Alignment to College and Career Ready Standards: Overall Summary

The materials reviewed for Grade 7 do not meet the expectations for alignment to the CCSSM in the areas of focus and coherence. The materials do not devote the majority of class time to the major work for Grade 7. The materials are coherent but not consistent with the standards for Grade 7. There are some Grade 8 standards taught and assessed at Grade 7, but the omission of these assessment items would not significantly impact the structure of the materials. There are explicit connections between major clusters. The supporting work is used to enhance the major clusters.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
0
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

Does Not Meet Expectations

+
-
Gateway One Details

The materials reviewed for Grade 7 do not meet the expectations for Gateway 1. The materials do not devote the majority of class time to the major work for Grade 7. The materials are coherent but not consistent with the standards for Grade 7. There are some Grade 8 standards taught and assessed at Grade 7, but the omission of these assessment items would not significantly impact the structure of the materials. There are explicit connections between major clusters. The supporting work is used to enhance the major clusters. Since the materials reviewed for Grade 7 do not meet the expectations for alignment to the CCSSM in the areas of focus and coherence, they were not reviewed for rigor and the MP.

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 materials reviewed for Grade 7 meet the expectations assessing material at the Grade 7 level. There are eight questions throughout the units that assess topics that are in future grades and should be omitted.

The majority of the concepts assessed in the Grade 7 units were on the standards for Grade 7. There were a few assessment items that were topics in future grades. There are questions on four unit tests that are testing CCSSM from grades above Grade 7. On the Shapes and Designs unit test, question 6 is on angles and transversals, which is the Grade 8 standard 8.G.A.5. On the Stretching and Shrinking unit test, question 7 is the Grade 8 standard on similarity (8.G.A.4). Question 6, Moving Straight Ahead unit test, is on systems, which is the Grade 8 standard 8.EE.C.8. On the Filling and Wrapping unit test, questions 8 and 9 are on volume and surface area of cones and cylinders, which is the Grade 8 standard 8.G.C.9.

Skipping these assessment problems does not compromise the integrity of the Grade 7 grade standards. The major work of Grade 7 is still assessed appropriately.

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 materials reviewed for Grade 7 meet the expectations for assessing material at the grade level with the following exceptions - there are assessment questions throughout the year that would need to be skipped:

  • On the Shapes and Designs unit test, question 6 is on interior/exterior angles and transversals which are the Grade 8 standard 8.G.A.5. In the initial review, question 6 was also identified as a concern; however, given that vertical and adjacent angles are formed from transversals, it is a reasonable connection. Teachers can skip Investigation 2, which is the one connected to the Grade 8 concept.
  • On the Stretching and Shrinking unit test, question 7 is the Grade 8 standard 8.G.A.4 on similarity. In the initial review, questions 5 and 6 were also identified as a concern; however, they could be reasonable connections to grade-level work, especially if question 6 is solved with scale factor. Teachers can skip Investigation 4, which is the one connected to the Grade 8 concept.
  • On the Moving Straight Ahead unit test, question 6 is on systems, which is the Grade 8 standard 8.EE.C.8.       This entire unit should be moved to Grade 8 with the exception of Investigation 3 which does cover major work of Grade 7.
  • On the Filling and Wrapping unit test, questions 8 and 9 are on volume and surface area of cones and cylinders, which is the Grade 8 standard 8.G.C.9. Teachers can skip Investigation 4, which is the one connected to the Grade 8 concept.

Skipping these assessment problems does not compromise the integrity of the Grade 7 standards. The major work of Grade 7 could still be 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.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 7 do not meet the expectations for spending the majority of class time on the major clusters for Grade 7. Grade 7 has less than 50% of the work on the major clusters of 7.RP.A, 7.NS.A, 7.EE.A and 7.EE.B. Out of the 8 units for Grade 7, the only two units focused on this work were Accentuate the Negative and Comparing and Scaling. The unit Moving Straight Ahead has the majority of the work on linear relationships that is Grade 8 CCSSM. The unit What Do You Expect is work on the additional cluster of 7.SP.C and this unit is more than twice as long as the unit Comparing and Scaling which is a unit on the major work of 7.RP.A. The unit Filling and Wrapping has work with volume and surface area of cylinders and cones, which are Grade 8 CCSSM.

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 spending the majority of class time on the major cluster for Grade 7.

  • Grade 7 has less than 50% of the work on the major clusters of 7.RP.A, 7.NS.A, 7.EE.A and 7.EE.B.
  • Out of the 8 units for Grade 7, the only two units focused on this work were Accentuate the Negative and Comparing and Scaling.
  • The unit Moving Straight Ahead has the majority of its work on linear relationships that is Grade 8 CCSSM.
  • The unit What Do You Expect is work on the additional cluster of 7.SP.C and this unit is more than twice as long as the unit Comparing and Scaling which is a unit on the major work of 7.RP.A.
  • The unit Filling and Wrapping has work with volume and surface area of cylinders and cones, which are Grade 8 CCSSM.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
5/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 7 partially meet the expectations for coherence. There are areas where the materials have strong connections and areas that could be stronger. The Grade 7 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 edition 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 CCSS. 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 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 What Do You Expect, Samples and Populations and Stretching and Shrinking there are problems that use supporting work to enhance 7.RP.A.
  • In all the units, there is evidence of the supporting work enhancing 7.NS.A.
  • Much of the work in Grade 7 is geometry-based and tied to similarity which is a Grade 8 standard.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 partially meet the expectations for being able to be taught in one school year.

  • The Grade 7 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.
  • While overall it is viable for a school year, the amount of time on the major work for Grade 7 is less than 65% of the year (as reflected in the rating for 1b), which means that teachers will need to find supplemental materials to cover the standards.

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 materials reviewed for the Grade 7 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 is found in several units (e.g., Let's Be Rational, Variables and Patterns) using informal methods of solving.
  • Grade 7: Solve real-life 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 to 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:

  • In Prime Time, work with 6.NS.B.4 begins with finding 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 LCM 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, which is 7.NS.A.
  • Comparing Bits and Pieces begins developing the ideas of positive and negative numbers on a number line and absolute value which is 6.NS.C. This leads to 7.NS.A in Accentuate the Negative with operations on rational numbers. This also leads into 8.NS.A on approximating rational numbers (although not the 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 students launch the problem and summarize 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 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 refers to work in unit rates in prior Grade 6 unit Comparing Bits and Pieces.
  • Accentuate the Negative in Grade 7: Problem 4.2, refers to 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, 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
+
-
Indicator Rating Details

The materials reviewed for Grade 7 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 Accentuate the Negative where two of the highlights are to understand the relationship between a number and its opposite and to develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers.

There are many links between major clusters in this curriculum.

  • In Comparing and Scaling investigation 1, students are asked to recognize and represent proportional relationships between quantities (7.RP.A) and use variables to represent quantities in a real work or a mathematical problem and construct simple equations (7.EE.B).
  • In Accentuate the Negative investigation 2, students are asked to understand subtraction of rational numbers as adding the additive inverse (7.NS.A) and solve multi-step real-world and mathematical problems posed with positive and negative rational numbers (7.EE.B)
  • In Moving Straight Ahead investigation 3, students are asked to explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation (7.RP.A) and understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related (7.EE.A).
  • 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

Not Rated

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.
0/8

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.
0/2

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
0/2

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
0/2

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
0/2

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
0/10

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
0/2

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2

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.
0/2

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2

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: Fri Feb 13 00:00:00 UTC 2015

Report Edition: 2014

Title ISBN Edition Publisher Year
null 9780133280869 null null null
null 9780133296754 null null null

About Publishers Responses

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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.

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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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