Alignment

Focus & Coherence

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Rigor & Mathematical Practices

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Meets Expectations
Partially Meets Expectations
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Usability

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Meets Expectations
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### Alignment

The instructional materials reviewed for Grade 8 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 8 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 ONE

### Focus & Coherence

MEETS EXPECTATIONS

The instructional materials reviewed for Grade 8 meet the expectations 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. There are 146 out of 180 days (81%) that are spent directly on the major work of the grade.

For coherence, each of the supporting modules also contains lessons that specifically address major work of the grade. A review of the table of contents, module overviews, and content, shows that the materials develop according to grade level progressions and that the materials give all students extensive work with grade-level problems. 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. Overall the Grade 8 materials are coherent and consistent with the standards.

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#### Focus

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The instructional materials reviewed for Grade 6 assess topics only at this grade level. The mid-module and end-of-module assessments only address grade-level content. There are no examples of above-level assessments in the student edition. 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 major work of the grade. Sixty-seven percent (67%) of the days are suggested for major work of the grade. Three of the six modules are designated as major work of the grade, and two other modules contain lessons related to the major work. Overall the instructional materials meet the criteria for grade level assessment the time devoted to the major work of the grade.

#### Criterion 1a

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

The instructional materials reviewed for Grade 8 assess topics only at this grade-level. For example, the mid-module and end-of-module assessments deal with grade-level content. Also, there are no examples of above-level assessments in the student edition. Overall, the instructional material meets the expectations for focus within assessment.

2/2
##### 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.

The instructional materials reviewed for Grade 8 meet the expectations for assessing the grade-level content. There is no content of future grades assessed.

• All of the mid-module and end-of-module assessments are aligned to the grade level standards 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

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Students and teachers using the materials as designed devote the large majority[1] of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Grade 8 are developed so that students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. For example, 146 of the 180 days (81%) of the days are spent directly on major clusters. All of modules 1, 2, 3 and 4 and half of modules 5, 6 and 7 focus on Grade 8 major clusters. Overall the instructional materials meet the criteria for the time devoted to the major work of the grade.

4/4
##### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 8 does meet the expectations for spending the majority of class time on the major cluster of each grade. Overall the instructional materials do meet the criteria outlined in the CCSS publisher guidelines for the time for the major work of the grade.

• According to the front matter of each module, 146 out of 180 days (81%) are spent directly on the major work of the grade. The remaining lessons also make specific connections to the major work.
• All of modules 1, 2, 3 and 4 and half of modules 5, 6, and 7 focus on Grade 8 major clusters.
• The second half of module 5 requires students to use functions to solve problems involving geometry.
• Module 6 requires students to use functions and expressions and equations to solve problems of statistics and probability.
• Module 7 focuses on number sense within the understanding of expressions and equations.

#### Coherence

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The instructional materials reviewed for Grade 8 meet the expectations for coherence and consistency with the Common Core State Standards. Clearly, the supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Also, the majority of the chapters and 81% of the respective days allocated in the timeline align to the major work of this grade. Furthermore, the Grade 8 materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials also develop by the grade-by-grade progressions in the standards. Overall, the Grade 8 materials address the key aspects of coherence and consistency with the standards.

#### Criterion 1c-1f

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Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

2/2
##### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 8 meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, most of the chapters and the respective days allocated in the timeline align to the major work of this grade level. Furthermore, the chapters and the individual lessons support focus and coherence to the major work of the grade level.

• Modules 5, 6 and 7 contain lessons on the supporting standards.
• Each of these modules also contains lessons that specifically address major work of the grade.
• All of these lessons flow together coherently because the concepts are discussed in relationship to one another.
• 8.F (using functions to solve) is enhanced by 8.G.C (perimeter and area of common and complex shapes).
• 8.EE (setting up equations) is enhanced by 8.SP (patterns and fitting lines in scatter plots).
• 8.EE and 8.F (using equations and graphs of functions) is enhanced by 8.SP (linear vs. nonlinear modeling of data).
• 8.EE (setting up equations and solving) is enhanced by 8.NS (simplifying radical expressions).
• 8.EE (using integer exponents) is enhanced by 8.NS (decimal expansion).
• 8.EE and 8.G (volume and area equations) is enhanced by 8.NS (simplifying radical expressions).
• 8.G.B (Pythagorean Theorem) is enhanced by 8.G.C (geometry problems).
• Only some of work on statistics and probability and on introductory geometry cannot be linked to a major cluster area.

2/2
##### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Grade 8 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 180 designated days for all of the modules.
• Each module has built in days for assessment, review and extra practice. This allows for adjustments needed throughout a school year because of school activities, weather days and a teacher's professional judgment as to pacing.
• The following are the designated days for each module:
• Module 1 (EE): 13 lessons + 7 days = 20 days
• Module 2 (G): 16 lessons + 8 days = 24 days (2 optional)
• Module 3 (G): 14 lessons + 6 days = 25 days (1 optional)
• Module 4 (EE): 31 lessons + 10 days = 41 days (1 optional)
• Module 5 (F): 11 lessons + 4 days = 15 days
• Module 6 (F/SP): 14 lessons + 6 days = 20 days
• Module 7 (NS/EE/G): 23 lessons + 12 days = 35 days
• TOTAL: 180 days (optional lessons included)

2/2
##### 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.

The instructional materials reviewed for Grade 8 meet the expectations for the material to be consistent with the progressions in the standards. The materials develop by the grade-by-grade progressions in the standards.

• 8.NS (focus on rational number approximation and an introduction to irrational numbers)-Vocabulary & representations (decimal division, number lines) are directly related to the progressions document.
• 8.EE (focus on radicals with integer exponents, proportional relationship connections, solving linear equations and simultaneous linear equations)- Vocabulary and representations (primarily connecting equations to tables and graphs) are directly related to the progressions document.
• 8.F (focus on understanding and comparing functions and using functions to model relationships between quantities)-Vocabulary and representations (ratio tables, linear/nonlinear equations, scatter plots, two-way tables) are directly related to the progressions document. This is a direct of functions to bivariate data (SP) in Module 6 and volume & area (G) in Module 5.
• 8.SP (focus on bivariate data (both linear & nonlinear))-Vocabulary and representations (scatter plots, two-way tables) are directly related to the progressions document. The Grade 8 curriculum deeply connects bivariate data to linear equation relationships (EE/F).
• 8.G (focus on congruence, similarity, Pythagorean Theorem, and volume of cylinders, cones, and spheres)-Vocabulary and representations (rigid motions, geometric figures) are directly related to the progressions document.
The instructional materials reviewed for Grade 8 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 grade level problems.
• Modules contain a large mix of tasks that are grade level appropriate.
• There are occasional comments within the teacher material to help teachers best reach low-level, high-level, English language learners and students with disabilities.
• The same comments can be found in the online "how to implement" Guide.

The instructional materials reviewed for Grade 8 partially meet the expectations 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.

• Teacher materials include a module overview that includes a narrative explaining how grade-level standards are introduced and what students will be doing in developing concept understanding. The connection to prior grade-level standards and how they progress into current grade-level standards is included.
• Notes for discussion in individual teacher lessons will also reference prior knowledge at various times.
• There are no explicit connections made for the students in the student material.
• However, some of the narrative reminds students of previously learned material within the grade when it is expected to be recalled.

2/2
##### 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.

The instructional materials reviewed for Grade 8 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.

• Both teacher and student materials occasionally end with a lesson summary that reviews the student outcomes. They are written in language that can be easily aligned to learning objectives (CCSSM standards) and cluster headings
• Most of the standards are clearly connected to their cluster headings in these modules. However, in module 4 standards 8.EE.5 and 8.EE.6 do not explicitly connect for the teacher or the student to their cluster heading. Lessons and tasks do not require students to demonstrate how they "understand the connections between proportional relationships, lines and linear equations" although all are addressed. The lessons and tasks do not connect these concepts beyond what naturally occurs with lessons following one another.
• There are some standards within a cluster that are taught in a module different than the majority of the standards in a cluster. For example, expressions (8.EE.2) is in module 7 rather than module 1 with the other standards in this cluster. This standard is about square and cube root symbols and evaluation, and it is taught alongside 8.NS.1 and 8.NS.2, which are about rational and irrational numbers and their approximations.

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. Overall the materials foster coherence through connections at the Grade 8.

• In module 6, lessons 8-12 have students work with scatter plots and linear models of association in bivariate measurement data (8.SP.1-3) by discussing proportional relationships, lines, linear equations and linear functions (8.EE.5-8, 8.F.3-4).
• In module 7, topics A and B, have students work with radicals and integer exponents (8.EE.2) with specific attention to irrational numbers (8.NS.1-2). Students continue this work to Pythagorean Theorem problems (8.G.6-8).
• Teacher notes do not refer to 8.G.A in addition to 8.EE.B.6, but the broad connection exists.

GATEWAY TWO

### Rigor And Mathematical Practices

MEETS EXPECTATIONS

The instructional material for the Grade 8 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 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 MPs. 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 meaning of Standards for Mathematical Practice. Overall the Instructional materials meet the quality expectations for gateway 2 in rigor and mathematical practices.

#### Rigor and Balance

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The materials reviewed for Grade 8 meet the expectation 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 8, procedural skill and fluency is most evidenced in modules 1 and 7, which develop 8.EE and 8.NS. 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 8 materials meet the criteria for rigor and balance.

#### Criterion 2a-2d

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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.

2/2
##### 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.

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings meeting the expectations for this indicator.

• Generally, lessons develop understanding first through explicit discussion outlined in the teacher lessons.
• Closing activities often ask students to verbally review important vocabulary or apply lesson discussion to a specific problem to demonstrate understanding.
• Problems sets required students to apply lesson discussion and build from lesson to lesson.
• Module 2 focuses on the conceptual understanding of G.1, 2, 5, 6, and 7. Tasks and activities develop a solid understanding of congruence and similarity along with the Pythagorean Theorem. This development of understanding continues into Module 3 with a greater focus on similarity (G.3, 4, 5, 6, 7).
• Module 4 provides students with ample opportunity to develop understanding of EE. 5,6,8a.
• Module 7 brings back conceptual understanding for students on NS.1 and G.6, 7, 8.

2/2
##### 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.

Materials give attention throughout the year to individual standard that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

• Procedural skill and fluency is evident in modules 1 and 7, which develop 8.EE and 8.NS.
• Besides an abundance of examples throughout the lessons, there are also computation activities designed to develop procedural skill and lead to fluency.
• Similarly, multiple lessons often cover a major cluster and offer ample practice of the required skill.
• For example, in module 4, lessons 24-30 continue to the develop 8.EE.8 using multiple methods

2/2
##### 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

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.

• Application of the mathematical concepts is abundant throughout each module.
• Introduction of new concepts is frequently done through examples that involve applications, and lessons often reinforce those skills.
• Similarly, as students work with functions in module 6 (8.F), the work leads into bivariate data (8.SP), a natural extension.
• Overall most lessons develop some sense of application which aligns with the publishers criteria, which suggests students increase their application as they near higher grades.
• Specifically application is addressed in topic D of module 4 by having students use distance-time graphs to learn about linear equations, as well as create their own equations to represent real-world situations.
• Topic E of module 4 include problems that apply the Pythagorean Theorem to real-world situations.
• Teachers frequently introduce new concepts by posing a problem to students and then structuring discussion around that problem (or set of problems) based on questions provided in the teacher materials.
• It is common for the problems used in classwork and problem sets to include applications that are relevant to the concepts in the standards.
• Very often, the application problems reinforce previously learned skills as well as provide context for the mathematical concepts introduced in the lessons.

2/2
##### 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.

The three aspects of rigor are not always treated together and are not always treated separately meeting the expectations for this indicator. There is a balance of the three aspects of rigor within the grade.

• Conceptual understanding, procedural skill and fluency, and application are integrated into each module as needed.
• When appropriate, separate procedural skill and fluency activities are included in the series.
• At other times, skill and fluency are part of application and conceptual understanding exercises.
• Specifically, in module 4 (Linear Equations), topic A is very procedural, because students write and solve linear equations using specific steps. Topics B and C expand on the procedures presented in Topic A by relating linear equations to application problems involving constant rate.
• Also included are specific lessons focusing on the understanding of possible solutions and equations characteristics. In addition, there is a balance of the three aspects of rigor in included assessments

#### Mathematical Practice-Content Connections

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The materials reviewed for Grade 8 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 student 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 occasionally 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.

#### Criterion 2e-2g

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

2/2
##### Indicator 2e

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

There is a clear articulation of connection between Standards of Mathematical Practice (MP) and content. Materials regularly and meaningfully connect MPs to the Standards for Mathematical Content within and throughout the grade

• All modules at the Grade 8 level list the focus MP in the module overview and expand on each practice's connection to the module.
• Throughout the lessons MPs are called out for the teacher
• Module 3, for example, lists MP3, MP4 and MP6 as MP focus standards. Here the practice standards are explained with examples demonstrating the connection and development of the standards to the content.
• On page 40, MP8 is easily seen by the blue line and box containing "MP8" off to the side of the discussion, clearly calling attention to where the practice standard is being developed within the lesson. Although the MPs are identified, they could be integrated more effectively within lessons.
• The MPs are identified in the margin within teacher material.

1/2
##### Indicator 2f

Materials carefully attend to the full meaning of each practice standard

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

• Module 3: page 19, MP5 and 3, MP5 is not reaching the full meaning of the standard as students are directed to use specific tools. The class discussion does have students construct viable arguments but does not explicitly have them critique the reasoning of others.
• There are very few MPs identified in modules 2 and 3 (approximately 15 in module 2 and 10 in module 3).
• MP7 is called out on page 119 (lesson 11). However, this is a brief prompt asking students to explain-or teachers to tell-that the slope, fraction or ratio in a problem is the rate for that problem.
• Tasks identified as MP4 (Modeling with Mathematics) often present a visual representation of the problem instead of encouraging the students to create the model.

##### Indicator 2g

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

2/2
##### 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.

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 very few examples of students being asked to analyze the arguments of others in the lesson material or practice exercises.
• There are opportunities for students to analyze the work of another - but it is usually in a problem set and not with another student's work within the classroom.

1/2
##### 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.

Materials rarely assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• Module 1 does discuss MP.3 in the introduction. However, further guidance, specifically within the lessons, may be beneficial for educators.
• MP3 was identified as a focus MP in modules 1, 2, 3 and 4.
• However, in module 3, MP3 was only identified for teacher reference on pages 148-49, and part of it was more of a formal proof.
• In module 4, it was identified in the teacher materials on pages 19, 22, and 70. One of these occasions included a critique of the reasoning of others. The others were all construction of viable arguments.
• There are several natural opportunities for teachers to have students analyze the work of others-and some of the student problem sets ask them to do so-but prompts for doing this are not provided.

2/2
##### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

Materials very explicitly attend to the specialized language of mathematics.

• Correct mathematical terminology is always used, enforced, and reinforced.
• Explicit detail is always used in student-teacher discussion and explanation of process
• At the beginning of each module, terminology that is new or recent-as well as terms that should be familiar-is specifically highlighted for the teacher and defined and, in some cases, examples are provided.
• The terminology that is used in the modules is consistent with the terms in the standards.
• Relevant vocabulary is highlighted for students throughout the lessons and is reiterated at the end of each lesson (when relevant).

GATEWAY THREE

### Usability

PARTIALLY MEETS EXPECTATIONS

The Grade 8 materials reviewed partially met the expectations for usability. Foremost, the materials met the criterion for use and design. 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. The design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. 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. On the other hand, the materials reviewed do not meet expectations for the criterion of assessment for Grade 8. The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Also, the materials reviewed for Grade 8 do not meet expectations for the criterion for differentiated instruction. There are limited notes-in the margins and boxes of the teacher materials-providing teachers with strategies for meeting the needs of a range of learners, and a variety of solution strategies are not always encouraged. Overall the Grade 8 material partially meets the criterion for usability.

#### Criterion 3a-3e

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

The materials meet the criterion for use and design. The underlying design of the materials make 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 in order 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 8 meet the expectations for this criterion.

2/2
##### 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.

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

• The lessons usually follow a sequence that includes classwork typically facilitated by the teacher: opening exercises, scaffold examples, exploratory challenges, discussion topics, and other examples. These problems or asks 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. The exit ticket is usually, but not always, aligned to problems in the exercises and the problem sets.
2/2
##### Indicator 3b

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

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.
2/2
##### 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.

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 explain their work, justify their reasoning and also 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.
2/2
##### Indicator 3d

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

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.
##### Indicator 3e

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

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 or grade-with both a lesson number and page number.
• The lessons are clearly named; the class work 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

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•  0
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•  5
•   6
•  8

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

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 begins with an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of math from Kindergarten through Grade 12. Overall, the material reviewed for the Grade 8 partially meet the expectations for this criterion.

1/2
##### Indicator 3f

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

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 that are asked through the lessons (class work) as well as the exercises, problems, exit tickets and assessments.
• However, suggestions on how to adjust a lesson or modify the questions a teacher asks to guide instruction based on the needs of students-for example if a part does not go well or students need additional practice or clarification before going on-are not included.
• 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.
• If teacher are not confident with the sequence of the mathematics or the purpose of the scaffolded questions, they may struggle to guide the instruction in a meaningful way and become frustrated that the outcome is not what is expected.
1/2
##### 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.

Materials contain a teacher edition that has 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. Typically there are not suggestions as to what common mistakes are for teachers should watch out for.
• Often, the scaffolding provided is as simple as "remind students that...." Furthermore, there are limited, if any, suggestions for how to modify lessons/questions/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 availability of technology-not even a calculator-and therefore no guidance on how to use it.
2/2
##### 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.

The materials contain a teacher edition (in print or clearly distinguished and accessible as such in digital materials) that sometimes contains full, adult-level 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, usually there are no additional explanations for teachers either before or within the lessons.
• If a concept is something the teacher is not familiar with, 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 they can build their understanding beyond the problems in the lesson.
2/2
##### 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.

The materials do contain a teacher edition (in print or clearly distinguished and accessible as such 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 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.
• 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).

The materials do provide a list of lessons in the teacher edition (in print or clearly distinguished/accessible as such in digital materials), cross-referencing the standards covered and providing pacing guide on the estimated instructional time for each lesson, chapter and unit.

• 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 takes time 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.

The materials do not contain strategies for informing parents or caregivers about the mathematics program nor offer suggestions for how they can help support student progress and achievement.

• The materials do not contain strategies for informing parentsâ€”however, there are great 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.

The materials do not contain explanations of the instructional approaches of the program 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

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•  0
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•   5
•  6
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•  10

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

The materials reviewed do not meet expectations for the criterion of assessment on the Grade 8. 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 the Grade 8 do not meet the expectations for the assessment criterion.

0/2
##### Indicator 3m

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

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.
1/2
##### Indicator 3n

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

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

• Although the materials do not typically provide strategies for identifying and addressing common student errors or misconceptions, there are several areas where teachers can do so.
• There are not 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.
2/2
##### Indicator 3o

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

The materials provide opportunities for ongoing review and practice but not strategies for feedback.

• The materials provide several opportunities for ongoing review and practice.
• Within a lesson there are three sets of practice problem: class exercises, problem sets, exit slips. Each promotes both increasing understanding of a concept as well as developing procedural skill/fluency.
• Beyond a lesson or module, future modules typically incorporate practice of previous learning.
• In Grade 8, students begin with writing linear equations and then use that knowledge in the modules on linear functions, functions from geometry, and also similarity.
• There are no provisions for or discussion on how to provide meaningful feedback to students.
##### Indicator 3p

Materials offer ongoing formative and summative assessments:

1/2
##### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

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 noted 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 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 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.
1/2
##### 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.

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 worked out 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.

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

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•   7
•  8
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•  10
•  12

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

The materials reviewed for Grade 8 does 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. There are limited notes in the margins and boxes of the teacher materials that provide teachers with strategies for meeting the needs of a range of learners and a variety of solution strategies are not always encouraged. Although there occasionally there are challenge problems, there are minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons. A strong point is that the materials attempt to provide a balanced portrayal of various demographic and personal characteristics. Overall, the materials do not meet the criterion for differentiated instruction.

1/2
##### Indicator 3r

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

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 into lesson development so that teachers pose problems as they progress through more rigorous processes or 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.
1/2
##### Indicator 3s

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

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 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.
• The lists online mirror the strategies in the teacher materials and do not offer additional clarification or suggestions.
• There is a concern that the suggestions provided are not enough to guarantee that all students have content that is accessible.
1/2
##### Indicator 3t

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

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

• A variety of solution strategies are not always encouraged.
• Sometimes teachers are asked to lead students through a particular task rather than providing students with an opportunity to create a solution path on their own.
• Although most tasks allow students to use 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.
• For example, in module 4, lesson 16, students learn to find the slope of a nonvertical line. In this lesson, teachers guide students through finding the slope of a line where the horizontal distance is not 1. However, instead of having students explore that no matter which points on the line they choose they will get the same slope, they structure the process, thus eliminating the opportunity for students to apply their own reasoning to arrive at this conclusion.
• Sometimes teachers are asked to lead students through a particular task rather than providing students with an opportunity to create a solution path on their own.
• Although most tasks allow students to use multiple entry points and can be solved using a variety of strategies, paths, and/or models, the materials sometimes undermine this concept by providing tasks that explicitly state how to solve it or which representation to use.
1/2
##### 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).

The materials suggest some options for 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).

• 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/problem.
• Materials and lists online mirror the strategies in the teacher 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
1/2
##### Indicator 3v

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

Materials sometimes provide opportunities for advanced students to investigate mathematics 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 math provided in the classroom lessons.
2/2
##### Indicator 3w

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

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.

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

• Often suggestions for grouping are made but there is rarely any mention of why to have a student 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.

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.

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

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

##### 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.

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.

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.

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.

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