# Standards

CMP 1 was based on the 1989 NCTM Curriculum and Evaluation Standards for School Mathematics. CMP 2 was based on a 2000 revision of these NCTM Standards, Principles and Standards for School Mathematics. The NCTM Standards emphasized understanding of important mathematical ideas and skills with a focus on problem solving, reasoning and proof, communication, connections, and representations.

## CMP and the Common Core Standards for Mathematical Content

The widespread adoption of the Common Core Standards for Mathematics called for thoughtful examination of the relationship of the Standards for Mathematical Content to CMP. This examination was central in guiding the authors in the development and placement of the mathematics in CMP3 in a way that aligns with the content standards while staying true to the CMP philosophy. As a result, CMP3 incorporates all of the Standards for Mathematical Content, as well as the Standards for Mathematical Practice. The details of the relationship of CMP3 content to the Mathematical Content standards are in Units & CCSS and CCSS & Units. At a broader level, visit Changes: CMP2 to CMP3 which summarizes the changes in content from CMP2 to CMP3.

## CMP and the Common Core Standards for Mathematical Practice

The Common Core Standards for Mathematical Practice were already embedded in the CMP curriculum. They come alive in the CMP classroom as students and teachers interact around a sequence of rich tasks to discuss, conjecture, validate, generalize, extend, connect, and communicate. As a result, students develop deep understanding of concepts and the inclination and ability to reason and make sense of new situations.

The heart and soul of the Mathematical Practices have been the foundation of the CMP classroom from its beginning, especially the practice “make sense of problems and persevere in solving them.” In CMP, one additional practice has been critical in helping students develop new and deeper understandings and strategies. New knowledge is developed by connecting and building on prior knowledge. In the process, understanding of prior knowledge is extended and deepened.

# Our additional practice

Build on and connect to prior knowledge in order to build deeper understandings and new insights.

Students use many of the Mathematical Practices each day in class. To enhance students’ meta-cognition of the role of the Mathematical Practices in developing their understanding and reasoning, examples of student reasoning that reflect several of the Mathematical Practices are given at the end of each Investigation in the Student Edition. The teacher support offers additional examples of student reasoning. Below is an explanation of how CMP addresses mathematical practices throughout the student editions.

## Make sense of problems and persevere in solving them

This mathematical practice comes alive in the Connected Mathematics classroom as students and teachers interact around a sequence of rich problems, to conjecture, validate, generalize, extend, connect, and communicate.

## Reason abstractly and quantitatively

As students observe, experiment with, analyze, induce, deduce, extend, generalize, relate and manipulate information from problems, they develop the disposition to inquire, investigate, conjecture and communicate with others around mathematical ideas.

## Construct viable arguments and critique the reasoning of others

The student and teacher materials support a pedagogy that focuses on explaining thinking and understanding the reasoning of others.

## Model with mathematics

The student materials provide opportunities to construct, make inferences from, and interpret concrete, symbolic, graphic, verbal, and algorithmic models of quantitative, statistical, probabilistic and algebraic relationships.

## Use appropriate tools strategically

Problem settings encourage the selection and intelligent use of calculators, computers, drawing and measuring tools, and physical models to measure attributes, and represent, simulate and manipulate relationships.

## Attend to precision

Students are encouraged to decide whether an estimate or an exact answer for a calculation is called for, to compare estimates to computed answers, and to choose an appropriate measure or scale depending on the degree of accuracy needed.

## Look for and make use of structure

Problems are deliberately designed and sequenced to prompt students to look for interrelated ideas, and take advantage of patterns that show how data points, numbers, shapes or algebraic expressions are related to each other.

## Look for and express regularity in repeated reasoning

Students are encouraged to observe and explain patterns in computations or symbolic reasoning that lead to further insights and fluency with efficient algorithms.