## Alignment: Overall Summary

The instructional materials reviewed for enVisionMATH California Common Core Grade 6 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for focus and coherence in Gateway 1 as they meet expectations for focus and meet expectations for coherence. In Gateway 2, the instructional materials partially meet the expectations for rigor and balance, and they partially meet the expectations for practice-content connections. Since the instructional materials do not meet expectations for both Gateways 1 and 2, evidence was not collected regarding usability in Gateway 3.

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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
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## 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 reviewed for enVisionMATH California Common Core Grade 6 meet expectations for focus on major work and coherence in Gateway 1. For focus, the instructional materials do not assess topics before the grade level in which the topic should be introduced, and they devote the large majority of class time to the major work of the grade. For coherence, the instructional materials have supporting content that engages students in the major work of the grade, include an amount of content designated for one grade level that is viable for one school year, and foster coherence through connections at a single grade.

### 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 reviewed for enVisionMATH California Common Core Grade 6 do not assess topics before the grade level in which the topic should be introduced. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level standards.

### 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 enVisionMATH California Common Core Grade 6 meet expectations for assessing grade-level content. Most of the assessments include material appropriate for Grade 6; however, above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

In the Teacher Edition, a Topic Test is available for each of the fourteen topics. The instructional materials assess content that is above grade level or not aligned to a standard.

• In the Topic 3 Topic Test, questions 4 and 6, students find how many combinations are possible from given information. Question 4 states, “Jorge has 16 quarters to spend on arcade games. He only wants to play pinball and the racing game. If each game takes 2 quarters to play and he plays both games at least one time, how many different combinations of time can Jorge play the two games?” (7.SP.8)
• In the Topic 3 Topic Test, question 7 states, “The table shows the number of miles, m, hiked by the hiking club in h hours. Write an equation that fits the pattern.” Students write a two-step equation as the solution. (7.EE.4)
• In the Topic 3 Topic Test, questions 9, 11, and 12 assess two-step equations. Question 11 states, “The temperature was 6 degrees celsius and increased 2 degrees celsius each hour for 6 hours. The equation y = 6 + 2x shows the relationship between x, the number of hours, and y, the temperature. Make a table. What is the temperature after 5 hours?” Students create a table after analyzing a two-step equation. (7.EE.4)
• In the Topic 3 Performance Assessment, questions 2 and 3 assess two-step equations. Question 2 states, “Write an equation that fits the pattern you found in problem 1 above.” The solution that is provided is h = 3d + 2. (7.EE.4)
• In the Topic 8 Topic Test, question 8 states, “An amusement park charges $2 for admittance and$1.50 for each ride. If R equals the number of rides and C equals the total cost, copy and complete the T-table for the equation C = $2 +$1.50R to show the relationship between total cost and the number of rides taken.” Students analyze a two-step equation to complete a table. (7.EE.4)

Examples of the instructional materials assessing grade-level content include:

• In the Topic 2 Topic Test, question 6 states, “Which graph represents the solutions of the inequality $$p \geq 10$$?” Students identify which solution to an inequality is correct. (6.EE.5)
• In the Topic 6 Topic Test, question 13 states, “How many 3/4 foot long pieces of ribbon can be cut from a ribbon that is 7 3/8 feet long?” Students divide fractions by fractions to solve real-world problems. (6.NS.1)
• In the Topic 14 Topic Test, question 4 states, “The ages of the girls in the dance recital are listed below. What are the median and mode of the ages? 7, 6, 8, 6, 8, 7, 8, 7, 8, 6” Students calculate the median and mode of a set of data. (6.SP.3)

### Criterion 1b

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

Students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. The instructional materials devote approximately 90 percent of class time to the major work of Grade 6.

### 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 enVisionMATH California Common Core Grade 6 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 9 out of 14, which is approximately 64 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 134 out of 149, which is approximately 90 percent.
• The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 27 out of 30, which is approximately 90 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each topic. As a result, approximately 90 percent of the instructional materials focus on 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 enVisionMATH California Common Core Grade 6 meet expectations for coherence. The instructional materials have supporting content that engages students in the major work of the grade, include an amount of content designated for one grade level that is viable for one school year, and foster coherence through connections at a single grade.

### 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 enVisionMATH California Common Core Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting content is used to support the major work of the grade. For example:

• In Topic 4 Lesson 4-2, students evaluate addition and subtraction expressions. The supporting standard 6.NS.3 engages students with the major work standard 6.EE.2c when students evaluate expressions that include decimals. Independent Practice question 13 states, “t - 0.48; t = 5.187”
• In Topic 5 Lesson 5-6, students evaluate expressions with decimals. The supporting standard 6.NS.3 engages students with the major work standard 6.EE.2c when students evaluate algebraic expressions that include decimals. Independent Practice question 16 states, “Evaluate each expression for x = 1.8, x = 5, and x = 6.4. 3x + 1.2x
• In Topic 6 Lesson 6-1, students use the greatest common factor and the distributive property to rewrite each sum. Independent Practice problem 16 states, “In 15 -18, use the GCF and the distributive property to rewrite each sum. 34 + 51” The supporting standard 6.NS.4 engages students with the major work standard 6.EE.3.
• In Topic 12 Lesson 12-1, students find the area of rectangles as well as the length of one side of a rectangle. The supporting standard 6.G.1 engages students with the major work standard 6.EE.2c when students use and manipulate the area formula to solve area problems involving variables. Guided Practice question 5 states, “In the example at the top, suppose Tessa used 24 ft squared of fabric to cover a bulletin board that is 3 ft. wide. How long is the bulletin board? Explain how you found the answer.” A sample answer is given using variables for length and width.

### 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

Instructional materials for enVisionMATH California Common Core 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 154 days.

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.

The instructional materials consist of 107 lessons that are listed in the Table of Contents. Lessons are structured to contain a Daily Review, Develop Concept-Interactive, Develop Concept-Visual, Close/Assess and Remediate, and Center Activities.

The instructional materials consist of 47 reteaching lessons and assessments that are listed in the Table of Contents. These include Reteaching, Topic Tests, Performance Assessments, Placement Test, Benchmark Tests, and End-of-Year Test.

The yearlong pacing guide lists Topic 6 to be covered for 15 days in November and 15 days in December for a total of 30 days. However, the pacing guide lists Topic 6 as a total of 15 days. There is a discrepancy with Topic 10 that lists 7 days in February and 6 days in March in the yearlong pacing guide as well as a total of 13 days listed in the pacing guide.

The publisher does not provide information about the suggested time to spend on each lesson or the components within a lesson. The Implementation Guide has a chart that suggests times for a multi-age classroom. The lessons within the multi-age classroom are structured differently than a single-age classroom. The multi-age lessons are structured to contain Problem Based Interactive Learning, Guided Practice, Center Activities, Independent Practice, Small Group Strategic Intervention, and Digital Assignments/Games. The suggested time for the multi-age lesson is 50-75 minutes per lesson.

### 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 enVisionMATH California Common Core Grade 6 partially meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials do not clearly identify content from prior and future grade levels and do not use it to support the progressions of the grade-level standards.

Prior and future grade-level work is not clearly identified within each lesson. For example:

• In Topic 3 Lesson 3-4, the Teacher Edition lists the standard 6.EE.6 as the focus of the lesson. Students determine all the possible combinations within a group. This is future grade-level content and is aligned to 7.SP.8b.
• In Topic 10 Lesson 10-6, the Teacher Edition lists the standard 6.RP.3d as the focus of the lesson. Students use ratio and rate reasoning to solve real-world and mathematical problems to change between customary units of measurement. This is prior grade-level content and is aligned to 5.MD.1.
• In Topic 12 Lesson 12-1, the Teacher Edition lists the standard 6.G.1 as the focus of the lesson. Students find the area of rectangles and squares. This is prior grade-level content and is aligned to 4.MD.3.
• In Topic 13 Lesson 13-3, the Teacher Edition lists the standard 6.G.2 as the focus of the lesson. Students calculate volume with all whole numbers. This is prior grade-level content and is aligned to 5.MD.5b.

Some of the lessons include a section in the Teacher Edition called, Link to Prior Knowledge. The Link to Prior Knowledge poses a question or strategy that has previously been learned for students to connect to the current lesson. The Link to Prior Knowledge does not explicitly identify standards from prior grades. For example:

• In Topic 8 Lesson 8-3, the Link to Prior Knowledge states, “Which operation does separating the leather string into equal parts represent? Division. On the board, display the division expression to represent the problem. 4 divided by 2/3” The publisher does not connect this prior knowledge to a specific prior grade level.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

The majority of lessons within the 16 topics focuses on and provides students with extensive opportunities to practice grade-level problems. Within each lesson, students practice grade-level problems within a Daily Common Core Review, Practice, Reteaching, Enrichment, and Quick Check activities. For example:

• In Topic 10 Lesson 10-5, the Teacher Edition lists standard 6.RP.3b as the focus of the lesson. Students solve unit rate problems including those involving constant speed. Independent Practice question 7 states, “distance = 568 mi; time = 8 h; rate = ___”
• In Topic 6 Lesson 6-8, the Teacher Edition lists standard 6.NS.1 as the focus of the lesson. Students divide mixed-number equations and apply the concept to solve word problems. Problem Solving question 36 states, “The biggest diamond ever found weighed 1 ½ pounds uncut. If this diamond were cut into 3 equal pieces. How much would each piece weigh?”
• In Topic 9 Lesson 9-1, the Teacher Edition lists standard 6.RP.1 as the focus of the lesson. Students write ratios three different ways to express the ratios in a part-to-part and part-to-whole relationship. Independent Practice question 6 states, “A person’s blood type is denoted with the letters A, B, and O, and the symbols + and -. The blood type A+ is read as A positive. The blood type B- is read as B negative. Use the data file to write a ratio for each comparison in three different ways. O+ donors to A+ donors.”

The instructional materials contain a Common Core State Standards Skills Trace for each topic that can be found in the Printable Resources section of the Program Resources Document. This document contains the grade-level standards for each topic and the standards from previous and future grade levels that are related to the standards focused on in the specified topic. The document states specific topic numbers from previous and future grades and their related grade-level standards.

• In Topic 3, the Skills Trace lists the standards 6.EE.6 and 6.EE.9 as the focus of the topic. These standards are linked to a “Looking Back” list where it lists the standard 5.OA.3 as the focus in Topic 15 within the Grade 5 instructional materials. The standards 6.EE.6 and 6.EE.9 are also linked to a “Looking Ahead” list where it lists the standards 6.EE.2c, 6.EE.6, and 6.EE.7 as the focus in Topics 4, 5 and 6 within the current Grade 6 instructional materials.

### 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 enVisionMATH California Common Core Grade 6 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Each topic is structured by a specific domain, and the learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

• In Topic 6 Lesson 6-1, the lesson objective states, “Students will find common factors and the greatest common factors of numbers.” This is shaped by the cluster 6.NS.B, Compute fluently with multi-digit numbers and find common factors and multiples.
• In Topic 10 Lesson 10-1, the lesson objective states, “Students will find the unit rate for a given rate.” This is shaped by the cluster 6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
• In Topic 12 Lesson 12-2, the lesson objective states, “Students will develop and use formulas for the areas of parallelograms and rhombuses.” This is shaped by the cluster 6.GA, Solve real-world problems and mathematical problems involving area, surface area, and volume.

Instructional 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 the connections are natural and important.

• In Topic 1 Lesson 1-6, cluster 6.EE.A connects to cluster 6.EE.B when students write expressions using variables. Independent Practice question 10 states, “Write an algebraic expression for each situation. 12 less than 7 times a number x.
• In Topic 6 Lesson 6-9, cluster 6.EE.A connects to cluster 6.NS.A when students evaluate expressions at specific values of their variables including word problems involving division of fractions by fractions. Problem Solving question 19 states, “The expression 9 1/3 $$\div$$ d can be used to find how many days of feed the bin holds, where d is the amount of feed a horse eats each day. Explain how to use the expression to find the days of feed for a horse that eats 1/6 cubic feet of feed each day.”
• In Topic 14 Lesson 14-1, cluster 6.SP.A connects to cluster 6.SP.B when students identify statistical questions and interpret data. Independent Practice question 11 states, “Kim asked her class, 'How many other states have you visited?' She got the following responses: 0, 1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0. Make a dot plot to display the data.”

## Rigor & Mathematical Practices

#### Partially Meets Expectations

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Gateway Two Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 6 partially meet expectations for rigor and mathematical practices. The instructional materials partially meet expectations for rigor by meeting expectations on giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. The instructional materials also partially meet the expectations for practice-content connections by meeting expectations on explicitly attending to the specialized language of mathematics and prompting students to construct viable arguments and analyze the arguments of others.

### 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.
6/8
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Criterion Rating Details

The instructional materials for enVisionMATH California Common Core Grade 6 partially meet expectations for rigor and balance. The instructional materials meet expectations for giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. However, the instructional materials partially meet expectations for giving attention to conceptual understanding and applications.

### 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 enVisionMATH California Common Core 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 present a Problem-Based Interactive Learning activity (PBIL) and a Visual Learning Bridge (VLB) within each lesson to develop conceptual understanding. However, the PBIL and VLB are teacher-directed and do not offer students the opportunity to practice conceptual understanding independently through the use of pictures, manipulatives, and models.

Overall, the instructional materials do not consistently provide students opportunities to independently demonstrate conceptual understanding throughout the grade level.

• In Topic 6 Lesson 6-8, the Overview of PBIL states, “Students divide mixed numbers by using models and improper fractions.” In the teacher-directed PBIL activity, students use a ruler to model the division of 5 1/2 inches by 1 3/8 inches. In the Develop the Concept: Visual section, the process for changing a mixed number to an improper fraction is described, as well as using the reciprocal of a fraction to create an equivalent multiplication problem to solve. The directions for the Independent Practice state, “In 9 through 20, find each quotient. Simplify, if possible.” Students do not demonstrate the conceptual understanding of dividing mixed numbers independently as fractions are shown as sample answers in the 12 problems in the Independent Practice.
• In Topic 9 Lesson 9-2, the Overview of PBIL states, “Students interpret and use ratios and equivalent ratios.” In the teacher-directed PBIL activity, students draw pictures to represent a ratio of rock songs to hip-hop songs. The Develop the Concept: Visual section of the lesson describes the procedural steps of finding equivalent ratios. The directions for the Independent Practice state, “In 9 through 16, write three ratios that are equivalent to the given ratio.” Students do not demonstrate the conceptual understanding of equivalent ratios independently as ratios in reduced form are shown as sample answers in the eight problems in the Independent Practice.
• In Topic 10 Lesson 10-3, the Overview of PBIL states, “Students use unit rates to solve proportions.” In the teacher-directed PBIL activity, students create a table to find the unit rate to solve a word problem. The directions for the Independent Practice state, “In 5 through 12, find the unit rate.” Students do not demonstrate the conceptual understanding of unit rates independently as written unit rates are shown as sample answers in the eight problems in the Independent Practice.
• In Topic 12 Lesson 12-2, the Overview of PBIL states, “Students find the area of a parallelogram.” In the teacher-directed PBIL activity, students create a parallelogram on paper and cut a triangle from one side and move it to the other side to form a rectangle. The directions for the Independent Practice state, “Find the area of each parallelogram or rhombus.” Students do not demonstrate the conceptual understanding of finding the area of a parallelogram independently as solutions are shown as sample answers in the eight problems in the Independent Practice.

### 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 enVisionMATH California Common Core Grade 6 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials provide regular opportunities for students to attend to the standards 6.NS.2 and 6.NS.3, Fluently divide multi-digit numbers using the standard algorithm, and fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

The instructional materials develop procedural skill and fluency throughout the grade level.

• In Topic 4 Lesson 4-5, Develop the Concept: Visual section of the lesson develops procedural skill when multiplying decimals by describing the thought process and presenting several step-by-step examples. The What You Think section states, “Find 0.36 x 4. Multiplying 0.36 x 4 is like adding 0.36 four times on a decimal model. The product is the total area shaded. 0.36 x 4 = 1.44”
• In Topic 5 Lesson 5-2, Develop the Concept: Visual section of the lesson develops procedural skill when modeling division of a four-digit number by a two-digit number in three separate steps. Step 2 states, “Divide the hundreds. Multiply and subtract. Continue the process.” The Independent Practice section includes a template for filling in the numbers to the division problem when practicing the standard algorithm for multi-digit division.
• In Topic 5 Lesson 5-5, Develop the Concept: Visual section of the lesson develops procedural skill when modeling division of decimal numbers in three separate steps. Step 2 states, “Multiply the divisor and dividend by the same power of 10 and place the decimal in the quotient.”

The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level.

• In Topic 4 Lesson 4-2, the Independent Practice provides students with 12 practice problems involving addition and subtraction of decimals. Problem 15 states, “9.501 - 9.45”
• In Topic 5 Lesson 5-3, the Problem Solving section of the lesson provides several multi-digit division practice word problems for students to demonstrate knowledge of procedural skill. Problem 38 states, “Darci wants to buy a computer that costs $1,308. She works at the grocery store where she earns$11 an hour. How many hours will she have to work to earn enough money to purchase the computer?”
• In Topic 7 Lesson 7-4, the Common Core Review provides students with a word problem involving the addition and subtraction of decimals. Problem 6 states, “Dom bought a T-shirt and coffee mug at a sports store. The coffee mug cost $11.50. If c equals the cost of the T-shirt and Dom spent$27 in all, write the equation that shows the cost of the T-shirt and mug. Then find the cost of the T-shirt.”

### 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 enVisionMATH California Common Core Grade 6 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Each topic includes at least one Problem Solving lesson that can be found at the end of the topic. These lessons offer students opportunities to integrate and apply concepts and skills learned from earlier lessons. Within each individual lesson, there is a section titled, Problem Solving, where students practice the application of the mathematical concept of the lesson. However, the applications of mathematics in Problem Solving are routine problems.

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade level. Examples of routine applications, where a solution path is readily available, are:

• In Topic 2 Lesson 2-3, students use addition and subtraction equations to solve word problems. Problem Solving problem 32 states, “The world record for a hot-air balloon flight is 65,000 feet high. Most hot-air balloons fly 62,150 feet below this height. At what height do most hot-air balloons fly? Use the equation h + 62,150 = 65,000.”
• In Topic 2 Stop and Practice, students determine if a statement involving equations is true or false and explain their reasoning. Number Sense problem 23 states, “In the equation 18h = 108, h will be less than 5.”
• In Topic 3 Lesson 3-2, students analyze different tables of values to determine a pattern and write an equation. Problem Solving problem 11 states, “To celebrate their 125th anniversary, a company in Germany produced 125 very expensive teddy bears. The bears, known as the “125 Karat Teddy Bears,” are made of mohair, silk, and gold thread and have diamonds and sapphires for eyes. The chart at the right shows the approximate cost of different numbers of these bears. Based on the pattern, how much does one bear cost?”
• In Topic 6 Lesson 6-8, students use division of mixed numbers to solve real-world problems. Problem Solving problem 30 states, “How many 3/4 ft. pieces can you cut from a 6 1/2 ft. ribbon?”
• In Topic 9 Lesson 9-4, students use ratios to solve word problems. Problem Solving problem 14 states, “Alberta found that 6 cars passed her house in 5 minutes. How many cars would you expect to pass her house in 2 hours?”
• In Topic 10 Lesson 10-8, students apply ratios and unit rates to solve word problems. Independent Practice problem 10 states, “A truck driver started the year making $0.35 per mile. Halfway through the year, she received a raise and began earning$0.43 per mile. She drove 48,000 miles the first 6 months and 45,000 miles the second 6 months. How much did she earn for the year?”

### 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.
2/2
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Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 6 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Lessons include components that serve to develop the three aspects of rigor. These include a Daily Common Core Review, Problem-Based Interactive Learning, Develop the Concept: Visual, Guided and Independent Practice, and Problem Solving. All three aspects of rigor are present independently throughout each topic in the materials. For example:

• In Topic 6 Lesson 6-6, students practice the procedural skill of dividing fractions by multiplying by the reciprocal. The lesson provides 26 procedural-based problems. Independent Practice problem 8 states, “In 7 through 22, find each quotient. Simplify, if possible. 1/2 $$\div$$ 1/4”
• In Topic 7 Lesson 7-6, students apply knowledge of positive and negative numbers to solve word problems. Independent Practice problem 5 states, “Amy spent $9 at the movies, earned$18 for babysitting, and bought a book for $7. She had$13 left. How much money did she have at the start?”
• In Topic 9 Lesson 9-3, students develop conceptual understanding of ratios when drawing a diagram to solve problems. Independent Practice problem 5 states, “For 5 through 8, draw a diagram to solve the problem. A cashier sells 7 DVDs for every 3 CDs she sells. How many CDs does the cashier sell if she sells 35 DVDs?”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

• In Topic 5 Lesson 5-4, students develop conceptual understanding of dividing decimals by a whole number while practicing the procedural skill of the standard algorithm of division of decimals when using place-value models and templates to solve a problem. Guided Practice problem 1 states, “Copy and complete. 304.75 $$\div$$ 53”
• In Topic 8 Lesson 8-3, students develop conceptual understanding of distance on a coordinate place and apply the use of absolute value when determining the distance between two points to solve word problems.
• In Topic 14 Lesson 14-8, students practice the procedural skill of finding the mean, median, mode, and range to solve a word problem. Problem Solving problem 21 states, “The table at the right shows 2 students’ scores for their last 9 games bowled. For the next meet, the coach needs to choose his top bowler. If the coach bases his decision on one of the following criteria, which player should he choose? In your answers, back up your decisions using measures of center and measures of variability. Player with the best average. Player who is the most consistent.”

### 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 reviewed for enVisionMATH California Common Core Grade 6 partially meet expectations for practice-content connections. The instructional materials explicitly attend to the specialized language of mathematics and prompt students to construct viable arguments and analyze the arguments of others. The instructional materials partially meet expectations for identifying and using the mathematical practices to enrich mathematics content within and throughout the grade and assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for enVision Grade 6 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

Mathematical Practice standards are identified in three places within the Teacher Edition: Problem-Based Interactive Learning activity, Guided Practice exercises, and Problem-Solving exercises. Throughout the teacher and student editions, there is a symbol that indicates that one or more MP is being used. Key phrases such as “Look for Patterns," "Use Tools," and "Reason" identify which practice is being highlighted. At the beginning of each lesson, all eight mathematical practices are listed. A check mark is placed beside each practice that is to be addressed within the lesson.

Examples of MPs that are identified but do not enrich the mathematical content include:

• In Topic 7 Lesson 7-1, MP8 is identified with the icon and the key word “Generalize.” Question 8 states, “Which integers do you use for counting?”
• In Topic 7 Lesson 7-4, MP5 is identified with the icon and the key word “Use Tools.” Question 9 states, “How can you use a vertical number line to compare two numbers?”

An example of MPs that are identified and enrich the mathematical content include:

• In Topic 9 Lesson 9-2, MP3 is identified with the icon and the key word “Writing to Explain.” Question 32 states, “The ratio of the maximum speed of Car A to the maximum speed of Car B is 2:3. Explain whether Car A or Car B is faster.” Students construct an argument, although, they do not have to critique the reasoning of others in this problem.

Examples where the MPs are incorrectly labeled:

• In Topic 7 Lesson 7-2, MP5 is identified in the PBIL activity. However, students are given two positive and two negative numbers and directed to order them from least to greatest. Students are instructed to use a number line or thermometer to help them, and both tools are provided within the student edition. Therefore, students are not selecting tools strategically.
• In Topic 11 Lesson 11-2, MP3 is identified with the icon and the key word “Communicate.” Question 8 states, “How is the decimal point moved when changing from a decimal to a percent?” This question does not require a viable argument or a critique of the reasoning of others. According to the teacher edition, students need to state that one moves the decimal point two places over to the right.

Overall, all eight math practices are included within the curriculum and are not treated as separate standards. However, the standards are not used to enrich the content. They are aligned to some of the problems as an explanation to what math practice students might need to use to solve the problem.

### 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 enVisionMATH California Common Core Grade 6 do not meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of each of the eight MPs. The MPs are defined in both the topic and lesson narratives, as appropriate, but are not fully attended to when students interact with the aligned problems in the materials.

The materials do not attend to the full meaning of three or more MPs. Examples that demonstrate this include:

MP1 Make sense of problems and persevere in solving them.

• In Topic 9 Lesson 9-2, MP1 is identified for question 34 in the Problem Solving section. Question 34 states, “Wildlife officials want to increase the population of wild salmon. Use the information in the picture below to determine which ratio shows how many salmon eggs may be needed to produce 18 adult salmon.” It is a multiple-choice question, and the teacher is given information on how to make sense of problems by reminding students to gather information from the caption for the picture.
• In Topic 11 Lesson 11-1, MP1 is identified for question 16 in the Problem Solving section. Question 16 states, “Draw a picture or use a proportion to find each percent.” There are three fractions given that the student changes into percents.

MP4 Model with mathematics.

• In Topic 10 Lesson 10-8, MP4 is identified for question 13 in the Independent Practice section. Question 13 states, “October 31 is National Knock-Knock Joke Day. To honor the day, Annika wants to give 3 different knock-knock jokes to each friend. Make a table that shows how many jokes she will need to collect for 1 to 5 friends. Write an expression that describes the relationship.” The teacher is informed to remind students to find the labels to use for the table.
• In Topic 13 Lesson 13-2, MP4 is identified for question 3 in the Guided Practice section. Question 3 states, “Use your work in exercise 1 to write a formula for the surface area of a cube. Let s equal the length of each side.” The teacher is informed, “If students have difficulty writing a formula...then refer them to the net they drew...”

MP5 Use appropriate tools strategically.

• In Topic 12 Lesson 12-7, MP5 is identified in the PBIL. Students use square tiles to make pentominoes. The teacher is encouraged to remind students that pentominoes and grid paper are tools they can use to solve problems about geometric shapes.
• In Topic 13 Lesson 13-5, MP5 is identified in the PBIL. Students use unit cubes to find the volume and surface area of pictured solids. The teacher is informed that students should see that objects such as unit cubes can be used to help model and find the volume and surface area of prisms.

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

### 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.
2/2
+
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 6 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Students justify their work and explain their thinking; however, evaluating and critiquing the work of others are found less often in the materials. Students critique the reasoning of in problems that ask them if they agree or disagree with a statement or solution.

Student materials prompt students to both construct viable arguments and analyze the arguments of others. Examples that demonstrate this include:

• In Topic 7, Lesson 7-3, Problem solving Question 21 states, “Critique Reasoning. Albert and rebecca toss horseshoes at a stake that is 12 feet away from where they are standing. Whoever is closer to the stake wins. Albert’s horseshoe lands 3 feet in front of the stake and Rebecca’s lands 2 feet past the stake. Albert says that -3 is less than 2, so he wins. Explain whether Albert is correct.”
• In Topic 6, Lesson 6-2, Guided Practice Question 6 states, “Construct Arguments. Grant finds juice bottles that come in packages of 3, but can only find applesauce in packages of 8. Will the LCM change? Explain.”
• In Topic 14, Lesson 14-1, Problem Solving Question 15 states, “Jo says “How do you get to school each morning?” is not a statistical question because each student who answers it can give only one answer. Do you agree with Jo? Explain.”

An example where there is a missed opportunity to construct viable arguments and analyze the arguments of others include:

• In Topic 6, Lesson 6-2, Problem Solving Question 28 states, “Ron is working to find the LCM of 4 and 6. Is his work shown below correct?” Students critique the reasoning of others; however, they are not asked to justify their conclusion.

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 6 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The Teacher Edition contains a Mathematical Practice Handbook which defines each math practice and includes question stems for each MP to help the teacher engage students. MP3 offers the following questions stems: “How can I use math to explain why my work is right?”, “How can I use math to explain why other people’s work is right or wrong?”, and “What questions can I ask to understand other people’s thinking?”

The materials label multiple questions as MP3 or parts of MP3; however, those labeled have little information assisting teachers to engage students in constructing viable arguments or to critique the reasoning of others. The information that the materials provide is not specific and are often hints or reminders to give students while they are solving a problem.

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 Topic 3, Lesson 3-2, Problem Solving Question 12 states “Writing to Explain. Explain how you can find a pattern in the chart showing the cost of “125 Karat Teddy Bears.” Use the pattern to write a rule and an equation.” No teacher guidance is given for this question.
• In Topic 6, Lesson 6-4, Problem Solving Question 32 states, “Writing to Explain. A bowl of soup holds 7 ounces. If a spoonful holds 1/6 ounce, how many spoonfuls are in 3 bowls of soup? Explain.” No teacher guidance is given for this question.

Examples where teachers are supported, although generally, to assist students in constructing viable arguments and analyzing the arguments of others include:

• In Topic 10, Lesson 10-8, PBIL identifies MP3 as the mathematical practice being used in the activity. The teacher note states, “Remind students that as they learn to write good mathematical explanations, they will become better able to communicate their own mathematical thinking.”
• In Topic 14, Lesson 14-1, Problem Solving Question 15 states, “Critique Reasoning. Jo says How do you get to school each morning? Is not a statistical question because each student who answers it can give only one answer. Do you agree with Jo? Explain.” Teacher guidance for this MP is “Remind students to check for reasonableness when solving each problem.”

### Indicator 2g.iii

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 6 meet expectations for attending to the specialized language of mathematics.

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

• Within the Yearlong Curriculum Guide, a list is provided for the Key Math Terms that are used each month of the school year.
• The teacher and student editions include a Review What You Know section at the beginning of every topic. This section reviews vocabulary used in prior topics along with introducing the vocabulary in the current topic. Students complete this activity by inserting the correct vocabulary word into a sentence to correctly identify its definition.
• Within Review What You Know, the new vocabulary listed for Topic 11 includes: proportion, ratio, fraction, and decimal.

The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them.

• In the student materials, vocabulary terms can be found highlighted in yellow within the Visual Learning Bridge across the top of the pages. A definition in context is provided for each term and is used in context during instruction, practice, and assessment.
• In the Implementation Guide, Teacher Edition, as well as the Student Edition, a complete Glossary is included and can be referred to at any time.
• No examples of incorrect use of vocabulary, symbols, or numbers were found within the materials.

Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of Mathematics.

## Usability

#### Not Rated

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

### Criterion 3a - 3e

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

### Indicator 3a

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

### Indicator 3b

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

### Indicator 3c

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

### Indicator 3d

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

### Indicator 3e

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

### Criterion 3f - 3l

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

### Indicator 3f

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

### Indicator 3g

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

### Indicator 3h

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

### Indicator 3i

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

### Indicator 3j

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

### Indicator 3k

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

### Indicator 3l

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

### Criterion 3m - 3q

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

### Indicator 3m

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

### Indicator 3n

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

### Indicator 3o

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

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

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

### Indicator 3p.ii

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

### Indicator 3q

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

### Criterion 3r - 3y

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

### Indicator 3r

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

### Indicator 3s

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

### Indicator 3t

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

### Indicator 3u

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

### Indicator 3v

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

### Indicator 3w

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

### Indicator 3x

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

### Indicator 3y

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

### Criterion 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: 2018/10/24

Report Edition: 2015

Title ISBN Edition Publisher Year
enVisionMATH California Common Core - Grade 6 9780328792733 Pearson 2015

## 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.

## Math K-8

K‑8 Evidence Guide K‑8 Review 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.