Sometimes pictures are easier to understand than numbers.

Solving a mathematics problem can often be frustrating, especially to students who are less comfortable with imagining abstract situations. The mathematical model can alleviate this difficulty, building a bridge between the mathematical world and the real world. A mathematical model is a simple, visual way of representing a problem so that both the situation and the solution become easier to imagine. While problems differ in what model should be used, you can apply a general strategy of model-building to many problems.

Before you even choose a model to use, you need to wrap your head around the overall goings-on in the problem. For this phase, ignore the numbers and look at how changes occur in the problem. Because many basic math problems involve changes over time or contain multiple steps, you can make this process easier by mentally dividing the problem into phases. For example, consider the problem, “During a sale, a bookstore sold 1/2 of all its books in stock. On the following day the store sold 4,000 more books. Now only 1/10 of the books in stock before the sale remain in the store. How many books were in stock before the sale?” This problem has three phases: before the sale, the sale day, and the day after the sale. Your model should represent these three phases separately.