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.
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10.
Guess and Check
a. Substitute Given Choices (multiple
choice format)
b. Trial and Error (open-ended format) |
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.)
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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.
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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.
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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.
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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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After June
Coultas, Ed.D., James Swalm, Ed. D, Roslynn Wiesenfeld, M.S., 1995,
Stragegies for Success in Mathematics, Steck-Vaughn Co., Texas.
Method
The
Four Step Method is a process commonly used to solve a variety of story
problems.
| 1.
Analyze |
Analyze
the information so you can understand what you must do. |
| 2.
Choose |
Choose
a strategy you think may help you solve the problem. |
| 3.
Solve |
Solve
the problem using the strategy you chose. |
| 4.
Check |
Check
your answer. Read the problem again and see if your answer makes
sense. |
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