## Alignment: Overall Summary

The instructional materials for Dimensions Math Grade 8 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 and devote less than 65% of instructional time to the major work of the grade. For coherence, the instructional materials are not coherent and consistent with the Standards. The instructional materials foster coherence through connections at a single grade, but the materials partially contain supporting work that enhances focus and coherence simultaneously by engaging students in the major work of the grade. Since the materials do not meet the expectations for focus and coherence in Gateway 1, they were not reviewed for rigor and the mathematical practices in Gateway 2 or usability in Gateway 3.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
4
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
N/A
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

#### Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials reviewed for Dimensions Math Grade 8 do not meet expectations for focus and coherence in Gateway 1. For focus, the instructional materials do not meet the expectations for assessing grade-level standards, and the amount of time devoted to the major work of the grade is less 65 percent. For coherence, the instructional materials are not coherent and consistent with the Standards. The instructional materials foster coherence through connections at a single grade, but the materials partially contain supporting work that enhances focus and coherence simultaneously by engaging students in the major work of the 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 8 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 8 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 8A and 8B, 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:

• Students solve equations with rational exponents using the properties of exponents (N-RN.2). For example, in Workbook 8A page 5, problem 20 part a states, “Solve the equation $$4(3^w)=9^2+9^{(w/3)}-2(3^{(w+1)})$$.” There are similar problems on pages 2, 4 and 7.
• Students factor quadratic expressions (A-SSE.B). For example, in Workbook 8A page 19, problem 1 part a states, “Factorize each of the following. $$w^2+9w+14$$.” Parts b through f are similar, and there are also similar problems on pages 14, 15 and 20-24.
• Students find equivalent expressions for rational expressions (A-APR.6). For example, in Workbook 8A, page 25, problem 2 part j states, “Simplify each of the following. $$(2x-3y)/(2x+y)^2 \div (8x-12y)/(3y+6x)$$.” Parts a through i are similar as well as problem 3. Also, page 29 problem 20 states, “Simplify $$((x^2 - 4x - 12)(2x + 3)^2)/(2x^2 - 9x - 18)$$.” There are similar problems on pages 22 and 31.
• Students solve quadratic equations (A-REI.4). For example, in Workbook 8B page 71, problem 3 part a states, “Solve the following equations by using the quadratic formula, giving your answers correct to 3 significant figures. $$x^2 +7x +12 = 0$$.” Parts b through h are similar. There are also similar problems on pages 72-78 of Workbook 8B and pages 17, 22, 24 and 30-32 in Workbook 8A.
• Students graph quadratic functions expressed symbolically (F-IF.7a). For example, in Workbook 8B page 10, problem 28 states, “The points (-5, q+2) and (1, q+2) lie on the graph of the quadratic function $$y = -x^2 + (p - 7)x +7p$$, where p and q are constants. The y-coordinate of the maximum point of the graph is 25. a) Find the line of symmetry of the graph. b) Hence, find the values of p and q.” There are similar problems on pages 6-10.

### 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.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Dimensions Math Grade 8 do not meet expectations for devoting the large majority of class time to the major work of the grade. The instructional materials spend less than 65% of instructional time on the major work of the grade.

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The instructional materials reviewed for Dimensions Math Grade 8 do not meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7.5 out of 14, which is approximately 53 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 27 out of 54, which is approximately 50 percent.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 41 out of 82, which is approximately 50 percent.
• In Grade 8, four of the 14 chapters do not address major work, or supporting work connected to major work.

A lesson-level analysis (which includes lessons and sublessons) is most representative of the instructional materials because it addresses the amount of class time students are engaged in major work throughout the school year. As a result, approximately 50 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.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Dimensions Math Grade 8 do not meet expectations for being coherent and consistent with the Standards. The instructional materials foster coherence through connections at a single grade, but the materials partially contain supporting work that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The instructional materials do not include an amount of content that is viable for one year, do not attend to the full intent of some standards, and do not give all students extensive work with grade-level problems.

### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Dimensions Math Grade 8 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

There are limited connections between supporting work and major work, and some connections are missed. Connections are not explicitly stated.

Examples of supporting work that engage students in the major work of the grade include:

• In Chapter 12, students solve linear equations (major standard 8.EE.7b) in volume problems (supporting standard 8.G.9), such as solving for height given volume and base area.
• In Chapter 13, students describe patterns, such as positive or negative and linear or nonlinear association (major standard 8.F.5) for scatter plots of bivariate data (supporting standard 8.SP.1).

Examples of missed connections between supporting and major work include:

• In Chapter 13, students draw a line of best fit and estimate the slope, but they do not identify y-intercepts, write equations for the line of best fit, or use linear models to solve problems in the context of bivariate measurement data, which are missed opportunities to connect supporting standard 8.SP.3 to the major standard 8.F.4.
• In Chapter 10, there is a missed connection between approximating irrational numbers (supporting standard 8.NS.2) and the Pythagorean Theorem (major cluster 8.G.B). When given irrational lengths, students calculate to three significant figures rather than estimate an answer.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
+
-
Indicator Rating Details

The instructional materials for Dimensions Math Grade 8 do not 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 82 days. The total days were computed in the following manner:

• Each lesson was counted as one day of instruction.
• A “lesson” with subsections (i.e., 1a, 1b, 1c) counted as three lessons or three days.
• A practice day was added to each chapter.

The suggested amount of time for the materials is not viable for one school year, and/or the expectations for teachers and students are unreasonable. Significant modifications would be necessary for the materials to be viable for one school year. In addition, there are several lessons that are off-grade level, which, if not completed, would reduce the number of days provided in the materials.

### 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
+
-
Indicator Rating Details

The instructional materials for Dimensions Math Grade 8 partially meet expectations for being consistent with the progressions in the standards. For the chapters that address Grade 8 standards, the materials generally follow the progression of grade-level standards, though they don’t always meet the full intent of the standards. In addition, lessons utilize standards from prior and future grade levels, though these are not always explicitly identified in the materials. There are multiple chapters that address content from future grades which interferes with students having extensive work with grade-level problems.

The “Notes on Teaching” in Teaching Notes and Solutions provide some direction for teachers to explicitly relate the content to prior learning:

• In Exponents and Scientific Notation, (Book A, page 1), “The idea of exponents has been introduced in Grade 7. In this chapter, students will study the laws of indices and the meaning of negative and rational indices.”
• In Expansion and Factorization of Algebraic Expressions (Book A, page 4), “The distributive law of multiplication that is used to multiply an algebraic expression by a single term has been introduced in Grade 7. In this chapter, we will extend it to find the product of two algebraic expressions (a+b) and (x+y).”

The instructional materials do not attend to the full intent of some standards. Examples include:

• In Chapter 13, students use scatter plots to describe the correlation between two variables, but students do not “use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept” (8.SP.3).
• For 8.NS.A, the materials provide a brief overview of irrational numbers (8.NS.1) in Lesson 1.7B, but students do not determine if a number is rational or irrational. Students do not plot irrational values on a number line or compare those values to other numbers (8.NS.2).
• For 8.F, students do not compare the properties of two functions that are represented in different ways (8.F.2) or sketch a graph for a function that has been described verbally (8.F.5).

The materials do not give all students extensive work with grade-level problems for some standards. Examples include:

• In Lesson 1.3, there are two examples that show the evaluations of “the square root of a small perfect square” and “the cube root of a small perfect cube” (8.EE.2), but students do not make such evaluations themselves.
• In Chapter 2, students solve simple pairs of linear equations by inspection (8.EE.8b) in one problem (page 67, #1c).

The following lessons and chapters address content that aligns to standards above Grade 8, which detracts from students having extensive work with grade-level problems:

• Lesson 1.3: Fractional Exponents (N-RN.A)
• Chapter 3: Expansion and Factorization of Algebraic Expressions (A-APR.1)
• Chapter 4: Quadratic Factorization and Equations (A-SSE.3, A-REI.4)
• Chapter 5: Simple Algebraic Fractions (A-APR.6)
• Lesson 8.2: Graphs of Quadratic Functions (F-IF.7a,8a)
• Lesson 12.3: Cones (G-C.5)

### 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
+
-
Indicator Rating Details

The instructional materials for Dimensions Math Grade 8 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, and there are correlations between Dimensions Math Grade 8 learning objectives and CCSSM cluster headings. Examples include:

• In Chapter 10, some learning objectives are: “State Pythagorean Theorem and its converse; apply Pythagorean Theorem to solve problems; and determine whether a triangle is right-angled given the lengths of its three sides.” These objectives are shaped by 8.G.B, “Understand and apply the Pythagorean Theorem.”
• In Chapter 1, some learning objectives are: “State and apply the laws of exponents; simplify an expression involving exponents; and solve equations involving exponents.” These objectives are shaped by 8.EE.A, “Work with radicals and integer exponents.”

The materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade. Examples include:

• In Lesson 9.2, students define, evaluate, and compare functions (8.F.A) while using functions to model relationships (8.F.B).
• In Chapter 8, students examine the equation y = mx +b (8.F.A) to interpret the unit rate as the slope of a graph (8.EE.B).

Students do not connect the Pythagorean Theorem (8.G.B) to work with radicals (8.EE.A) in Lessons 10.1, 10.2 and 10.3.

## Rigor & Mathematical Practices

#### Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

### 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.

### 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.
N/A

### 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.
N/A

### 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
N/A

### 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.
N/A

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
N/A

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
N/A

### Indicator 2g

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

### 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.
N/A

### 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.
N/A

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
N/A

## 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

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

### 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

### 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

Report Published Date: Mon Nov 12 00:00:00 UTC 2018

Report Edition: 2015

Title ISBN Edition Publisher Year
Dimensions Math Textbook 8A 978-981-4250-62-7 Star Publishing Pte Ltd 2013
Dimensions Math Textbook 8B 978-981-4250-63-4 Star Publishing Pte Ltd 2013
Dimensions Math Workbook 8A 978-981-4250-64-1 Star Publishing Pte Ltd 2015
Dimensions Math Workbook 8B 978-981-4250-65-8 Star Publishing Pte Ltd 2014
Dimensions Math Teaching Notes and Solutions 8A 978-981-4250-68-9 Star Publishing Pte Ltd 2013
Dimensions Math Teaching Notes and Solutions 8B 978-981-4250-69-6 Star Publishing Pte Ltd 2014

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

## Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric 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.

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