Lesson 5: Solving Equations - Applications

How do we use distribution and CLT to simplify and expression before solving.

How do we isolate a variable to find a solution to a one-step linear equation?

How can you check that your solution is correct?

Inverse operations; Equality

2G (CCS HSA.REI.A.1) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Lesson Description
Section 3.4 focuses on the application of linear equations through word problems. The lesson introduces a consistent, multi-step strategy for approaching applications: defining a variable, translating key phrases into algebraic expressions, setting up an equation, solving it, and—crucially—interpreting the result within the context of the original problem. Key application types include:

Number problems (e.g., "The sum of three consecutive integers...").

Direct translation problems using keywords like "more than," "product of," and "is."

Basic geometric applications (e.g., finding dimensions of a rectangle given its perimeter).

Simple interest or uniform motion (distance = rate × time) at an introductory level.

Purpose
The purpose of this section is to develop mathematical literacy. It forces students to move beyond rote calculation and engage in critical thinking. By learning to "decode" language into symbols, students see algebra as a functional tool for solving practical dilemmas rather than an abstract set of rules. This section is vital for student success in subsequent science and business courses, where the primary challenge is often setting up the problem rather than solving the arithmetic.

Depth of Knowledge (DOK) Level
DOK Level 2 & 3

Level 2 (Skills and Concepts): Translating standard phrases into algebraic symbols and applying a known formula (like perimeter) to a specific scenario.

Level 3 (Strategic Thinking/Complex Reasoning): Students must analyze a paragraph, filter out irrelevant information, determine the relationship between unknown quantities, and construct a mathematical model from scratch. It requires a deeper level of logic to verify if the "solved" number actually makes sense in the "real-world" context

Class and online work

Use practice problems 6-11, pages 92-93 to assess students' understanding of the lesson concepts