Course 3 Unit 3 - Symbol Sense and Algebraic Reasoning
1st Edition

In Courses 3 and 4, the mathematical strands in the Contemporary Mathematics in Context program become increasingly blended within units. For example, in Course 3, the content in Unit 2, Modeling Public Opinion, is primarily from the discrete mathematics and statistics and probability strands. Another example is Course 3, Unit 7, Discrete Models of Change. This unit contains content from both the discrete mathematics and the algebra and functions strands. (See the descriptions of Course 3 Units.)

In Courses 1 and 2 of the Contemporary Mathematics in Context program, students have developed a robust understanding of linear, exponential, power, inverse power, and quadratic models. They have also studied Course 3, Unit 1, Multiple-Variable Models. This unit develops student ability to construct and reason with linked quantitative variables and relations involving several variables and constraints.

Unit Overview

Symbol Sense and Algebraic Reasoning develops student ability to represent and draw inferences about algebraic relations and functions using symbolic expressions and manipulations.

Unit Objectives
  • To develop a more formal understanding of functions and function notation
  • To reason about algebraic expressions by applying the basic algebraic properties of commutativity, associativity, identity, inverse, and distributivity
  • To develop greater facility with algebraic operations with polynomials, including adding, subtracting, multiplying, factoring, and solving
  • To solve linear and quadratic equations and inequalities by reasoning with their symbolic forms
  • To prove important mathematical patterns by writing algebraic expressions, equations, and inequalities in equivalent forms and applying algebraic reasoning

Sample Overview

Lesson 4 of this unit develops student ability to solve linear equations by applying the field properties and to solve quadratic equations and inequalities by factoring, by using the quadratic formula, and by using technology. Students also learn how to identify whether a quadratic function has 0, 1, or 2 zeroes and how to determine the axis of symmetry and the distance between the zeroes for a quadratic function.

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.

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How the Algebra and Functions Strand Continues

In Course 3, students will study one additional algebra and functions unit, Families of Functions. This unit reviews and extends student understanding of the basic function families and develops student ability to adjust function rules to match patterns in tables, graphs, and problem conditions

Four units in Course 4 extend student understanding of algebra and function concepts in preparation for post-secondary education. Students develop understanding of the fundamental concepts underlying calculus, of inverse functions, and of logarithmic functions and their use in modeling and analyzing problem situations. Students also extend their ability to use polynomial and rational functions to solve problems and to manipulate symbolic representations of exponential, logarithmic, and trigonometric functions.

A unit that develops understanding and skill in the use of standard spreadsheet operations while reviewing and extending many of the basic algebra topics from Courses 1-3 is included for students intending to pursue programs in social, management, and some of the health sciences or humanities.

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