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Problem Solving Strategies

The computation strategies and approaches described below can be used by parents and teachers to foster students' understanding of a variety of math problems. They are not all inclusive nor mandates for instruction, but are presented merely as a resource.

There are a number of strategies that may be used in solving math problems. Teaching students how to use the different strategies when they work in mathematics will provide them with the greater ability to deal with the variety of math problems that they will encounter.

 1. Organize Information a. Draw a Picture b. Make a Chart, Graph, Table or Organized List c. Sort the Data 10. Guess and Check a. Substitute Given Choices  (multiple choice format) b. Trial and Error  (open-ended format)

1. Organize Information
Draw a Picture
When you organize your information you can approach the problem in one or more ways. By drawing a picture or diagram, and labeling it with the correct information, your calculations will take less time and create less confusion. Sometimes, drawing a picture or diagram will help you to see a way to solve the problem that you might not have thought about without drawing the picture.

Make a Chart, Graph, Table, List or Organized List
Making a chart, table, list, or graph allows you to clearly examine data. A chart, graph, or table not only helps in making comparisons but also allows the reader to find numerical information, which may be needed to make decisions to solve the problem. When you see data in an organized chart, table, list or graph, this allows you to draw conclusions more easily than you could by just looking at a set of unorganized numbers. Organizing your information like this allows you to see patterns or trends.

Sort Data
Data is sometimes easier to analyze when it is sorted. This is especially true when finding the median (the number in the middle of a group of numbers when arranged in increasing or decreasing order) or the mode (the number that appears most frequently in a group of numbers). Sorting data into categories can help you in these and other processes. There are many different ways to sort numbers. When the information is well organized, you can solve the problem a lot easier.

2. Use Manipulatives to Model the Information
Using real materials to model the information may help solve the problem. Blocks, counters, rulers, protractors, compasses, dice, play money and squared materials are some examples of materials that you may use the information given in a problem.

3. Estimate
Calculations involving decimals and very large numbers are often made easier by using numbers about the same size as those in the problem and then doing the calculation. This requires that you be familiar with rounding off.

4. Substitute Simple Numbers or Making a Simpler Problem
Using simple numbers to make an easier problem can sometimes solve problems. Taking simple numbers and using them for the given numbers can give you a clearer picture. You can then use the same idea for the larger numbers.

5. Translate into a Number Sentence
People use language to communicate in a clear way. By translating English phrases/ sentences into "Math" phrases/ sentences (in mathematics, phrases are called expressions, and sentences are called equations or inequalities), solutions become clearer. This can be done because there are many English words that have math symbols to match them.

6. Look for a Patternk for a PatternPattern
In some problems it is helpful to find a pattern within a group of items. This lets you look at the problem as something that happens over and over.

7. Use a Formula
Using a formula can solve certain mathematical problems. A formula is a set of directions that is always true for a particular situation. When applying a formula, take the given information and substitute each piece of data into the formula. Then carry out mathematical operations indicated by the formula.

8. Apply a Rule or Definition
Many times problems require the knowledge of certain rules or definitions. It is necessary to know these rules for without them; the student is unable to obtain the correct answer. (E.g. order of operations, sum of angles in a triangle is 180 degrees, etc.)

9. Form a Ratio or Proportion
A ratio is a way to compare two numbers. When two ratios are set equal to each other, the equation is called a proportion. When a problem compares the same things in two different situations, you can use a proportion. This will help you solve the problem.

10. Guess and Check
The answers to many problems can be determined by substitution or trial and error. We can use the choices offered in a multiple-choice problem and substitute them in the given problem. Obviously, only one of the choices is going to be the correct answer. By using substitution, we can sometimes avoid more complicated and time-consuming solution methods.

11. Work Backwards
It is sometimes necessary for you to start with the information given at the end of a problem and compute your data working toward the information presented at the beginning of a problem.

12. Logical Thinking
All problems require logical reasoning, but there is a group of problems that offers a set of conditional data that you must use to eliminate choices that are false and select an answer that is true. Usually a chart, diagram, or picture can be used to organize the information given in these problems. Once the information is organized, you can eliminate choices that do not meet the conditions asked for in the problem and then select the logically correct answer.