# 2.8: Problem-Solving Strategies: Guess and Check; Work Backward

## Learning Objectives

At the end of this lesson, students will be able to:

- Read and understand given problem situations.
- Develop and use the strategy:
*Guess and Check.* - Develop and use the strategy:
*Work Backward.* - Plan and compare alternative approaches to solving problems.
- Solve real-world problems using selected strategies as part of a plan.

## Vocabulary

Terms introduced in this lesson:

- guess and check
- working backwards

## Teaching Strategies and Tips

Use Example 1 to introduce *guess and check.* Teachers are encouraged to postpone solutions involving systems of equations (two variables) until chapter *Solving Systems of Equations and Inequalities.*

Allow students to strategize from their guesses. The guessing process will often lead to unexpected patterns that can serve to make better guesses along the way:

- In Example 2, one guess yields a sum of , which is half of the desired ; therefore, the initial numbers should be multiplied by .
- In Example 4, note the pattern given by the relation: when Nadia’s age is decreased by , her father’s age decreases by . This observation leads to the answer.
- In Example 6, allow students to keep guessing until the
*total costs*are the same. Students may notice however that for an increase of , the difference between total costs falls by .

Use Example 3 to show how to *work backward.* Reverse the steps starting with the result until the unknown is obtained.

General Tip: Teachers are encouraged to compare alternative approaches to some of the problems.

## Error Troubleshooting

General Tip: Remind students to check their work. Ask: *Does the answer make sense?*