Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for Grade 6 partially 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 mathematical practices are embedded into rich problem solving tasks. However, Focus and Coherence (Gateway 1) are lacking in some indicators, in particular, not spending at least 65 percent of time on major work of grade-level standards.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
8
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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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 6 partially 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. However, they do not spend the majority of time on major work, and non-major work rarely, directly reinforces the major clusters of the grade.

Overall, Grade 6 meets expectations for assessment, amount of content provided for a year, and making connections across concepts. However, Grade 6 materials only partially meet expectations in time devoted to major work (including non-major content enhancing major work) and identifying connections to prior knowledge from earlier grades. Therefore, the overall rating for Gateway 1 is partially 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 6 meets the expectations for focus within assessment. The focus for Grade 6 assessments was appropriate for the major work of the grade, but the materials also assess students on above grade-level content, such as scale factor, steepness of graphs for equations, and formal proportions. Overall, the instructional material does not assess any content from future grades that would impact the integrity of grade-level standards if those questions were modified or omitted.

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 material reviewed for Grade 6 meets the expectations for focus within assessment. Overall, the instructional material assesses grade-level content. However, there are a few questions that include content from future grades within the suggested summative assessment of each chapter.

The materials reviewed for indicator 1A 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.

  • The summative assessments focus on grade level topics.
  • All assessments and topics relate to Grade 6 standards or below except for the specific questions noted below.
  • In those instances, the problems are mathematically reasonable connections and within the scope of Grade 6 ability. They could also be easily adapted or skipped without impacting the integrity of the grade level work, so they do not impact the over score of meeting expectations.
  • The above grade level content that was assessed on the chapter summative tests includes the following:
    • Chapter 4, problem 4 is about scale factor and similarity that aligns to 7.G.1 and 8.G.4.
    • Chapter 4, problem 6 asks students to “write a proportion” which aligns to 7.RP.2.
    • Chapter 7, problem 5 and Chapter 8, problem 2 involve graphs of equations and comparing steepness which is informally introduced in Grade 7 related to unit rates (7.RP.2).
  • In Chapter 8, problem 7 assesses stem and leaf plots which, while mathematically reasonable for Grade 6, are not in CCSSM.

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectations for focus within major clusters. The amount of time spent on major work is 53 percent and there is a significant amount of time spent on work from future grades. Overall, the instructional material does not spend the majority of class time in the major clusters of the grade.

Indicator 1b

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

The instructional materials reviewed for Grade 6 do not 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 not 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, approximately 53 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 materials.

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 counted). Days for assessments, chapter closure, mid-course and full course closure reflections are not included in the data.

  • Chapters – Approximately 59 percent of time is spent on major work.
  • Lessons – Approximately 53 percent of time is spent on major work.
  • Days – Approximately 53 percent of time is spent on major work.
  • It is a concern that a large portion of the instructional days are more closely aligned with Grade 7 work. Examples include:
    • Three lessons in Chapter 3 that involve computation of integers.
    • Two lessons in Chapter 4 that include similarity and scale factor.
    • Four lessons in Chapter 9 that are application work with percent.
  • In the pacing guide, it would be very beneficial to plan for more days on the lessons that address major work of the grade rather than so many days on future work or stand-alone lessons.
  • 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. Although there were some connections found between non-major clusters and major clusters, such as in lessons 2.3.3, 6.1.2 and 7.2.3, these connections were not strong enough to be included as addressing major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 6 only partially meet the expectations for coherence and consistency with the CCSSM. The Grade 6 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. However, there is limited evidence of supporting content enhancing coherence by reinforcing the major work of the grade. In addition, 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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 partially 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 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 determining when lessons that are not major clusters directly support major work.
  • The strongest support comes from geometry lessons, specifically area, supporting the major work of expressions and equations, which require the students to use formulas/equations to solve problems.
  • There was also significant support linking the number system standards to both expressions and equations and ratios and proportional relationships. Examples include dividing decimals to find equivalent rates, using decimal operations in percent problems, calculating equivalent measurements and writing repeated factors as exponents.
  • There were several instances where the supporting work missed opportunities to connect to major work. One example of this is Chapter 8 on statistics could easily have made strong connections to both number system and expressions and equations, but did not.
  • However, much of the supporting work is “stand-alone” lessons that do not make connections to major work. Examples include multiple lessons on central tendency, work with data displays and scatterplots, and basic computation such as multiplying decimals.

Indicator 1d

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

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

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.

  • The lessons plus a chapter closure and assessment days equal 142 days.
  • The work is viable for one school year.
  • The number of days fall within the 140-190 range suggested.
  • According to the Teacher Guide alignment, all Grade 6 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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 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 6 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.

Throughout the entire series in the Teacher's Guide, content connections made are within the current course, but 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 helps make connections such as:
    • “Your work with similar figures and scale drawings will lay the foundations for much of the rest of the chapter.”
    • “In 5.2, you will continue your earlier study of probability.”
    • “Since the concepts in this chapter lay the foundation for simplifying and solving equations, they will be revisited throughout the entire course.”
    • “In section 3.1, you learned about the multiple representations of portions, now you will return to the idea of portions as you develop strategies for finding parts of parts.”
  • 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 it does tie to grade-level work with reasonable connections, but there are no explicit connections made to prior or future standards.
  • The materials do address the depth of the standards for the grade level.
  • Concept development supports the expected progression of the grade.

1.e.ii

The instructional materials reviewed for Grade 6 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 default strategy for helping all students engage in the problems.
  • There is a good balance of time devoted to each standard, though a slightly disproportionate amount is allocated to statistics and probability considering it is supporting work and detracts from time that could be spent on the major work of the grade.

1.e.iii

The instructional materials reviewed for Grade 6 only 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 support grade level work by developing conceptual understanding.
  • Some 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.
  • 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 learning from prior grades.
  • 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
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • Generally, chapter titles and lesson objectives make connections to CCSSM cluster headings, though never verbatim, and it's not always clear/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 a domain. They include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Overall the materials foster coherence through connections at the Grade 6.

  • One of the design principles of the entire course is that 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 6 includes 25 lessons that have significant connections either within a cluster or across domains. Some examples include:
    • In lesson 2.3.3: 6.NS.B and 6.EE.A are connected as students use factors to write expressions of products using the area model.
    • In lessons 6.1.2, 7.2.3: 6.NS.1 and 6.NS.2 are connected as students use the standard algorithm for division to understand division of fractions.
    • In lessons 9.1.1, 9.1.2: 6.G and 6.NS.B are connected as students use decimal computation to find volume and surface area.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials for Grade 6 meet the expectation for rigor and mathematical practices. The materials provide a solid balance of conceptual understanding, procedural skill and fluency, and application throughout every unit 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.

Criterion 2a - 2d

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

The materials reviewed for Grade 6 meet the 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 6, procedural skill and fluency is evident in almost every unit, which develop the relevant standards. In addition, application of the mathematical concepts is evident throughout each unit. 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
+
-
Indicator Rating Details

Materials meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

  • 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 their understanding.
  • Chapters 2, 3, 4, 5, 6 and 7 all include work directly related to the clusters that address conceptual understanding (6.RP.A, 6.NS.A, 6.EE.A, 6.EE.B, 6.EE.C). Conceptual understanding is built through strategies such as:
    • Using rectangles to multiply and work with distribution.
    • Creating a "concept catcher" (page 90).
    • The "Giant 1" for the multiplicative identity.
    • Percent grids to "see" fractions, decimals, percents.
    • Frogs jumping on a number line for integers and absolute value.
    • Algebra tiles for combining like terms, variables, area, perimeter.
  • 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 meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

  • 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. For example, in Chapter 9, the students are still practicing the skill of “solve equations for x” and using the “distributive property” while learning about volume and percents. The program model suggests about one-fifth of the homework be on new material and the rest review previous concepts.
  • The skills are frequently embedded in an engaging activities such as the “magic square” or “tweaking the data.”
  • Procedural skill and fluency that develop the clusters that emphasize it (6.EE.A , 6.EE.B) is evident in Chapters 2, 4, 6 and 7. 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 (Rates & Unit Rates, Solving & Graphing Inequalities)
    • Learning logs (Using a Super Giant 1, Fraction Division)
    • Spiral homework
    • Checkpoint problems - with extra practice if not mastered (Area & Perimeter, Rewriting Variable Expressions)
  • There was strength in developing procedural skill and fluency when using the distributive property and combining like terms.

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

Materials meet the expectations 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 "Croakie the Talented Frog," "Which is Sweeter?" and "Shopping Shirley."
  • 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, 5, 6, 7, 8 and 9 all explicitly provide opportunity for students to engage in application in the standards of Grade 6 (6.RP.A.3, 6.NS.A.1, 6.EE.B.7, 6.EE.C.9) that specify application. Examples include:
    • Birthday Bonanza - 18 million people on Earth share your birthdate; (ratios, proportions).
    • Dora's Dollhouse - 3/4' pieces from an 8' board; (division with fractions).
    • Memory Lane - taking a trip down memory lane; (integers).
    • Training for the Triathlon - swimming, biking, running; (comparing rates).

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

  • Conceptual and procedural knowledge as well as application of knowledge and skills are balanced throughout the course, including the chapter assessments.
  • There are multiple lessons where two or all three, of the aspects are interwoven.
    • For example: Lesson 5.3.2 - finding area of a parallelogram - starts with an online tech tool called Area Decomposer where students can cut pieces of shapes to try to rearrange them into a rectangle exemplifies conceptual development which moves into fluency by having students work with paper/pencil to draw cuts on original figures and then draw what the final figure would look like, showing how the pieces move. Students then return to concept development by exploring measurements on parallelograms and rectangles to establish what represents the base and height, then to fluency practicing measuring for several parallelograms until they begin to generalize and are prompted to discover that the area of parallelograms is the same as rectangles, therefore just A=b*h.
  • 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.
    • For example: Lesson 2.2.3 - exploring relationships between area and perimeter and what happens if one changes using base 10 blocks is a very conceptual lesson.
    • For example: Lesson 7.1.1 on comparing rates is very application based. Students are given a problem-solving situation and data about fundraising for a field trip which they have to analyze to make a recommendation. This is followed by multiple extensions which require further analysis with ratio comparisons, though students are never given that as a solution path - they have to figure out how to best compare options.

Criterion 2e - 2g.iii

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

The materials reviewed for Grade 6 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 always used, enforced, and reinforced. Overall, the materials meet the expectations for the practice-content connections criterion.

Indicator 2e

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

The 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. 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 practice standards 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. For example:
    • MP1 - 4.2.1 Mystery Mascot, 9.2.3 Shopping Shirley.
    • MP2 - 3.1.2 Portions as Percents, 7.1.1 Comparing Rates.
    • MP3 - 9.3.3 How is it Changing?, 6.1.1 Fair Shares.
    • MP4 - 2.3.1 Using Rectangles to Multiply, 5.1.3 Describing Parts of Parts.
    • MP5 - 2.2.1 Exploring Area, 6.2.3 Perimeters of Algebra Tiles.
    • MP6 - 9.3.1 Trail to the Treasure of Tragon, 4.2.1 Enlarging Shapes.
    • MP7 - 9.3.2 How Does it Grow?, 5.3.2 Area of a Parallelogram.
    • MP8 - 4.1.3 Using Variables to Generalize, 7.2.2 Another Division Strategy.
  • 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.

  • There is a section in the Teacher's Guide under Core Structure and Components that:
    • Defines each MP and provides a rationale about how this program addresses that practice overall.
    • Shows a chart on page 54 that identifies the problem tasks that integrate multiple MPs.
  • The prep section for every lesson in the Teacher's Guide identifies the MP for the lesson and how it's related, for example:
    • 2.1.1: "This lesson is an opportunity for the students to engage with mathematics through a variety of graphical representations. This is their first opportunity to focus on models. Students, in discussing these models, identify important quantities and map relationships. They will learn about whether each model makes sense and has served its purpose."

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
+
-
Indicator Rating Details

The materials meet the expectations 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 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.
    • Examples include: What can we compare? How else can we represent it? How are they related? Is there another way to see it? How is it the same (or different)? How can you show it?
  • Students construct viable arguments through activities such as explaining their thinking or justifying steps.
    • For example in a single lesson (7.1.2), students are asked to: Justify your answer (7-15c). Explain your reasoning (7-16a and 7-19c). How do you know? (7-17b).

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
+
-
Indicator Rating Details

The materials meet the expectations 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, such as “Who agrees? Who disagrees? Why is there a disagreement? Explain.” This would create an environment in the mathematics classroom that is rich with constructing viable arguments and critiquing the reasoning of others.
  • Teachers are encouraged to assign tasks that require students to consistently engage in debate. The course is designed for students to work in teams and have them collaborate and explain their thinking to each other.
  • The teacher guide links 1-2 MPs to each lesson –
    • For example: 8.1.5 – The goals of today’s lesson is for students to construct three different representations of a single set of data and decide with representation is most useful.
    • Continuing with 8.1.5, the Teacher's Guide prompts teachers to structure this lesson as a Participation Quiz to help focus students on explaining their reasoning and justifying their choice in data.
    • 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?”
  • Teachers also are encouraged to assign tasks that require students to consistently engage in debate.
  • The course is designed for students to work in teams and have them collaborate and explain their thinking to each other.

Indicator 2g.iii

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

The materials meet the expectations 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 terms are bolded 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.
  • The text makes connections between mathematics terms such as “mean” and “arithmetic average.” The students are required to learn the correct mathematics terminology with support for how they might hear it outside the mathematics classroom.
  • There is vocabulary that seems unique to CPM such as the “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

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

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.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

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

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

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.
0/2

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.
0/2

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.
0/2

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

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

Indicator 3l

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

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

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

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
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.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

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).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

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

Indicator 3y

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

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

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

Indicator 3ab

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

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

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

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

Additional Publication Details

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

Report Edition: 2013

Title ISBN Edition Publisher Year
null 978-1-60328-194-2 null null null
null 978-1-60328-196-6 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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