Chapter 3, students engage simultaneously in Standards 7.NS.A and 7.EE.A, as they simplify, add, subtract, factor and expand linear expressions involving positive and negative number coefficients. For example, in Section 3.1, Try It, Problem 9, students simplify 2s - 9s + 8t - t. In Section 3.3, Try It, Problem 5, students use the distributive property to simplify the expression -3/2 (a - 4 - 2a).
• In Chapter 4, students use operations with integers, Cluster 7.NS.A to solve problems using numerical and algebraic expressions and equations, Cluster 7.EE.B.
• In Chapter 5, Domain 7.RP connects ratio with computations with rational numbers 7.NS, as students explore rates and unit rates. For example, in Section 5.6, students analyze proportional relationships and use them to solve real-world problems.
• Chapter 6, the problems and activities provide connections between the skills and understandings of Cluster 7.EE.B to those of Cluster 7.RP.A as students write proportions and equations to represent and solve percent problems, and to write equations to solve problems involving discounts and markups. In Section 6.3, Practice, Problem 23, students write and solve an equation to determine the percent of sales tax on a model rocket costing $24 with a sales tax of$1.92.
• Chapter 8, Section 8.4, students use random sampling to draw inferences about a population, connecting 7.SP.A with drawing informal comparative inferences about two populations, 7.SP.B.

## Rigor & Mathematical Practices

#### Partially Meets Expectations

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Gateway Two Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet the expectations for rigor and mathematical practices. The materials partially meet the expectations for rigor by reflecting the balances in the Standards and giving appropriate attention to procedural skill and fluency. The materials partially meet the expectations for practice-content connections, they identify the Standards for Mathematical Practices, and attend to the specialized language of mathematics, but do not attend to the full intent of each practice standard.

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
5/8
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Criterion Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 partially meet the expectations for rigor and balance. The instructional materials give appropriate attention to procedural skill and fluency, but only partially give appropriate attention to conceptual understanding and application, due to the lack of opportunities for students to fully engage in the work. The materials partially address these three aspects with balance, treating them separately but never together. Overall, the instructional materials partially help students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
1/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 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 Exploration section where students develop conceptual understanding of key mathematical concepts through teacher-led activities. For example:

• In Chapter 1, Section 2, Exploration 1 (7.NS.1.d), students are taught to add integers with chips and using number lines. “Write an addition expression represented by the number line. Then find the sum.” After these examples, students are asked to use conceptual strategies (number line or chips).
• In Chapter 3, Lesson 2, Exploration 1, students use algebra tiles to model a sum of terms equal to zero and simplify expressions. In the Concepts, Skills and Problem Solving section, students have two additional problems where they use algebra tiles to simplify expressions. (7.EE.1)
• Chapter 1, Section 4, “Subtracting Integers,” Exploration 1 asks students to work with partners and use integer counters to find the differences and sums of several problems with two different representations. For example, “4 - 2” and “4 + (-2)”; “-3 - 1” and “-3 + (-1)” and “13 - 1”.  Student pairs are asked to generate a rule for subtracting integers. Students who can’t generate a rule are prompted to use a number line. After working independently students share their rule with a partner and discuss any discrepancies. (7.NS.1)
• Chapter 4, Section 1 “Solving Equations Using Addition or Subtraction” Exploration 1, students are asked, “Write the four equations modeled by the algebra tiles. Explain how you can use algebra tiles to solve each equation.” (7.EE.3)

The instructional materials do not always provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. The shift from conceptual understanding, most prevalent in the Exploration Section, to procedural understanding occurs within the lesson.  The Examples and “Concepts, Skills, and Problem Solving” sections have a focus that is primarily procedural with limited opportunities to demonstrate conceptual understanding. For example:

• In Chapter 3, Section 2, only Problems 8 and 9 ask students to demonstrate conceptual understanding. For example, Problems 10-17 ask students to “Find the Sum.”  Problem 10: “(n+8) + (n-12)”; Problem 16: “(6-2.7h) + (-1.3j-4).” Problems 19-26 ask students to “Find the difference.” Problem 19: “(-2g+7) - (g+11)”; Problem 26: “(1-5q) - (2.5s+8) - (O.5q+6)”. (7.EE.1)
• In Chapter 2, Section 2, Concepts, Skills & Problem Solving, the majority of the questions require procedural knowledge and do not ask students to demonstrate conceptual understanding. For example, Problems 13-28 ask students to “Find the quotient, if possible”, such as Problem 16: “-18 ÷ (-3)"; and Problem 22: “-49 ÷ (-7)”. (7.NS.1)

### Indicator 2b

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 meet expectations that they attend to those standards that set an expectation of procedural skill. The instructional materials attend to operations with rational numbers (7.NS.A), using the properties of operations to generate equivalent expressions (7.EE.1), and solving real-life and mathematical problems using numerical and algebraic expressions (7.EE.B). For example:

• In Chapter 1, Lesson 5, students subtract rational numbers. Examples 1-3 provide step-by-step explanations of the procedural skill of rational numbers. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of subtracting rational numbers. (7.NS.1)
• In Chapter 2, Lesson 1, students multiply rational numbers. Examples 1-3 provide step-by-step explanations of the procedural skill of multiplying rational numbers. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of multiplying rational numbers. (7.NS.2)
• In Chapter 3, Lesson 4, students factor expressions. Examples 1-3 provide step-by-step explanations of the procedural skill of factoring an expression. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of factoring an expression. (7.EE.1)
• In Chapter 4, Lesson 1, students solve equations using addition and subtraction. Examples 1-3 provide step-by-step explanations of the procedural skill of solving an equation using addition and subtraction. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of solving an equation. (7.EE.4.a)

In each lesson there is a “Review & Refresh” section, which provides additional practice for skills previously taught. Within these sections are further opportunities to practice the procedural skills. For example:

• In Chapter 2, Lesson 2, there are four problems requiring multiplication of rational numbers. For example: “Problem 1: 8 x 10; Problem 2: -6(9); Problem 3: 4(7); Problem 4: -9(-8)”. (7.NS.2)
• In Chapter 3, Lesson 4, there are three problems requiring simplifying expressions. For example: “Problem 1: 8(k-5); Problem 2: -4.5(-6+2d); Problem 3: -1/4(3g-6-5g)”. (7.EE.1)
• In Chapter 4, Lesson 1, there are four problems asking students to factor out the coefficient of the variable term.  For example: "Problem 1: 4x-20; Problem 2: -6y-18; Problem 3: -2/5w + 4/5; Problem 4: 0.75z - 6.75”. (7.EE.4.a)

In addition to the Student Print Edition, Big Ideas Math: Modeling Real Life Grade 7 has a technology package called Dynamic Classroom. The Dynamic Student Edition includes a middle school game library where students can practice fluency and procedures. The game library is not specific for any one grade in grades 6-8, so teachers and students may select the skill for which they wish to address. Some of the activities are played on the computer. For example, the game “Tic Tac Toe” allows up to two players to practice solving one-step, two-step, or multi-step equations. The game “M, M & M” allows up to two players to practice mean, median, and mode. There are also non-computer games within the game library that are printed and played by students. For example, “It’s All About the Details” is a game that reinforces details about shapes and played with geometry game cards that are also included and prepared by the teacher. In addition to the game library, the Dynamic Student Edition includes videos that explain procedures and and can be accessed through the bigideasmath.com website.

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
1/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of mathematics.

The instructional materials present opportunities for students to engage in application of grade-level mathematics; however, the problems are scaffolded through teacher-led questions and procedural explanation. The last example of each lesson is titled, “Modeling Real Life,” which provides a real-life problem involving the key standards addressed for each lesson. This section provides a step-by-step solution for the problem; therefore, students do not fully engage in application. For example:

• Chapter 5, Lesson 1, Example 3, Modeling Real Life, “You mix 1/2 cup of yellow paint for every 3/4 cup of blue paint to make 15 cups of green paint. How much yellow paint do you use?” Students are given two methods to solve the questions with both methods being explained and answered. For example, “Method 1: The ratio of yellow paint to blue paint is 1/2 to 3/4. Use a ratio table to find an equivalent ratio in which the total amount of yellow paint and blue paint is 15 cups.” [A completed ratio table with annotated description as to how it was filled out is included.] “Method 2: You can use the ratio of yellow paint to blue paint to find the fraction of the green paint that is made from yellow paint. You use 1/2 cup of yellow paint for every ¾ cup of blue paint, so the fraction of the green paint that is made from yellow paint is 2/5 [included equation and solution]. So, you use  2/5 ⋅ 15 = 6 cups of yellow paint.” (7.RP.1)
• Chapter 1, Lesson 1, Example 3, Modeling Real Life, “A moon has an ocean underneath its icy surface. Scientists run tests above and below the surface. [Table Provided] The table shows the elevations of each test. Which test is deepest? Which test is closest to the surface?” The explanation from this point provides students with step-by-step directions on how to solve the problem. “To determine which test is deepest, find the least elevation. Graph the elevations on a vertical number line. [Vertical line provided.] The number line shows that the salinity test is deepest. The number line also shows that the atmosphere test and the ice test are closest to the surface. To determine which is closer to the surface, identify which elevation has a lesser absolute value. Atmosphere:  ∣0.3∣  = 0.3  Ice:  ∣−0.25∣  = 0.25 So, the salinity test is deepest and the ice test is closest to the surface.” (7.NS.1)

Throughout the series, there are examples of routine application problems that require both single and multi-step processes; however, there are limited opportunities to engage in non-routine problems. For example:

• Chapter 2, Lesson 1, Problem 17, “On a mountain, the temperature decreases by 18°F for each 5000-foot increase in elevation. At 7000 feet, the temperature is 41°F. What is the temperature at 22,000 feet? Justify your answer.” (7.NS.3, multi-step, routine)
• Chapter 3, Lesson 4, Problem 41, Dig Deeper, “A square fire pit with a side length of s feet is bordered by 1-foot square stones as shown. [Diagram provided] a. How many stones does it take to border the fire pit with two rows of stones? Use a diagram to justify your answer.” (routine) "b. You border the fire pit with n rows of stones. How many stones are in the nth row? Explain your reasoning.” (non-routine) (7.EE.3)
• Chapter 6, Lesson 3, Problem 32, Dig Deeper, “At a restaurant, the amount of your bill before taxes and tip is \$19.83. A 6% sales tax is applied to your bill, and you leave a tip equal to 19% of the original amount. Use mental math to estimate the total amount of money you pay. Explain your reasoning. (Hint: Use 10% of the original amount.)” (7.RP.3, routine)

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
1/2
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Indicator Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

The instructional materials present opportunities in most lessons for students to engage in each aspect of rigor, however, these are often treated together. There is an over-emphasis on procedural skill and fluency. For example:

• In Chapter 4, Lesson 3, Solving Two-Step Equations, students begin with an Exploration example that uses algebra tiles to show the steps for solving an equation and the relationship to the properties of equality. These examples show the conceptual solving of an equation through models. The lesson shifts to a procedural steps of solving two step equations with Examples 1: “-3x + 5 = 2” and Example 2: “x/8- 1/2 = -7/2”. Example 3 is a procedural example of solving two step equations by combining like terms “3y - 8y = 25”. The lesson progresses to independent application of the skill in Concepts, Skills, and Problem Solving. Students solve equations procedurally.
• Chapter 6, Lesson 1, Fractions, Decimals and Percents, students begin the lesson with an Exploration activity where they compare numbers in different forms based on a variety of strategies. Example 1, presents a conceptual model of a decimal using a hundredth grid, and how to convert a decimal to a percent. Example 2, shows the students how to procedurally build on what they have learned to convert a fraction to a decimal to a percent using division. The lesson then moves to independent practice in Concepts, Skills, and Problem Solving where students procedurally convert between decimals, percents, and fractions.
• Chapter 7, Lesson 2, Experimental and Theoretical Probability, students’ learning begins with an Exploration activity in which students conduct two experiments to find relative frequencies (Flip a Quarter and Toss and Thumbtack) to understand the concept behind probability. The lesson moves on to Example 1, Finding an Experimental Probability by utilizing a formula. “$$P(event) =\frac {number of times the event occurs}{total number of trials}$$”, and Example 2, Finding a Theoretical Probability, by utilizing the  formula “$$P (event)= \frac{number of favorable outcomes}{number of possible outcomes}$$”. Example 3, shows the steps for applying each formula to compare probabilities. The bar growth shows the results of rolling a number cube 300 times. How does the experimental probability of rolling an odd number compare with the theoretical probability?” The independent practice in Concepts, Skills, and Problem Solving has the students finding an experimental probability and theoretical probability based on an event.
• Chapter 9, Lesson 1, Circles and Circumference, begins with Exploration 1, where students use a compass to draw circles and conceptually see the length of the diameter and circumference. Exploration 2, continues to explore diameter and circumference through hands on modeling. The lesson continues with three examples showing the steps of applying the formula for finding radius, circumference, and perimeter of a circle. The independent work of the students is within the Concepts, Skills, and Problem Solving in which students are asked to procedurally solve for the radius, diameter, circumference and perimeter.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/10
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Criterion Rating Details

The instructional materials for Big Ideas Math: Modeling Real Life Grade 7 partially meet the expectations for practice-content connections. The materials identify the practice standards and explicitly attend to the specialized language of mathematics. However, the materials do not attend to the full meaning of each practice standard.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet expectations for identifying the Mathematical Practices (MPs) and using them to enrich 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 1, Lesson 4, Subtracting Rational Numbers, Exploration 1 (MP2), students work with a partner in answering the following questions: a. Choose a unit fraction to represent the space between the tick marks on each number line. “What expressions involving subtraction are being modeled? What are the differences? b. Do the rules for subtracting integers apply to all rational numbers? Explain your reasoning. You have used the commutative and associative properties to add integers. Do these properties apply in expressions involving subtraction? Explain your reasoning.” MP2 is identified in the teaching notes, “The number line helps students see that the rules for subtracting rational numbers shouldn’t be different from the rules for subtracting integers.”
• Chapter 8, Lesson 1, Samples and Populations, Example 2 (MP3), students are given the scenario, “You want to know how the residents of your town feel about adding a new landfill. Determine whether each conclusion is valid.” Students are provided with information about the survey. MP3 is identified in the teaching notes, “Ask a volunteer to read part (a). Then ask whether the conclusion is valid. Students should recognize that the sample is biased because the survey was not random—you only surveyed nearby residents. Ask a volunteer to read part (b). Then ask whether the conclusion is valid. Students should recognize that the sample is random and large enough to provide accurate data, so it is an unbiased sample.”
• Chapter 5, Lesson 4, Writing and Solving Proportions, Example 3 (MP1), students are provided with two examples of solving proportions using cross products. MP1 is identified in the teaching notes, “As you work through the problems with students, share with them the wisdom of analyzing the problem first to decide what method makes the most sense.”

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. For example:

• Chapter 9, Lesson 1, Circles and Circumference, Exploration 2 - Exploring Diameter and Circumference, students work with a partner and find the circumference and diameter of a circular base. They determine whether the circumference or diameter is greater and by how much. “Math Practice - Calculate Accurately,” students are asked, “What other methods can you use to calculate the circumference of a circle? Which methods are more accurate?”
• Chapter 6, Lesson 1, Fractions, Decimals, and Percents, Concepts, Skills & Problem Solving, Problem 39, “MP Problem Solving", “The table shows the portion of students in each grade that participate in School Spirit Week. Order the grades by portion of participation from least to greatest.”
• Chapter 2, Lesson 4, Multiplying Rational Numbers, Concept Skills, & Problem Solving, Problems 10-12. “MP Reasoning”, “Without multiplying, tell whether the value of the expression is positive or negative. Explain your reasoning.”

MP7 and MP8 are under-identified in the series, both are identified in four of the ten chapters.

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
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Indicator Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 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, and MP5: Use appropriate tools strategically.

MP1: The instructional materials present few opportunities for students to make sense of problems and persevere in solving them. For example:

• Chapter 2, Lesson 3, Laurie’s Notes, Example 1, “Mathematically proficient students are able to plan a solution. Choosing between methods may help students be more efficient and accurate when writing fractions as decimals. Complete part (a) as a class. The first step is to write the mixed number as an equivalent improper fraction. Then divide the numerator by the denominator. Point out that the negative sign is simply placed in the answer after the calculations are complete. Discuss the Another Method note with students. Point out that to find an equivalent fraction with a denominator that is a power of 10, you multiply the numerator and denominator by powers of 2 or 5. This is not possible for repeating decimals. Complete part (b) as a class. Remind students to always divide the numerator by the denominator, regardless of the size of the numbers!” In Example 1, the solution is provided for students and therefore they do not have to persevere in solving the problem.

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

• Chapter 5, Lesson 5, Laurie’s Notes, Example 3, “Ask students to explain why the graph represents a ratio relationship and to identify the unit rate. Plotting the ordered pairs confirms that x and y are proportional. ‘What is the constant of proportionality?’ 16. ‘What is the equation of the line?’ y = 16x. Students can use the equation to find the area cleaned for any amount of time.” Students are analyzing a given model, not using a model to solve a problem.
• Chapter 7, Lesson 3, Laurie’s Notes, Example 1, “The tree diagram helps students visualize the 8 outcomes in the sample space.” Students are provided with a worked out example, and do not create a tree diagram as a way to model a problem independently.

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. For example:

• Chapter 8, Lesson 2, Laurie’s Notes, Example 2, “Students can use calculators to quickly find the mean of each sample.” Teachers direct students to use calculators.
• Chapter 7, Lesson 2, Laurie’s Notes, Exploration 1, “Combine the results for each experiment. As the data are gathered and recorded, several students with calculators can summarize the results.” Students are not selecting their own tool in this example.

### Indicator 2g

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

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
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Indicator Rating Details

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 partially meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

“You be the Teacher”, found in many lessons, presents opportunities for students to critique the reasoning of others, and construct arguments. Examples of where students engage in the full intent of MP3 include the following:

• Chapter 4, Lesson 2, Problem 28, You Be the Teacher, “Your friend solves the equation -4.2x=21. Is your friend correct? Explain your reasoning.” The student work is provided to examine.
• Chapter 6, Lesson 1, Problem 20, You Be the Teacher, “Your friend uses the percent proportion to answer the question below. Is your friend correct? Explain your reasoning. ‘40% of what number is 34?’” The student work is provided to examine.

The Student Edition labels MP3 as “MP Construct Arguments,” however, these activities do not always require students to construct arguments. In the Student Edition, “Construct Arguments” was labeled only once for students and “Build Arguments” was labeled once for students. For example:

• Chapter 2,  Lesson 1, Construct Arguments, students construct viable arguments by writing general rules for multiplying (i) two integers with the same sign and (ii) two integers with different signs. Students are prompted to “Construct an argument that you can use to convince a friend of the rules you wrote in Exploration 1(c).”
• Chapter 8, Lesson 4, Exploration 1, Build Arguments is identified in the Math Practice blue box with the following question, “How does taking multiple random samples allow you to make conclusions about two populations?”

### Indicator 2g.ii

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 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:

• In Chapter 1, Lesson 4, Subtracting Integers, students are shown an example of subtracting integers. In Laurie’s notes, teachers are prompted, “Ask students if it is possible to determine when the difference of two negative numbers will be positive and when the difference of two negative numbers will be negative.”
• In Chapter 5, Lesson 2, Example 1, students find a unit rate based on given information. In Laurie’s notes, teachers are prompted, “There are several ways in which students may explain their reasoning. Take time to hear a variety of approaches.” This is labeled as MP3, but there is no support for teachers to assist students in constructing a viable argument or critiquing the thoughts of others.
• Chapter 1, Lesson 2, Example 2, The Teacher’s Guide is noted with MP3 with the following directions, “‘When you add two integers with different signs, how do you know if the sum is positive or negative?’ Students answered a similar question in Example 1, but now they should be using the concept of absolute value, even if they don’t use the precise language. You want to hear something about the size of the number, meaning its absolute value.” There is no reference to MP3 in the Student Edition in this Lesson.

### Indicator 2g.iii

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

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 7 meet expectations that materials use precise and accurate mathematical terminology and definitions when describing mathematics and the materials support students to use precise mathematical language.

• The materials attend to the vocabulary at the beginning of each chapter in the Getting Ready section. For example, in the Getting Ready section for Chapter 3, students read, “The following vocabulary terms (like terms, linear expression, factoring an expression) are defined in this chapter. Think about what each term might mean and record your thoughts.” In Laurie’s Notes for the chapter, teachers are provided with the following notes regarding the vocabulary: “A. These terms represent some of the vocabulary that students will encounter in Chapter 3. Discuss the terms as a class. B. Where have students heard the word like terms outside of a math classroom? In what contexts? Students may not be able to write the actual definition, but they may write phrases associated with like terms. C. Allowing students to discuss these terms now will prepare them for understanding the terms as they are presented in the chapter. D. When students encounter a new definition, encourage them to write in their Student Journals. They will revisit these definitions during the Chapter Review.”
• Key vocabulary for a section is noted in a box in the margins of the student textbook, along with a list of pages where the students will encounter the vocabulary. Vocabulary also appears in some of the Key Ideas boxes. For example, in Chapter 6, Lesson 4, the Key Idea box contains the definition for percent of change, percent of increase, and percent of decrease with an equation of how to find each.
• Each chapter has a review section that includes a list of vocabulary important to the unit and the page number the students will find the terms. For example, in Chapter 4, Review, teachers are given the prompt: “As a review of the chapter vocabulary, have students revisit the vocabulary section in their Student Journals to fill in any missing definitions and record examples of each term.” In the Student Edition, the terms and page number are provided and students are asked to “Write the definition and give an example of each vocabulary term.” Additionally, there is a Graphic Organizer Section where students need to create a “Summary Triangle” for each concept.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. For example:

• The Chapter 4, Laurie’s Notes, Chapter 4 Overview states, “Be sure to use precise language when discussing multiplying or dividing an inequality by a negative quantity. Use language such as, “The direction of the inequality symbol must be reversed.” Simply saying, “switch the sign” is not precise.”
• In Chapter 7, Chapter Exploration includes a list of vocabulary words related to probability. Laurie’s Notes (page T-282) guides teachers to have students use contextual clues and record notes and definitions related to the mathematical terms throughout the chapter.
• In Chapter 9, Section 9.4, Laurie’s Notes, “Motivate, guides teachers to play a game that will help students remember vocabulary and their meanings relating to triangles.”
• In Chapter 2, Lesson 1, Laurie’s Notes remind teachers that “students should say, “Negative 5 times negative 6 equals 30”. Teachers are advised to respond to students saying, “minus 5”, by reminding them that minus represents an operation.
• In Chapter 8, Lesson 1, Laurie’s Notes, teachers are asked to discuss the following, “Define unbiased sample and biased sample. Give a few examples of each. Then ask students to write the definitions in their own words and share an example of each type of sample. The size of a sample can have a great influence on the results. A sample that is not large enough may not be unbiased and a sample that is too large may be too cumbersome to use. As a rule of thumb, a sample of 30 is usually large enough to provide accurate data for modest population sizes.”
• In Chapter 7, Lesson 1, Laurie’s Notes, teachers are asked to “Discuss the vocabulary words: experiment, outcomes, event, and favorable outcomes. You can relate the vocabulary to the exploration and to rolling two number cubes. ‘What does it mean to perform an experiment at random?’ All of the possible outcomes are equally likely. Ask students to identify the favorable outcomes for the events of choosing each color of marble. green (2), blue (1), red (1), yellow (1), purple (1) Be sure students understand that there can be more than one favorable outcome. ‘What are some other examples of experiments and events? What are the favorable outcomes for these events?’ Sample answer: An experiment is rolling a number cube with the numbers 1–6. An event  is rolling a number greater than 4, with favorable outcomes of 5 and 6.”

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

#### Not Rated

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

### Criterion 3a - 3e

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

### Indicator 3a

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

### Indicator 3b

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

### Indicator 3c

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

### Indicator 3d

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

### Indicator 3e

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

### Criterion 3f - 3l

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

### Indicator 3f

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

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

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

### Indicator 3i

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

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

### Indicator 3l

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

### Criterion 3m - 3q

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

### Indicator 3m

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

### Indicator 3n

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

### Indicator 3o

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

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

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

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

### Indicator 3q

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

### Criterion 3r - 3y

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

### Indicator 3r

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

### Indicator 3s

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

### Indicator 3t

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

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

### Indicator 3v

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

### Indicator 3w

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

### Indicator 3x

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

### Indicator 3y

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

### Criterion 3aa - 3z

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

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

### Indicator 3ab

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

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

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

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A
abc123

Report Published Date: 2019/12/05

Report Edition: 2019

Title ISBN Edition Publisher Year
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

## Math K-8 Review Tool

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

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

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

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

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

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

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

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

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

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

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

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

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