1.7: Problem-Solving Plan
Learning Objectives
At the end of this lesson, students will be able to:
- Read and understand given problem situations.
- Make a plan to solve the problem.
- Solve the problem and check the results.
- Compare alternative approaches to solving the problem.
- Solve real-world problems using a plan.
Vocabulary
Terms introduced in this lesson:
- “read and understand the problem”
- knowns
- unknowns
- “solve the problem”
- “check and interpret the answer”
Teaching Strategies and Tips
In this lesson, students are introduced to problem solving and a new plan that will be used throughout the book.
Some common strategies that students will learn are listed here for easy reference:
- draw a diagram
- make a table
- look for patterns
- guess and check
- work backward
- use a formula
- read and make graphs
- write equations
- use linear models
- use dimensional analysis
- use the right type of function for the situation
It is helpful to advise students that when translating sentences into expressions and equations, they should not attempt to solve the entire problem all at once. Instead, students should read the problem “phrase by phrase”; translate one phrase, then move on to the next.
Teachers can ask their students to reread the question, rephrase it, or even read it aloud.
Estimation is a good habit to develop as it helps confirm the answers students obtain after solving a problem.
Error Troubleshooting
The following list includes possible sources of mistakes for students while solving an applied problem:
- Not listing the given information
- Not restating the question being asked in your own words
- Not selecting a variable to represent the unknown quantity
- Not clearly stating what the variable represents
- Not looking for possible patterns
- Not looking up a definition or formula
A common mistake students make is checking their answers in the equations that they constructed instead of in the original wording of the problems.