When writing a problem string, there are several things to consider.
- How can you encourage students to construct mathematical relationships?
- What progression of problems can help?
- How will you model student thinking?
Here are the first three problems in a problem string around solving linear equations.
Some number doubled is 16.
Some number doubled and then add 2 is 16.
Some number doubled and then add 1 is 16.
The following is what that problem string might look like as the teachers asks each question one at a time, fields students responses, and models student strategies using equations and an open number line model.
Notice that each problem has "=16" in it. Look again at the open number line models. How does this affect the solution to each problem? Because doubling a number and then doing things to that results in the same 16, therefore the number, n, must change. This is a desirable connection for students to make.
It's not the only connection we could make with such problems. Stay tuned for another option coming soon.