## Alignment: Overall Summary

The instructional materials reviewed for Grade 6 meet the expectation for alignment to the Common Core State Standards. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Also, the majority of the chapters and the respective days allocated in the timeline align to the major work of this grade. For coherence, supporting work is clearly connected to the focus of the grade and is done so in a meaningful way. Coherence is also evident in the instructional materials including problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. The Grade 6 materials are coherent and consistent with the standards. The instructional material meets the expectations for the criterion of rigor and balance with a perfect rating. Within the concept development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. Procedural skill and fluency are evident, with an abundance of examples and computation activities which stress fluency in conjunction with the skill. Application of the mathematical concepts is abundant throughout each module. In the instructional materials, the three aspects are balanced within the lessons and modules. The instructional materials also meet the expectations for the criterion of practice-content connections. They meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. However, weaknesses were noted in the identification of the latter and in attending to the full meaning of each practice standard. Overall, the Instructional materials meet the quality expectations for alignment to the Common Core State Standards.

|

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

|

## Gateway 3:

### Usability

0
22
31
38
25
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

+
-
Gateway One Details

The instructional materials reviewed for Grade 6 meet the expectation for alignment to the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Also, the majority of the chapters and the respective days allocated in the timeline align to the major work of this grade. For coherence, supporting work is clearly connected to the focus of the grade and is done so in a meaningful way. Coherence is also evident in the instructional materials including problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. The Grade 6 materials are coherent and consistent with the standards.

### Criterion 1a

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

The instructional materials reviewed for Grade 6 assess topics only at this grade level. For example, the mid-module and end-of-module assessments cover grade-level content. There are no examples of above-level assessments in the student edition. Overall, the instructional material meets the expectations for focus within assessment.

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectations for assessing the grade-level content. There is no content of future grades assessed. Overall, the instructional materials assess grade-level topics.

• All assessment Items are at grade level and aligned to one or more of the grade-level standards.
• Mid-module and end-of-module assessments are aligned to grade-level content and do not assess content above the specified grade level.
• The rubrics for each assessment indicate which standards are assessed in each question. Every question aligns to at least one grade-level standard.

### 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
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 are developed so that students and teachers using the materials as designed devote the large majority of class time to the grade's major work. Sixty-seven percent of the days are suggested for major work of the grade. Three of the six modules are designated as major work and two others contain lessons related to major work. Overall the instructional materials meet the criteria for the time devoted to the major work of the grade.

### Indicator 1b

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

The instructional materials reviewed for Grade 6 meets the expectations for spending the majority of class time on the major cluster of each grade. Overall the instructional materials meet the criteria outlined in the CCSSM publisher guidelines for the time for the major work of the grade.

• 6.RP.1-3, 6.NS.1, 6.NS.5-8 and 6.EE.1-9 standards are major work of the grade.
• Modules 1, 3 and 4 focus on the major work, and Modules 2 and 5 contain lessons related to the major work.
• The modules in bold are modules aligned to the major clusters of the grade.
• Module 1: 29 lessons + 6 days = 35 days (ratio and unit rates)
• Module 2: 19 lessons + 6 days = 25 days (operations and fractions)
• Module 3: 19 lessons + 6 days = 25 days (rational numbers)
• Module 4; 34 lessons + 11 days = 45 (expressions and equations)
• Module 5: 19 lessons + 7 days = 26 days (area, surface area, volume)
• Module 6: 22 lessons + 3 days = 25 days (statistics)
• Of the 180 days, 120 days (67%) are spent on the major clusters of the grade.

### Criterion 1c - 1f

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

The instructional materials reviewed for Grade 6 meet the expectations for coherence and consistency with the CCSSM. The majority of the chapters and the respective days allocated in the timeline align to the major work of this grade. Supporting work is connected to the focus of the grade in a meaningful way. Each module begins with an overview of the foundational standards that have been taught and learned previously and focus, both of which were being addressed in the module. Ample narrative exists throughout the modules explaining how the materials develop from previous material and, sometimes, how the material will be addressed in the future. Coherence is also evident in the instructional materials by the inclusion of problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade.

### Indicator 1c

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

The instructional materials reviewed for Grade 6, by engaging students in the major work of the grade, simultaneously meet the expectations for the supporting content-enhancing focus and coherence. Overall, the majority of the chapters and the respective days allocated in the timeline align to the major work of this grade level. The chapters and the individual lessons support focus and coherence to the major work of the grade level.

• Supporting work is clearly connected to the focus of the grade and is done so in a meaningful way.
• Module 2 is a strong example of how supporting work, 6.NS.2-4, is presented in a way that connects to the focus of the grade, providing ample opportunity to work with fractions and ratios.
• In lesson 1 of module 5, students are asked to solve a problem using equations and fractions (dividing fractions). These two concepts link the topic of area back to previous learning from this grade level.
• Within lesson 12 of module 6 (statistics), students must perform operations with decimals which support previous learning from the grade level.

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. Overall, the amount of content that is designated for this grade level is viable for one school year.

• There are 181 designated days for all of the modules with one day labeled optional.
• Each module has built in days for assessment, review and extra practice. This allows for adjustments needed throughout a school year resulting from school activities, weather days and a teacher's professional judgment as to pacing.
• The following are the designated days for each module:
• Module 1: 29 lessons + 6 days = 35 days (ratio and unit rates)
• Module 2: 19 lessons + 6 days = 25 days (operations and fractions)
• Module 3: 19 lessons + 6 days = 25 days (rational numbers)
• Module 4; 34 lessons + 11 days = 45 (expressions and equations)
• Module 5: 19 lessons + 7 days = 26 days (area, surface area, volume)
• Module 6: 22 lessons + 3 days = 25 days (statistics)

### 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 reviewed for Grade 6 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grades is identified, although materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not often made to content in future grades. Overall, the materials in Eureka-Grade 6 identify the progressions from prior grades in the standards.

• Each module begins with an overview of standards being addressed in the module: here, foundational standards that have been taught and learned previously and focus.
• When appropriate, the connections to lessons and/or topics from previous grade levels are called out at the beginning of a given topic. For instance, in module 5, lesson 16, the beginning information specifies that the upcoming lessons are a continuation of topics A and B from module 5 in the Grade 5 materials.
• Ample narrative exists throughout the modules explaining how the materials develop from previous material and sometimes how the material will develop in the future.
• Teachers are provided with sufficient information to help see the connections in the standards, tasks, modules and lessons.

The instructional materials reviewed for Grade 6 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

• The materials provide students with extensive work with grade level problems.
• Modules contain a large mix of tasks that are grade level appropriate. Each module also contains at least one extensive problem set designed to help develop students' procedural skill/fluency.
• There are occasional comments within the teacher material to help teachers best reach English language learners (ELLs) or below-grade-level students, and little guidance is provided on how to support students that are above grade-level.

The instructional materials reviewed for Grade 6 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials only generally relate grade-level concepts explicitly to prior knowledge from earlier grades.

• Each module lists the foundational standards at the beginning of the module to explicitly connect prior learning to current learning.
• Educators may find it more beneficial to see these connections called out in the lessons as they occur.
• The student material makes no explicit connections to prior knowledge from earlier grades. However, some of the narrative reminds students of previously learned material within the grade when it is expected to be recalled.

### 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 reviewed for Grade 6 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

• When both teacher and student materials sometimes end with a lesson summary that reviews student outcomes, they are written in language that can be easily aligned to learning objectives (CCSSM standards) and cluster headings.
• The first sentence in topic A directly connects the 6.RP standards in the module to the cluster heading.
• Module 3's overview also connects the RP standards to the cluster heading. In this module there is also a student outcome that says, "Students extend their understanding of the number line, which includes zero and numbers to the right, which are above zero, and numbers to the left, which are below zero."

The instructional materials include problems and activities that serve to connect two or more clusters in a domain. They include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important.

• In module 2 of Grade 6, the clusters within the number system are intertwined. The clusters are: "apply and extend previous understandings of multiplication and division to divide fractions by fractions" and "compute fluently with multidigit numbers and find common factors and multiples." The integration of these standards allows students to see and build connections within the number system and the operations.
• In module 4, lessons 3, 4, 10 and 11, students use their skill in recognizing common factors (6.NS.4) to rewrite expressions (6.EE.3).
• Module 4, lesson 7, stresses writing, reading, evaluating and transforming the volume formulas V = lwh and V = Bh (6.G.2, 6.EE.2).
• In module 4, lesson 25, equations of the form px = q (6.EE.7) are unknown-factor problems; the solution will sometimes be the quotient of a fraction by a fraction (6.NS.1).

## Rigor & Mathematical Practices

#### Meets Expectations

+
-
Gateway Two Details

The instructional material for the Grade 6 meets the expectation for rigor and mathematical practices. The instructional material meets the expectations for the criterion of rigor and balance with a perfect rating. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. Procedural skill and fluency is most evident in modules 2, 3 and 4, with an abundance of examples and computation activities that stress fluency in conjunction with the skill. Application of the mathematical concepts is abundant throughout each module. In the instructional materials, the three aspects are balanced within lessons and modules. The instructional materials also meet the expectations for the criterion of practice-content connections. They meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials are strong in rigor and in regard to emphasis on supporting the standards' emphasis on mathematical reasoning. However, improvements should be made in fully attending to the MPs being identified and used to enrich mathematics content and materials and attending to the full meaning of each practice standard. Overall the Instructional materials meet the quality expectations for Gateway 2 in rigor and mathematical practices.

### 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.
8/8
+
-
Criterion Rating Details

The materials reviewed for Grade 6 meet the expectations for this criterion by providing a balance of all three aspects of rigor throughout the lessons.

Within the concept development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. In Grade 6 Procedural skill and fluency is most evident in module 2, 3, and 4, which cover 6.NS and 6.EE. Application of the mathematical concepts is abundant throughout each module. Overall, introduction of new concepts is done through examples that involve applications, and lessons often follow that are application reinforcements of the skills. The three aspects are balanced within the lessons and modules. Overall, the Grade 6 materials meet the criteria for rigor and balance.

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

The materials reviewed in Grade 6 for this indicator meet the expectations by attending to conceptual understanding within the lesson.

• Module 1 assesses all of the specific content in 6.RP in various questions. Students were required to create and explain visual models (i.e., fraction models, ratio models, etc.) as part of their understanding on a regular basis.
• In Eureka-Grade 6, the development of division of fractions is structured in a way that includes several high-quality conceptual problems that allow students to work with several models, when applicable, and engage in discussion about the representations.
• The lessons are scaffolded in a way that gradually builds on and expands concepts from previous lessons.
• The lessons also structure the language of division in a way that helps transition students from the conceptual development to building fluency with the procedures.

### 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
+
-
Indicator Rating Details

The materials reviewed in Grade 6 for this indicator meet the expectations by attending to fluency and procedural work within the lessons.

• Procedural skill and fluency is most evident in modules 2, 3 and 4, which cover 6.NS and 6.EE. In addition to an abundance of examples throughout the lessons, there are also specific computation activities that provide practice with procedural skill designed to build fluency.
• Similarly, small-group and whole-class activities are sometimes included as opening or closing activities stressing the importance of procedural skill and fluency to the development of a concept, like simplifying ratios (e.g., module 1, lesson 12).
• Within the module on division of fractions, the review team identified the development of procedural fluency to be rushed. The unit spends a tremendous amount of time building conceptual understanding, but it is difficult to determine if there is sufficient time for students to gain fluency with the operations. Additionally, fluency in division of fractions is not assessed.
• However, the materials do continue to spiral back to previous concepts throughout the next lessons and modules.

### 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
2/2
+
-
Indicator Rating Details

The materials reviewed in Grade 6 for this indicator meet the expectations by attending to application within the lessons.

• Application of the mathematical concepts is abundant throughout each module. Overall, the introduction of new concepts is done through examples that involve applications, and lessons often follow that reinforce application skills.
• For example, module 1 uses application to develop 6.RP and the transition from ratios to tables to equations to graphs.
• Similarly, as students solve equations in module 4 (6.EE), they must develop the equation based on given information and then solve.
• In module 2, most of the problems are presented within a real-world context so that students can see the application of the math (division) to contextual situation.
• Students are also asked to apply mathematics to solve problems.
• There is a balance of introducing the concepts using real-world situation and also having students apply their understanding in order to solve application problems.

### 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
+
-
Indicator Rating Details

The materials reviewed in Grade 6 for this indicator meet the expectations by providing a balance of rigor. The three aspects are not always combined together nor are they always separate.

• Conceptual understanding, procedural skill and fluency, and application are integrated into each module as needed. When needed, separate fluency activities are included in the series. At other times, the procedural skill are part of application and conceptual understanding exercises.
• In module 1, lessons 1, 2, 10, 14, 15, 16 and 17 spend the majority of the time developing the concepts of ratios and unit rates.
• Lessons 8, 12, 13 and 18 continue to develop the concepts, but also require work finding equivalent ratios and rates using specific procedure to compute.
• The remaining lessons, as well as those already mentioned, give the students ample practice using ratios and unit rates in real-world application problems.
• There is a balance of the three aspects of rigor in included assessments.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
+
-
Criterion Rating Details

The materials reviewed for Grade 6 partially meet the criterion of meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. The latter are often identified and used to enrich mathematical content. However, there are missed opportunities for identifying MPs in the materials. Materials sometimes attend to the full meaning of each practice standard. Throughout the lessons, the materials prompt students in constructing viable arguments concerning grade-level mathematics detailed in the content standards. Students are also directed to explain responses in practice sets and exit ticket questions. Occasionally, the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others. On the other hand, materials very explicitly attend to the specialized language of mathematics. Correct mathematical terminology is always used, enforced and reinforced. Overall, the materials meet the expectations for the practice-content connections Criterion.

### Indicator 2e

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

The Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content.

• All modules at the Grade 6 level list the focus MPs in the module overview and expand on each practice's connection to the module.
• The summary in the overview is helpful because they specifically explain how the practice relates to the particular math concepts and lessons within the modules.
• For example, MP1, MP3, MP4 and MP6 are all called out in module 5 (page 7) and include some specific explanation of how they connect to the content in the module.
• The modules do not all find ways to address every practice standard, which is more realistic than forcing all of the practice standards into each module.
• Within the teacher lesson notes for each lesson, the mathematical practices are again called out when appropriate, sometimes several times throughout the lesson when practices are emphasized throughout the lesson. These notes assist teachers in understanding what students should be doing to engage with the practice standard.

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

Materials sometimes attend to the full meaning of each practice standard.

• On page 14 of module 1 (MP6), students are asked to use terminology appropriately and accurately and are pushed to be accurate and precise in their descriptions.
• On page 19 (MP.6) students are again asked to use precise language to answer questions.
• Furthermore they are given specific questions using mathematical terminology to determine if they understand the language with precision.
• Module 2, page 19 (MP 1, 2, 3, and 5) is a good example of representing a problem with a model and creating the quantitative equations. It also allows students to choose the model, although SMP.5 is not listed. The task indirectly asks students to evaluate each other's work (MP3), but this standard is not listed. Referencing the MP is often not done when it could be.
• Page 40 is labeled MP5, which is not fully aligned to the standard since the practice problem led students through the lesson using a tape diagram. Students would likely then also use a tape diagram in example 2, which does not support them in independently choosing the appropriate tool.
• Page 64 (MP7) opens by saying teacher should "continue to guide students to create the table shown." Depending on how much guidance is given this practice standard may not be met.

### 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

Materials frequently prompt students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Occasionally materials prompt students to analyze the arguments of others.

Throughout the discussion portion of each lesson, students are expected to explain the mathematics leading to understanding content and solving problems.

Students are also directed to explain responses in problem-set and exit ticket questions.

There are examples of students being asked to analyze the arguments of others in the lesson material or practice exercises.

### 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

Materials are limited in assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

The teacher material frequently provides quality questions the teacher can pose to students to elicit their reasoning, but it falls short in providing teachers directions to then have students critique the reasoning of others.

It is not until module 3 that students and teachers are given the opportunity to reach the full meaning of MP3 with explicit mention to the educator. Even here, on page 81, teachers are not given a great deal of information to help facilitate this.

Pages 7 and 8 of module 5 give some help to educators regarding MP3.

MP3 was not identified as a focus MP until modules 5 and 6.

In module 2, MP3 is identified for teacher reference a very limited number of times. However, it was not it a focus in teacher-student discussion and instruction.

### Indicator 2g.iii

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

Materials very explicitly attend to the specialized language of mathematics.

• Correct mathematical terminology is always used, enforced and reinforced.
• At the beginning of each module, terminology that is new or recent is specifically highlighted and defined (and examples provided in some cases) for teachers as are terms that should be more familiar.
• Explicit detail is always used in student-teacher discussion and explanation of process.
• The terminology that is used in the modules is consistent with the terms in the standards.
• Furthermore, relevant vocabulary is highlighted for students throughout the lessons and is reiterated at the end of each lesson (when relevant). This allows students to use their own resources in future lessons to review the relevant vocabulary and/or equations associated with such terms as "area" or "pi."

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
+
-
Criterion Rating Details

The materials meet the criterion for use and design. The underlying design of the materials makes a distinction 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. The design of assignments is not haphazard; exercises do seem to be given in intentional sequences. Furthermore, the design is not distracting or chaotic but supports students in engaging thoughtfully with the subject.

Additionally, in most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives. Overall, the materials reviewed for Grade 6 meet the expectations for this criterion.

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

The underlying design of the materials does distinguish between problems and exercises meeting the expectations for this indicator.

• The lessons usually follow a typical sequence that includes classwork typically facilitated by the teacher: opening exercises, scaffold examples, exploratory challenges, discussion topics and other examples. These problems or tasks are usually labeled "examples" and are intended to be the learning portion of the lesson.
• Following the classwork, and sometimes within the class work, there is usually a set of "exercises" that are to be completed within the class period either individually or with a partner. These "exercises" generally reinforce and/or extend the process(es) explored in the classwork.
• Next, there is usually an additional set of problems that are labeled "problem set." The problems in the problem set typically mirror the problems in the class exercises but appear to be done with extra class time or outside of structured class time.
• Lastly, lessons with closure also include an "exit ticket," which is usually, but not always, aligned to problems in the exercises and the problem sets.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
+
-
Indicator Rating Details

The design of assignments is not haphazard; exercises do seem to be given in intentional sequences meeting the expectations for this indicator.

• Problem sets typically follow the sequence in classroom work.
• Problem sets generally build from simpler problems to more complex ones with either more steps or more challenging numbers (fractions, decimals, etc.).
• Problems often allow students to both apply new knowledge (such as solving equations) to prior understandings (such as using integers, fractions, decimals) in order to solve problems.
• Therefore, it appears students are increasing fluency of prior skills while developing understanding of new math concepts.

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

There is a variety in what students are asked to produce meeting the expectations for this indicator.

• Throughout a module-and often within a given lesson-students are asked to produce answers and solutions as well as to explain their work, justify their reasoning and use appropriate models.
• Sometimes only one aspect is specified, such as only requiring an answer, and other times a problem requires students to provide an answer, provide an explanation or steps, include a diagram and/or use a model.
• Because problems require different responses, the type of response is intentional-such as requiring models when a concept is introduced and then not requiring the same model when a more concrete or procedural method for solving similar problems is developed.

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
+
-
Indicator Rating Details

The manipulatives are almost always faithful representations of the mathematical objectives they represent and when appropriate are connected to written models meeting the expectations for this indicator.

• In most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives.
• When appropriate, multiple models are introduced-such as using both an area and a number-line model for dividing fractions in module 2.
• However, there was an inconsistency in the model. In module 2, lesson 3, both example 1 and 2 use an area model. But in one, 8/9 is represented by shading 8 of 9 sections and using a bracket to show the whole as all 9 parts. In the other, 9/12 is shaded, but the bracket only continues to the 9 parts, Therefore, a teacher who may not be familiar with this manipulative/model may be confused by the inconsistency (there did not appear to be any other instructions about how to use these representations.)

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Narrative Evidence Only
+
-
Indicator Rating Details

The visual design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

• The student materials are clear and consistent between modules within a grade level as well as across grade levels.
• Each lesson is clearly labeled-and provides consistent numbering for each module/grade-with both a lesson number and page number.
• The lessons are clearly named, the classwork and examples within them are labeled as well as another section for exercises-which are typically completed within class-and then the problem sets.
• When appropriate, a section for lesson summary and/or vocabulary is included at the end of the lesson but before the problem sets.
• The exit slips are separate and provide space for a name and date.
• There are no distracting or extraneous pictures, captions or "facts" within lessons.

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
6/8
+
-
Criterion Rating Details

The materials reviewed partially meet the criterion for teacher planning and learning. The materials partially support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Materials contain a teacher edition with ample and useful annotations and, sometimes, suggestions on how to present the content in the student edition and in the ancillary materials. The strongest point is that each module has an overview section at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Overall, the material reviewed for Grade 6 partially meet the expectations for this criterion.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
1/2
+
-
Indicator Rating Details

The materials partially support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

• The strength of the materials is the quality of the questions asked through the lessons (classwork) as well as the exercises, problems, exit tickets and assessments.
• However, the materials do not include instructions or guidance for how to adjust a lesson or the questions that a teacher asks to guide instruction based on the needs of students.
• The materials provide effective learning experiences if the teacher both understands the content and also has a wealth of pedagogical practices for guiding discussions through questioning strategies that they are able to incorporate with ease.
• There is not sufficient guidance for how to group students or structure questions that can support all students in accessing the material.
• If a teacher is not confident with the sequence of the math or the purpose of the scaffolded questions, she/he may struggle to guide the instruction in a meaningful way and become frustrated that the outcome is not what is expected.

### 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.
1/2
+
-
Indicator Rating Details

Materials contain a teacher's edition with ample and useful annotations and that sometimes includes 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.

• The materials are structured in a way that teachers could present the content effectively if all students engage in the mathematics and learn in the same way.
• However, if students struggle with a concept or problem, there is little guidance for teachers in how to appropriately remediate or revisit a problem. There are no suggestions for how to address or identify common mistakes or challenges that students may have with the content.
• Often, the scaffolding provided is to "remind students." There are limited, if any, suggestions for how to modify lessons, questions and/or problem sets for students who already understand the content of the given lesson.
• Beyond an occasional link to video, there are no suggestions for teacher or student on the use of technology, including a calculator, and therefore no guidance on how to use such technology.

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

The materials contain a teacher edition (in print or clearly distinguished or accessible in digital materials) that sometimes contains full explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

• The teacher edition gives a clear process for each step of the solution to the problems posed to students.
• However, there are not always consistent explanations for teachers either before or within the lessons.
• If a concept is something teachers are not familiar with, such as dividing fractions, they must study the examples given to create their own understanding of the strategies students should be using.
• Although deeper explanations should not be needed for most lessons, it would be helpful for teachers to have access to supplementary materials that further develop an idea so that they can build their understanding beyond the problems in the lesson.

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

The materials do contain a teacher edition (in print or clearly distinguished or accessible 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 12.

• Each module has an overview section at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of math Kindergarten through Grade 12.
• Knowledge required from prior modules and/or grades is explicitly called out in this section.

### 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).
Narrative Evidence Only
+
-
Indicator Rating Details

The materials do provide a list of lessons in the teacher edition (in print or clearly distinguished/accessible as a teacher 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).

• The materials provide a curriculum overview that specifies the standards addressed in each module.
• Each module organizes the lessons into topics and clearly states which lesson(s) align to each standard.
• It would be helpful to have all of the information in one document for ease of reference-it is tedious to go through each model to determine which lessons address which standards and to quickly see that all of the standards are addressed throughout the year.

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The materials do not contain strategies for informing parents or caregivers about the mathematics program and give suggestions for how they can help support student progress and achievement.

• The materials do not contain strategies for informing parents. However, there are many resources online.
• There should be clear links to these in the teacher materials because they are hard to find and unless you specifically look for them, there is no way to know they even exist.

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Narrative Evidence Only
+
-
Indicator Rating Details

The materials do not contain explanations of the program's instructional approaches and identification of the research-based strategies within the teaching materials.

• There are no connections to research-based strategies within the lessons.
• Materials are available online (in the FAQ section) that suggest connections to research-based strategies, but they are not specific to modules or content, nor are they in-depth, specific to modules and content, or very helpful to teachers.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
4/10
+
-
Criterion Rating Details

The materials reviewed do not meet expectations for the criterion of assessment on Grade 6.

The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Materials sometimes provide strategies for teachers to identify and address common student errors and misconceptions. A strong point is that the materials provide opportunities for ongoing review and practice.

The materials offer some formative and summative assessments, notably by the mid-module and end-of-module assessments that assess particular standards and have rubrics specifically aligned with those standards. Overall, the materials reviewed for Grade 6 do not meet the expectations for the assessment criterion.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2
+
-
Indicator Rating Details

The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels.

There are no strategies or assessments that are specifically for the purpose of assessing prior knowledge.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
1/2
+
-
Indicator Rating Details

Materials sometimes provide strategies for teachers to identify and address common student errors and misconceptions.

• Although the materials do not always provide strategies for identifying and addressing common student errors or misconceptions, there are several opportunities within each lesson where teachers can do so.
• There are no suggestions for how to address specific common errors on problem sets or homework. Such suggestions would support teachers in knowing how to intervene when these errors are observed.

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
+
-
Indicator Rating Details

The materials provide opportunities for ongoing review and practice.

• The materials provide several opportunities for ongoing review and practice.
• Within a lesson there are three sets of practice problems: class exercises, problem sets and exit slips. These opportunities promote both increasing understanding of a concept as well as developing procedural skill and fluency.
• Beyond a lesson or module, future modules typically incorporate practice of previous learning.
• In Grade 6, after students learn the operations with rational numbers, they are expected to use those skills in the next lessons to further develop both understanding and procedural skill and fluency.
• There are no provisions for specific feedback for teachers or instructions on how to best provide meaningful feedback to students.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
Narrative Evidence Only

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

Within the teacher materials, summative assessments do clearly denote which standards are being emphasized, and items used as formative assessments do not clearly denote which standards are being emphasized.

• Each standard is aligned to one or more lessons as denoted at the beginning of each topic.
• The mid-module and end-of-module assessments appear to be developed to fully assess a particular standard, and the rubrics specify which item aligns to which standard.
• However, problems within exit slips and problem sets-which could be used as formative assessment tasks-are not explicitly aligned to a specific standard or group of standards.
• The lessons are grouped in a way that the standards are addressed, but each specific lesson and the problems within it do not necessarily align to a particular standard. Therefore, it becomes challenging for teachers to easily make notes about which students are attaining or struggling with a specific standard prior to scoring the formal assessments that are provided and clearly aligned to standards.

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

Formative assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.

• Each mid-module and end-of-module assessment includes a rubric as well as completed solutions for correct responses.
• There are no strategies or suggestions for follow-up provided.
• There are no rubrics or scoring guidelines for any formative assessments tasks (nor are any items or tasks identified as formative assessment opportunities).

### Indicator 3q

Materials encourage students to monitor their own progress.
Narrative Evidence Only
+
-
Indicator Rating Details

The materials do not encourage students to monitor their own progress.

• There are no evident strategies or opportunities for students to monitor their own progress.
• Objectives or outcomes for each lesson and/or assignment are not provided to students in any of the student materials.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
7/12
+
-
Criterion Rating Details

The materials reviewed for Grade 6 do not meet expectations for the criterion for differentiated instruction. Materials sometimes provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. In the margins and boxes of the teacher materials, there are some limited notes that provide teachers with strategies for meeting the needs of a range of learners, but a variety of solution strategies are not always encouraged. Although occasionally there are challenge problems, there are minimal opportunities for advanced students to go beyond the math provided in the classroom lessons. A strong point is that the materials provide a balanced portrayal of various demographic and personal characteristics. Overall, the materials do not meet the criterion for differentiated instruction

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
+
-
Indicator Rating Details

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

• Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
• The sequencing and scaffolding are built in to the lesson development so that teachers pose problems as they progress through more rigorous processes and skills.
• However, the reasons that the problems and/or strategies are selected for sequencing scaffolding are rarely explicit.
• The best place to find an explanation of how the lessons develop is in the module and topic overviews where the structure of how the lessons build and develop is discussed in a narrative form.
• There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
+
-
Indicator Rating Details

The materials sometimes provide teachers with strategies for meeting the needs of a range of learners.

• The materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners.
• There are some limited notes in the margins/boxes of the teacher materials. Sometimes the suggestions are very simple-"use questioning strategies" or "remind students of a definition"-and do not offer relevant suggestions that will impact the outcome of a lesson/problem.
• The lists online mirror the strategies in the teacher's materials and do not offer additional clarification or suggestions.

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
1/2
+
-
Indicator Rating Details

The materials frequently (but not always) embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

Although most tasks allow students to utilize multiple entry points and to solve problems using a variety of strategies, paths and/or models, the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.

### 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).
1/2
+
-
Indicator Rating Details

e materials suggest some options for support, accommodations and modifications for English language learners (ELLs) and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

• Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners.
• There are some limited notes in the margins and boxes of the teacher materials. Sometimes the suggestions are very simple-"use questioning strategies" or "remind students of a definition"-and do not offer relevant suggestions that will affect the outcome of a lesson or problem.
• Lists online mirror the strategies in the teacher's materials and do not offer additional clarification or suggestions.
• What is provided is not enough to guarantee that all students have content that is accessible.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
+
-
Indicator Rating Details

Materials sometimes provide opportunities for advanced students to investigate mathematical content at greater depth.

• Occasionally there are "challenge" problems.
• It is difficult to determine if those tasks were optional for the entire class, scaffolded for the class or if they were explicitly for students who needed advanced mathematics.
• There were minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
+
-
Indicator Rating Details

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

The materials provide a balanced portrayal of various demographic and personal characteristics.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
Narrative Evidence Only
+
-
Indicator Rating Details

The materials provide limited opportunities for teachers to use a variety of grouping strategies.

• Suggestions for grouping are made but there is often no mention of why a student should work within a certain group size.
• Within the lessons, there are no group roles, no group expectations, etc., to help teachers enhance the involvement of every student.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
Narrative Evidence Only
+
-
Indicator Rating Details

Materials do not encourage teachers to draw upon home language and culture to facilitate learning.

There is no evidence of teachers needing to draw upon home language and culture to facilitate learning.

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

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Narrative Evidence Only
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

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.).
Narrative Evidence Only
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

### 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.
Narrative Evidence Only
+
-
Indicator Rating Details

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

abc123

Report Published Date: 2015/03/04

Report Edition: 2013-2014

Title ISBN Edition Publisher Year
9781118965313

## 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

Teacher edition and student edition were reviewed.

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 teacherâ€™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.