Problem-solving is at the heart of mathematics. Many problems, however, are difficult to solve and therefore require methods and strategies to assist in finding the solution. It is here that our study of algebra begins, as we learn how to write and solve the most basic types of equations--linear equations. Consider the following problem:
Mr. Banks wants to build a new vegetable garden that will fit within the 60 feet of fencing that he already owns. He also knows that ideally he wants his garden to be 4 feet longer than it is wide. Given this information, how long and wide should he make his new garden?
Without the aid of an equation and a process for solving it, the problem above can be a challenging problem. However, in Unit 1 we will begin by examining the process of solving linear equations and then explore how this process can be applied in order to solve problems like the one listed above.
Guiding Questions for Unit 1:
How does our understanding of basic algebraic properties help us solve linear equations and linear inequalities?
What is the value and purpose of solving a formula for a given variable?
How can linear equations and linear inequalities be used to solve application problems?
Lessons in Unit 1:
Lesson 1: Solving One-Step Linear Equations
Lesson 2: Solving Multi-Step Linear Equations
Lesson 3: Solving Inequalities
Lesson 5: Translating into Expressions and Equations