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Report Overview
Summary of Alignment & Usability: Connected Mathematics Project 3 | Math
Math 6-8
The instructional materials reviewed for Grade 6–8 do not meet the requirements for alignment to the Common Core State Standards. The materials do not consistently devote the majority of class time to the major work for Grade 6. The materials are not always coherent and consistent with the CCSSM. The materials have some assessment items that go beyond the grade level standards in all three grades. Since the instructional materials reviewed for Grade 6–8 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 mathematical practices.
6th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 7th Grade
Alignment 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.
7th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
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.
Gateway 1
v1.0
Criterion 1.1: Focus
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 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 1.2: Coherence
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
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 1.3: Coherence
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
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 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
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
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.