# Methods - Modeling

Children must learn to model word problems. While there are other ways to solve word problems (that is, by using shortcuts) children cannot understand those other ways without the ability to make models.

Of course it is obvious that children are not born with the ability to make models. In this example it is clear that Trixie does not know how to model a Hard Subtraction 1 problem - she simply doesn't understand the question and so she has no way to solve the problem. One way or another Trixie must learn what to do - the question is, "How is she to do that?"

I believe that modeling should be explicitly taught. The 12 types of word problems should be systematically introduced and children should be provided with clear direction on how the problems are to be solved. Can there be any doubt that I did the right thing in the examples above by telling Trixie and Rose exactly what to do?

Here is some general advice on teaching your child to model word problems. The videos on the Addition, Subtraction, Multiplication and Division tabs illustrate these principles and more.

 You can start when your child is as young as 2. Easy Addition and Easy Subtraction are the easiest models to learn and it makes sense to start there. One word problem a day, or even one every few days is more than enough. Try to work them into ordinary play situations. Try to make them funny. You don't want problem solving to turn into boring work.
• Some problem types are typically harder to learn than others. I would follow examples of Easy Addition and Easy Subtraction with examples of Easy Multiplication, Easy Measurement Division, Easy Partitive Division, and Combinations.

• Hardest of all are Hard Addition, Hard Subtraction 1, Hard Subtraction 2, and Hard Multiplication.

• I think it reasonable to expect that by the time your children are 7 they know how to model all 12 types of word problems (and be able to use some shortcuts as well.)

• Although I do believe in systematically introducing all 12 types of problems, I don't believe in teaching only one type at a time. Mix the problems up. For example, your child need not be expert with Easy Addition before being introduced to Easy Subtraction.

• Keep the numbers small - under 10 to begin with and always under 20. Larger numbers just make the counting tedious and error prone - and contribute nothing to learning to model.

• Remember, you are teaching your child to model. It is the modeling process that is important - not speed or even the right answer. Nor is it important that your child be able to name the different problem types - in fact, I wouldn't use the names at all.
 (back) (next)