The Xs and Whys of Algebra

Key Ideas and Common Misconceptions

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulation of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world.

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Description

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulation of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In The Xs and Whys of Algebra: Key Ideas and Common Misconceptions, Anne Collins and Linda Dacey provide a set of thirty research-based modules designed to engage all students in m...read more

Anne M. Collins

Anne Collins has thirty years of teaching experience, having taught all grade levels K-12, as well as undergraduate- and graduate-level courses. She has been providing mathematics content professional development institutes and courses for teachers for the past fourteen years.

Linda Dacey

Linda Dacey, professor of mathematics and education at Lesley University, began her career teaching at the elementary level and, early in her career, received an NSF grant to develop a model program for preparing middle school teachers.

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Contents
Introduction
EXPRESSIONS
Walking the Cartesian Coordinate Plane
Simplifying Expressions
Generalizing Patterns
Geometric Patterns
Equivalence of Expression
Input/Output
Problem Solving with Patterns
Posing Problems
EQUATIONS
Equal Sign as a Balance
Solving Equations
Graphing Equations
Solving Linear Equations
Equivalent Expressions
Meaning of Slope
Working with Slope
Interpreting Graphs
Systems of Linear Equations
Linear Inequalities
Posing Problems for Inequalities
Absolute Value as Distance
Absolute Value Inequalities
FUNCTIONS
Am I a Function?
Linear Functions
Solving Problems Using Ordered Pairs
Exponential Growth
Exponential Decay
Appendix