Diagrams and Sketches

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Modeling is one of the fundamental applications of mathematics concepts. Mathematicians use models to make sense out of situations that seem ambiguous and messy. Most of the time they have to ask their own questions and use their models to find out more information. We can create this type of endeavor in the classroom, too, and provide students with the opportunity to hone their modeling and problem solving skills.

Here's an example that a student could explore with one of the models from the Modeling Situations page...

• Each morning, a math teacher runs a total distance of 42 city blocks, and always chooses a rectangular running path. This morning his rectangular path was twice as long as it was wide.

Here's one possibility:

Here's another approach...

In both instances, we've discovered some new information - the length and width of the rectangular running path. We've made sense out of an ambiguous situation!

Here are a few more situations, and some possible models that could be used to make sense of them. Remember that it's okay to be creative. There are many ways to model the situations, and find out more information about them.

• The sum of two numbers is 40, and their difference is 14...

• Of the girls on the basketball team last fall, 1/2 also played soccer, 1/4 also played volleyball, and 1/8 were also in the choir. The remaining three girls weren't in other activities. No one was in more than 2 activities.

• There are 3 secret numbers. The first number is twice the second number. The third number is twice the first number. Their sum is 112.

• The perimeter of Square A is 24 linear units. The area of Square A is four times the area of Square B.

The idea of modeling situations will receive much emphasis in our further explorations of math concepts in Visual Mathematics / Math Alive! activities. We will see how these ideas can be applied to Algebra, Geometry, Probability, and Number Theory. Try to model situations you encounter at home or in your neighborhoods. It's good practice!

For more basic information, visit the Modeling Situations page.