Problem Solving: A Mathematical Guide

When solving math problems, there are several computation methods and clue words you can use to arrive at the correct answer

Trial and Error

A tested logical guess is often the quickest way to solve a problem. The trial, or first guess, will probably not be the right answer, but it should help you figure out a better, more reasonable guess.

Computation Methods

There are several methods you can use to solve problems.

Mental Math is calculating in your head. This method is used with small numbers, memorized facts, and multiples of 10s, 100s, and 1000, etc...

Object/Diagram is using a drawing or object to represent or model the problem.

Pencil/paper is used when a calculator is not handy and the problem is too difficult to solve mentally.

Use a calculator or computer to find answers to problems involving large numbers or when a quick answer is needed.

Trial and error is making a guess at an answer and trying to see if it works. This method is used when you are unsure of what to do or if none of the other methods work.

Word Problem Operations

First, choose which operation to use: addition, subtraction, multiplication, or division. Certain clue words can help you choose which operation to use, but you should also pay attention to the context of the problem.

Addition: in all, sum, total, altogether, more than, combined

Subtraction: less, less than, how much more/less, difference, decrease, compare

Multiplication: join, combine, twice, triple, times more

Division: divide, separate, split, how many

Find a Pattern

Look for a way to describe relationships. Then, use the pattern to solve your problem.

Draw a picture

Use a diagram, list, chart, graph, or table such as in a problem about geometry or physical objects, or to get a visualization of what is happening in your problem.

Work Backwards

You can work backwards, from the end to the beginning, to solve a problem when the final result is given but the original parts are not or when the problem includes a series of steps that can be reversed (division and multiplication). Working backwards is also used when the problem is complicated at the beginning and simpler at the end.

Multi-Step Problems

When working with multi-step problems, plan each step needed to solve each part to arrive at your answer.

Hidden Questions

Some information is not stated in problems. First, find what information you need and decide how you can use the data in the problem to find this information.