1.8: Problem-Solving Strategies: Make a Table; Look for a Pattern
Learning Objectives
At the end of this lesson, students will be able to:
- Read and understand given problem situations.
- Develop and use the strategy: Make a Table.
- Develop and use the strategy: Look for a Pattern.
- Plan and compare alternative approaches to solving the problem.
- Solve real-world problems using selected strategies as part of a plan.
Vocabulary
Terms introduced in this lesson:
- “make a table”
- “look for a pattern”
Teaching Strategies and Tips
In this lesson students learn how to develop and use the methods: make a table and look for a pattern.
Teaching Tip: Review key phrases with students such as: What? How much? When? How long? Where? How far? (and even Who? and Why?). If students’ answers (with appropriate units) do not answer the key phrase in the problem, then the student needs to return to it and either back-substitute to obtain the correct answer or start over by labeling the variables differently to answer the key phrase.
In Example 1, the key phrase is How much was the total bill? By distilling this question from the rest of the problem, a student understands what is unknown: the total bill (how much the pizza costs). At this point, a variable can clearly be defined.
The strategy make a table enables the problem-solver to recognize patterns and relationships within numerical data organized in tables. Students sometimes need help with table headings. In Example 2, the units are weeks, minutes per day, and minutes per week. By extracting this information and laying it out on paper, a student can readily infer the column headings.
Look for a pattern has the problem-solver create only a minimum of rows until a pattern can be established and used to obtain the answer.
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