There are a number of strategies that may be used in solving math problems. In fact, a problem usually often be solved by different methods. Learning to use the different strategies will enable you to deal with the variety of math problems that you will encounter.
Commonly used strategies are:
- Organize Information – Draw a Picture / Diagram, Make a Chart, Graph, Table or Organized List , Sort the Data
- Build Models
- Estimate
- Substitute with Simple Numbers
- Write a Number Sentence
- Look for a Pattern
- Use a Formula
- Apply a Rule
- Form a Ration or Proportion
- Guess and Check – Substitute Given Choices or Trial and Error
- Work Backwards
- Logical Thinking
1. Organize Information
Draw a Picture/Diagram
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 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. Build Models
Using real materials to model the information may help solve the problem. Blocks, counters, rulers, dice, and play money are some examples of materials that you may use to interpret the information given in a problem.
3. Estimate
Calculations involving decimals and very large numbers are often made easier by using manageable numbers about the same size as those in the problem and then doing the calculation (eg. use 0.5 instead of 0.50021 or 1000 instead of 999). This requires that you be familiar with rounding off.
4. Substitute with Simple Numbers
Substituting given numbers with simple numbers can give you a clearer picture of the problem and thus the solution can become more obvious. You can then use the same idea for the larger numbers.
5. Write a Number Sentence
Translate the descriptive phrases/ sentences into Mathematical equations. This way, solutions become clearer.
6. Look for a Pattern
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
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. They can be written as two numbers separated with a colon, or as a fraction. To compare ratios, write them as fractions. When two ratios are set equal to each other, the equation is called a proportion. A proportion is an equation with a ratio on each side. When a problem compares the same things in two different situations, you can use a proportion.
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. Using the trial and error method would require you making intelligent guesses as to what the answer should be. Intuitive skills such as logical thinking and deduction skills are important in such instances.
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.
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