## Big Ideas Math: Modeling Real Life

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#### Additional Publication Details

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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## Report for 6th Grade

### Overall Summary

The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 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.

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

### Focus & Coherence

The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

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

The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 6 meet the expectations for assessing the grade-level content and if applicable, content from earlier grades.

Above grade-level assessment items could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Overall, summative assessments focus on Grade 6 standards with minimal occurrences of above grade-level work. Examples of assessment items which assess grade-level standards include:

• Chapter 3, Test A, Item 3, students will find missing values in a ratio table. (6.RP.3.a)
• Chapter 5, Performance Task, students are given four different real-life situations and use algebraic expressions to predict change over time. They answer the following questions for each data set:
1. “What is the first recorded value in the data set?”
2. “How much does the recorded value change each time period? Does the recorded value change by approximately the same amount each period?”
3. “Write an expression for the form ax + b to model the data set, or explain why this type of expression is not appropriate.”
4. “Use the expression to predict the next value, if possible.” (6.EE.6)
• Chapter 7, Alternative Assessment Item 1, students solve problems involving the shape of a park with a base of 200 feet and a height of 130 feet. Students form different shapes, then choose one to find the area and perimeter of the park. When given the dimensions, they draw possible shapes again and find the area. Next, they put shapes together to label and find the dimensions and finally determine the square footage of the entire park. Rubrics are provided to score student work. (6.G.A)

Examples of assessment items which are above grade-level content, but can easily be modified:

• Chapter 6, Quiz, Item 7, students write an equation that will be written in the form px + q =r. (7.EE.4a)
• Chapter 6, Test A and B, Item 11, students write a word sentence as an equation, that is in the form px + q =r.  (7.EE.4.a)
• Chapter 6, Alternative Assessment, Item 1e, students write an equation that is in the form px + q =r. (7.EE.4a)

#### 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 6 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 75% 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 6 meet expectations for spending a majority of instructional time on major work of the grade. This includes all the clusters in 6.RP.A, 6.NS.A & C, 6.EE.A, B, and C.

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 6.5 address major work of the grade, or approximately 65%
• There are 156 lessons, of which 117 address major work of the grade, or approximately 75%
• There are 156 instructional days, of which 117 address major work of the grade, or approximately 75%

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 75% 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 6 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' | 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 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting Domain 6.G enhances focus and coherence with the major standards/clusters of the grade, especially clusters 6.NS.A, 6.NS.C and 6.EE. There are natural connections including the use of fractions and decimals as the dimensions of the geometric figures. For example:

• In Chapter 4, Section 4.1, Area of Polygons, 6.G.1 is connected to the major work of 6.EE.2c as students evaluate the formula of polygons by substituting specific values into the expression.
• In Chapter 5, Section 5.5, Common Factors and Multiples, 6.NS.4 is connected to the major work of applying the properties of operations to generate equivalent expressions, 6.EE.3. Students use common factors to rewrite expressions using the distributive property.
• In Chapter 7, Section 7.1, Area, Surface Area, and Volume, Example 1, 6.G.1 is connected to 6.EE.3 as students use their equation solving skills to assist in solving problems using the formula for the area of a parallelogram.
• In Chapter 7, Sections 7.1-7.3, 7.5-7.7, and Chapter 8, Sections 8.6-8.8, domain 6.G is connected to domain 6.EE, as students connect their work with expressions and equations to problems with areas of triangles (6.G.1) and volumes of right rectangular prisms (6.G.2).
• Chapter 8, Section 8.6, Draw Polygons in the Coordinate Plane, 6.G.3 is connected to the major work of solving real-world math problems by graphing, 6.NS.8. Students graph the vertices of a secret chamber and determine the perimeter.
##### 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 6 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 156 days.

The pacing shown in the Teacher Edition includes a total of 156 days.  This is comprised of:

• 126 days of 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. It should be noted that the work of solving inequalities in Section 8.8 of Chapter 8 is work from a future grade (7.EE.4b). 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' | 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 6 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 3, Section 3.2, “Students have drawn tape diagrams (or bar models) in earlier grades. In this lesson, tape diagrams are used to solve ratio problems.”
• 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, the Chapter 7 Overview states, “This chapter on geometric measurement is a strand in mathematics that connects numbers and the computational work students have learned to the study of geometry. In previous work, students explored two- and three-dimensional shapes. Now they will extend measurement concepts by deriving various area, surface area, and volume formulas.”
• Each chapter’s Learning Targets and Success Criteria chart lays out the progression of learning for the chapter. In Chapter 7, the learning target for Section 7.1, is “Find areas and missing dimensions of parallelograms.” For Section 7.2, the learning target is “Find areas and missing dimensions of triangles, and find areas of composite figures”, and for Section 7.3, the learning target is “Find areas of trapezoids, kites, and composite figures.” (6.EE.2; 6.G.1)

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 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 Chapter 3, Getting Ready for The Chapter, students begin to develop an understanding of the concept of a ratio as they write ratios, learn the term ratio, and begin to write ratios for various situations throughout the whole lesson and in the practice section. In Section 3.4, proficient and advanced students develop mastery with 6.RP.1 as they solve problems.
• In Chapter 3, Section 3.6, Concepts, Skills and Problem Solving, all students solve the You Be The Teacher, Problem 43, “Your friend converts 8 liters to quarts (work is shown in a diagram). Is your friend correct? Explain your reasoning.” (6.RP.3.d) However, students considered emergent or proficient in using ratio reasoning to convert measurement units (6.RP.3d) solve Problem 54, “You are riding on a zip line. Your speed is 15 miles per hour. What is your speed in feet per second?” and Problem 55, “Thunder is the sound caused by lightning. You hear thunder 5 seconds after a lightning strike. The speed of sound is about 1225 kilometers per hour. About how many miles away was the lightning?” Advanced students also solve Problem 56, “Boston, MA, and Buffalo, NY, are hit by a snowstorm that lasts 3 days. Boston accumulates snow at a rate of 1.5 feet every 36 hours. Buffalo accumulates snow at a rate of 0.01 inch every minute. Which city accumulates more snow in 3 days? How much more snow?”
• In Chapter 9, Section 9.3, Scaffolding Instruction, teacher guidance notes: “Finding median and mode is fairly easy for students, but their depth of understanding is apparent when students analyze the best measure of center, describe the effect of an outlier, and explain how changes to a data set affect the measures of center.”
• “Emerging: Students can find the median and mode, but they may need practice using these statistics in different situations and choosing a measure of center to represent a data set.  Students may benefit from guided instruction with the examples." (6.SP.2-3)
• “Proficient: Students understand the meaning of median and mode, find them efficiently, and can apply them in different situations.  Have students check their progress using the Try It exercises before completing the Self-Assessment exercises.” (6.SP.2-3)

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. For example:

• Chapter 1, Section 1.1, “In prior courses, students evaluated whole-number powers of 10. In this lesson, they will begin to evaluate other bases as well.” (6.EE.1). In Exploration 1, students write 10 x 10 using an exponent. This builds from their previous knowledge of using base 10 from previous grades (5.NBT.2).
• Chapter 2, Section 2.2, “In the previous course, students divided unit fractions by whole numbers and vice versa. The first exploration contains fractions other than unit fractions, which is the next step in the progression of fraction division (6.NS.1)."
• Chapter 7, Section 7.1, “In prior courses, students used rectangular area models to represent one- and two-digit multiplication. In this course, they used area models to represent the Distributive Property, which provides the basis for this chapter’s work with using the definition of the area of a rectangle to derive the formula for the area of a parallelogram.” In Example 1, students use the area model to find the area of a parallelogram.
• Chapter 8, Section 8.1, explicitly connects students’ prior work of locating fractions on a number line, 3.NF.2, and of making line plots, 4.MD.4, 5.MD.2, to represent points on a number line with negative numbers, 6.NS.6. For example, “Students will build upon their experiences with finding non-negative numbers on a horizontal or vertical number line to develop the number line to the left of 0 or below 0.”
• Chapter 10, Section 10.1, “Students know how to use dot plots to display and analyze data. Now they will add another data display to their toolkits, stem-and-leaf plot.”
##### 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 6 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, or if it completes the learning, or if students are learning, or extending learning. For example:

• In the Teacher Edition, Chapter 3, Section 3.1, and in the student edition, the “Learning Target” is identified as “Understand the concepts of ratios and equivalent ratios”. This connects to Cluster heading 6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
• In Chapter 2, Section 2.2, students multiply fractions. In Section 2.3, students divide fractions and apply and extend previous understandings of multiplication and division to divide fractions by fractions. This connects to Cluster heading 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• In Chapter 8, Section 8.3, students place integers on a number line. This connects to Cluster heading 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• In Chapter 5, Section 5.1,  Learning Goals: “Evaluate algebraic expressions given values of their variables." This connects to cluster heading for 6.EE.A, Apply and extend previous understandings of numbers to the system of rational numbers.
• In Chapter 6, Sections 6.2 and 6.3, students explain the solution strategy of using inverse operations and properties of inequalities. This connects to  for 6.EE.A, Apply and extend previous understandings of numbers to the system of rational numbers.

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:

• Chapter 4, Section 4.3, Exploration 1 connects 6.RP.A to 6.NS.7 as students represent four numbers written as decimals, fractions, and percents by placing the numbers on a number line drawn on the floor, to order the numbers from least to greatest and to explain how to determine the placement of the numbers.
• Chapter 6, Section 6.4, Exploration 1 serves to connect the work of using ratio reasoning 6.RP.A to solve problems 6.EE.C. Given a ratio table and its graph for an airplane traveling 300 miles per hour, students determine which quantity is dependent, describe the relationship between the two quantities, and then use variables to write an equation that represents the relationship between time and distance.
• Chapter 9, Section 9.2, Practice Problem 20, students find the mean monthly rainfall, and compare the mean monthly rainfall for the first half of the year with the mean monthly rainfall for the second half of the year. This connects and extends their cluster work of computing fluently with multi-digit numbers, specifically decimals, 6.NS.B, to the cluster work of summarizing and describing distributions, 6.SP.B. In Section 9.4, students connect knowledge about fractions, decimals, and percents as they identify the quartiles and interquartile range as they solve problems.

### Rigor & Mathematical Practices

The instructional materials for Big Ideas Math: Modeling Real Life Grade 6 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 6 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' | 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 6 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 3, Section 1, Exploration 2, “Using Ratios in a Recipe,” students are directed to “Work with a partner. The ratio of iced tea to lemonade in a recipe is 3:1. You begin by combining 3 cups of iced tea with 1 cup of lemonade. A. You add 1 cup of iced tea and 1 cup of lemonade to the mixture. Does this change the taste of the mixture? B. Describe how you can make larger amounts without changing the taste.” The teaching notes direct the teacher not to teach but to listen to the conversations and take notes on the answers students are getting in order to reference the answers when discussing equivalent ratios in the lesson. (6.RP.1)
• In Chapter 5, Section 5, Exploration 1, “Finding Dimensions,” students are directed to work with a partner in solving the following? “A. The models show the area (in square units) of each part of a rectangle. Use the models to find missing values that complete the expressions. Explain your reasoning. B. In part (a), check that the original expressions are equivalent to the expressions you wrote.  Explain your reasoning. C. Explain how you can use the Distributive Property to rewrite a sum of two whole numbers with a common factor.” Throughout this exploration, the teacher is encouraged to listen to conversations and have volunteers share their strategies to the class. (6.EE.1)
• In Chapter 5, Section 4, Exploration 1, “Using Models to Simplify Expressions,” students are given three models to “simplify expressions”. Through these models, students are able to see how the distributive property is applied. (6.EE.1)
• In Chapter 6, Section 2, Exploration 2, students are asked to work with a partner as they look at an equation as a balanced scale. They are asked, “A. How are the two sides of an equation similar to a balanced scale? B. When you add weight to one side of a balanced scale, what can you do to balance the scale?  What if you subtract weight from one side of a balanced scale? How does this relate to solving an equation? C. Use a model to solve x + 2 = 7. Describe how you can solve the equation algebraically.” (6.EE.5)
• In Chapter 3, Section 2, Example 1, “Interpreting a Tape Diagram” students are shown how to use a tape diagram to solve problems. For example, “The tape diagram represents the ratio of blue monsters to green monsters you caught in a game. You caught 10 green monsters. How many blue monsters did you catch?” While the problem is modeled using a tape diagram for students, the solution is explained to the students. (6.RP.1)

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 is completed 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 5, Section 5, Example 1, “Factoring Numerical Expressions”, students are shown how to find the GCF by listing the factors of two numbers and circling the common factors. (6.NS.2)
• In Chapter 6, Section 3, “Concepts, Skills and Problem Solving”, there are missed opportunities to demonstrate conceptual understanding. Problems 16-35 have students “Solve the equation. Check your solution.” Problem 16: “s/10 = 7”; Problem 26: “13 = d ÷ 6” Problem 33: “7b ÷12 = 4.2.” (6.EE.5)

##### 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 6 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 6 including multi-digit division (6.NS.2) and multi-digit decimal operations (6.NS.3) and applying previous understandings of arithmetic to algebraic expressions (6.EE.A). For example:

• In Chapter 2, Lesson 4, students add and subtract decimals. Examples 1-3 provide step-by-step explanations of the procedure for adding and subtracting decimals. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill with the addition and subtraction of decimals. (6.NS.3)
• In Chapter 2, Lesson 5, Examples 1-3 provide step-by-step explanations of the procedural skill of multiplying decimals. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of multiplying decimals. (6.NS.3)
• In Chapter 2, Lesson 6, Dividing Whole Numbers, students learn to divide whole numbers. Examples 1-3 provide step-by-step long division instruction. In the Concept, Skills, and Problem Solving section, students have many opportunities to demonstrate their skill of dividing whole numbers. (6.NS.2)
• In Chapter 5, Lesson 1 Algebraic Expressions, students learn to write algebraic expressions using exponents and evaluate algebraic expressions. Examples 1-6 provide step-by-step instructions. The Concepts, Skills, and Problem Solving section provides many opportunities for students to demonstrate their procedural understanding. (6.EE.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 fluencies for Grade 6. For example:

• In Chapter 7, Lesson 1, there are three problems requiring adding or subtraction of decimals: “Problem 10: 2.36 + 15.71; Problem 11: 9.035 - 6.114; Problem 12: 28.351 - 019.3518”. (6.NS.3)
• In Chapter 9, Lesson 2, there are four problems requiring division of decimals: “Problem 9: 11.7÷9; Problem 10: 5⟌72.8 ; Problem 11: 6.8 ⟌28.56; Problem 12: 93÷3.75”. (6.NS.2)
• In Chapter 7, Lesson 5, students to solve equations in four problems. For example: "Problem 8: s-5=12; Problem 9: x+9=20; Problem 10: 48=6r; Problem 11: m/5=13”. (6.EE.A)

In addition to the Student Print Edition, Big Ideas Math: Modeling Real Life Grade 6 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' | 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 6 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. In addition, there are few non-routine problems presented. For example:

• In Chapter 2, Lesson 2, there are several, multi-step, routine problems that students solve independently. For example, Problem 64: “You use 1/8 of your battery for every 2/5 of an hour that you video chat. You use 3/4 of your battery video chatting. How long did you video chat?” Problem 67: “You have 6 pints of glaze. It takes 7/8 of a pint to glaze a bowl and 9/16 of a pint to glaze a plate. a. How many bowls can you completely glaze? How many plates can you completely glaze? b. You want to glaze 5 bowls, and then use the rest for plates. How many plates can you completely glaze? How much glaze will be left over?” Part C is an example of a non-routine application: “c. How many of each object can you completely glaze so that there is no glaze left over? Explain how you found your answer.” (6.NS.1)
• Chapter 3, Lesson 2, Example 4, Modeling Real Life, “In a seven-game basketball series, a team’s power forward scores 8 points for every 5 points the center scores. The forward scores 60 more points than the center in the series. How many points does each player score in the series? The ratio of the forward’s points to the center’s points is 8:5. Represent the ratio using a tape diagram.” The tape diagram is given to the students and a step-by-step breakdown explanation is given about how to solve the ratio using a tape diagram. (6.RP.3)
• Chapter 6, Lesson 1, students explore multiple examples of routine application problems. Problem 11, “After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams that started the competition.” (6.EE.7)

Overall, there are limited opportunities for students to engage in non-routine problems throughout the grade level.

##### 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 6 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 also an over-emphasis on procedural skill and fluency. For example:

• In Chapter 4, Lesson 1, Percents and Fractions, Introduction, students build conceptual understanding of percent as they consider the meaning of the word “percent.” In the Exploration section, students interpret models with a partner by determining the percent, fraction, and ratio shown by each model. In these sections, students are building conceptual understanding. In Example 1, students use both models and numbers to write percents as fractions. In Example 2, students write fractions as percents without models, using a modeled procedure. In the Concept, Skills, & Problem Solving, the focus is on procedural skill and fluency, and application.
• In Chapter 9, Lesson 2, Mean, the first two examples provide students an opportunity to build an understanding of mean as a “fair share” or “balanced share”. In the Self-Assessment section, students write answers to questions that focus on conceptual understanding. For example, “Is the mean always equal to a value in the data set? Explain. Explain why the mean describes a typical value in a data set. What can you determine when the mean of one set is greater than the mean of another data set? Explain your reasoning.” In Example 1, students learn a procedure to find the mean. In Example 2, students learn to compare means using a double bar graph. In Example 3, students learn how an outlier affects the mean. In Concepts, Skills, & Problem Solving, students find the mean in both isolated number sets and story problems.
• In Chapter 6, Lesson 3, Solving Equations Using Multiplication or Division, students build conceptual understanding in Exploration 1, where they solve an equation using a tape diagram, and Exploration 2, where they solve an equation using a balance. The lesson shifts to a focus on procedural understanding and fluency, providing annotated step-by-step solutions in Examples 1: “Solve w/4 =12, Solve 2/7x=6”; Example 2: “Solve 65=5b”; and Example 3: “The area of a rectangular LED ‘sky screen’ in Beijing, China is 7500 square meters. The width of the sky screen is 30 meters. What is the length of the sky screen?”

#### 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 6 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 6 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 1, Powers and Exponents, Exploration 1, MP7, students work with a partner to complete a table with the headings: Repeated Factors, Using an Exponent, and Value. MP7 is identified in the teaching notes, “Understanding how to represent repeated factors using an exponent requires students to recognize the pattern or structure of the expression."
• Chapter 4, Lesson 3, Comparing and Ordering Fractions, Decimals, and Percents, Example 1, MP2, students determine “which is greater, 17/20 or 80%”. MP2 is identified in the teaching notes, “Take time to review and analyze the efficiency of the different strategies."
• Chapter 7, Lesson 3, Areas of Trapezoids and Kites, Example 4, MP1, students approximate the number of people in one-square mile of a Virginia County (shaped like a trapezoid) given the dimensions of the county with a population of 21,100. The teaching notes identify MP1, “Students look for an entry point and plan a solution pathway which is defined in the example. They use diagrams to help define the problem and ask if the answer makes sense, which can be completed as shown in the Check Reasonableness note.”

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 2, Lesson 1, Fractions and Decimals, Concepts, Skills, & Problem Solving (Directions for Problems 12-14). “MP Choose Tools” is identified, “A bottle of water is 1/3 full. You drink the given portion of the water. Use a model to find the portion of the bottle of water that you drink.” [Problem 12. 1/2; Problem 13. 1/4; Problem 14. 3/4).
• Chapter 5, Lesson 2, Writing Expressions, Self-Assessment for Concepts & Skills, Problem 11. “MP Precision” is identified, “Your friend says that the phrases below have the same meaning. Is your friend correct? Explain your reasoning. ‘the difference of a number x and 12’ and ‘the difference of 12 and a number x.’"
• Chapter 6, Lesson 4, Writing Equations in Two Variables, Exploration 1 (Blue Box). Students are given a ratio table and graph depicting an airplane traveling 300 mph. Students “a. Describe the relationship between the two quantities. Which quantity depends on the other quantity? b. Use variables to write an equation that represents the relationship between the time and the distance. What can you do with this equation? Provide an example. c. Suppose the airplane is 1500 miles away from its destination. Write an equation that represents the relationship between time and distance from the destination. How can you represent this relationship using a graph?” In a blue box labeled “Math Practice - Look for Patterns” students are asked, “How can you use the patterns in the table to help you write an equations.”
##### 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 6 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, MP6: Attend to Precision, and MP7: Look for and make use of structure.

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

• Chapter 6, Lesson 3, Laurie’s Notes, Example 2, “Work through the problem. Being clear about notation and symbols will help students make sense of the mathematics and how to work towards the solution. Discuss the last step in the solution. This can be confusing for students because of the 5 on each side of the equation. On the left, 5 is the ones digit in a two-digit number. On the right, 5b means 5 times the value of b. If the equation had been written as 65 = b(5), it would have been even more confusing. Remember that students may not yet be comfortable with multiplication represented as 5b.” The solution is presented, so students are trying to make sense of the procedures, not the problem itself. They do not need to independently solve the problem.
• Chapter 4, Lesson 4, Laurie’s Notes, Example 6, “Students should know a variety of ways to find a number such that 120 is 60% of that number. It is important that students find an approach to solving a problem that makes sense.” Example 6 is solved for the student, with step-by-step reasoning and procedures.

MP4: The instructional materials present few opportunities for students to model with mathematics. Many MP4 notations are used in the Example sections throughout the grade level. In these examples, the work and a step-by-step description is provided for the student, eliminating students’ use of models. For example:

• Chapter 3, Lesson 5, Rates and Unit Rates, Example 2, “A piece of space junk travels 5 miles every 6 seconds. a)How far does the space junk travel in 30 seconds? b) How many seconds does it take for the space junk to travel 2 miles” Ratio tables are provided and filled in/answered for the students to use.
• Chapter 8, Lesson 1, Laurie’s Notes, Example 1, “There is an intentional effort in this lesson to display number lines in two orientations: horizontal and vertical. These two models will help students graph in the coordinate plane. The models also make connections to common contexts, such as a thermometer. A vertical number line should remind students of the thermometer in Exploration 8.1. For part (b), draw a vertical number line and graph −5 and −3.” Students are provided with the model and a detailed description on how to use the model to compare numbers.

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. The instructional materials present limited opportunities for students to choose tools strategically, as the materials indicate what tools should be used.

• Chapter 7, Lesson, 4, Exploration 2, Student Edition, “Work with a partner. Draw the front, side, and top views of each stack of cubes. Then find the number of cubes in the stack. An example is shown at the left.” Laurie’s Notes, “If possible give each pair of students six cubes. To see each view, students need to be at ‘eye level’ with the solid.”
• Chapter 9, Lesson 5, Laurie’s Notes, Example 2, “A dot plot is again used to organize the data. It is then modified to record the distance of each data value from the mean.” Students are provided two line plots and the solution to the problem.

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

• In Chapters 1, 2, 4, 5, and 6, MP6 is noted in the Example sections. Students are not attending to precision because the solutions are given in the Student Edition.
• Chapter 10, Lesson 1, Laurie’s Notes, Example 1, “Discuss with students the need to have a key that describes how to read the data in the plot. Explain the key in the solution.” The students are directed to a solution and directed to notice the key provided.

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

• Chapter 5, Lesson 6, Laurie’s Notes, Preparing to Teach, “Students will use the structure of mathematics to break down and solve complex problems.” This is general and not specific for any one problem addressed in the unit.
• Chapter 2, Lesson 2, Laurie’s Notes, Example 2, “Point out to students how division is represented differently in the two problems. Before starting part (a), you may want to ask if the problem could be written another way.” Students are not using structure to solve a problem, but are directed to look at the structure of a problem that was solved for them.
##### 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 6 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. For example:

• Chapter 2, Lesson 1, Problems 52 & 53, You Be the Teacher, “Your friend finds the product. Is your friend correct? Explain your reasoning.” The student is provided work to examine.
• Chapter 5, Lesson 5, Problem 56, You Be the Teacher, “Your friend factors the expression 24x + 56. Is your friend correct? Explain your reasoning.” The student is provided work to examine.
• Chapter 9, Lesson 5, Problem 22, You Be the Teacher, “Your friend finds and interprets the mean absolute deviation of the data set 35, 40, 38, 32, 42, and 41. Is your friend correct? Explain your reasoning.” The student is provided work to examine.

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

• Chapter 2, Section 7, Exploration 1, Construct Arguments is identified in the Math Practice blue box with the following question, “Why do the quotients in part (b) have the relationship you observed?”
• Chapter 9, Lesson 1, Exploration 2, Build Arguments is identified in the Math Practice blue box with the following question, “How can comparing your answers help you support your conjecture?”
• Chapter 10, Lesson 4, Exploration 1, Construct Arguments is identified in the Math Practice blue box with the following question, “Explain why the shapes of the distributions in Exploration 1 affect which measures best describe the data.”
##### 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 6 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 3, Lesson 2, during the self-assessment teachers are prompted to have students share their thinking. “Discuss the language and clarity of explanations. Then ask, “If you were unclear before, did any of the explanations help you make sense of this question?”
• In Chapter 8, Lesson 8, Example 4, students are shown how to set up and solve an inequality. Laurie’s Notes identify MP3, “Mathematically proficient students take into account the context of the problem. Students should consider the number of times a person needs to ride a bus in a 30-day period when deciding whether a 30-day pass saves money.” There is no support provided to assist teachers to engage students in MP3.
##### 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 6 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 Getting Ready for Chapter 5, students read, “The following vocabulary terms (algebraic expression, variable, constant, equivalent 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 5. Discuss the terms as a class. B. Where have students heard the word constant 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 constant. 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 3, Lesson 1, the Key Idea box contains the definition for ratio in words (“A ratio is a comparison of two quantities. Ratios can be part-to-part, part-to-whole, or whole-to-part comparisons. Ratios may or may not include units.”), examples (six examples of ratio statements that could be made to describe a provided picture of cats and dogs), and an algebra example (“The ratio of a to b can be written as a:b.”)
• Each chapter has a review section that includes a list of vocabulary important to the unit and the page number where the students will find the terms. In the Chapter 5 Review, the Teaching Edition prompts teachers, “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.”  Additionally, a Graphic Organizer Section is included for students to create examples and non-examples of the key vocabulary terms for the chapter.

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

• In Chapter 1, Lesson 1, Laurie’s Notes alert teachers to a common error of saying $$3^5$$ means multiply 3 five times, and reminds them that there are actually only four multiplications to perform, and that the number 3 is written five times which means there are five factors of 3.
• Teachers are prompted in Laurie’s Notes to have students use precise mathematical language. For example, Laurie’s Notes in the Chapter 2 Overview states, “Throughout this chapter, and course, be sure to use precise language when reading decimals. Always say, “two and five-tenths” instead of “two point five.” You want students to understand the fractional part in the numbers 2.5 and that will not be evident if point terminology is used.”
• In Chapter 4, Section 4.2, this suggestion is offered for reinforcing the meaning behind moving the decimal point when writing percents as decimals: Say, “23 percent, 23 per one hundred, or 23 hundredths”.  This strategy also calls attention to the correct reading a decimal amounts, and the meaning of percent.

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

### Usability

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

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

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

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
##### Indicator {{'3ad' | indicatorName}}
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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###### Alignment
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###### Usability
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