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Connected Mathematics Project 3
2014

Connected Mathematics Project 3

Publisher
Savvas Learning Company f/k/a Pearson
Subject
Math
Grades
6-8
Report Release
02/13/2015
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
Does Not Meet Expectations
Our Review Process

Learn more about EdReports’ educator-led review process

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Note on review tool version

See the top of the page to confirm the review tool version used for this report:

Report for 6th Grade

Alignment Summary

The instructional materials reviewed for Grade 6 do not meet the expectations for alignment to the CCSSM. The materials do not devote the majority of class time to the major work for Grade 6. 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 minor assessment items that go beyond the Grade 6 standards, which could be skipped without impacting the integrity of the materials.

6th Grade
Gateway 2

Rigor & Mathematical Practices

NE = Not Eligible. Product did not meet the threshold for review.
NE
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Usability (Gateway 3)
Not Rated
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 6 do not meet the requirements for Gateway 1. The materials do not devote the majority of class time to the major work for Grade 6. 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 minor assessment items that go beyond the Grade 6 standards, which could be skipped without impacting the integrity of the standards. Since the instructional materials reviewed for Grade 6 do not meet the requirements for alignment to the CCSSM in the areas of focus and coherence, they were not reviewed for rigor and the MPs.

Criterion 1.1: Focus

02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 6 meet the expectations for assessing material at the Grade 6 level with one “non-structural” exception described below.

The majority of the concepts assessed in the Grade 6 units met the standards for Grade 6. However, there were a few assessment items on one test that are testing standards above grade level. On the Decimal Ops unit test, questions 3–5 assess application of percent (7.RP.A.3), which could be skipped without impacting the integrity of the grade level standards.

Indicator 1A
02/02
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.

The instructional materials reviewed for Grade 6 meet the expectations for assessing material at the grade level with one “non-structural” exception - the materials assess topics that are in future grades for “using percents.”

  • On the Variables and Patterns unit test, question 6 uses “function,” which is a Grade 8 standard. However, the problem can be solved in ways appropriate to Grade 6 standard 6.EE.C.9.
  • On the Decimal Ops unit test, questions 3–5 are on application of percents, which is a Grade 7 standard 7.RP.A.3. The Grade 6 standard, 6.RP.A.3.C, is the actual skill of calculating percent. However, application is mathematically reasonable, the unit is in the last half of the year, and removing the questions and lesson would not impact the integrity of the grade level standards. It only involves one section of the unit, investigation 4: using percents, which could simply be skipped or not assessed.

*Evidence updated 10/27/15

Criterion 1.2: Coherence

00/04
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.

The instructional materials reviewed for Grade 6 do not meet the expectations for spending the majority of class time on the major cluster for Grade 6. Grade 6 contained approximately 50% of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 6.EE.C.

Indicator 1B
00/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 6 do not meet the expectations for spending the majority of class time on the major cluster for Grade 6. The instructional materials reviewed for Grade 6 had only approximately 50% of the work on the major clusters for 6.RP.A, 6.NS.A, 6.NS.C, 6.EE.A, 6.EE.B and 6.EE.C.

  • The units Prime Time, Comparing Bits and Pieces, Decimal Operations and Variables and Patterns have lessons that specifically address this major work.
  • There are also lessons in many units that are supporting cluster concepts but they are used to enhance the major work.
  • Two examples of this are in Prime Time where 6.NS.B is found throughout investigations 2-4 but it is used to enhance the work with 6.RP.A.
  • In Covering and Surrounding in investigation 3, 6.G.A is used to enhance the understanding of 6.NS.C.

Criterion 1.3: Coherence

05/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 6 partially meet the expectations for coherence. There are areas where the materials have strong connections and areas that could be stronger. The Grade 6 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
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 6 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 Comparing Bits and Pieces there are problems in investigations 1 and 2 that use supporting work of fractions operations to enhance the major work 6.NS.C and 6.RP.A.
  • In Prime Time, Covering and Surrounding and Decimal Ops, there is work with equations while working on area, and greatest common factor and lowest common multiple decimal operations that supports the major work of 6.EE.A.
  • There are lessons asking students to determine equivalence between fractions, decimals and percents that is not part of Grade 6 work. This section was not completed alongside 6.RP.A or 6.NS.C, which would have enhanced the major work.
  • In Prime Time there was a heavy emphasis on greatest common factor and lowest common multiple that was not connected to more work with integers for 6.NS.C.
  • There are problems in Data About Us that could have tied into integers and enhance the major work of 6.NS.C
Indicator 1D
01/02
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 6 partially meet the expectations for being able to be taught in one school year.

  • The Grade 6 materials could be completed within the timeline of 180 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 6 is less than 65% of the year, which means that teachers would need to find supplemental materials in order to effectively cover the standards.
Indicator 1E
01/02
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.

The materials reviewed for Grade 6 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 -- found in several units (e.g., Let's Be Rational, Variables & Patterns) using informal methods of solving.
  • Grade 7: Solve real-life and mathematical problems using numerical and algebraic expressions and equations-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-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, 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 Grades 6 and 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, 7.NS.A, 8.NS.A):

  • 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 begins the work with 6.NS.B.4 in Prime Time.
  • 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 operations on rational numbers in Accentuate the Negative (7.NS.A). This also leads into 8.NS.A on approximating rational numbers.
  • 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 experience the problem launch and summary in the same way and that the differentiation comes during the explore phase of the problem.
  • There are 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 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."
  • Looking for Pythagoras in Grade 8: Problem 4.2, refers to earlier work with rational numbers.
  • It's in the System in Grade 8: Problem 2.1 refers to the previous Grade 8 unit Say it With Symbols and the Grade 7 unit Moving Straight Ahead that work with solving equations.
  • Thinking with Mathematical Models in Grade 8: Problem 1.1 refers to several previous units in Connected Mathematics 3 using tables, graphs and equations to explore variables.
  • Butterflies, Pinwheels Wallpaper in Grade 8: Problem 4.1 refers to previous work in the Grade 7 unit Stretching and Shrinking with enlargements and reductions.
Indicator 1F
02/02
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.

The materials reviewed for Grade 6 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 Prime Time, where the mathematical highlights state "...Develop strategies for finding factors and multiples, least common multiples and greatest common factors; and use exponential notation to write repeated factors." This follows one strand, Expressions and Equations, which says to use properties of operations to generate equivalent expressions. (6.EE.A.3-4, 7.EE.A, 8.EE.A.1)
  • Prime Time: Equivalent Expressions: Understand why two expressions are equivalent.
  • Comparing Bits and Pieces: Equivalence: Understand equivalence of fractions and ratios. Use equivalence to solve problems.
  • Another example is in Comparing Bits and Pieces: Ratios, Rational Numbers Equivalence. This unit refers to relationships that exist between ratios, ratio reasoning proportions and using them in real-world problems while working on fraction and decimal operations (6.RP.A).

There are many links between major clusters in this curriculum.

  • In Variables and Patterns students solve unit rate problems including those involving unit pricing and constant speed (6.RP.A) and use variables to represent two quantities in a real-world problem that change in relationship to one another (6.EE.C).
  • In Let's be Rational students apply and extend previous understanding of multiplication and division to divide fractions by fractions (6.NS.A), and identify parts of an expression using mathematical terms (6.EE.A).
  • In Decimal Ops students interpret and compute quotients of fractions solve word problems involving division of fractions by fractions (6.NS.A) and solve real world and mathematical problems by writing and solving equations in the form p+x=q and px=q (6.EE.B).
  • Comparing Bits and Pieces connects 6.NS.C with 6.RP.A.
  • Decimal Ops connects multiplying and dividing decimals with 6.RP.A, 6.EE.A and 6.EE.B.
  • Data About Us uses data to compute with numbers, measure and graph data connects 6.SP.A, 6.SP.B and 6.RP.A.
  • Variables and Patterns analyzes relationships among variables 6.EE.A, 6.EE.B, 6.EE.C and 6.RP.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.
Overview of Gateway 2

Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2.1: Rigor

NE = Not Eligible. Product did not meet the threshold for review.
NE
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.
Indicator 2A
00/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Indicator 2B
00/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
Indicator 2C
00/02
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
Indicator 2D
00/02
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.

Criterion 2.2: Math Practices

NE = Not Eligible. Product did not meet the threshold for review.
NE
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
Indicator 2E
00/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
Indicator 2F
00/02
Materials carefully attend to the full meaning of each practice standard
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
00/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
Indicator 2G.ii
00/02
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.
Indicator 2G.iii
00/02
Materials explicitly attend to the specialized language of mathematics.

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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.
Indicator 3H
00/02
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.
Indicator 3I
00/02
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.
Indicator 3J
Read
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).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
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.
Indicator 3AD
Read
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.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.