The Five Most Powerful Representational Strategies


Hyde, 2006
“The two common strategies of looking for a pattern and using logical reasoning always should be used in problem solving… Mathematics is the science of patterns… Logical reasoning is essential to doing mathematics.” (p. 10)

Along with looking for patterns and using logical reasoning, there are five very powerful representational strategies.


  • Discuss the problem in small groups (language representations using auditory sense).
  • Use manipulatives (concrete, physical representations using tactile sense).
  • Act it out (representations of sequential actions using bodily kinesthetic sense).
  • Draw a picture, diagram or graph (pictorial representations using visual sense).
  • Make a list or table (symbolic representations often requiring abstract reasoning

Try it: Create a mathematical representation of the situation below. Choose the type of representation you want to use.
Amanda’s grandmother said that she will put money into a savings account for Amanda if Amanda will also save some money. She said she would put twice as much money as Amanda saves, plus $12, each time Amanda adds money to her savings account.

Here’s another problem to try:
At the beginning of the day, 3 people know a secret. Each person tells a new person the secret every hour. Therefore, the number of people who know the secret doubles every hour.
How many representations can you make for this problem? Would it be easier for some of your students to start with one kind of representation rather than another?