Introduction to�Connected Mathematics3 (CMP)

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Connected Mathematics – A Complete Middle School Curriculum

• The overarching goal of CMP is to help students and teachers develop mathematical knowledge, understanding, and skill along with an awareness of and appreciation for the rich connections among mathematical strands and between mathematics and other disciplines. The CMP curriculum development has been guided by our single mathematical standard:

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• Mathematical ideas are embedded in a carefully sequenced set of tasks to allow students to develop deep mathematical understandings and meaningful skills.

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• Problems embed the Common Core State Standards for Mathematics (CCSSM) and the Standards for Mathematical Practice.

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• CMP helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among representations for fluency in both conceptual and procedural knowledge.

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Overarching Goal of Connected Mathematics

• Help students and teachers develop
• mathematical knowledge, understanding, and skill
• an awareness of and appreciation for the rich connections among mathematical strands and between mathematics and other disciplines.
• Curriculum development has been guided by our single mathematical standard:

All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency.

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Guiding Principles 

• CMP is problem-centered. Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the Problems in an Investigation.
• CMP identifies big ideas and goes for depth. Ideas are explored through these mathematical tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
• CMP has coherence. The underlying concepts, skills, or procedures supporting the development of a key idea are identified and included in an appropriate development sequence. The curriculum builds and connects from Problem to Problem, Investigation to Investigation, Unit to Unit and grade to grade.
• CMP intertwines conceptual and procedural knowledge. The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations to produce fluency in both conceptual and procedural knowledge.

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Guiding Principles, continued

• CMP develops skills and concepts as needed. Concepts and skills are developed, as appropriate, to solve interesting and challenging problems.
• CMP promotes inquiry-based instruction. Classroom instruction focuses on inquiry and investigation of mathematical ideas embedded in rich problem situations through rich classroom discourse and collaborations.
• CMP promotes effective use of technology. The curriculum reflects the information-processing and delivery capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem solving to new tasks.
• CMP has high expectations of all students. All students are asked sophisticated mathematical questions and are expected to persevere in their explorations to these questions, looking for patterns, generalizing, validating, and sharing and critiquing each other’s work.

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Criteria for Mathematical Tasks

To be effective, problems must embody critical concepts and skills and have the potential to engage students in making sense of mathematics. And, since students build understanding by reflecting, connecting, and communicating, the problems need to encourage them to use these processes.

Each CMP Problem has some or all of the following characteristics:

• Embeds important, useful mathematics
• Promotes conceptual and procedural knowledge
• Builds on and connects to other important mathematical ideas
• Requires higher-level thinking, reasoning, and problem solving
• Provides multiple access points for students
• Engages students and promotes classroom discourse
• Allows for various solution strategies
• Creates an opportunity for teacher to assess student learning

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College of Natural Science

Goals for Student Engagement

Students develop deep understanding of mathematical concepts, skills, and procedures by solving problems. In the process, they:

• Observe patterns and relationships in a situation:
• Conjecture, test, discuss, verbalize, and generalize;
• Discover salient mathematical features of patterns and relationships and abstract the underlying mathematical concepts, processes, and relationships;
• Develop a mathematical language for representing and communicating ideas; and
• Make sense of and connect mathematics abstracted from their experiences.

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College of Natural Science

The Three Phases of the CMP Instructional Model

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College of Natural Science

CMP Assessment Dimensions

https://connectedmath.msu.edu/components/assessment/

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CMP Teacher Support

• The teacher support for each Unit includes a discussion of the mathematics underlying the Investigations, mathematical and problem-solving goals for each Investigation, planning charts, standards correlations, connections to other Units, in-depth teaching notes, answers, labsheets, teaching aids, parent letters, and an extensive assessment package.
• The teacher support engages teachers in a conversation about what is possible in the classroom around a particular lesson. Suggestions are made about how to engage the students in the mathematics task in the launch, how to promote student thinking and reasoning during the exploration of the Problem, and how to summarize with the students the important mathematics embedded in the Problem. Support for this Launch–Explore–Summarize sequence occurs for each Problem in the curriculum.

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Mathematical Units by Grade

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Grade 6

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Grade 7

Grade 7

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Grade 7

Grade 8

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Grade 7

Grade 8/Algebra

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Grade 8 and Algebra 1 - Two Paths

Appendix A of the Common Core State Standards for Mathematics (CCSSM) and the PARCC Model Content Framework for Mathematics both suggest required standards that an Algebra I course would comprise. Connected Mathematics 3 (CMP3) is aligned with both sets of recommendations and is also a good fit for Algebra 1 courses designed by local school districts. Therefore, CMP3 students completing all 23 units in Grades 6, 7, and 8 will be prepared to take college-level courses, including calculus, by their senior year of high school.

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More About CMP

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College of Natural Science

Research Overview Available

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https://connectedmath.msu.edu/research/connected-mathematics-a-research-overview/

College of Natural Science

CMP Observation Guide Available

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The intent of the Guide is to inspire rich conversations among teachers, mentors, coaches, and administrators around the teaching and learning of mathematics in a productive classroom environment. 

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The guide may help provide a vision of a CMP classroom.

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https://connectedmath.msu.edu/teacher-support/support-for-teaching/cmp-classroom-observation-guide-working-together-to-support-teacher-and-student-learning/

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College of Natural Science

Classroom Videos

These videos were created to provide classroom teachers a vision of how the curriculum might play out in the classroom and to stimulate their curiosity about promising classroom practices that engage students in rich and deep mathematical conversations.

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https://connectedmath.msu.edu/video/

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College of Natural Science

Strengths of Connected Mathematics

• Is organized around important mathematical ideas and processes.
• Is a problem-centered curriculum that uses an inquiry-based instructional model.
• Develops deep understanding of key mathematical ideas, reasoning, and skills.
• Substantially raises the level of mathematical thinking and reasoning of students.
• Has high expectations of all students.
• Promotes long-term retention of mathematical concepts, processes, and skills.

• Connects mathematical ideas within a unit, across units, and across grade levels.
• Provides homework that emphasizes practice with skills and problems solving.
• Incorporates technology throughout the curriculum.
• Offers multidimensional assessment tasks.
• Provides extensive support for teachers.
• Is based on 3 decades of experience and research.

CMP is a complete mathematics curriculum for grades 6–8, Connected Mathematics, it:

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https://connectedmath.msu.edu/

College of Natural Science