Course 1 Unit 2 - Patterns of Change
1st Edition

Patterns of Change is the second unit in Course 1 of the Contemporary Mathematics in Context curriculum. In Unit 1, Patterns in Data, students have developed the ability to make sense out of real-world data through the use of graphical displays. Students can describe distributions by the shape of the distribution, including variation, and by using summary statistics. (See the descriptions of Course 1 Units.)

Unit Overview

One of the most important transitions from elementary to secondary school mathematics is the emergence of algebraic concepts and techniques. Algebra allows one to study numerical patterns, quantitative variables and relationships among those variables, and important patterns of change in those relationships.

The intent of this unit, which precedes the study of linear models, is to focus students' attention on the variety of types of change inherent in real situations. This unit will provide students with a broad picture of patterns of change so that linear models, as studied in the next unit, will be seen as a specific type of change.

Objectives of the Unit
  • To begin developing students' sensitivity to the rich variety of situations in which quantities vary in relation to each other
  • To develop students' ability to represent relations among variables in several ways - using tables of numerical data, coordinate graphs, symbolic rules, and verbal descriptions - and to interpret data presented in any one of those forms
  • To develop students' ability to recognize important patterns of change in single variables and related variables

Lesson Overview

In Lesson 1, students build and study mathematical models for two-variable data. They look for patterns of change and make predictions that go beyond the data.

In Lesson 2 (a portion of which is included on this web site - see below), student attention is again focused on patterns of change in variables. The investigations in this lesson encompass the basic ideas of iterative or recursive change that are present in computer models of problem situations. (Expressed in algebraic symbolism, one common model for such change is yn + 1 = yn + ayn + b.) Finally, students utilize the iteration capabilities of a graphing calculator to think about patterns of change.

In the remainder of the unit, students write and use symbolic rules to model situations which are linear and nonlinear, thus setting the stage for the next unit, Linear Models.

Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

View the Unit Table of Contents and Sample Lesson Material

We have provided for your perusal a file containing the Patterns of Change Table of Contents and another containing sample material from Lesson 2.

How the Algebra and Functions Strand Continues

Patterns of Change is the first of seven algebra and functions units in the first three years of the Contemporary Mathematics in Context curriculum. Algebraic reasoning and skill is developed over time with most of the abstract symbolic mathematics developed in Course 3. In Course 4, students continuing on to college will continue to develop these skills. (See the CPMP course descriptions.)

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