Topic: The Basics
Subtopic: Introduction to Algebra
Overview
This lesson covers the basic processes of simplifying algebraic expressions. The two most important of these is the "distributive law" and "collecting like terms". Take your time with these and pay close attention to the signs. There is lots of new terminology to learn. One caution to note is the difference between an "algebraic expression" and an "algebraic equation". The former may be able to be simplified but can never be solved. But an equation contains an equals sign and can therefore be solved (and the answer checked by substitution). Another caution is that when you do check a solution in an equation (or evaluate an expression for a given value) be sure to substitute the value in using parentheses or you may make sign errors. E.g., evaluating x2y given that x=-3 and y=-2 would be (-3)2(-2)=-18 and not -32*-2=18 nor (. (Do you see why the latter is wrong? If not, discuss in class!)
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 1.1.1 Evaluate algebraic expressions
- 1.1.2 Check if a given value is actually a solution to an equation
- 1.1.3 Translate words into an algebraic expression or equation
- 1.1.4 Model real-life data with an algebraic equation
- 1.1.5 Recognize the properties of algebra: commutative, associative
- 1.1.6 Collect like terms
- 1.1.7 Use the distributive law (forward and backward)
- 1.1.8 Apply order of operations to simplify an expression
- 1.1.9 Factor an algebraic expression via the distributive law
Terminology
Define: variable, constant, algebraic expression, term, coefficient, exponent, power, order of operations, "like" terms, equivalent expression, commutative property, associative property, equation, solution, equation vs. expression, distributive law, factor, factor vs. term
Text Notes
Text: Intro & Inter Algebra for CS 3ed by Blitzer, sect. 1.4 & 1.8
- ch 1.4 pg 43-45 includes definitions of the commutative and associative properties. Personally I care more that you know how these rules work than what there names are. For instance it is important to know that x*y = y*x but not as important that this is the "commutative law of multiplication" (IMO).
- ch 1.4 pg 46-50 covers the distributive property (a.k.a. distributive law), combining like terms (a.k.a. collecting like terms), and simplifying expressions. These three processes are the guts of chapter 1. Learn them well! This material is needed to build a strong foundation of beginning algebra skills.
- ch 1.8 Focus on working with exponents and using order of operations to simplify an expression. Examples 1-11 are all very important to study to be sure that you have all the basic skills needed to move forward to chapter 2.
- ch 1.8 pg 90-91 examples 12-13. This text introduces some pretty heavy-weight applications and "mathematical models" right from the get go primarily to provide motivation for the algebra that you are beginning to learn. Try to follow all the steps, but your main focus should be the step of evaluating a given formula by plugging-in a given value for a variable. We will cover evaluating formulas and solving word problems in more detail throughout the course.