Development of the Math Strands
The “Connected” in Connected Mathematics has several meanings. First, there are contexts that connect to the world in which students live. Second, there are mathematical ideas that serve as unifying themes to connect Units and strands together. Lastly, goals are developed in symbiotic tandem with each other, and over Units and grade levels. The result is a coherent whole.
Within each CMP Unit, the Problems are carefully sequenced to address important goals. This might imply that the goals are a discrete, linear sequence, but goals are often developed in parallel, as well as in sequence.
Example
While exploring relationships among variables in Variables and Patterns, students are simultaneously beginning to develop strategies for solving equations, two prominent goals for CMP’s Algebra and Functions strand.
Likewise, organizing Units by mathematical strands does not imply that all the goals for each Unit are related to the same strand. A Unit might be listed in the one strand but also carry key mathematical goals for another strand. For example, Looking For Pythagoras, while primarily about the Pythagorean Theorem, also carries forward the development of the Number and Operations strand by introducing students to irrational numbers and the set of real numbers. The Pythagorean Theorem also leads naturally to the equation of a circle and other important ideas.
Not only does goal development transcend the boundaries of a strand, but some mathematical ideas are so powerful that they permeate several strands and serve as unifying themes. Two of these overarching themes are proportional reasoning and mathematical modeling.
This section provides an overview to the development of the four mathematical strands, Number, Operations, Rates, and Ratio, Geometry and Measurement, Data and Probability, and Algebra and Functions and two of the unifying themes.
As you study the goals, the development of the mathematics in each strand, and in the collection of Units that comprise each grade-level course, it will be helpful to ask:
- What are the big ideas of the strand and key objectives of each Unit in the strand?
- How are the key concepts of the strand developed in depth and complexity over time?
- What connections are made between the Units of this strand and those of other strands which are interpreted in the sequence of Units?
- How are the unifying themes reflected in the strands? Units?