Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for Grade 7 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) is 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

|

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

|

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 7 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 7 meets expectations for assessment, amount of content provided for a year, and making connections across concepts. However, Grade 7 materials 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."

Criterion 1a

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

The instructional material reviewed for Grade 7 meets the expectations for focus within assessment. The focus for Grade 7 assessments was appropriate for the major work of the grade. The materials also assess students on Grade 8 content, such as similarity and solving equations where collection of like terms must occur. 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
+
-
Indicator Rating Details

The instructional material reviewed for Grade 7 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 7 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 7 grade ability. They could also be easily adapted or skipped without impacting the integrity of the grade-level work, so they do not impact the overall score of meeting expectations.
  • The above grade level content that was assessed on the chapter summative test includes the following:
    • Chapter 6, problem 4 - Scale factor is grade level but similarity is 8.G.4.
    • Chapter 3, problem 2; Chapter 7, problem 7; Chapter 8, problem 3 – all three are instances of solving equations where collection of like terms must occur which is Grade 8 (8.EE.7).
    • Chapter 7, problems 3 and 4 both assess stem and leaf plot, which isn’t 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 7 do not meet the expectations for focus within major clusters. The amount of time spent on major work is 59 percent with minor additional support from content in the non-major clusters that directly connects with major work. Overall, the instructional material does not spend the majority of class time in the major clusters of each 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 7 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 59 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 57 percent of time is spent on major work.
  • Lessons – Approximately 58 percent of time spent on major work.
  • Days – Approximately 59 percent of time is spent on major work.
  • It is a concern that the development of procedural competency with expressions and equations is not adequately addressed throughout the lessons.
    • There are several lessons devoted to vocabulary and concept development using algebra tiles, but only one lesson where kids are prompted to record and move away from tiles to paper and only four equations for homework. From that point on, students are expected to use/solve equations in application situations and when they are in the spiraling review homework.
    • One of those homework problems in particular is a "checkpoint" homework problem, which means there is some additional practice in the back of the book (24 problems) if teachers choose to use it. Although, they are multi-step with variables on both sides, which is actually a Grade 8 standard.
    • Students do not seem to have a strong opportunity to develop any real fluency with the process for solving equations which is very valuable for future grades.
  • 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; however, we did not find evidence strong enough to support this.

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 7 partially meet the expectations for coherence and consistency with the CCSSM. The Grade 7 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 on 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 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 seeing when lessons that are not major clusters directly support major work.
  • The strongest support comes from the nine probability lessons supporting the major work of both number sense (using rational numbers) and expressions and equations (converting among forms).
  • There was also significant support linking geometry with ratios and proportions as students used ratios to solve scaling problems.
  • However, much of the supporting work is “stand-alone” lessons that do not make connections to major work. This was evident in sections on statistics, angle measures, and probability.
  • There were several instances where the supporting work missed opportunities to connect to major work. One example of this is in Chapter 9 on geometry which could have easily tied volume formulas to expressions and equations, but lessons never got to a formula, staying on "how many cubes fill up the space" until students were supposed to use a formula in homework. It was unclear if this was expected to be prior knowledge.

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

The instructional materials reviewed for Grade 7 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades.

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 147 days.
  • The content is viable for one school year.
  • According to the Teacher's Guide alignment, all Grade 7 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 7 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 7 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 are made within the current course – they never explicitly tie to prior or future work.

  • On the chapter introduction page and almost every lesson, students are given a very clear overview of what the chapter will be and helps make connections such as:
    • Lesson 4.2.2 states, "In Lesson 4.2.1, you learned that you could identify proportional relationships by looking for a constant multiplier. Today you will revisit the earlier situation...."
    • Chapter 6 – “you will extend what you know about comparing expressions…”
  • 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 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 supports the expected progression of the grade.

1.e.ii

The instructional materials reviewed for Grade 7 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, but 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 some concerns:

  • There is a disproportionate amount 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.
  • Several standards in ratios and proportions are only addressed in one or two lessons throughout the year and 7.RP.3 is not addressed at all in the correlation guide provided for teachers, though there is evidence of the content in the lessons.
  • Some lessons are misidentified such as in 6.2.6 and 6.2.7 where students are finding the number of solutions to an equation (null, identity), which are labeled as 7.EE.3,4, but this more closely aligns to 8.EE.7.

1.e.iii

The instructional materials reviewed for Grade 7 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.
  • The teacher materials also state that Chapter 1, which includes mostly review and preparation for grade level work, is “meant only as an introduction to the course”.

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 7 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

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

  • 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 7.

  • 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 7 includes 21 lessons that have significant connections either within a cluster or across domains. Some examples include:
    • In lessons 4.1.1, 4.1.2: 7.G.A and 7.RP are connected as students use scale factor to enlarge/decrease geometric figures.
    • In lesson 7.1.3: 7.RP, 7.NS and 7.EE.B are connected as students write equations and compute to solve percent problems.
    • In lesson 7.2.2: 7.RP and 7.G.A are connected as students write proportions to find lengths of sides of geometric figures.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials for Grade 7 meet the expectation for rigor and mathematical practices. 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 expectations 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
+
-
Criterion Rating Details

The materials reviewed for Grade 7 meet the expectation for this criterion by providing a balance of all three aspects of rigor throughout the lessons. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. In Grade 7, procedural skill and fluency is 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 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's 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, with questions like "How do you see it?" "How can you tell if 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 and 7 all include work directly related to the clusters that address conceptual understanding (7.NS.A, 7.EE.A). Examples of this are:
    • Percent bars;
    • Ratio tables;
    • Multiple representations of the constant of proportionality;
    • Cecil, the tightrope walker, for adding integers;
    • Algebra Tiles for combining like terms, variables, comparing expressions; and
    • Positive/Negative chips for integers.
  • 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
+
-
Indicator Rating Details

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

  • There is evidence of the opportunity to develop fluency and procedural skills in every chapter.
  • 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 reviews previous concepts.
  • The skills are frequently embedded in an engaging activity such as the silent board game or the human graph.
  • Procedural skill and fluency, from the clusters that emphasize it (7.NS.A, 7.EE.A.1, 7.EE.B.4), is evident in Chapters 2, 3, 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 (Integers, Proportional Relationships in Graphs and Tables);
    • Learning logs (Evaluating Algebraic Expressions, Unit Rate);
    • Spiral homework; and
    • Checkpoint problems - with extra practice if not mastered (Unit Rates & Proportions, Simplifying Expressions).
  • Beyond the lessons, the suggested chapter tests also require students to demonstrate fluency and procedural skill.

Indicator 2c

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

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.
  • There are multiple non-routine problems throughout the chapters such as Robert’s New Hybrid Car, What Are You Eating, Fencing the Basketball Court, Community Service, Renting the Hall, and Birthday Sweets.
  • Chapters 2, 4, 5 and 7 all explicitly provide opportunity for students to engage in application in the standards of Grade 7 (7.RP.A, 7.NS.A.3, 7.EE.B.3) that specify application. Application is developed through non-routine problem solving such as:
    • Shopping Deals - (finding and using percentages);
    • The Yogurt Shop - charged by weight (proportional relationships);
    • Maverick Movie Theater - sizes of popcorn (volume and scaling); and
    • Alvin, the Deep Submergence Vehicle -- ocean depths (integers).
  • Students are frequently presented with problems in real world situations that are relevant to them.
  • Students must also apply their understanding through teaching others.
  • Beyond the lessons, the suggested chapter tests also require students to apply their knowledge.

Indicator 2d

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

The three aspects of rigor are not always treated together and are not always treated separately, thereby meeting the expectations for this indicator. 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.
  • There are multiple lessons where two, or all three, of the aspects are interwoven.
    • A mixed lesson, application and conceptual, is 7.1.5. The community service club is painting senior citizen apartments and need to figure out how many can be done in a day. Previously only 4/7 of the club was able to do 9 apartments, how many can the whole club complete? Students are guided through a possible process with the president of the club visualizing with algebra tiles and being able to create an equation to solve the problem.
  • 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.
    • An example of a fluency lesson is 2.2.1. Cecil, the tightrope walker, has to combine lengths to get across. In various ways of presenting the problem, students solve about 35 addition of integer problems in the lesson.
    • An example of a conceptual lesson is 3.2.2. It begins with an exploration with integer tiles to find multiple ways to represent a value and identifying efficient steps, followed by creating an argument to answer the question, "Do you think that every subtraction problem can be rewritten as an addition problem that gives the same result?" In the next problem, they have to justify, "When would rewriting subtraction problems into addition problems be useful?" The answers to these are shared/discussed in class. The lesson ends with a Learning Log entry called "Connecting Addition and Subtraction" which needs to include examples and diagrams.
  • In addition, there is a balance of the three aspects of rigor in included 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
+
-
Criterion Rating Details

The materials reviewed for Grade 7 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 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
+
-
Indicator Rating Details

The materials meet the expectation for ensuring that the MPs are 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 on 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 mathematical practices 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
+
-
Indicator Rating Details

The materials meet the expectation 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; 9.3.1 Maverick Movie Theater Popcorn, 9.1.1 Bubble Madness
    • MP2; 2.2.1 Composing Integers, 8.3.1 Intro to Angles
    • MP3; 7.2.1 Proportional Relationships, 2.3.1 Choosing a Scale
    • MP4; 9.3.3 Estimating Fish Populations, 7.1.2 Scaling Quantities
    • MP5; 4.3.1 Combining Like Terms, 6.2.1 Solving Equations
    • MP6; 8.1.1 Measurement Precision, 3.1.2 Scale Drawings
    • MP7; 3.1.1 Grouping Expressions, 5.2.4 Probability Tables
    • MP8; 9.3.2 Delightful Design, 3.2.2 Addition and Subtraction, 9.1.1 Circumference, Diameter and Pi
  • 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 55 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, in 4.2.3 "Students will use tables and graphs to make sense of problems...Attending to precision is important today as students must be careful when specifying units of measure."

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

  • The materials have questions throughout every lesson to encourage students to construct viable arguments and critique each other’s reasoning with heavy emphasis on group work.
  • Students are consistently being asked to verify their work, find mistakes and look for patterns or similarities.
  • Students construct viable arguments through activities such as explaining their thinking or justifying steps. For example in a single lesson (5.3.2), students are asked to justify their answers, present work so that someone could make sense of it, explain their reasoning, and show their solution.

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 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 3.3.3, the Teacher's Guide states "As you circulate, listen for the abstract and quantitative reasoning, the construction of viable arguments and critiquing of others’ reasoning and attention to precision in team discussions."
    • In 3.3.3, the Teacher's Guide prompts teachers throughout the lesson description to ask questions such as "How can you tell? What does your answer represent? and Do you have enough information to keep working?" There are also prompts about having teams do Think-Pair-Share and Hot Potato with different problems so they have to explain their thinking and asking students to justify solutions.
    • This is true for every lesson. Any page you flip to includes questions 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 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 bolded in the context of the lesson, and then, it is 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.
  • 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 978-1-60328-207-9 null null null
null 978-1-60328-209-3 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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