Math
Chris Johnson and Paul Carroll
The Connected Mathematics Program (CMP2) used by the sixth and seventh grades and the College Preparatory Mathematics (CPM) algebra I curriculum used by the eighth grade are rich with areas inviting additional insights and open to diverse methods of problem-solving, creating an open-ended structure that is more permissive of individual differences. While much of the content of these programs is parallel to that of standard middle school textbooks, how students learn and the role of the teacher in their learning may be significantly different.
Our mathematics courses support a philosophy of teaching and learning in which the teacher is a facilitator of learning rather than a dispenser of knowledge, and the students are active participants in constructing and explaining mathematics. Activities promote mathematical reasoning, problem-solving, and communication skills. Students work in small and large groups as well as individually to explore concepts, make conjectures, and form generalizations. They learn to respect and value other opinions as they create and eagerly present a variety of approaches and solutions to problems. In so doing, students have an opportunity to experience mathematics in meaningful and challenging ways while obtaining a solid conceptual basis for further study in mathematics.
Read more»The CMP series in both sixth and seventh grade consists of several units, each developing a major mathematical concept through a series of investigations. The problems are designed to allow students to uncover the mathematics that is embedded in the situation. The sixth grade year begins with Prime Time, where students explore number theory and concepts involving factors, multiples, primes, and composites. From there, the first of three units focusing on rational numbers, Bits and Pieces 1, provides opportunities for understanding fractions, decimals and percents. Subsequent units on rational numbers interspersed between other topics deal with operations and applications. Other topics include a geometry unit that promotes reasoning about shapes, as well as properties of these shapes and their angles, as well as a measurement unit that emphasizes area and perimeter relationships of both regular and irregular, curved, and straight-sided figures.
In seventh grade, the students study pre-algebra, beginning with Variables and Patterns, which is an introduction to algebra, using tables, graphs and symbols as representations. Similarity concepts are developed in Stretching and Shrinking before exploring rate, ratio, proportion, percent, and proportional reasoning in Comparing and Scaling. Through activities from Accentuate the Negative, students develop an understanding and use of integers before Moving Straight Ahead highlights linear relationships expressed in words, tables, graphs, and symbols. The study of volume and 3-D measurement in Filling and Wrapping extends our study of geometry before concluding the year with What do You Expect, a unit on probability.
Eighth grade algebra begins by briefly reviewing arithmetic operations with integers, order of operations, and some aspects of geometry, especially area. Quickly though, students move into writing and solving equations, solving and graphing systems of equations, examining geometric and algebraic ratios through a variety of activities, and finally factoring quadratics. The end of the year will bring problems that begin to tie algebraic concepts together by formalizing our work with relations, functions, non-linear graphs, and solving inequalities. Lastly, the students will revisit quadratic equations more formally and work out a derivation of the quadratic formula.
Although those represent some of the mathematical topics for each year, the changes we hope to see in your children go beyond acquiring the fundamentals of algebra. We hope that they develop a greater sense of involvement and excitement about mathematical thinking, a greater sense of confidence and trust in their own abilities, a greater ability to clearly explain their thoughts and procedures both in writing and in conversation, and a greater awareness of the diverse skills and approaches that are embraced in mathematics and that can be discovered in each student.
