Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for Grade 8 meet expectations for Alignment to Common Core. Rigor and mathematical practices (Gateway 2) are very strong for this series. The instructional materials provide an excellent, seamless balance of conceptual understanding, procedural development, and application. The MPs are embedded into rich problem solving tasks. In addition, for Focus and Coherence (Gateway 1), those problem solving tasks connect multiple clusters and domains. The majority of time is spent on major work, and non-major work often directly reinforces the major clusters of the grade.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
32
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 8 meet expectations for Focus and Coherence. The materials do primarily assess grade-level work. A true strength is providing rich, grade-level problems for all students that connect multiple clusters and domains. In addition, they spend the majority of time on major work, and non-major work often directly reinforces the major clusters of the grade.

Overall, Grade 8 meets expectations for assessment, amount of content provided for a year, making connections across concepts, and time devoted to major work (including non-major content enhancing major work). The Grade 8 materials partially meet expectations in identifying connections to prior knowledge from earlier grades. The overall rating for Gateway 1 is meets expectations.

Criterion 1a

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

The instructional material reviewed for Grade 8 meets the expectations for focus within assessment. All of the summative assessment questions focus on grade-level topics or below. Overall, the instructional material does not assess any content from future grades.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each chapter.

The materials reviewed for this indicator were the Individual Chapter Tests that are pre-made for Chapters 2-9. Chapter 1 does not have an individual test. Also, the online component for Core Connections has an extensive item bank that can be used to create individual assessments.

  • All assessments and topics relate to Grade 8 standards or below.
  • The summative assessments focus on grade level topics.
  • No above grade-level content was assessed on the chapter, summative tests.

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional material reviewed for Grade 8 meets the expectations for focus within major clusters. The amount of time spent on major work is 76 percent with additional support from content in the non-major clusters that directly connects with major work. Overall, the instructional material spends the majority of class time on the major clusters of the grade.

Indicator 1b

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

The instructional materials reviewed for Grade 8 meet the expectations for focus within major clusters. This program integrates a spiral curriculum, including in homework and on assessments. Overall, the instructional material does spend the majority of class time on the major clusters of each grade.

Three perspectives were considered: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of instructional days devoted to major work. The number of days, at approximately 76 percent, devoted to major work is the most reflective for this indicator because it addresses the amount of class time spent on concepts, especially given the spiraling nature of the curriculum.

For the purpose of consistency when calculating, all lessons (even those labeled optional) are included in the data and the maximum number of days in the range suggested was included (for example, if a lesson was labeled 1-2 days, 2 days was used). Days for assessments, chapter closure, mid-course and full course closure reflections are not included in the data.

  • Chapters – Approximately 72 percent of time is spent on major work.
  • Lessons – Approximately 76 percent of time is spent on major work.
  • Days – Approximately 76 percent of time is spent on major work.
  • We also reviewed the non-major clusters to determine if they could be factored in due to how strongly they support major work of the grade and found that there are connections made to major work in the supporting clusters.
  • Grade 8 does spend the majority of time on major work because 76 percent meets the threshold of 65 percent.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 8 meet the expectations for coherence and consistency with the CCSSM. The Grade 8 materials do include lessons that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials also provide all students with extensive work at grade-level problems. Lessons are consistent with the depth and progressions in the standards. In addition, there is evidence of supporting content enhancing coherence by reinforcing the major work of the grade. However, connections to prior knowledge or content from prior grades are not explicitly identified.

Indicator 1c

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

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. To determine this, we looked at the student lessons that were not major work to identify connections and support they provided to the major clusters. We also considered if there were missed opportunities to make strong connections. In the Teacher's Guide, the lessons are correlated to standards, so there was some guidance in determining where connections were being made.

  • In general, the standards alignment in the Teacher’s Guide is accurate, therefore it is a reliable source for seeing when lessons that are not major clusters directly support major work.
  • The strongest support comes from Chapter 7 on statistics, specifically scatterplots and lines of best fit, which connect strongly to both expressions and equations and functions.
  • There was also significant support linking geometry with both number system and expressions and equations as students wrote and solved Pythagorean theorem equations where solutions had to be approximated.
  • Also, Chapter 10 on geometry provided many connections to expressions and equations when students used formulas/equations to solve problems.
  • There is some supporting work as stand-alone lessons that do not make connections to major work.
  • There were no glaring instances where the supporting work missed opportunities to connect to major work.

Indicator 1d

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

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. The Teacher’s Guide offers three different pacing plans –

  • One for traditional schedules
  • One for block schedules
  • One for Acceleration – combining Course 2 and 3 into one year

The traditional plan was used to determine the number of instructional days since it seemed to best represent the way the course was designed.

The pacing provided by the publisher is reasonable for lessons to be completed in the time suggested.

  • Lessons plus a chapter closure and assessment days equal 148 days.
  • This is viable for one school year.
  • This falls within the 140-190 range suggested.

According to the Teacher's Guide alignment, all Grade 8 standards are included.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 8 partially meet the expectation to be consistent with the progressions in the standards. Materials do provide all students with extensive work at grade level problems. However, content from prior grades is rarely identified and materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections are also not made to content in future grades. Overall, the materials in Grade 8 are consistent with the depth and progressions in the standards, but explicit connections to prior or future grade-level content are never identified for teachers or students.

1.e.i

Throughout the entire series in the Teacher's Guide, content connections made are within the current course – they never explicitly tie to prior or future work.

  • On the chapter introduction page, students are given a very clear overview of what the chapter will be, and it helps make connections such as:
    • Chapter 5 – “In the last chapter, you….:
    • Chapter 8 – “In previous chapters, you have investigated….in 8.1, you will …”
  • Chapter overviews include a chart with a column of “Concepts Introduced/Reviewed” as well as identifying “Section Content Revisited”, but they are within the course.
  • Each chapter overview includes “Where is this going?” that makes connections to extensions of the concept later in the year since this curriculum spirals.
  • Teacher notes at the beginning of each lesson sometimes include a mathematical background section – these provide information, but do not make direct connections to prior or future work.
  • When off grade-level material is present, it is sometimes labeled as “preparation for” and does tie to grade-level work with reasonable connections, but it does not make explicit connections to prior or future work.
  • The materials do address the depth of the standards for the grade level.
  • Concept development aligns to the expected progression of the grade.

1.e.ii

The instructional materials reviewed for Grade 8 meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do consistently give students extensive work with grade-level problems, however there is extensive dependency on peer interactions for learning concepts that could be a significant challenge for many students. All students are expected to do the same work.

  • Students have ample opportunity to engage deeply in grade-level work.
  • Every lesson requires student teams to start by solving non-routine problems where clear pathways or expected answers are not obvious.
  • Problems presented are frequently relevant, authentic, and require students to make connections.
  • Some problems develop through multiple extensions throughout the entire course, spiraling back with new connections.

Working with a collaborative team is the main strategy for helping all students engage in the problems.

There is a fair balance of time devoted to each standard, with the following concern. Based on correlations provided in the Teacher's Guide:

  • Several standards in Expressions and Equations are only addressed in one or two lessons throughout the year which indicates weak development of an important concept. Examples include:
    • EE.3 and 4, which involve using scientific notation, are only correlated in one lesson each (8.2.1 and 8.2.4).
    • EE.5 which makes connections between unit rate, slope, and proportional relationships is only correlated in two lessons (1.2.1 and 7.2.4).
    • EE.8.A and EE.8.B, which relate to simultaneous linear equations, are only correlated in one and two lessons, respectively (5.2.1 and 5.2.3, 5.2.4).

1.e.iii

The instructional materials reviewed for Grade 8 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades other than noting that certain lessons are “preparation for” a grade-level standard.

  • Lessons identified as “preparation for” lessons (less than one-fourth) support grade level work by developing conceptual understanding.
  • Approximately 15 lessons are not aligned to a standard at all, these lessons generally review or build concepts necessary for grade-level standard understanding, which could be explicitly linked to previous standards. Examples include: background review on interpreting graphs, vocabulary for writing algebraic expressions, using algebra tiles to simplify and compare expressions, extending patterns.
  • Connections between concepts are addressed on the chapter introduction page, so students can begin to see how content relates (see 1.e.i for examples), though concepts are never explicitly connected to prior learning.
  • Within the teacher materials, each chapter contains narrative stating topics that may be “reintroduced” from previous courses.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 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.

  • Generally, chapter titles and lesson objectives make connections to CCSSM cluster headings, though never verbatim, and it's not always clear or obvious.
  • The Teacher's Guide does connect every cluster heading to problems that address it, with each one being engaged in multiple times throughout the course.
    • Correlation is available in two forms: 1) CPM Core Connections as aligned to the CCSSM and 2) CCSSM as aligned to CPM Core Connections.
    • Teacher lessons have the CCSSM of the lesson listed in the upper right hand corner of the opening pages of instruction information.
  • For the teacher, when looking into the actual lessons, the chapter overview makes the alignment to CCSSM clusters easier to see.

The instructional materials do include problems and activities that serve to connect two or more clusters in cases where these connections are natural and important. Overall the materials foster coherence through connections in Grade 8.

  • One of the design principles of the entire course is: Mathematics is a coherent, intellectual system, not a collection of disjointed facts, and needs to be taught in a way that makes this coherence clear.
  • Grade 8 includes 34 lessons that have significant connections either within a cluster or across domains. Some examples include:
    • In lessons 7.3.1, 7.3.2: 8.SP and 8.F.B are connected as students use equations to make predictions and associations involving data.
    • In lessons 9.2.2, 9.2.5, 9.2.7: 8.EE.A and 8.G are connected as students write equations to solve Pythagorean theorem problems.
    • In lesson 9.2.3: 8.EE.A, 8.G.B and 8.NS are connected as students find side lengths of triangles using equations and approximations of irrational numbers.
    • In lesson 9.2.4, 10.1.1: 8.NS and 8.EE.A are connected as students find decimal approximations of roots.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials for Grade 8 meet the expectation for rigor and MPs. The materials provide a solid balance of conceptual understanding, procedural skill and fluency, and application in units and in assessments. There are many lessons where each aspect of rigor is the focus as well as many where they are combined. Students have the opportunity to learn, practice, and understand the relevance of the grade-level concepts. In addition, the MPs are embedded within the rich, problem-based learning routinely and naturally. This includes an emphasis on constructing viable arguments. Therefore, The materials meet the expectation for Gateway 2.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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-
Criterion Rating Details

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. In each lesson, concept-development occurs through problem-based tasks and concrete representations as indicated by the standards and cluster headings. In Grade 8, procedural skill and fluency is evident in every unit, which develop the relevant standards. In addition, application of the mathematical concepts is evident throughout each unit in rich, problem-solving situations. Beyond the lessons, there is a balance of the three aspects of rigor included in every assessment. Overall, conceptual development, procedural skills and fluency, and application are all strongly represented and the three aspects are balanced within the units.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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-
Indicator Rating Details

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.

  • Evidence for this indicator is found throughout all of the chapters, including the chapter assessments.
  • Generally, lessons develop understanding through the group work that students complete in the lessons.
  • There are extensive suggestions in the teacher guide for every lesson describing the purpose of the lesson and how to guide study teams to develop their understanding of a concept.
  • Teacher questioning during instruction is designed to lead to conceptual understanding: How do you see it? How can you tell it’s correct? What is the pattern? Is there a different way?”
  • Students are consistently being asked to communicate with their group and explain for understanding.
  • Chapters 1, 3, 5, 6 and 7 all include work directly related to the clusters that address conceptual understanding (8.F.A, 8.EE.B, 8.G.A). Conceptual understanding is built through strategies such as:
    • Patterns (ex: exponent rules, Pythagorean);
    • Graphing/comparing transformations;
    • Multiple representations of Linear Equations; and
    • Algebra Tiles for solving and comparing equations.
  • The materials provide evidence of high-quality conceptual problems using concrete representation, algebra tiles, experimenting, verbalization, online activities/tools, multiple representations, and interpretation.
  • Students are required to use previous learning to construct new learning.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

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

  • There is evidence of the opportunity to develop fluency and procedural skills in every chapter, including the chapter assessments.
  • Fluency is especially evident in the constantly spiraling homework. According to the publisher, about one-fifth of the homework is on new material and the rest of the homework review previous concepts.
  • The skills are frequently embedded in an engaging activity such as the silent board game or the human graph.
  • Standards that emphasize procedural skill and fluency are 8.EE.C.7, 8.EE.C.8b and 8.G.C.9, and they are evident in Chapters 2, 3, 5, 9 and 10. Procedural skill and fluency is developed through strategies such as:
    • Examples and repetition in practice;
    • Chapter closures have problems with solutions - if students miss them, they are directed back to the relevant lesson ("Need Help?") and to additional practice problems that align with what they missed ("More Practice");
    • Math Note boxes reinforce vocabulary and concrete examples (Angle Vocabulary, Line of Best Fit);
    • Learning logs (Pythagorean Theorem, Slope & Steepness);
    • Spiral homework; and
    • Checkpoint problems - with extra practice if not mastered (Solving Equations, Scatterplots & Associations).
  • Students would benefit from having more opportunity to develop fluency and procedural skills in solving equations, including simultaneous linear equations. There were limited situations to practice the process before the knowledge was expected to be routinely applied.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The materials meet the expectation for being 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.

  • There is evidence of the opportunity to work with engaging applications of the mathematics in every chapter, including the chapter assessments.
  • There are multiple non-routine problems throughout the chapters such as Newton’s Revenge, the Line Factory and the TV Antenna.
  • Students are frequently presented with problems in real-world situations that are relevant to them.
  • Students must also apply their understanding through teaching others.
  • Chapters 3, 4, 5 and 9 all explicitly provide opportunity for students to engage in application with standards of Grade 8 (8.EE.C.8.C, 8.F.B) that specify application. Application is developed through non-routine problem solving such as:
    • Newton’s Revenge – could someone be too tall to ride the roller coaster (scatterplot, data collection/analysis and prediction);
    • Iditarod Trail Sled Dog Race – when did they meet, who traveled faster, how long was the race (systems);
    • Biking the Triathlon – interpreting lines on a graph – speed, distance, rate (slope, data analysis); and
    • Personal Trainer – collect/organize biking data (scatterplot, line of best fit).

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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-
Indicator Rating Details

The materials meet the expectation for the three aspects of rigor not always being treated together and not always being treated separately. There is a balance of the three aspects of rigor within the grade.

  • There are multiple lessons where two, or all three, of the aspects are interwoven.
    • Lesson 10.1.2 presents students with a task to provide input to a sports company designing a new bag given the constraint of using only a piece of fabric that is 40" x 52" and that will hold the most. Students are encouraged to build conceptual understanding through modeling with paper and practice fluency by calculating volume of different shapes/sizes, then applying their discoveries to the size given and make a recommendation with rationale. They're further encouraged to generalize their learning about the volume of cylinders versus rectangular prisms.
  • There are also multiple lessons where one aspect is the clear focus, which is almost equally split among all three aspects, with perhaps a slight emphasis on conceptual development.
    • Lesson 3.1.1 "What is the Rule?" is clearly focused on fluency and procedural skill because the lesson is entirely 12 in-and-out tables for students to complete and generalize a rule.
    • Lesson 7.1.2 "Is there a relationship?" is all application - organizing and analyzing data from car advertisements about odometer reading and cost.
  • In addition, there is a balance of the three aspects of rigor included in assessments, all pre-made individual assessments contain questions on conceptual understanding, procedural skill and fluency, and application.

Criterion 2e - 2g.iii

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

The materials reviewed for Grade 8 meet the criterion of meaningfully connecting the Standards for Mathematical Content and the MPs. The latter are clearly identified in teacher materials and used to enrich mathematical content in problem-solving tasks. Problems attend to the full meaning of each practice standard multiple times throughout the year. Throughout the lessons, the materials consistently prompt students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Students are often directed to explain responses in practice and tasks. Teacher materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others. In addition, materials very explicitly attend to the specialized language of mathematics. Correct mathematical terminology is used, enforced, and reinforced. Overall, the materials meet the expectations for the practice-content connections criterion.

Indicator 2e

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

The materials meet the expectations for the MPs being identified and used to enrich mathematics content within and throughout each applicable grade.

  • There is a clear articulation of connection between MPs and content standards. Materials regularly and meaningfully connect MPs throughout the lessons.
  • There is a chart in the Teacher’s Guide that aligns the MPs with the course, including an in-depth explanation of how they are “deeply woven into daily lessons.”
  • Every unit identifies the MPs used in the teacher chapter overview page.
  • In the Teacher's Guide, each unit specifically relates how the listed standards are used in the unit and for each lesson. These are logical connections and integrated with the content.
  • Teachers are reminded to encourage the use of MPs in team discussions even if they aren’t identified.
  • Most lessons incorporate multiple MPs as students have the opportunity to deeply engage with authentic mathematics of the grade.
  • All eight MPs are represented throughout the course.
  • Connections are not made in the student materials until the end of the book in the End-of-Course Reflection when students are asked to discuss/reflect on the entire course about them. The questions and problems in this section clearly facilitate students understanding and making connections to the MPs, though there is concern that the reflection could easily be skipped by teachers if instructional time for the regular lessons runs short.

Indicator 2f

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

The materials meet the expectations for attending to the full meaning of each practice standard.

  • Each practice is addressed multiple times throughout the year. Over the course of the year, students have ample opportunity to engage with the full meaning of every MP. Examples include:
    • MP1 in 8.1.1 "Profit, Profit, Profit," 10.1.2 "Comparing Gym Bags," 10.2.2 "Fifty Nifty Necklaces."
    • MP2 in 5.1.1 "Changing Forms," 6.2.2 "Undoing Dilation," 7.2.2 "Biking the Triathlon," 9.2.2 "Part of Pythagorean Relationship."
    • MP3 in 4.1.1 "Tile Pattern Team Challenge/Presentation," 6.2.1 in group work on dilations and in 7.1.2 in determining line of best fit as a team.
    • MP4 in 5.2.2, which models saving money to purchase bicycles and how saving at different rates creates different equations and graphs; 7.1.3 experimenting with different factors that will affect plant growth and modeling this mathematically; and 9.2.5 with applications of Pythagorean theorem.
    • MP5 in 3.1.3, that says, “Be ready to defend your math position with all the math tools you have.” (i.e., students choose), and in 3.2.4 “Did you use algebra tiles to solve...Why or why not?” where again, students were given the choice.
    • MP6 in 3.1.4 "Precise Labeling," 8.2.4 which asks students to make an exact computation and in 9.2.1 when it says to "Be as specific as you can."
    • MP7 in 3.1.7 "Goofy Graphing," 4.1.1 "Tile Pattern Team Challenge," 6.1.3 "Describing Transformations."
    • MP8 in 8.2.3, that looks at structure of positive exponents to extend pattern to negative exponents, and 9.2.4 where students determine whether decimals repeat, terminate, or neither.
  • MPs are embedded in lessons, assessments, mid-year and end-of-year reflection, and puzzle investigator problems.
  • There are clear definitions for all the practices as well as where they are addressed in the curriculum.
  • The core structure and components section of the Teacher's Guide defines each MP and provides a rationale of how the program addresses each math practice. On page 52 a chart identifies problem tasks that integrate multiple MPs.
  • In the Teacher Guide the prep section for every lesson identifies the MP(s) and connects the MP(s) to the content of the lesson. For example, 4.1.2 states "Students continue reasoning and quantitatively while working with patterns. Today they makes the connection more explicit, looking for and making use of the structure of a linear equation."

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The materials meet the expectation for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

  • Students are consistently being asked to verify their work, find mistakes and look for patterns or similarities.
  • The materials have questions built throughout every lesson to encourage students to construct viable arguments and critique each other’s reasoning with heavy emphasis on group work.
  • Students construct viable arguments through activities such as explaining their thinking or justifying steps.
    • For example in 9.2.1, students are asked to the following: "Justify your conclusion. Explain your reasoning. How do you know? Do you agree? Is Cisco correct? Why or Why not? What was his mistake? Explain your choice."
    • In 10.1.3 students are asked to explain why Dan’s and Jan’s work is different but they have the same answer.
    • In 5.1.1, students are asked to justify how many feet a tree grew in a year.
    • In 2.1.5, students are asked "Why does it work? as they are developing a method to simplify both sides of the Expression Comparison Math.

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.
2/2
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Indicator Rating Details

The materials meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

  • Teachers are encouraged throughout the Teacher’s Guide to ask students questions.
    • Teachers ask questions such as “Who agrees? Who disagrees? Why is there a disagreement?”
    • For example in 2.1.1, the Teacher's Guide states that "The goals of today’s lesson is for students to begin using algebra tiles as an appropriate tool. While using this tool, they will begin to look for and make use of the structure of algebraic notation as they combine like terms."
    • Also in 2.1.1, the Teacher's Guide prompts teachers throughout the lesson description to ask questions such as “What is different? How do we know? Why can I?” There are also prompts about having pairs check each other on different problems so that they have to explain their thinking and prompts asking students to justify solutions.
    • This is true for every lesson. Any page you flip to includes question prompts like, “What information do you need? How can you check? What does this mean? Help me understand how? Why did you? Did anyone else?"
  • The course is designed for students to work in teams and have them collaborate and explain their thinking to each other.
  • Teachers also are encouraged to assign tasks that require students to consistently engage in debate.

Indicator 2g.iii

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

The materials meet the expectation for explicitly attending to the specialized language of mathematics.

  • Each chapter ends with a vocabulary list of words used in the unit that includes words from previous learning as well as new terms. Students are referred to the glossary and it is suggested that they record unfamiliar words in the Learning Log.
  • Each chapter includes a resource page of concept map cards with the vocabulary of the chapter.
  • Throughout the unit, these terms are used in context during instruction, practice, and assessment.
  • Vocabulary is bold in the context of the lesson, then pulled out specifically in “Math Notes” sections in each chapter.
  • There are suggestions like “Encourage students to use appropriate vocabulary, referencing the word wall when necessary.” Sometimes they even list specific words that should be included.
  • In some instances, the text is slow to introduce vocabulary such as “slope” – it is developed as “change” or “rate” in through many lessons before it’s called slope. Or starting with “flip, slide, turn” before transformations are labeled. It seems intentional that students have the concept before linking vocabulary to it.
  • There is vocabulary that seems unique to CPM such as the “Equal Values Method” for solving systems, which is just a specific case of substitution and “Giant 1” or “fraction busting” or “the 5-D process” as strategies.
  • The terminology that is used in the course is consistent with the terms in the standards.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

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

The instructional materials for Grade 8 meet expectations for Use and Design to Facilitate Learning. Within the lessons of Grade 8, students have ample problem solving tasks in addition to exercises to develop skills. The lessons progress in a natural, coherent sequence that builds knowledge and homework that constantly spirals to include review of the concepts. Students are expected to use manipulatives to represent their thinking and build knowledge as well as showing their learning in a variety of other ways. The layout of the book is not confusing or visually distracting, it is easy to find any section that may be needed in a lesson. Overall, this section meets expectations for each indicator.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

The materials meet the expectation for the underlying design of the materials distinguishing between problems and exercises.

Each student lesson begins with “core mathematical content (page 4)” - usually a non-routine, problem-solving team challenge or game, then includes further learning (i.e., math notes box, learning log, more practice), then homework, called “review/preview” that allows them to practice mathematics concepts and to prepare for future mathematics concepts because this is a spiral text.

New mathematics is usually taught through completion of core problems, sometimes referred to as tasks, by collaborative groups with the teacher acting as the facilitator, leading the students through guiding questions and activities. Each lesson is designed so that students solve only a few complex problems.

Following the core problems is the “Review & Preview” section that includes 4-7 problems, which may also be scaffolded. Even within this spiral review, there are non-routine problems as well as routine exercises, designed to build mastery over the course of the year. Students have multiple opportunities to be exposed to previously learned concepts throughout the year.

Indicator 3b

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

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

The sequence of lessons develops in a coherent flow that naturally builds students’ mathematical foundations. The chapters are divided by similar content. For example, in Chapter 9, Angles and Pythagorean Theorem, section 9.1 is angles, section 9.2 is Pythagorean theorem, clearly indicating to students that, while connected in the big picture, this is different than what they just worked on.

  • Within each section, topic development is sequential.
  • Lessons are numbered by chapter.topic.lesson: for example, 4.1.3.
  • Problems are numbered sequentially throughout the entire chapter, classwork, and homework: for example, 6-83 is the 83rd problem in Chapter 6.

Homework spirals and includes practice of what was learned in that lesson, review of previous concepts, and introduction of what’s coming. This is intentionally spaced practice to constantly review key concepts and lay foundation for what’s coming. The review and preview section problems build on each other, starting with simpler problems and building to more complex problems, most problems are scaffolded with parts a and b allowing students to have an entry point into the problem and then moving to more complex math. The program’s philosophy is to embed the mixed, spaced practice throughout the course of the year, teaching students to rely on both recall of how to solve a problem and to identify what type of problem it is.

Each chapter ends with Closure for students to consolidate understanding or correct misunderstandings. Full mastery of a concept is not always intended after the daily lesson. Partial mastery of material is often reviewed and revisited in further lessons, building to full mastery.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

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

Throughout various lessons and within the problem sets, students are asked to produce answers and solutions as well as to describe their answers, discuss ideas, make conjectures, explain their work and reasoning, make sketches and diagrams, justify their reasoning and use appropriate models. Students are asked to show all work, including: checking of solutions, drawing visual representations in the form of figures, tables, graphs, etc., writing equations, explaining steps and reasoning, and justifying responses.

Students are asked to represent their thinking using multiple representations. Within the collaborative class structure, students are constructing viable arguments and critiquing each other's reasoning, using equation mats, drawing tables and creating graphs, writing equations, looking for patterns, explaining their reasoning both verbally and in writing, and making explicit connections between the variety of representations. There is a Learning Log in each lesson that allows students to make connections and reflect on their learning.

Indicator 3d

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

The manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models, which meets the expectations for this indicator.

Manipulatives are appropriately used and explained. Algebra tiles are the primary manipulative used at this level. This program makes heavy use (especially during Grades 6 and 7) of algebra tiles to make concrete, accurate representations of very abstract concepts. The tiles are used so often that students would really learn these concepts well.

Most of the manipulatives used in CPM are commonly available, and many schools may already have them such as rulers, protractors, angle rulers, cubes, square tiles, counters, spinners, and dice. There is a materials list provided on page 7 that includes general supplies like graph paper, sticky dots, masking tape as well as grade-level specific materials for activities like ribbon, straws, tracing paper, models of solids. Manipulatives and/or models accurately and consistently represent the related mathematics.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The visual design is not distracting or chaotic, and it supports students in engaging thoughtfully with the subject. The student materials are consistent between chapters within a grade level as well as across grade levels.

The entire series was designed with 11 key assumptions about student learning in place. These can be found on pages 6-7 of the teacher edition and include the belief: "The structure of the lessons and the layout of the textbook help students focus on mathematics and eliminate distractions."

The visual design of this program is very basic and clearly focused on the mathematics. The student materials are in black and white, making use of models, diagrams, and simple pictures to illustrate concepts. The program explicitly states “the color in the book is the students’ excitement and engagement with mathematics” ( page 7 Course Structure and Components). There are no distracting or extraneous pictures, captions or "facts" within lessons.

Each lesson and homework set is clearly labeled and provides consistent numbering system. Each chapter gives an overview of the chapter, guiding questions, bulleted list of what students will learn, and a chapter outline. Each lesson has a heading in the form of a question and then followed by a title, intended to build student interest and provide students with objectives. “Review & Preview” Problems are always labeled and easily identified within the materials. At the end of each chapter, there is a clearly labeled Closure section.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
5/8
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Criterion Rating Details

The instructional materials for Grade 8 partially meet expectations for Teacher Planning and Learning for Success with CCSSM. Teachers are provided with detailed, extensive materials to prepare for every lesson including suggestions for managing the study team structure, prompts/questions to guide students in the content, possible modifications, and pacing. However, the teacher materials do not provide adult-level explanations and examples for teachers to improve their own knowledge. Within a course, lessons are connected or referenced so students see a continuation of knowledge. There is thorough research and rationale provided explaining the program’s instructional approach as well as several areas of support for parents. 

Indicator 3f

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

Materials support teachers in planning and providing effective learning experiences through teacher questioning, which meets expectations for this indicator.

This is a strength of the program with multiple questions for each lesson/problem throughout all of the Grade 8 units. Prompts and questions are provided in the teacher edition for both the lesson activity and daily closure. These questions are not generic, but are designed to focus students on the core concept of the lesson.

Some lessons contain a narrative titled “Team Strategies” that offers suggestions for management of the collaborative teams during activities. Teachers are often given suggested teaching strategies that incorporate higher level thinking.

Sample questions are also provided to assist ELL students and students who have more difficulty with the mathematics concepts in the Universal Access section of each lesson. Additionally, teachers are prompted to reflect on student learning after the lesson in order to prepare for the next daily lesson or unit.

However, this guidance is provided in long, narrative form and requires teachers to spend significant time “digging in” in order to prepare the lesson. If teachers do not use narrative information fully in preparation of each lesson, they may struggle to guide the instruction and use questioning techniques effectively.

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.
2/2
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Indicator Rating Details

The materials meet the expectation for the teacher’s edition having many suggestions on presenting the content to students.

The preparatory materials presented for each lesson are extensive - generally two to five narrative pages of suggestions, scripts, prompts, things to look for, tips for strategies, universal access, homework, pacing, and guiding questions. The multi-page lesson overview also gives narrative information about the mathematics content, including connections to MPs, information to assist teachers in understanding connections being made within and across chapters, and the core problems to focus on for each lesson. The teacher’s edition, text, assessments and additional resources are also online and some include videos that may generate interest in the lesson.

The Universal Access guide gives teachers support on helping struggling students, but it is simplistic and doesn’t help teachers in identifying the root cause of why students maybe be struggling or how to address the needs of the struggling students. Extensive information is offered on management of collaborative teams, including specific methods/techniques that can be used for various activities and helping students to work together and share their thought process and mathematics learning.

In-print and online, teacher guidance is available for use of various technologies, including examples such as graphing calculators and an online transformation tool available to the teacher and students. Individual problems include notes on when to use a form of technology.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2
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Indicator Rating Details

The materials do not meet the expectation for the teacher’s edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

At 8th Grade, this text clearly expects teachers of mathematics to know the math and does not provide background teaching of the concepts. Problems have answers but without explanation, and the answers give little support to teachers' own understanding. Teachers may glean some knowledge through the guidance provided during the lesson to assist teachers in helping students to successfully solve the problems.

There are some print resources available outside of the teacher edition:

  • The “Math Notes” that students are expected to record frequently contain background knowledge.
  • Teachers do have access to the Parent Guide which provides an alternative explanation of some key ideas along with additional practice problems.
  • There are also “Homework Help Tips” available for students/parents that may benefit teachers as well if they need support with some of the problems.
  • A teacher with limited content knowledge would have to develop their background outside of the resources provided.

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.
1/2
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Indicator Rating Details

The teacher’s edition does not clearly explain the role of specific grade-level mathematics in the context of the overall mathematics for grades 6-12.

  • Teacher’s editions do not connect the learning from previous grade levels or explain how standards build on one another throughout the program.
  • The resources do not contain materials that explain the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.  
  • However, each chapter does include a section called “Where Is This Going?” that helps the teacher understand how this unit builds toward students’ future math learning, usually within the grade-level course, but in some instances toward future course work – this is evident in chapters 8 and 10 where work is connected to Algebra.

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).
0/0
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Indicator Rating Details

The teacher’s edition contains a detailed planning chart of each lesson and estimated pacing of the problems as well as assessment and mathematical reflections. There is a Course Planning Timeline in “Preparing to Teach This Course” that lists the number of days per chapter at-a-glance.

Every chapter includes a lesson pacing guide for the chapter as well as assessment days that should be allotted. Every lesson suggests the amount of time/class periods needed.

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.
0/0
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Indicator Rating Details

The materials do contain strategies for informing parents or caregivers about the mathematics program and give suggestions for how they can help support student progress and achievement. Parents have extensive online access to tips, reviews, and how to help their student. Online resources are noted in Teacher’s edition – page 33 - in Course Structure and Components.

The book “Parent Guide with Extra Practice” for Courses 1-3 is available in print and online. It contains general course information, questioning suggestions, keys for student success, content explanations, examples, and practice problems with answers aligned by topic and chapter. There is also Homework Help available online for parents and students to access.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

The materials do contain explanations of the program's instructional approaches and identifies the research-based strategies within the teaching materials. The teacher edition provides a section called Course Structure and Components which describes the program’s design principles, including articles that synthesize research on their key elements: cooperative learning, problem-based learning, and spaced practice. The explanations contain specific relationships between these topics and the instruction suggested within the series.

Online, there is an extensive section called “About CPM” that includes philosophy, mission, vision, program description, research base, and more. The teacher materials contain a “Team Support Guidebook” explaining the use of Study Teams: Effective Learning and Teaching Strategies.

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
8/10
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Criterion Rating Details

The instructional materials for Grade 8 partially meet expectations for assessment. Materials offer some resources and tools to help teachers collect ongoing data about student progress on the standards. The Grade 8 materials do include pre-assessments and they do identify problems in each lesson that may cause student errors or misconceptions. There is constant review built into the course because of the spiral homework and, for several concepts, spiral lessons. Because of the team structure, students receive a lot of feedback from their peers and teachers have prompts in the teacher guide to help orchestrate discussion, although students may not receive direct teacher feedback individually on a routine basis. Pre-made assessments do not indicate the standards being assessed, though it is possible to create assessments by selecting questions based on certain standards. Assessments have generic scoring guides provided, but they may not be specific enough to accurately interpret current student performance. Students are expected to monitor their progress and there are several ways for this to happen built into the program. Overall, while there are solid components in assessment, there are also significant gaps resulting in only partially meeting expectations.

Indicator 3m

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

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

  • There is a pre-course diagnostic assessment to gather information about skills from prior grade levels.  
    • Questions are aligned to standards from the previous grade to assess background content knowledge
    • There is a good balance of content with 4-5 questions per cluster
  • Within the grade level, there are multiple opportunities to check for student understanding before they move to the next chapter.  
  • There is an assessment bank resources with a test generator online providing teachers with flexibility to create assessments to meet their needs.

Indicator 3n

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

Materials meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions. Within each lesson of the Teacher’s Guide, trouble spots for students are embedded within the “Suggested Lesson Activity” and ideas about how to address those possible misunderstandings are provided.

Often, possible questions to ask students are offered that allow for students to discuss misconceptions and to lead them toward deeper, more accurate understanding of the math concepts.

In the student tasks, students are presented with situations which are based on common misconceptions and asked to identify mistakes or provide rationales, which presents opportunities for “teachable moments.”

Indicator 3o

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

Materials meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

This program is very strong in on-going review; the program’s philosophy of how to build mastery is research-informed, where mastery is best achieved over time. The materials provide several opportunities for ongoing review and practice, particularly in the daily spiral homework and mid/end of year course reflections.

Each chapter ends with a “Chapter - Closure” lesson. This lesson contains several activities which provide students with multiple ways to review and prove what they have learned. Each chapter has a checkpoint problem that is material that students are supposed to have mastered at this point, generally a review from content learned in prior years. Students are provided with additional practice in the back of the book if the checkpoint concept is not mastered.

Practice of both basic skills and major concepts is spaced throughout the curriculum. Teacher Planning offers prompts to orchestrate discussion which gives students instant feedback on their thinking and processes. The teacher materials do not offer provisions on how to provide feedback to students regarding homework assignments. A concern is that because of the structure of study teams for learning students may not routinely receive specific individual feedback.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

The materials partially meet the expectation for assessments clearly denoting which standards are being emphasized.

Pre-made summative chapter assessments do not denote the standards.

Some assessments are connected to standards, however they cover numerous topics from various chapters, making standards alignment difficult.

There is a test generator online which allows the selection of questions based on standards.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details

The materials partially meet the expectation for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The teacher materials contain generic 4-point and 6-point rubrics that may be used when evaluating formative and summative assessment. The tests include solution keys, and there are suggested feedback forms provided for presentations.

CPM provides multiple strategies for assessment:

  • These include individual tests, team tests, participation quizzes, student presentations, portfolios, homework, and class observations.
  • Most of the suggested assessments are designed to be formative, providing feedback to both teacher and student about their progress toward mastery of both mathematical skills and concepts.

The only suggestion for follow up is student revision including error analysis. There are no follow-up suggestions connected directly to the assessments. The teacher materials suggest that assessments must be designed to meet the needs of individual classes. However, this guidance may not be enough for many teachers.

It is a concern that scoring help provided is too generic. Rubrics are not aligned to specific assessments or tasks within each chapter and therefore may not provide enough guidance to teachers to interpret current student performance.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

The materials do encourage students to monitor their own progress. Students are expected to complete a Learning Log, and they also should create a portfolio with justification for the items they include. They are expected to reflect in closure sections, and chapter 10 requires reflection back over the entire course.

Because CPM is taught using the collaborative approach with the teacher acting as the facilitator, students are encouraged to monitor not only their own progress but also to help members of their study teams understand and master all concepts.

Each chapter’s closure lesson contains activities and narrative intended to help the student reflect on the concepts they have learned and may need to practice before moving forward and assessment. The “Checkpoint problems are designed to support students in taking responsibility for the development of their own skills” (page 31, Team Support and Universal Access).

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
11/12
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Criterion Rating Details

The instructional materials for Grade 8 meet expectations for differentiated instruction. In the teacher materials, there are many suggestions about making content accessible to all students and strategies for addressing the whole range of learners, including ELL students. This includes allowing multiple entry points into problems and multiple pathways for solutions, as well as opportunities for advanced students to go deeper. However, many of the suggestions are very non-specific or not practical, especially for students who are struggling. The text does provide a balanced portrayal of demographic and personal characteristics, though does not emphasize home language or culture in the learning. While there is concern about success with the lowest students, there is enough support provided to justify meeting expectations for differentiation.

Indicator 3r

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

The materials meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners:

  • Scaffolding and sequencing is built in to lesson development and specific problems to help students master concepts.
  • Each suggested lesson activity gives support to teachers to help engage all students through use of different strategies.
  • Throughout the Teacher's Guide, many lessons include specific scaffolding suggestions, including probing questions, for concepts that students may struggle with. These can often be found in the Suggested Lesson Activity and/or the Universal Access section that is included with many lessons. Ex:  Lesson 4.1.2 has a suggestion for students who are having a hard time seeing pattern growth to use one color to shade each level of growth.

  • Every lesson also has a section of “Team Strategies” with tips on how to facilitate collaboration.
  • Each lesson identifies the “core problems” in case some of the work needs to be reduced.
  • Specific problems that may need scaffolding are identified. Example: “Academic Literacy & Language Support: A useful sentence starter for the Learning Log entry in problem 4-57 could be ‘In order to tell if a shape has been enlarged correctly…’”
  • Specific problems that may provide additional challenge are identified. Example: “Additional Challenge: Problem 4-56 is provided for students or teams who have time or the inclination to reduce by a more challenging multiplier.”

Indicator 3s

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

The materials meet the expectation for providing teachers with strategies for meeting the needs of a range of learners:

  • The program is designed with varying levels of problems. Students who need more time can focus on the core problems of the lesson (which are listed in each lesson plan). On-level students can solve more problems, and advanced learners can additionally incorporate the enrichment and extension problems built into the latter part of each lesson.
  • There is a “Universal Access” tab in the teacher’s edition. It provides suggestions for Special Education students, ELL, and Advanced students. They are non-specific suggestions, though there is repeated emphasis on the benefits of the study team structure.
  • Some lessons contain a narrative titled “Universal Access” with suggestions to support ELL, low-level, and high-level students on specific concepts. These tips are specific to the lesson's content.
  • Students have access to an online tutorial website for homework help. It provides hints and step-by-step solutions intended to help students understand homework concepts.
  • Homework also includes varying levels of problems that could challenge more advanced students.

Indicator 3t

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

The materials meet the expectation for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

A variety of solution strategies is always encouraged in the problem tasks, and students are given opportunities to create solution paths on their own.

Study teams are encouraged to use collaboration to solve tasks that lead to understanding and mastery of concepts in most lessons. Students are encouraged to make observations and brainstorm to solve the tasks within their study team.

Lessons include richer problems with multiple entry points and teacher suggestions for scaffolding lower performing students consistently through teacher’s edition.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
1/2
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Indicator Rating Details

The materials partially meet the expectation for providing support, accommodations, or 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).

This series is clearly designed with best practices for all students in mind, however, there is nothing explicitly differentiated or modified for lower or ELL students, other than translating assessments into Spanish.

The teacher materials contain a “Universal Access Guidebook” offering general information about how the CPM series supports students at all levels. Universal Access provides non-specific strategies to help all learners have access to the math concepts. However, some of the suggestions are not very helpful, such as: It is suggested that students who struggle stay after school for additional tutoring/support or do additional practice at home found in the Parent Guide, don’t do enrichment or extension, concentrate on the review portion of the homework, encourage parent participation with homework, and use the homework help online. Or possibly be re-assigned to an appropriate course.

Some lessons contain a narrative titled “Universal Access” with suggestions to support ELL students on specific concepts. These materials are language-intensive, so there is concern that ELL or special needs students would be overwhelmed by the reading and vocabulary. There is also concern that the suggestions provided are not enough to guarantee that all students have content that is accessible. In addition, there is extensive dependency on peer collaboration for learning concepts, which may intimidate students who struggle or lack self-confidence.

Indicator 3v

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

The materials meet the expectation for providing opportunities for advanced students to investigate mathematics content at greater depth.

Problems that are not identified as “core problems” in each lesson are considered enrichment or extension problems, allowing students to investigate deeper application. In the back of the book, there is a section of Puzzle Investigator Problems that offers challenging situations.

There is a pacing option provided to accelerate students through Courses 1-3 to be able to enroll in Algebra I in Grade 8.

The teacher materials contain a “Universal Access Guidebook” offering general information about how the CPM series supports students at all levels. Some lessons contain a narrative titled “Universal Access” with suggestions to support high-level students on specific concepts. The study team structure provides opportunity for advanced students to deepen their understanding by helping their group. Students are frequently encouraged to reflect on their learning, providing opportunities for advanced students to make connections.

Indicator 3w

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

The materials meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

No examples of bias were found.

Pictures, names, and situations present a variety of ethnicities and interests.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
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Indicator Rating Details

Materials provide opportunities for teachers to use a variety of grouping strategies.

Lessons are intended for cooperative learning groups, or study teams, with specific roles assigned, typically in groups of 4.

It is suggested that special education students work with one partner rather than a team of 4 to encourage collaboration and a sense of safety.

Teachers are provided with abundant support and rationale for setting up and facilitating study teams for collaborative learning and problem based learning.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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Indicator Rating Details

There is limited evidence of the instructional materials encouraging teachers to draw upon home language and culture to facilitate learning. The materials provide parent welcome letters and unit overview letters that are available in English and Spanish.

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

The instructional materials for Grade 8 do support Effective Technology Use to enhance student learning. Technology plays a vital role in this program, though it is not a requirement for success. There is online access to the complete text, homework, and homework help. There are interactive tools and virtual manipulatives to go with lessons. There is a test generator for teachers, although there is no online assessment option. There is extensive research, rationale, and resource links for parents. However, there is not any type of online, collaborative community. Digital materials are accessible and available in multiple platforms.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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Indicator Rating Details

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.

Digital access is part of the CPM package for teachers, students, and parents. It is web-based and compatible with multiple internet browsers and wireless devices.

The digital access includes, but is not limited to, the textbook, extra practice, and homework help.

Accessibility was tested on Chrome, Firefox, Safari, an iPhone, and an iPad. All access was successful. It is not compatible with Internet Explorer.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

Materials partially include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

There are “Student Activities” online that could easily be used as opportunities for assessment such as the Keylock Puzzle to evaluate skill with transformations.

For actual tests, there is not a clear way for teachers to assess student understanding using technology.

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.
0/0
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Indicator Rating Details

Materials can be easily customized for individual learners.

Teachers have the ability to create customized assessments using the extensive online CPM assessment bank.

Teachers have the ability to add notes to their personal online textbook for future reference.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

Materials do not include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g., websites, discussion groups, webinars, etc.).

CPM offers a monthly technology newsletter, video resources, teacher and parent tips and technology support as needed.

CPM does not provide an opportunity for teachers and/or students to collaborate directly with each other.

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.
0/0
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Indicator Rating Details

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the MPs.

Materials offer teacher and student access to various technologies that can be used throughout the curriculum, there are many resources on their website.

Some lessons include e-tools intended to help students understand concepts such as using algebra tiles, the keylock game for transformations, and graphing calculators.

There are homework hints online.

There is also parent support online as well as links to other sources of support.

Additional Publication Details

Report Published Date: Mon Mar 14 00:00:00 UTC 2016

Report Edition: 2013

Title ISBN Edition Publisher Year
null 978-1-60328-221-5 null null null
null 978-1-60328-223-9 null null null

About Publishers Responses

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

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

Educator-Led Review Teams

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

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

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

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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