Solving Two-Step Equations by Undoing Operations
About this lesson
Students solve think-of-a-number puzzles by working backwards, then use the same undoing idea to solve two-step equations. They finish by writing puzzles for a partner to solve. It takes about 15 minutes and needs only the board, scrap paper and pencils.
- Grade
- 7
- Subject
- Math
- Time
- 15 min
- Prep
- 3 min
Objective
Students will solve two-step linear equations by undoing operations in reverse order and check each solution by substituting it back into the equation.
Prep
3 min: write these 8 equations on the board: 3x + 4 = 19, 2x − 5 = 11, 5x + 2 = 37, x/4 + 3 = 8, 6x − 7 = 29, x/3 − 2 = 5, 4x + 9 = 1, 7x + 10 = 3
Materials
- whiteboard and markers
- scrap paper
- pencils
Steps
- Say, 'I'm thinking of a number. I multiply it by 3, add 4 and get 19. What is my number?' Ask a student to explain how they worked backwards: subtract 4, then divide by 3, so the number is 5.
- Write 3x + 4 = 19 beside the puzzle and show that it is the same problem. Model undoing the last operation first: subtract 4 from both sides, then divide both sides by 3. Check by substituting: 3(5) + 4 = 19.
- Have students solve the board equations on scrap paper for 5 minutes. Each solution must include a substitution check, and the last two have negative answers.
- In pairs, each student writes one think-of-a-number puzzle and its matching equation. Partners swap and solve, then check each other's answers by substitution.
- Call on two pairs to share a puzzle with the class, and have everyone solve it on their paper.
Quick Check
Write 5x − 3 = 22 on the board and have students hold up their paper. Look for x = 5 and the steps add 3, then divide by 5.
Differentiation
Make it easier: Start with one-step equations such as x + 7 = 12 and 4x = 28 before moving to two-step equations.
Make it harder: Give equations with the variable on both sides, such as 5x + 3 = 2x + 18, or have students write puzzles with three operations.
Good For
- Review
- Supply teacher
- Early finishers
- Morning warm-up
