Problem-Solving Strategies

By Mari Taira

Introduction

Strategies for problem-solving help students understand and find a process for solving problems. Sometimes, the strategies are the solution process. There are ten of them and they include: Act Out or Use Objects, Draw a Picture/Diagram, Draw a Table, Make an Organized List, Guess and Check, Find a Pattern, Work Backwards, Use Logical Reasoning, Make it Simpler, and Brainstorm.

I. Act Out or Use Objects

Acting out a problem, or using objects to solve problems help students get visual images of the information and solution process of a problem. This also helps the students to remember the process for future use. Using counters or colored chips are fine for this strategy.

II. Draw a Picture or Diagram

Drawing pictures or diagrams help students understand and control the data in the problem. Diagrams are mostly requisite when the problem involves mapping. This also gives a visual to help.
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III. Draw a Table

Drawing tables help keep track of data, find missing data, and get data that is needed in the problem. Tables are an organized arrangement of data, and so students may find patterns in them.

This is an example of a word problem that could be solved with a table:

Fiona got chocolate candies for good behavior every month. In January, she got 2. In February, she got 10. In March, she got 18. If the pattern continued, how many chocolate candies would she have gotten in June?

IV. Make an Organized List

Lists help students organize their thinking. Recording data helps to review what has been done, and what still needs to be done. This helps students to see data in an orderly way.

This is an example of a word problem in which a list may help:

You earn extra money during the summer by mowing your neighbors' lawns. You can mow five lawns an hour and need to mow 37 lawns. How long will it take you to mow all the lawns?

V. Guess and Check

When there are lots of information in a problem, or the problem has big numbers, guessing the answer, then checking it can easily get students to the answer. With each guess, the students get closer and closer to the real answer. This is also helpful when making a list is too much work. This strategy can be combined with other ones to figure out a problem.

This is an example of a word problem that requires guess and check:

Sally is thinking of two numbers. The product of the two numbers is thirty-six. The sum of the two numbers is 15. What are the 2 numbers?

VI. Find a Pattern

Patterns are systematic repetitions that are either numerical, visual, or behavioral. Patterns help to find out what happens in the future. To find a solution, patterns are usually extended. Tables are very useful and help to reveal patterns. his is used to solve lots of different problems with lots of different strategies as well.
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VII. Work Backwards

When a problem gives the ending but asks for the beginning, working backwards can help to get the answer. Students can start at the ending answer and work their way backwards to get the starting data.

This is an example of a word problem that requires working backwards:

Katherine bought some chocolate bars. She ate 3 of those chocolate bars. Then she bought 5 more chocolate bars and ate two of those. She has four chocolate bars left. How many bars did she have in the beginning?

VIII. Use Logical Reasoning

Logical reasoning is used for all problems, but some include different conditional statements: "if...then," "if...then...else," "if something is true, then...," and "if something is not true, then..." The data is usually in a chart and these problems require lots of reasoning.
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IX. Make it Simpler

When solving complex problems, they can be made simple by either reducing numbers, or reducing the amount of data given in the problem. The simple representation then may give out a process for the complex representation.

This is an example of a word problem with extra information:

Sammy found 2 folders, four markers, and some crayons. He found twelve times as many crayons than markers. How many crayons did he find?

X. Brainstorm

Brainstorming is used when all of the other strategies do not work. When students cannot think of a similar problem that they have solved before, they can look at the problem in new, creative ways.
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