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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 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
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
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.
Gateway 1
v1.0
Criterion 1.1: Focus
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
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
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
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
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
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
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
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
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.