### Classifying Word Problems

Mathematics educators have various ways of sorting word problems into different categories. Not all authors do this, but I begin in an obvious way.

• Any word problem that can be solved by adding is, first of all, an addition problem.
• Any word problem that can be solved by subtraction is, first of all, a subtraction problem.
• Any word problem that can be solved by multiplication is, first of all, a multiplication problem.
• Any word problem that can be solved by division is, first of all, a division problem.

For example, this problem may seem like an addition problem, but it is solved by subtraction, not addition. Therefore, in my system, it is a subtraction problem.

Rose had 3 snakes and then Eva gave her some more so that Rose now has 7 snakes altogether. How many snakes did Eva give Rose?

The next step for me is to further sort the addition problems, the subtraction problems, the multiplication problems, and the division problems. This sorting is done on the basis of how I would teach a child to solve them - that is, on the basis of what model I would help them to make. You have already seen on the Addition tab that in the case of addition problems there are two models - what I call Easy Addition and Hard Addition. You will see on the Subtraction, Multiplication, and Division tabs that there are 3 models for subtraction problems, 3 for multiplication, and 4 for division.

That is all there is to my system - 12 models and so 12 types of word problems. But I emphasize that other distinctions can be made. For example, while all Easy Addition word problems involve the joining of two sets of objects, some authors distinguish those problems in which the joining is explicitly described from those in which it is not. For those authors, these next two problems are of different types.

There are 3 boys in the classroom and 2 girls in the classroom. How many children are in the classroom altogether?

There were 3 boys in the classroom. Then 2 girls came into the classroom. How many children are in the classroom altogether?

Similarly, one might want to distinguish these two Hard Addition problems from one another.

There are 3 children in the gym. There are 2 more children in the auditorium than are in the gym. How many children are in the auditorium?

There are 3 children in the gym. There are 2 fewer children in the gym than are in the auditorium. How many children are in the auditorium?

Although I haven't built these lower level distinctions into my classification system, that is not to say that I don't think they are important. As you might imagine, some children, for example, might understand "there are 2 more children in the auditorium" and not understand "there are 2 fewer children in the gym." The implication is that in helping your children with any particular problem type you should provide many examples - phrasing the problems in many different ways to get at all of this diversity.

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