Using Diagrams to Solve Word Problems

Instructor: Lynne Hampson

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

In this lesson, you will learn the important role diagrams play in solving word problems. Some word problems can have a lot of information, which may create confusion when trying to find the answer. One way organize information is to use a diagram.

What is a diagram?

The word diagram simply means a drawing or a visual. In math, we use many types of diagrams. Venn Diagrams, bar graphs, basic drawings, pie charts, and tape diagrams are only a few of the diagrams used to solve problems. It is likely you have either used or seen at least one of these diagrams.

Every type of diagram helps to display information, making it easier to solve for what is missing. The missing information is called a variable, usually represented by a letter symbol, such as x or b.

Solving Word Problems

Let's pretend for a moment that a student is asked to solve an algebra word problem. The student begins willingly and is optimistic they can solve the problem. They understand the content of the first few sentences of the problem but figure out quickly that there is a lot of information being presented. It's hard to keep track of it all. The student continues their efforts, rereading the information, but even with their best effort, they cannot sort out or solve the problem.

When faced with a difficult word problem where the answer is not clear, there is still hope. Our brains work in a way that houses information, much like a computer. A computer with too many files open will likely freeze at some point. That is why we need to find a way to process the information from a word problem in a way that puts all of the information into one folder.

A diagram is a way to help your brain process a lot of information at once. It is a visual planning tool that takes some of the pressure off of remembering every single detail. Sometimes we have hard questions that require sifting through a lot of information to figure them out.

It becomes difficult to keep all of the information straight when faced with a problem, especially where numbers are involved. We have learned that people have different ways in which their minds interpret data. One way is to visualize the problem as if it is being played out on paper, much like a story.

Which diagram for which problem?

We will look at a few of the more popular diagrams used to solve math problems. Remember, a diagram is a drawing, so you can draw anything you want to help solve the problem.

  • Venn Diagram - Compares and contrasts information.

A word problem asks you to compare and contrast multiples of three and even numbers up to 50. A Venn diagram will help sort those numbers.


  • Pie Charts- A circle with colors separating each groups information by percentages.

There are four candidates running for president, therefore each has a separate color in the pie chart. This type of chart gives a quick, easy way to see how a whole is divided into its constituent parts.


  • Bar Graph- Compares values with one or more groups. It can also show and compare trends over a time period.

A problem lists the profits for a company over time. Time is on the x-axis and profit is on the y-axis of the graph. Two companies can be compared by using bars of different colors.


  • Tape Diagram- Places information into boxes.

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