Alignment

Focus & Coherence

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•
•
•  8
•
•
•
•  12
•  14 14

Rigor & Mathematical Practices

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•
•
•
•
•
•  11
•
•
•
•
•  16 16
•  18
Meets Expectations
Partially Meets Expectations
Does not Meet Expectations
Usability

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•  23
•
•   25
•
•
•
•
•
•  31
•
•
•
•
•
•  38
Meets Expectations
Partially Meets Expectations
Does not Meet Expectations

### Alignment

The instructional materials reviewed for Grade 7 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 7 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 Standards for Mathematical Content and Standards for Mathematical Practice. However, weaknesses were noted in identifying 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 7 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. The materials also develop by the grade-by-grade progressions in the standards. 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 7 materials are coherent and consistent with the standards.

#### Focus

•
•
•
•
•
•
•  0
•
•
•
•
•  6 6

The instructional materials reviewed for Grade 7 meet expectations for focus and assess topics only at this grade-level. For example, the mid-module and end-of-module assessments deal with grade-level content. There are no examples of above-level assessments in the student edition. The instructional materials reviewed for Grade 7 are developed so that students and teachers using the materials as designed devote the large majority of class time (67% is suggested) to the 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 and for the majority of the time devoted to the major work of the grade.

#### Criterion 1a

•
•
•  0
•  2 2

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

The instructional materials reviewed for Grade 7 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 7 meet the expectations for assessing the grade-level content. There is no content of future grades assessed.

• The rubrics for each assessment indicate which standards are assessed in each question.
• Most questions align to at least one grade-level standard.
• In the mid-module assessment for module 6, questions 3b, 3c and 3d do not align to a grade-level standard but are also not above-grade-level material.
• 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.

#### Criterion 1b

•
•
•
•
•  0
•
•
•  4 4

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.

The instructional materials reviewed for Grade 7 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, the Grade 7 material spends 145 of 180 days on major clusters. Three and a half of the six modules are designated as major work of the grade. Although modules 5 and 6 focus on statistics and probability and geometry, they contain lessons related to the major work and require understanding of expressions and equations, number sense, and ratio and probability. 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 7 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.

• The Grade 7 material spends 145 of 180 days on major clusters.
• All of modules, 1, 2 and 4 and half of module 3 focus on Grade 7 major clusters.
• The second half of module 3 requires students to set up equations before solving area, surface area and volume problems.
• Although modules 5 and 6 focus on statistics and probability and geometry; they also require understanding of expressions and equations, number sense, and ratio and probability.

#### Coherence

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  5
•
•  8 8

The instructional materials reviewed for Grade 7 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 the respective days allocated in the timeline align to the major work of this grade. Furthermore, the Grade 7 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 7 materials address the key aspects of coherence and consistency with the standards.

#### Criterion 1c-1f

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  5
•
•  8 8

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 7 meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the majority 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.

• 7.EE (setting up equations) is enhanced by 7.G (finding angle measures).
• 7.EE and 7.NS (setting up equations) is enhanced by 7.G (solving geometry problems).
• 7.RP (using proportional reasoning) is enhanced by 7.SP (random samplings with populations).
• 7.NS (solving problems involving rational numbers) is enhanced by 7.SP (calculating probabilities).
• Only some of the SP introductory work 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 7 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.
• It is important to note though that each module has built in days for assessment, review, and extra practice. This allows for adjustments needed throughout a school year due to school activities, weather days, and professional judgment to pacing by teachers.
• The following are the designated days for each module:
• Module 1 (RP/EE/G): 22 lessons + 8 days = 30 days
• Module 2 (NS/EE):       23 lessons + 7 days = 30 days
• Module 3 (EE/G):         26 lessons + 9 days = 35 days
• Module 4 (RP/EE/G): 18 lessons + 7 days = 25 days
• Module 5 (SP):             23 lessons + 2 days = 25 days
• Module 6 (G):               27 lessons + 8 days = 35 days
• TOTAL: 180 days
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 7 meet the expectations for the material to be consistent with the progressions in the standards. The materials do develop by the grade-by-grade progressions 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 standards.
• 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 information to help see the connections in the standards, tasks and modules or lessons.
• 7.RP (focus on proportional relationships, equation representation, and multi-step problems involving percents)-Vocabulary and representations (tape diagrams, double number lines, ratio tables and coordinate plane) are directly related to the progressions document. This shows a direct connection to scale drawings (G) in modules 1 and 4.
• 7.NS (focus on rational number understanding and operations and real-world application: vocabulary and equations)-Vocabulary and representations (equations from ratio tables, coordinate planes, tape diagrams, number lines, area models and geometric figures) are directly related to the progressions document. EE is deeply integrated into modules 1-4 of the Grade 7 curriculum.
• 7.EE (focus on application of properties in generating expressions and equations and real-world application of expressions and equations)-Vocabulary and representations (equations, expressions, tape diagrams, number lines) are directly related to the progressions document.
• 7.SP (focus on random sampling and inferences with populations and probability models)-Vocabulary and representations (dot plots, histograms, tree diagrams and tables) are directly related to the progressions document.
• 7.G (focus on geometric figures and relationships, angle measure, area, surface area, and volume)-Vocabulary and representations (tables, graphs, scale drawings, floor plans, geometric figures, and area models) are directly related to the progressions document
The instructional materials reviewed for Grade 7 meet the expectations 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 and fluency.
• An online "how to implement" guide contains general scaffolding examples for English language learners (ELLs), low-level learners, high-level learners and students with disabilities, but these are the same as the occasional comments within the teacher material. This guidance is often superficial.
The instructional materials reviewed for Grade 7 partially meet the expectations of relating grade- level concepts explicitly to prior knowledge from earlier grades.
• Teacher materials include a module overview (one per module) that has 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 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 7 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 sometimes end with a lesson summary that reviews student outcomes. The summaries are written in language that can be easily aligned to learning objectives (CCSSM standards) and cluster headings.
• The first paragraph of module 2 states on page 3, "Students build on previous understanding of rational numbers to add, subtract, multiply, and divide signed numbers." This appears to be making a connection to the cluster heading. However, the title of the cluster heading for this set of standards is "Apply and Extend Previous Understanding of Operations with Fractions [emphasis added] to Add, Subtract, Multiply, and Divide Rational Numbers." Few fractions are used throughout this topic in this module, thus not truly connecting the standards to the cluster heading.
• No mention of cluster headings is provided to students or made clear in the student material or student outcomes.
The instructional materials include problems and activities that serve to connect two or more clusters in a domain. They also 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 Grade 7.
• The connection of two or more clusters or domains often exists in the materials for teacher and student materials and is usually noted in the teacher material.
• It is noted in module 1, lessons 8-15, that 7.EE.B is connected to 7.RP.A as students develop and analyze equations using a constant of proportionality in real-life problems.
• Similar connections are made with these two standards in module 4 with percents and proportional relationships.
• In module 2, lessons 22 and 23 connect 7.EE.B to 7.NS.A after all operations with rational numbers have been covered.
• Module 3 combines two clusters within the expressions and equations domain. The clusters that are integrated are "use properties of operations to generate equivalent expressions" and "solve real-life and mathematical problems using numerical and algebraic expressions and equations."

GATEWAY TWO

### Rigor And Mathematical Practices

MEETS EXPECTATIONS

The instructional material for the Grade 7 meets the expectation for rigor and mathematical practices. 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 Standards for Mathematical Content and Standards for Mathematical Practice. The instructional materials are strong in rigor and in regard to emphasis on supporting the standards' emphasis on mathematical reasoning. Overall the Instructional materials meet the quality expectations for gateway 2 in rigor and mathematical practices.

#### Rigor and Balance

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  5
•
•  8 8

The materials reviewed for Grade 7 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 7, procedural skill and fluency is most evident in module 2, which extensively covers 7.NS. Besides an abundance of examples, there are also computation activities stressing fluency in conjunction with the skill. 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 are application reinforcements of the skills. The three aspects are balanced within the lessons and modules. Overall, the Grade 7 materials meet the criteria for rigor and balance.

#### Criterion 2a-2d

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  5
•
•  8 8

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 require students to apply lesson discussion, and this discussion builds from lesson to lesson.
• A thorough review of the assessments in module 2 found that all of the specific content in 7.NS was assessed in various questions. (Note: Grade 7 students will likely need more time working on operations with rational numbers in order to master the content.)
• Cluster understanding was also spread over several modules at the Grade 7 level. For example, 7.EE is evident in several lessons within modules 1, 2, 3 and 4 as proportional relationships, algebraic expressions and percentages are covered.

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 standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

• Procedural skill and fluency is evident in module 2, which extensively covers 7.NS.
• In addition to an abundance of examples throughout the lessons, there are some fluency tests that provide specific problems devoted to procedural skill and lead to fluency.
• A great deal of work is done with integer cards; game-like activities lead to the understanding as well as the skill. 7.EE is present in multiple modules (1, 2, 3 and 4) and students are constantly reviewing the basics of solving equations

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 applying the mathematics without losing focus on the major work of each grade, meeting the expectations for this indicator.

• 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.
• Module 1 uses application to develop 7.RP and represent proportional relationships.
• Module 4 continues the development of 7.RP and 7.EE with multiple applications involving percentages.
• Students are continually solving real-world problems related to the major focus of the grade level.

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.

There is a balance of the three aspects of rigor within the Grade 7 material meeting the expectations for this indicator. The three aspects of rigor are not always treated together and are not always treated separately.

• Conceptual understanding, procedural skill and fluency, and application are integrated into each module as needed.
• When applicable, 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, module 2 (rational numbers) tends to focus on procedural skill and fluency. However, built in to these lessons are activities designed to help the student understand the use of rational number operations. (For example, the focus of lesson is understanding subtraction of integers, not just the procedure itself.)
• Also included, when appropriate, are applications of operations involving rational number. (For example, lessons 19 and 20 apply rational numbers to percentages and investments.)
• In addition, there is a balance of the three aspects of rigor in included assessments.

#### Mathematical Practice-Content Connections

•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•  6
•
•   8
•  10

The materials reviewed for Grade 7 partially meet the criterion of meaningfully connecting Standards for Mathematical Content and 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 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

•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•  6
•
•   8
•  10

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 the Standards of Mathematical Practice (MPs) and content. Materials regularly and meaningfully connect MPs to the Standards for Mathematical Content within and throughout the grade.

• Throughout the lessons MPs are called out for the teacher.
• In the opening statements of all lessons and modules there is commentary connecting the appropriate mathematical practice standards to the content. For example, page 7 of Module 4 identifies MP1, MP2, MP5, MP6 and MP7 as focus standards for the module.
• They are explained with examples of how and where you can see connections and development of the practice standards within the content of the module.
• A clear and visual connection is made within the lessons by a blue line and the MP listed. For example, see MP2 on page 42 of module 4.

1/2
##### Indicator 2f

Materials carefully attend to the full meaning of each practice standard

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

• Module 3 generally does a good job attending to MP2, MP7 and MP8 in the discussion of equations and explanations.
• Throughout the materials, students use properties to prove expressions equivalent and substitution to prove equivalence.
• Questions in problem sets and exit tickets sometimes ask students to construct viable arguments (MP3), but these are not identified for the students.
• Frequently when MP5 is listed the task tells the students what tools to use.

##### 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 examples of students being asked to analyze the arguments of others in the lesson material or practice exercises; however, there are missed opportunities to prompt students to critique the reasoning of others.

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 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 with directions to then have students critique the reasoning of others.
• MP3 was not identified as a focus MP until modules 5 and 6.
• In module 3, MP3 was identified for teacher reference a very limited number of times (pages 20, 237 and 337). However, it was not a focus in teacher-student discussion and instruction.

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.
• At the beginning of each module, terminology that is new or recent is specifically highlighted and defined (examples are provided in some cases as well) for teachers, as are terms that should be familiar.
• The terminology 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).
• The highlighting and emphasis on vocabulary allows students to use their own resources in future lessons to review the relevant vocabulary and/or equations associated with such terms as "area" and "pi."

GATEWAY THREE

### Usability

PARTIALLY MEETS EXPECTATIONS

The Grade 7 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 that contains 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 7. The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Also, the materials reviewed for Grade 7 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 7 material only partially meets the criterion for usability.

#### Criterion 3a-3e

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  5
•
•  8 8

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 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 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 7 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 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.

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 built 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 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.

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 objects 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.
• In most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives. In Grade 7, module 4, lesson 3, a model of a percent number line is introduced to provide a visual model showing that 100% corresponds with the whole quantity. In the problem sets and the exit ticket, students are required to solve each problem with two different approaches-the visual model can be one of those (in addition to algebraic and numeric models). This model is consistently used throughout the module in lessons 3, 4, 5, 9 and 16.
• 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 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

•
•
•
•
•
•
•
•
•  0
•
•
•
•
•  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 mathematics from Kindergarten through Grade 12. Overall, the material reviewed for Grade 7 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 asked through the lessons (classwork) 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 teachers 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 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 on how to appropriately remediate or revisit a problem. Typically there are no suggestions as to what common mistakes new 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 and 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 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.
• 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 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 mathematics, 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 or accessible in digital materials), cross-referencing the standards covered and providing a 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 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.

The materials do not contain strategies for informing parents or caregivers about the mathematics program nor 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.

The materials do not contain explanations of the program's instructional approaches nor identify 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

•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•   4
•
•  6
•
•
•  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 Grade 7. 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 7 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 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.

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 problems: class exercises, problem sets, exit slips. Each promotes both increasing understanding of a concept as well as developing fluency.
• Beyond a lesson or module, future modules typically incorporate practice of previous learning.
• In Grade 7, after students work with solving equations they are expected to continue to solve equations in future lessons.
• 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.

0/2
##### 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

•
•
•
•
•
•
•
•
•
•
•
•
•  0
•
•
•
•
•
•
•   7
•  8
•
•  10
•  12

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

The materials reviewed for Grade 7 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. There are limited notes in the margins and boxes in the teacher materials that provide teachers with strategies for meeting the needs of a range of learners. 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 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 in to lesson development so that teachers pose problems as they progress through more rigorous processes and skills.
• However, the reasons why 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 margin notes and boxes in 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 provide 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.

A variety of solution strategies are not always encouraged. Sometimes teachers are asked to lead students through a particular task rather than provide them with an opportunity to create a solution path on their own. Although most tasks allow students to use multiple entry points and students can solve them using a variety of strategies, paths and/or models, the materials sometimes undermine this concept by using tasks that explicitly state how to solve a problem or which representation to use. In Grade 7, module 1, lesson 8 (example 1) students are presented with a situation about miles driven and amount of gas used and asked to determine if the mom will run out of gas. Instead of presenting the data and the question, the problem provides the data and a set of questions that guide students through finding the constant of proportionality; students then write an equation and use that equation to determine if the driver has enough gas to get to her destination. Since determining the constant was part of a previous lesson, students could have been directed to simply solve the problem-does the mom have enough gas to get to her destination-using more than one method. With multiple entry points and suggestions for sharing student work, the lesson could have been designed to encourage a variety of solution strategies and ended with the strategy that was the focus of the lesson. (Note: the last step of this problem does provide choice in using either an algebraic strategy or a numerical strategy but only that one step provides that choice.)

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. Often the suggestions are simple-"use questioning strategies" or "remind students of a definition"-and do not offer specific suggestions that will affect the outcome of a lesson or problem.
• Materials and lists available online mirror the strategies in the teacher materials and do not offer additional clarification or suggestions.
• The materials do not provide enough suggestions or content 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 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 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 a 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.

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

• There is no evidence of teachers being asked 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.