Pre-Algebra Out Loud

Learning Mathematics Through Reading and Writing Activities

Pat Mower

• Publisher: Jossey-Bass
• Year: 2016
• Print ISBN:
  9780470539491
• eBook ISBN:
  9781118234037
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

An essential guide for teaching students in grades 5-9 how to write about math

Learning to read and write efficiently regarding mathematics helps students to understand content at a deeper level. In this third book in the popular math 'Out Loud' series, Mower provides a variety of reading and writing strategies and activities suitable for elementary and middle school pre-algebra courses, covering such key skills as integers and exponents, fractions, decimals and percents, graphing, statistics, factoring, evaluating expressions, geometry and the basics of equations.

• Includes dozens of classroom tested  strategies and techniques
• Shows how reading and writing can be incorporated in any math class to improve math skills
• Provides  unique, fun activities that will keep students interested and make learning stick

This important guide offers teachers easy-to-apply lessons that will help students develop a deeper understanding of mathematics.

Chapter 1

The Basic Tools of Algebra

WHAT? Introduction

When middle school students begin a pre-algebra course, they are introduced to a magnificent new world of mathematical symbols and concepts. By this time, they have learned the basic operations of arithmetic: addition, subtraction, multiplication, and division. They still need to continue practicing these skills along with learning higher-order skills. After becoming familiar with the newness of algebra, students are able to incorporate the new with the old to solve more complex problems. This chapter has two mini-lessons: one focusing on the basic symbols and concepts of algebra and the other on solving a simple equation. The first lesson, which introduces pre-algebra students to the basics and general concepts of algebra, lays the foundation for the activities for reading and writing to learn pre-algebra. It may be used as content for any of the activities that follow.

WHY? Objectives

By doing the activities in this chapter, pre-algebra students will:

• Find the major mathematical topics in the lessons that follow and in any pre-algebra text and write them out for use in future activities
• Create a math glossary demonstrating their understanding of the concepts of algebra
• Use semantic word maps to show the relationship between certain algebraic concepts
• Construct and use a concept circle to focus on a large algebraic idea and its components, rules, and examples
• Use algebraic terms creatively, allowing them to learn, understand, and apply these terms in a short story
• Examine, write out, and explain each step in the process of an algebraic algorithm or method of operation

Mini-Lesson 1.1 The Big Ideas of Algebra

CCSS Standard 6.EE: Expressions and Equations

Apply and extend previous understanding of arithmetic expressions.

A toolbox full of all the basic tools of algebra certainly contains a definition of algebra: a generalization of arithmetic in which symbols or letters called variables represent numbers and to which many of the same arithmetic properties and operations apply. This definition encompasses some of the major algebraic concepts and tools. Adding the following definitions to our toolbox yields plenty of tools to help learn about algebra:

• A variable is a symbol that stands for a number or a range of numbers.
• The letters X or Y can represent any number, so they are variables.
• A constant is a fixed number. For example, in 2x + 8, the 8 is the constant.
• A coefficient is the multiplier next to a variable. For example, in 5x or 10a²b, the 5 and 10 are coefficients.
• The arithmetic operations are addition, subtraction, multiplication, and division: +, −, ×, ÷.
• A term is a variable or variables with a coefficient or a constant. For example, in 2, 4x, 6y and −8 are terms.
• An algebraic expression is a mathematical phrase that can contain numbers, operators (add, subtract, multiply, divide), and at least one variable (like x or y.) For example, 4x + 6y - 8 and 24ab - 3a²b are algebraic expressions
• Like terms are terms that have the same variable (raised to the same power) but may have different coefficients. For example, 2x, 5x, and 6x are like terms.

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Teaching Tip

When you introduce an exponential expression, such as x², show students the comparison of x with x². For example, if x=3, then x² = 9. This reinforces the idea that x and x² are two different variables and therefore not like terms.

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The following example describes many of these concepts:

−2x and 4 are terms. -2x + 4 is an algebraic expression.

These are useful tools for performing arithmetic operations.

Combining Like Terms

Completing an arithmetic operation on an algebraic expression requires collecting and combining like terms. Like terms can be thought of as similar things, like apples. For example, we can add the two like terms 4a and 5a by thinking of adding 5 apples to 4 apples to get 9 apples:

Note that 20ab and 36ab are like terms, but 15a and 23ab are not like terms. The variables a and ab are not the same variables. Similarly, 5x² and 7x² are like terms, but 5x² and 7x³ are not like terms and cannot be combined.

Here are some other examples of combining like terms:

Example 1:

. The 5x and 2x can be combined and the 3y and 6y can be combined because they are like terms, but since 3x and 9y are not like terms, the operation is completed when you get 3x + 9y, which is in simplified form.

Example 2:

. Here we moved, or commuted, the like terms 14a and 12a so they sat next to each other and then combined them by adding the coefficients. This is because the operat...

Table of contents

• Cover
• Jossey-Bass Teacher
• Other titles in Out Loud series
• Title Page
• Copyright
• About the Author
• Acknowledgments
• Introduction
• Chapter 1: The Basic Tools of Algebra
• Chapter 2: Exploring Infinite Sets
• Chapter 3: Topics in Integers
• Chapter 4: Number Theory
• Chapter 5: Fractions, Decimals, and Percents
• Chapter 6: Equations and Inequalities
• Chapter 7: Visualizing Algebra by Graphing Lines
• Chapter 8: Geometry
• References