Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 8 meet the requirements for alignment to the standards. The materials devote the majority of class time to the major work for Grade 8. The materials are coherent and consistent with CCSSM. There are explicit connections between major clusters. The supporting work is used to enhance the major clusters. The materials have some assessment items that go beyond the Grade 8 standards. The materials reviewed for Grade 8 meet expectations for rigor and MPs. Each unit offers multiple opportunities for hands-on, conceptual development, skills practice for fluency, and engaging real-life situations. There is a solid balance of the three areas of rigor, with fluency being slightly weaker than the others, though the easiest to supplement if needed. MPs are identified in the materials, are used to enrich the mathematics content, and have their full meaning represented. The instructional materials support the standards emphasis on mathematical reasoning by prompting students and teachers to construct and analyze viable arguments and explicitly attending to the specialized language of mathematics. Overall, the instructional materials address all aspects of rigor and meaningfully connect the CCSSM and the MPs.

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
12
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

|

Partially Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Grade 8 meet the requirements for Gateway 1. The materials devote the majority of class time to the major work for Grade 8. The materials are coherent and consistent with the CCSSM. There are explicit connections between major clusters. The supporting work is used to enhance the major clusters. The materials have some lessons and assessment items that go beyond the Grade 8 standards. Since the materials reviewed for Grade 8 meet the expectations for alignment to the CCSSM in the areas of focus and coherence, they were reviewed for rigor and the MPs.

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 materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. There are questions on four unit tests that are testing CCSSM from grades above Grade 8. Even though the materials assess topics that are in future grades, omission of these 8 assessment problems does not compromise the integrity of assessing the Grade 8 standards.

Indicator 1a

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

The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. There are eight questions throughout the units that assess topics that are in future grades and could be omitted.

  • On the Looking for Pythagoras unit test, question 7 is on using a 30-60-90 triangle, which is HSG.SRT.C.6. Teachers can skip Investigation 5, which is the one connected to the high school concept.
  • On the Growing, Growing, Growing unit test, questions 1, 2, 4 and 8 are high school exponential functions HSF.LE.A.1. This entire unit should be moved from Grade 8 with the exception of Investigation 5 which does cover major work of Grade 8.
  • On the Say It With Symbols unit test, question 5 is high school exponential and quadratic functions HSF.LE.A.1. Teachers can skip Investigation 4, which is the one connected to the high school concept.
  • On the It's in the System unit test, questions 4 and 6 have system of inequalities and graphing inequalities which are high school HSA.REI.B.3 and HSA.REI.C.5. Teachers can skip Investigations 3.3 and 4, which are the ones connected to the high school concept.
  • Two units are clearly identified as Algebra: Frogs, Fleas, and Painted Cubes and Function Junction, so are not being evaluated.

Skipping these eight assessment problems does not compromise the integrity of the Grade 8 standards. The major work of Grade 8 is still assessed appropriately.

*Evidence updated 10/27/15

Criterion 1b

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

The instructional materials reviewed for Grade 8 meet the expectations for the majority of class time being devoted to major work. Grade 8 has more than 65% of the work on the major clusters of 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, and 8.G.A. The units Thinking With Mathematical Models; Looking for Pythagoras; Growing, Growing, Growing; and Butterflies, Pinwheels, and Wallpaper had the majority of the lessons on major work. The only concern is that the units also contained work that is a high school standard and this could distract from the major work. A notation to teachers on where the distinctions are would be helpful to keep the focus on the major work.

Indicator 1b

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

The instructional materials reviewed for Grade 8 meet the expectations for spending the majority of class time on the major clusters for Grade 8. Grade 8 has more than 65% of the work on the major clusters of 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, and 8.G.A.

  • The units Thinking With Mathematical Models; Looking for Pythagoras; Growing, Growing, Growing; and Butterflies, Pinwheels, and Wallpaper had the majority of the lessons on major work.
  • The concern is that the units also contained work that is high school CCSSM and this could distract from the major work. A notation to teachers on where the distinctions are would be helpful to keep the focus on the major work. One example of this is in Growing, Growing, Growing. The work with exponential equations is a high school standard, but used as a counter example to solidify linear work could be helpful. Without more guidance, teachers and students could spend a lot of time working on lessons that are actually high school concepts. Another example is that in Say it With Symbols there are lessons on quadratic, exponential and linear functions. The focus of Grade 8 is supposed to be linear functions and the work on quadratic and exponential functions could take time away from the work on linear functions.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 8 partially meet the expectations for coherence. There are areas where the materials have strong connections and areas that could be stronger. The Grade 8 materials could be completed within the timeline of 170-190 days. The connections between standards to build understanding are strong. There are some off grade level topics that could be identified to help teachers and students know that these are topics that are beyond the CCSSM necessary for that grade. Each investigation within each unit lists the CCSSM that are taught. The mathematical highlights for each unit stress the clusters from CCSSM. All investigations in the student books contain the standards included in that lesson. Every investigation includes activities that connect two or more clusters in a domain, or two or more domains. There is no unit or investigation that only focuses on one aspect of the CCSSM. Connections are evident in all grade levels and in all units. This is a very strong aspect of Connected Mathematics 3.

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 8 partially meet the expectations for the supporting content enhancing the major work. There are areas where the materials have strong connections and areas that could be stronger.

  • In Thinking With Mathematical Models, the use of scatterplots to tie into linear equations enhances the major work of 8.EE.B.
  • In Looking for Pythagoras, there is an attempt to connect working with irrational numbers and 8.G.B.
  • There are connections made with linear equations and high school content standards in many of the units.

Indicator 1d

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

The instructional materials reviewed for Grade 8 meet the expectations for being able to be taught in one school year.

  • The Grade 8 materials could be completed within the timeline of 170-190 days.
  • This includes all lessons, mathematical reflections, Looking Back and Looking Ahead and all assessments.

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 materials reviewed for the Grade 8 partially meet the expectations for being consistent with the progressions in the standards. The connections between standards to build understanding are strong. There are some off grade level topics that could be identified to help teachers and students know that these are topics that are beyond the CCSSM necessary for that grade.

All three grade levels have major work on equations, EE.A and EE.B:

  • Grade 6: Reason about and solve one-variable equations and inequalities can be found in several units (e.g., Let's Be Rational, Variables and Patterns) using informal methods of solving.
  • Grade 7: Solve real-world and mathematical problems using numerical and algebraic             expressions and equations is primarily in Moving Straight Ahead where they start using symbolic equations and properties of equality.
  • Grade 8: Analyze and solve linear equations and pairs of simultaneous linear equations is found in It's in the System, where various methods of solving systems are explored.

All three grade levels have major work on ratio and proportional reasoning, 6.RP and 7.RP:

  • Grade 6: Comparing Bits and Pieces begins work with ratios/rates and proportions then continues the major work of Grade 6 ratio and proportion into Variables and Patterns.
  • Grade 7: Stretching and Shrinking works with ratios using scale factors and Comparing and Scaling continues the work by solving proportions using many strategies learned from Grade 6 and Grade 7.
  • Grade 8: Butterflies, Pinwheels and Wallpaper use the concepts of proportional reasoning in transformational geometry work.

All three grades have major work on the number system (6.NS.A, 6.NS.B, 6.NS.C to 7.NS.A to 8.NS.A):

  • Prime Time begins the work of 6.NS.B.4 when it asks students to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
  • This leads to finding the least common multiple in order to find common denominators for fractions in Comparing Bits and Pieces, Let's be Rational and Decimal Ops in Grade 6 and extends to ratios in Comparing and Scaling in Grade 7. This continues into Accentuate the Negative in Grade 7 with performing arithmetic operations with integers and rational numbers (7.NS.A).
  • Comparing Bits and Pieces begins developing the ideas of positive and negative numbers on a number lines and absolute value (6.NS.C). This leads to 7.NS.A in Accentuate the Negative with operations on rational numbers. The also leads into 8.NS.A on approximating rational numbers (although not major work of Grade 8).
  • Let's Be Rational begins 6.NS.A with students dividing fractions. This continues in Grade 7 with 7.NS.A in Accentuate the Negative.

There is limited support for differentiation of instruction.

  • There is guidance for the teacher in the book titled A Guide to Connected Mathematics 3 that discusses differentiation. This gives best practices from research to be used while working on the problem with all students.
  • Differentiation is embedded within the instructional model for Connected Mathematics 3 that all kids get the problem launched and summarized the same way and that the differentiation comes during the explore phase of the problem.
  • There were specific strategies and guidance for English language learners.
  • To help make differentiation more explicit, strategies need to be discussed in the teacher's unit planning pages and it needs to be tied into the specific problems so the teachers have guidance.
  • The guide has general best practices but what to use with specific parts of a unit would make it more accessible for teachers and students.

There are many places where the materials relate grade level concepts to explicitly to prior knowledge from earlier grades. These can be found in the student editions in the problems and in the teacher editions in charts and in a narrative called Mathematics Background.

  • Let's Be Rational in Grade 6: Page 3, "These situations require addition, subtraction, multiplication, and division of fractions, including mixed numbers. You will decided which operation makes sense in each situation;"  "You may already know shortcuts for working with fractions..."
  • Comparing and Scaling in Grade 7: Problem 2.3 references work in unit rates in the prior Grade 6 unit Comparing Bits and Pieces.
  • Accentuate the Negative in Grade 7: Problem 4.2 references work with the distributive property in Grade 6.
  • Accentuate the Negative in Grade 7: Page 3, "Most of the numbers you have worked with in math class have been greater than or equal to zero. However, ...;" "You will also learn more about the properties of operations on numbers." Page 4, "You will extend your knowledge of negative numbers." Page 8, "You have worked with whole numbers, fractions, and decimals in earlier units." Page 58, "You have already examined patterns in ..."
  • Thinking With Mathematical Models in Grade 8: Page 3, "In earlier Connected Mathematics units, you explored relationships between two variables. You learned how to find linear relationships from tables and graphs and then write their equations. Using the equations, you solved problems."

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 materials reviewed for Grade 8 meet the expectations for coherence. Each investigation within each unit lists the CCSSM that are taught. The mathematical highlights for each unit stress the clusters from CCSSM. All investigations in the student books contain the standards included in that lesson. Every investigation includes activities that connect two or more clusters in a domain, or two or more domains.

An example of this is in Butterflies, Pinwheels, and Wallpaper. Two of the highlights are identify congruent and similar triangles and quadrilaterals efficiently; and use properties of congruent and similar triangles to solve problems about shapes and measurements.

There are many links between major clusters in this curriculum.

  • In It's in the System, investigation 1, students analyze and solve pairs of simultaneous linear equations (8.EE.C) and define, evaluate and compare functions (8.F.A).
  • In Thinking With Mathematical Models, investigation 2, students graph proportional relationships, interpreting the unit rate as the slope of the graph (8.EE.B) and understand that a function is a rule that assigns to each input exactly one output. The graph of a function is a set of ordered pairs consisting of an input and the corresponding output (8.F.A).
  • In Growing, Growing, Growing, investigation 1, students compare properties of two functions each represented in a different way (8.F.A) and use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large quantities (8.EE.A).
  • Due to the nature of the problems being "investigations," there are very few instances where materials do not connect two or more clusters in a domain and almost all connect two or more domains. One example of this connection is in Thinking with Mathematical Models, investigation 2, Linear Models and Equations includes Expressions and Equations, Functions, and Statistics and Probability (8EE.B.5, 8.EE.C, 8.F.B.4, 8.F.A, 8.SP.A.1-8.SP.A.3).
  • In Looking for Pythagoras understanding real numbers connects to 8.G.A, 8.G.B and 8.EE.A.
  • In Butterflies, Pinwheels, and Wallpaper in lesson 1.1, 8.G.A.1, 8.G.A.1.A, 8.G.A.1.B, 8.G.A.1.C are all connected.
  • There is no unit or investigation that only focuses on one aspect of the CCSSM. Connections are evident in all grade levels and in all units. This is a very strong aspect of Connected Mathematics 3.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The materials reviewed for Grade 8 meet expectations for rigor and MPs. Each unit offers multiple opportunities for hands-on, conceptual development, skills practice for fluency, and engaging real-life situations. There is a solid balance of the three areas of rigor, with fluency being slightly weaker than the others, though the easiest to supplement if needed. MPs are identified in the materials, are used to enrich the mathematics content, and have their full meaning represented. The instructional materials support the standards emphasis on mathematical reasoning by prompting students and teachers to construct and analyze viable arguments and explicitly attending to the specialized language of mathematics. Overall, the instructional materials address all aspects of rigor and meaningfully connect the CCSSM and the MPs.

*Evidence updated 10/27/15

Criterion 2a - 2d

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

The materials reviewed for Grade 8 meet expectations for rigor and balance. Each unit offers multiple opportunities for hands-on, conceptual development, skills practice for fluency, and engaging real-life situations. In addition, teachers are provided with guidance for “how and why” questions that develop conceptual understanding. Students never have to wonder when they will use the skill because they are asked to apply what they’ve learned in each lesson. There is a solid balance of the three areas of rigor, with fluency being slightly weaker than the others, though the easiest to supplement if needed.

Indicator 2a

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

The materials reviewed for Grade 8 meet the expectations for developing conceptual understanding of key mathematical concepts. 

Each unit starts with a “Looking Ahead” problem, which poses a mathematical situation that they will be learning to solve.

Looking Ahead also provides explicit scaffolding to prior knowledge.

Investigation problems frequently involve hands-on activities or models and always involve students explaining why. These problems also frequently involve error analysis. All of these help develop conceptual understanding.

Some Investigation problems can carry throughout a unit, each time adding a layer of complexity to further develop conceptual understanding.

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

The materials reviewed for Grade 8 meet the expectations for giving attention to individual standards for developing procedural skills and fluency.

Each unit provides three or four “investigations” where students are given problems to solve that will help develop skills for the Looking Ahead problem.

Indicator 2c

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

The materials reviewed for Grade 8 meet the expectations for students spending sufficient time working with engaging applications of the mathematics.

The instructional materials provide relevant, real-world problems. For example, problems frequently focus on school events for Grade 8.

There are opportunities for students to make their own assumptions or simplifications of situations.

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 reviewed for Grade 8 meet the expectations for a balance of the three aspects of rigor.

Almost every investigation provides instructional problems that develop conceptual understanding within an application context.

Overall for the grade, practice problems are about half procedural practice and half application. Some units lean more one way than the other, but they balance out.

Students are asked to complete a “Looking Back” problem that puts everything together. The problem asks students to  explain their reasoning and to reflect to summarize learning for each unit.

The weakest area is fluency. Some students will need more skills practice for some concepts than provided in order to develop fluency.

Criterion 2e - 2g.iii

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

The materials reviewed for Grade 8 meet the expectations for practice content connections. Mathematical practices are identified in the materials, are used to enrich the mathematics content, and have their full meaning represented. The instructional materials support the standards emphasis on mathematical reasoning by prompting students and teachers to construct and analyze viable arguments and explicitly attending to the specialized language of mathematics. Overall, the instructional materials meaningfully connect the CCSSM and the MPs.

Indicator 2e

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

The materials reviewed for Grade 8 meet the expectations for identifying and using MPs.

 

At the beginning of each unit, the practices are listed along with bullets to help students understand how use them. Teachers are provided with explicit connections of the most prevalent practices and which problems they match. The practices are not explicitly labeled for students on the problems, though they use them routinely.

Indicator 2f

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

The materials reviewed for Grade 8 meet the expectations for attending to the full meaning of the MPs. 

For each investigation:

Teachers are provided with a rationale of how the MPs are used in the problems.

The last thing the students reflect on is a model of a student explanation of how the MP connected to a problem and identifying what other MPs were used, then asks students to identify the MP they used in a different problem.

Indicator 2g

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

Indicator 2g.i

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

Students are constantly prompted to explain, analyze, make connections, justify. There are frequent instances of “Do you agree with their reasoning? Why or Why not?”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

Teacher Planning for every investigation includes “Orchestrating the Discussion” that prompts mathematical reasoning such as “How did you know? Did you use this in your solution? Name another. Does this work for any? Etc..”

Indicator 2g.iii

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

Vocabulary is mathematical and grade-level appropriate.

Gateway Three

Usability

Partially Meets Expectations

Criterion 3a - 3e

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

The instructional materials meet expectations for use and design to facilitate student learning. Materials are well designed and take into account effective lesson structure and pacing. The materials meet the criterion for use and design. The underlying design of the materials makes a distinction between problems and exercises. In essence, the difference is that in solving problems students learn new mathematics, whereas in working exercises students apply what they have already learned in order to build mastery. Each problem or exercise has a purpose. The design of assignments is not haphazard; exercises do seem to be given in intentional sequences. Furthermore, the design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. Additionally, in most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives. Overall, the materials reviewed for Grade 8 meet the expectations for this criterion.

Indicator 3a

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

In the teacher edition, the section before the investigation starts is divided into the following sections:

  • Launch
    • Launch Video
    • Connect Prior Knowledge
    • Present Challenge
  • Explore
    • Provide for Individual Needs
    • Planning for Summary
  • Summary
    • Orchestrate Discussion
    • Reflect on Student Learning

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

The investigations are divided into problem sets, and they typically follow a sequence. For example, Investigation 1 could be divided into the following problems set: 1.1, 1.2, and 1.3.

At the beginning of each investigation problem set, there are some explanations and definitions given. Next, there is a set of problems to be completed within the class period. 

At the end of each investigation, there is a homework section. This section is divided into Application, Connection, and Extension sections. 

There is also a mathematical reflection section at the end of each investigation where students reflect on the mathematics content they have learned. During this section, there is also a connection between the mathematical practices used throughout the investigation.

Indicator 3b

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

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

On page 12 of A Guide to Connected Mathematics, the three phases of the CMP model are explained: launching, exploring, and summarizing. 

In the first phase, the teacher launches the problem with the whole class. Launches include connecting to prior knowledge as well as presenting the challenge of the problem.  

For the Explore phase, the nature of the problem suggests whether students work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem. As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem solving strategies. 

It is during the Summarize phase that the teacher guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The Summarize phase begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions and the strategies they used to understand the problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the problem and guides them in refining their strategies into more efficient, generalizable problem-solving techniques, or algorithms.

Indicator 3c

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

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

  • Throughout various investigations and within the problem sets, students are asked to produce answers and solutions as well as to describe their answers, discuss ideas, make conjectures, explain their work and reasoning, make sketches and diagrams, justify their reasoning, and use appropriate models.
  • Sometimes only one aspect is specified, such as only requiring an answer, and other times a problem requires students to provide an answer, provide an explanation or steps, include a diagram and/or use a model.

Because problems require different responses, the type of response is intentional, like requiring models when a concept is introduced and then not requiring the same model when a more procedural method for solving similar problems is developed.

Indicator 3d

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

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

On page 40 of A Guide to Connected Mathematics, an explanation is provided for the use of manipulatives in the instructional materials. Manipulatives are used only when they can help students develop understanding of the mathematical ideas.  

For example, in Filling and Wrapping, students find all the different rectangular arrangements possible for a given number of cubes. They find the surface area of each arrangement by creating a net (covering) for the arrangement that require the least and the most material to wrap. This activity sets the stage for developing the ideas of surface area and volume of rectangular prisms. 

Most of the manipulatives used in CMP are commonly available, and many schools may already have them. Included are rulers, protractors, angle rulers, cubes, square tiles, counters, spinners, and dice.

Two manipulatives are unique to CMP:

Polystrips are plastic strips that can be pieced together with brass fasteners to form polygons. They are used in Grade 7 to investigate the relationship among the side lengths of triangles and quadrilaterals. They also are useful in the Grade 8 Geometry unit, “Butterflies, Pinwheels, and Wallpaper.”  

The CMP Shapes Set is a set of polygons used in Grade 7 to explore sides, angles, and tilings.

Indicator 3e

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

The visual design is not distracting or chaotic but supports students in engaging thoughtfully with the subject.

  • The student materials are clear and consistent between investigations within a grade level as well as across grade levels.
  • Each investigation and problem set is clearly labeled and provides consistent numbering for each investigation and problem set with both a lesson number and page number.
  • The investigations are clearly named, and the problem set examples within each investigation are labeled. The homework section includes clear labels for the Applications, Connections, and Extensions sections. 
  • At the end of each Investigation, there is a clearly labeled Mathematical Reflection section.
  • There are no distracting or extraneous pictures, or captions within lessons.

Criterion 3f - 3l

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

Teacher Planning and Learning for Success with CCSSM: Materials support teacher learning and understanding of the standards. The materials reviewed meet the criterion for teacher planning and learning. The materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Materials contain a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition. The strongest point is that each module begins with an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Overall, the material reviewed for the Grade 8 meets the expectations for this criterion.

Indicator 3f

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

Materials support teachers in planning and providing effective learning experiences through teacher questioning. This is a strength of the program with multiple questions for each lesson/problem throughout all of the Grade 8 units. 

  • Lesson sections that include questions are Launch, Presenting the Challenge, Explore and Summarize.
  • Additionally, teachers are prompted to reflect on student learning after the lesson in order to prepare for the next daily lesson or unit.

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The teacher’s edition has many suggestions on presenting the content to students. 

  • The Launch section and Connecting to Prior Knowledge are the two beginning sections of each lesson.
  • The purple book contains ideas for technology implementation for student learning.

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.
2/2
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Indicator Rating Details

The teacher’s edition is an excellent resource for mathematics teachers to understand the mathematics of the unit and for teachers to expand their understanding of the mathematical concepts.

  • Mathematical background is included at the beginning of each unit. In the It’s in the System book, there are 13 pages of mathematical background for teachers to understand.

It’s in the System includes problems, explanations of problems, examples, and connections to CCSSM. 

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.
2/2
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Indicator Rating Details

The teacher’s edition clearly explains the role of specific grade-level mathematics in the context of the overall mathematics for grades 6-12.

  • Standards are aligned in Grades 6-12 (curriculum is only written for these grade levels--K-5 is not an option)
  • Teacher’s editions connect the learning from previous grade levels and explain how standards build on one another throughout the program.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The teacher’s edition contains a detailed planning chart of each Problem and estimated pacing of the problems as well as assessment and mathematical reflections. 

  • The standards are aligned for each investigation throughout the book.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The materials do contain strategies for informing parents or caregivers about the mathematics program and give suggestions for how they can help support student progress and achievement.

A parent letter is available for each of the 23 units in A Guide to Connected Mathematics. These letters provide valuable information about how parents can be helpful to their children in learning mathematics. The letters can be personalized to include teacher name and contact information. The letters can be sent home with students or can be sent electronically

Indicator 3l

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

The materials do contain explanations of the program's instructional approaches and identify the research-based strategies within the teaching materials.

A list on page 7 of A Guide to Connected Mathematics provides CMP’s guiding principles. Page 8 provides a rationale for a problem-centered curriculum. On page 10, a rationale is provided for depth versus spiraling. On pages 16–19, a theory and research rationale is provided for the following topics: cooperative learning and classroom discourse, teaching through problem solving, equity and motivation for learning, conceptual and procedural knowledge, formative assessment, mathematical knowledge for teaching, and teacher development and school change.

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
9/10
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Criterion Rating Details

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

The materials reviewed partially meet expectations for the criterion of assessment in Grade 8. The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Materials only sometimes provide strategies for teachers to identify and address common student errors and misconceptions. Reflections and problem sets - which could be used as formative assessment tasks - are not aligned to a specific standard or group of standards. The materials provide opportunities for ongoing review and practice. The materials offer formative and summative assessments, such as Notebook, Mathematical Reflection, Looking Back, Check Up, Partner Quiz, Unit Test, Self-Assessment, Project, and Group Work/Discussion. The materials do encourage students to monitor their own progress.

Overall, the materials reviewed for the Grade 8 partially meet the expectations for the assessment criterion.

Indicator 3m

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

In the first phase of each lesson, the teacher launches the problem with the whole class.  Launches include connecting to prior knowledge. 

Indicator 3n

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

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

  • In the Teacher Planning section, there were occasionally “Notes” about potential student errors.

They present situations and ask students to identify mistakes or provide rationale based on common misconceptions.

Indicator 3o

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

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

  • The materials provide several opportunities for ongoing review and practice, such as Notebook, Mathematical Reflection, Looking Back, Check Up, Partner Quiz, Unit Test, Self-Assessment, Project, and Group Work/Discussion.
  • Within a unit the set of practice problems includes Application, Connection, and Extension to promote both increased understanding of a concept as well as developing procedural skill/fluency.
  • Beyond a lesson, future lessons/units typically expand practice and depth of previous learning.

Teacher Planning offers a multitude of prompts to orchestrate discussion.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Assessments clearly denote which standards are being emphasized.

  • Each standard is aligned to one or more lessons as noted at the beginning of each topic.
  • The Check up and Unit Test appear to be developed to fully assess a particular standard and the scoring guidelines specify which item aligns to which standard.
  • However, reflections and problem sets—which could be used as formative assessment tasks—are not aligned to a specific standard or group of standards.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details
  • Formative assessments include scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.
  • Each Check up and Unit Test includes a scoring guideline as well as worked out solutions for correct responses but do not include suggestions for follow-up for below or above grade level students.
  • Although the rubric and scoring guidelines are complete, there are no strategies or suggestions for follow-up provided for the teachers.

Indicator 3q

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

The materials do encourage students to monitor their own progress. On page 57 the approach to self-assessment is explained. After every unit, students complete a self-assessment summarizing the mathematics they learned in the unit and the ideas with which they are still struggling. The self-assessment also asks students to provide examples of what they did in class to add to the learning of the mathematics. The goal of this activity is to have students reflect on their learning.

An explanation of the Mathematical Reflections questions is provided on page 83 of A Guide to Connected Mathematics. These questions provide an opportunity for the teacher and students to discuss the goals of the Investigation. After the class discussion, which can take place orally or in written form, students record their responses to the Mathematical Reflection questions to have a record of their current understandings.

Using the Mathematical Practices Reflections at the close of each Investigation allows students to name what they have done. Students demonstrate to themselves the power of the Practices.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
5/12
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Criterion Rating Details

The materials reviewed for Grade 8 do not meet expectations for the criterion for differentiated instruction. Materials sometimes provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content. There is little provided that would help struggling or ELL students access the content successfully. Although there are occasionally challenge problems, there are minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons. What is provided is not enough to guarantee that all students have content that is accessible. Overall, the materials do not meet the criterion for differentiated instruction.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
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Indicator Rating Details

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

  • Sequencing and scaffolding are embedded into lesson development, but materials provide few strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
  • In Teacher Planning pages, there is always a section called “Orchestrating Discussion” which offers suggestions of questions at varying levels to help students understand the content.
  • There is no evidence of an explanation of how the lessons develop.

There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
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Indicator Rating Details

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

  • The materials provide very general strategies to help teachers make the content accessible to a range of learners.
  • There are some questioning prompts in the Teacher Planning section under “Provide for Individual Needs.” However, they do not seem geared toward a struggling learner but are simply good discussion points for all students.
  • Occasionally, “Provide for Individual Needs” includes “Going Further” which offers approximately 100 challenge problems.
  • The homework problems always offer “Extensions.”
  • There is a concern that the suggestions provided are not enough to guarantee that all students have content that is accessible.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
1/2
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Indicator Rating Details

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

  • A variety of solution strategies are not always encouraged.
  • Students are given opportunities to create solution paths on their own.
  • Most tasks do not allow students to use multiple entry points; they start at the same place.
  • Students do have the opportunity to solve problems using a variety of strategies, paths and/or models, though the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.

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
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Indicator Rating Details

Materials provide little support, accommodations, or modifications for English language learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

  • This series is clearly designed with best practices for all students in mind; however, there is nothing explicitly differentiated or modified for struggling or ELL students, other than translating assessments into Spanish.
  • What is provided is not enough to guarantee that all students have content that is accessible.

Indicator 3v

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

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

  • Occasionally there are challenge problems.
  • There were minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.

Indicator 3w

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

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

Indicator 3x

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

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

  • Investigations are intended for cooperative learning groups, though there are no recommendations for forming groups or any mention of why to have a student work within a certain group size.
  • Within the lessons, there are no group roles, no group expectations, etc., to help teachers enhance the involvement of every student.

Indicator 3y

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

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

  • There is no evidence of teachers needing to draw upon home language and culture to facilitate learning.

Criterion 3aa - 3z

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

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

Indicator 3aa

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

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are platform neutral (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices:  Accessibility was tested on Chrome, Firefox, Safari, an iPhone, and an iPad. All access was successful.

Indicator 3ab

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

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology: There are multiple “Student Activities” in both Student Place and Teacher Place online that could easily be used as opportunities for assessment such as the Integer Product Game, Paper Pool, and the Transformation Tool. In addition, MathXL was developed to provide online readiness tests and skills assessments at the end of units as well as additional skills practice. There is also a test generator disk.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

Materials can be easily customized for individual learners.

  1. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations: Math XL can be used to assign students practice in areas not yet mastered.
  1. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic: There is a test generator disk that is customizable. However, there are no digital lessons that can be adapted.

Indicator 3ad

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

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.): There is no evidence of this component.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the MP: There is an extensive list of Digital Math Tools available in both Student Place and Teacher Place online including tools such as 3D Geometry, Algebra Tiles, Fraction Shapes, and Pattern Blocks. In addition, within the text, there are prompts to the student to go online to watch a video that demonstrates a point or application. And teachers have a disk that includes a Launch Video for each lesson.

Additional Publication Details

Report Published Date: Fri Feb 13 00:00:00 UTC 2015

Report Edition: 2014

Title ISBN Edition Publisher Year
null 9780133280876 null null null
null 9780133296761 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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