## Alignment: Overall Summary

The instructional materials for Dimensions Math Grade 6 do not meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus as they assess above-grade-level standards but do devote at least 65% of instructional time to the major work of the grade. For coherence, the instructional materials are partially coherent and consistent with the Standards. The instructional materials contain supporting work that enhances focus and coherence simultaneously by engaging students in the major work of the grade and foster coherence through connections at a single grade. In Gateway 2, the instructional materials meet the expectations for rigor and balance, but they do not meet the expectations for practice-content connections. Since the materials do not meet the expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
10
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

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

|

## 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

#### Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Dimensions Math Grade 6 partially meet expectations for focus and coherence in Gateway 1. For focus, the instructional materials do not meet the expectations for assessing grade-level standards, but the amount of time devoted to the major work of the grade is at least 65 percent. For coherence, the instructional materials are partially coherent and consistent with the Standards. The instructional materials contain supporting work that enhances focus and coherence simultaneously by engaging students in the major work of the grade 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.
0/2
+
-
Criterion Rating Details

The instructional materials reviewed for Dimensions Math Grade 6 do not meet expectations for not assessing topics before the grade level in which the topic should be introduced. The instructional materials include assessment items that align to standards above this grade level.

### 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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Dimensions Math Grade 6 do not meet expectations for assessing grade-level content. The FAQ page on the website for Singapore Math states, “There are currently no tests, but the workbook could be used as a test bank.” In Dimensions Math workbooks 6A and 6B, above grade-level items are present and could not be modified or omitted without a significant impact on the underlying structure of the instructional materials. For example:

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
+
-
Criterion Rating Details

The instructional materials for Dimensions Math Grade 6 do not meet expectations for practice-content connections. The instructional materials prompt students to construct viable arguments and analyze the arguments of others, and they partially assist teachers in engaging students to construct viable arguments and analyze the arguments of others and explicitly attend to the specialized language of mathematics.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Dimensions Math Grade 6 do not meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

Mathematical Practices are not identified in the materials. In the Syllabus, page 39, Mathematical Processes (Reasoning, Communication and Connections, Application and Modeling, and Thinking Skills and Heuristics) are identified, but these are not referenced in the remainder of the materials. Teachers are not provided with guidance or directions for how to carry out lessons to ensure students are developing the mathematical processes.

Examples where the Mathematical Practices are not identified and do not enrich the mathematics content include:

• For MP4, students use physical models in problems. For example, in Chapter 6 Section 6.1, Class Activity 1, students use blue and yellow blocks to model averages for player A and player B. However, students do not represent the situation mathematically with an equation or a method that would help them generalize information to draw conclusions.
• For MP5, students are directed which tools to use in problems, and students do not discuss which tools to select or use strategically. The instructional materials show different methods for solving problems, but students do not choose which method to use or which method would be most appropriate for problems.
• For MP7, the materials do not identify looking for and making use of structure. For example, in Chapter 1 BrainWorks Exercise #8, Daniel makes use of structure to write $$3^5$$ as an equivalent expression for $$3^2\times3^3$$. However, the materials do not identify the use of structure or provide guidance for teachers as to how MP7 could be used.

### Indicator 2f

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

The instructional materials reviewed for Dimensions Math 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 MPs.

For MP4 Model with mathematics, students solve real-world, contextual problems, but students do not model with mathematics in those problems. Examples of the materials not attending to the full meaning of MP4 include:

• In Student Workbook 6A, Lesson 1.4, students “draw a model and equation to match” for two real-world problems. On page 32 problem 3, students are prompted to “draw a model and solve” for a real-world problem. In these problems, there are no opportunities for students to revise initial assumptions or models once calculations have been made.
• In Lesson 2.1C, examples 14-16 show students how to use bar models to solve real-world problems and write the solution mathematically from the models. Problems like this are also encountered in Lessons 5.2 and 7.2. In these problems, students do not make assumptions, define quantities, or choose what model to use, and there are no opportunities for students to revise initial assumptions or models once calculations have been made.
• In Lesson 8.1C, students complete an example by using a given table to model the relationship in age between two children, creating an expression from the table, and using the expression to determine the age of one child. In Try It! on page 14, students complete a similar problem on their own. In this problem, students do not make assumptions, define quantities, or choose which model to use.

For MP5 Use appropriate tools strategically, the materials rarely demonstrate the use of tools to solve problems, other than a tape diagram. The instructional materials do not introduce and engage students in the use of various tools, including technology. Examples of the materials not attending to the full meaning of MP5 include:

• In Lesson 2.1, students are shown how to use a bar model as a mathematical tool for solving a problem involving multiplication of fractions. Other tools are not introduced or used, and students do not choose which tool to use.
• In Lesson 10.2, students are shown a number line to help define absolute value in the introduction. Further examples in the lesson show distance on a coordinate plane through the use of absolute value, but students do not choose which tools to use to find distances.
• In Lesson 12.2B, students are shown a net of a triangular prism, but students do not use nets as a tool for finding surface area in subsequent examples in the lesson.
• Students do not use ratio tables or number line diagrams in problems with ratios, rate, or percentages. They are shown tape diagrams as a tool for working with ratios, but students do not choose the tool.

For MP8 Look for and express regularity in repeated reasoning, there are limited opportunities for students to examine repeated calculations and look for general methods and/or shortcuts. Examples where students do not engage in MP8 include:

• In Lesson 2.2, the materials demonstrate how to divide a whole number by a fraction, draw a model to represent “how many 1/3’s and 2/3‘s are in 6,” and complete a table by using the reciprocal of the divisors to write equivalent multiplication expressions. Students are asked to: “(a) Look at the patterns in the divisors and the quotients. What happens to the quotient as the divisor gets smaller? (b) What do you notice about the quotients of the division expressions and the products of the equivalent multiplication expressions?” However, students are given a summary of the activity showing the generalization, “Dividing a whole number by a fraction is the same as multiplying by its reciprocal,” as an algebraic expression.
• In Lesson 3.2, the materials demonstrate what happens to a rational number written in decimal form as it is multiplied by powers of 10. Students relate their results to place value. Students do not look for and express regularity in repeated reasoning. In example 5 on page 81, students determine which decimal factors produce products of a given size, but the remainder of the lesson includes teacher-led explanations of the repeated reasoning rather than students engaging in the mathematical practice.
• On page 94, students divide rational numbers written in decimal form, but none of the divisions result in repeating decimals, which means students do not engage in MP8. In BrainWorks question 16 on page 94, students compare two different students’ reasoning about the value of repeating decimals, but they do not look for and express regularity in repeated reasoning themselves.

### Indicator 2g

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

### 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
+
-
Indicator Rating Details

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

The student materials include questions for discussion in the margins where students explain their thinking, and the teacher materials indicate students should discuss their explanations with a partner or in a group. The materials contain some problems where students are specifically asked to justify a claim with mathematics, build a logical progression of statements to explore the truth of a conjecture, or analyze situations by breaking them into cases. Examples include:

• In Chapter 1 page 4: “Which is greater: Two to the third power or three to the second power? Explain.”
• In Chapter 1 page 15: “Are 72 and 96 common multiples of 4 and 6? Explain.”
• In Lesson 5.1, problem 15 states, “A bag contains some red balls and blue balls. The ratio of the number of red balls to the number of blue balls is 4:7. If the total number of balls in the bag is not more than 40, what are the possible numbers of blue balls in the bag? Explain how you find the answers using equivalent ratios.”
• In Chapter 7 page 198, students explain whether they would want 10 percent of $20 or 20 percent of$10.
• In Chapter 13 page 199: “Can we arrange the data in descending order instead of ascending order? Why?”

The student materials include problems in each chapter for students to critique someone else’s work or explanation. The Workbooks contain additional similar tasks. Examples include:

• In Chapter 3 page 101 Write in Your Journal, students determine if 6.5 x 10 = 6.50 is a student’s correct application of the rule, “Add a zero when you multiply by 10,” and explain their reasoning.
• In Workbook 6A, Lesson 1.1B page 7, students explain Leo’s error in evaluating $$6^3$$ as 18.
• Chapter 7 page 209 states: “A shop owner sold 10 cell phones and made a total gain of 20 percent. What was her profit for each cell phone? A student solved this question as follows: 10 phones → 20 percent, 1 phone → 20%/10 = 2 percent. Her profit for each cell phone was 2 percent. Is this solution correct? Explain.”

### 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 Dimensions Math 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 instructional materials provide little assistance to teachers in engaging students in constructing viable arguments and analyzing the arguments of others, and the assistance that is provided is general in nature.

In the Syllabus page 13, the Mathematics Framework describes five components that make up Problem Solving: Attitudes, Metacognition, Processes, Concepts, and Skills. Under Processes, the syllabus describes how “in the context of mathematics, reasoning, communication, and connections take on special meanings.” On page 16, there is a section that describes ways “to help teachers focus on these components in their teaching practice,” and on page 18, the Syllabus states, “To support the development of collaborative and communication skills, students must be given opportunities to work together on a problem and present their ideas using appropriate mathematical language and methods.”

On page 39, the Syllabus specifies that Reasoning, Communication, and Connections include:

• Using appropriate representations, mathematical language (including notations, symbols and conventions), and technology to present and communicate mathematical ideas;
• Reasoning inductively and deductively, including: explaining or justifying/verifying a mathematical solution/statement; drawing logical conclusions; making inferences; and writing mathematical arguments; and
• Making connections within mathematics and between mathematics and the real world.

The syllabus does not give specific direction to teachers about creating these opportunities for students, and this information is not found in any of the other materials besides the Syllabus.

Within the remainder of the instructional materials, there are no prompts, suggested questions, or frameworks for teachers suggesting ways to engage students in constructing viable arguments and/or analyzing the arguments of others. There is no guidance for teachers as to what constitutes a viable mathematical argument, such as the use of definitions, properties, counterexamples, cases, or if-then statements, and there is no guidance for analyzing the arguments of others, such as repeating or restating to check for understanding, asking clarifying questions, or building on a previous idea.

The teacher materials contain some directions to engage students in discussions, but there is no guidance for teachers on constructing viable arguments or analyzing the arguments of others. Examples of directions for teachers to engage students in discussions include:

• On page 6, “Have students talk about DISCUSS boxes with a partner or group.”
• On page 17, “Have them solve the problem and share and discuss their solutions.”
• On pages 28 and 54, “Have students work together with a partner or in groups . . . then compare solutions with their partner or group. If they are confused, they can discuss together.”
• On page 60, “Have students study examples 18-20 and do Try It! 18-20 on their own, then compare their solutions with partners or in a group.”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Dimensions Math Grade 6 partially meet expectations for explicitly attending to the specialized language of mathematics.

In general, the materials accurately use numbers, symbols, graphs, tables, and mathematical vocabulary. However, the materials do include some vocabulary and definitions that are not consistent with the CCSSM. Examples include:

• In Lesson 1.1, “Remark” on page 2, the following information is given: “There will be a convention that when a difference between two numbers is asked for, it will be the larger minus the smaller unless otherwise specified. For division, the quotient of two numbers will be the larger divided by the smaller unless otherwise specified.” This may reinforce a common misconception that division is always the larger number divided by the smaller number.
• “Simplest form” is used in Chapter 2 with fractions and in Chapter 5 with ratios, but it is not used in the CCSSM.
• In Student Workbook 6A problem 6 page 15, “Cora and Alyssa solved the expression independently and got different solutions: $$6 + 3\times 6 \div2 + 4$$. Cora says that the solution is 19. Using the Order of Operations convention, which girl is correct? What was the other girl thinking?” The term convention is used once in the Remark section on page 3, but a formal definition or explanation of convention is not provided.
• Simplify is used throughout Chapter 8, but it is not used in CCSSM.

## 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: 2018/11/12

Report Edition: 2016-2017

Dimensions Math Teacher's Guide 6B

Dimensions Math Workbook 6B

Title ISBN Edition Publisher Year
Dimensions Math Workbook 6A 978‑1‑947226‑42‑5 Star Publishing Pte Ltd and Singapore Math Inc. 2017
Dimensions Math Teacher's Guide 6A 978‑1‑947226449 Star Publishing Pte Ltd and Singapore Math Inc. 2017
Dimensions Math Textbook 6A 978‑981‑4658‑22‑5 Star Publishing Pte Ltd and Singapore Math Inc. 2016
Dimensions Math Textbook 6B 978‑981‑4658‑23‑2 Star Publishing Pte Ltd and Singapore Math Inc. 2017

## 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.