Lesson 2: Solving One-Step Equations

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: This lesson expands on the properties of equality by introducing the Multiplication and Division Properties of Equality. Students will learn to isolate a variable in a single step by applying inverse operations. The curriculum covers four primary scenarios: Adding to undo subtraction. Subtracting to undo addition. Dividing to undo multiplication. Multiplying to undo division (including the use of reciprocals when dealing with fractional coefficients). Emphasis is placed on the formal algebraic habit of showing work on both sides of the equation to maintain balance.
Purpose: The purpose of Section 3.2 is to achieve procedural fluency. While many students can solve x + 5 = 12 mentally, this section teaches them the systematic "inverse operation" method required for the complex, multi-step equations in Chapter 4. By mastering one-step movements now, students eliminate the "guess and check" habit and replace it with a reliable mathematical strategy that works for integers, decimals, and fractions alike.
Depth of Knowledge (DOK) Level DOK Level 1 & 2Level 1 (Recall & Reproduction): Recalling the specific inverse for a given operation (e.g., knowing that division is the inverse of multiplication). Level 2 (Basic Application of Skill/Concept): Selecting and performing the correct operation to solve for a variable and verifying the result through checking. Students must process multiple steps: identify the operation being performed on the variable, determine the inverse, and apply it to both sides.

The Daytona 500 is widely considered to be the most important event of the NASCAR circuit. The distance around the track is 2.5 miles, and the race is a total of 500 miles. How many laps does it take to finish the race?

Ricardo is driving 780 miles to Memphis. He drove about 3/5 of the distance on the first day. About how many miles did Ricardo drive?

Class and online work

Use practice problem 5, page 90 to assess students' understanding of the lesson concepts