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.
Terms introduced in this lesson:
guess and check
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.
General Tip: Remind students to check their work. Ask: Does the answer make sense?