5. Vary Problem Types

Students should experience a variety of problem types related to addition, subtraction, multiplication, and division. The following charts from the 3rd and 5th grade SOL Curriculum Framework documents provide examples. The videos embedded next to the charts provide further explanation and examples.

Let's not skip the charts

If I asked 10 teachers to write a sample subtraction practical problem, chances are that most of them would write something like this:

• I saved $5,000 for a trip to Disney World, but I had to spend $1,457 of that money to fix my leaky roof. How much do I have now?

This is a great Separate, Result Unknown problem, but this is also the subtraction problem type with which we are most comfortable. If students only ever see Separate, Result Unknown problems, they will not develop a complete understanding of the subtraction operation. The same is true with multiplication and division. We don't want to get stuck always asking Equal Groups, Result Unknown problems.

Problem type charts are tools we can't afford to pass over. We need students to experience different types of problems in order to develop flexible problem solvers. As we are choosing or creating practical problems for students to experience, we can refer back to this chart to make sure we are covering a variety of problem types. If you need further assistance creating problems of a certain type, check out Greg Tang's Word Problem Generator where you can enter parameters and generate problems to meet your needs. For all problem types, remember that we want students focusing on the structure of problems, rather than key words.

If you're looking for an even more in depth resource, I recommend Mathmatize It! Going Beyond Key Words to Make Sense of Word Problems. I read this book this summer with a handful of teachers at RSP and found it to be thorough and useful.