4.3.1 Math Cycle

Before we jump in, let’s talk about some of the main steps in solving a real problem mathematically. These steps can be summarized in the mathematical modeling cycle shown below.

There are four main steps in this cycle:

  • Describe the problem concisely so that you are clear what you are trying to work out. This may involve discussing the problem with others.
  • Collect information and make assumptions so that you can use mathematics to solve it.
  • Decide what mathematical techniques to use, and carry out these calculations.
  • Work out what your results mean practically and check that they are reasonable. If they are not, you may need to refine the assumptions and go through the cycle again.

This sounds a little complicated, but with a little practice it’ll become second nature to you—you may well already be using the model but had just not realized it!

4.3 Using Math in the Real World

4.3.2 Insulating the Attic