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The Xs and Whys of Algebra

Key Ideas and Common Misconceptions

Anne Collins and Linda Dacey

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 manipulations 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.

 

Product Details

  • Author: Anne Collins and Linda Dacey
  • ISBN: 978-157110-857-9
  • Year: 2011
  • Media: 84 pp/flipchart
  • Grade Range: 7-9
  • Item No: WEB-0857

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 manipulations 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 mathematical learning that develops conceptual understanding, addresses common misconceptions, and builds key ideas that are essential to future learning.

For use in seventh- to ninth-grade courses focused on an introduction to formal algebra, this flipchart emphasizes five essential algebraic concepts: using variables meaningfully; using multiple representations for expressions; connecting algebra with number; connecting algebra with geometry; and manipulating symbols with understanding. The thirty research-based modules in this spiral-bound flipchart are designed to engage all students in mathematical learning that develops conceptual understanding, addresses common misconceptions, and builds key ideas essential to future learning.

Following the recommendations of the National Council of Teachers of Mathematics and the Common Core State Standards, the modules at this level are organized into three sections: Expressions, Equations, and Functions. Each module begins with the identification of its mathematical focus and the potential challenges and misconceptions associated with those ideas. The "In the Classroom" section then suggests instructional strategies and specific activities to implement with students. The "Meeting Individual Needs" section offers ideas for adjusting the activities to reach a broader range of learners. All modules are supported by one or more reproducibles (located in the appendix), and the "References/Further Reading" section provides resources for enriching your knowledge of the topic and gathering more ideas.

Teachers will want to keep this resource next to their plan book so they will have these ideas at their fingertips throughout the year.

Table of Contents

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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
Quadratic Functions
Modeling Quadratics
Solving Quadratic Equations
Exponential Growth
Exponential Decay
Appendix
Answer Key

About the Authors

Anne Collins
Anne Collins has thirty years of teaching experience having taught all grade levels K-12 including undergraduate and graduate level courses. >more

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. >more

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