In More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction, Dr. Marian Small discusses the turn-around strategy to create open questions.
Instead of asking “The legs of a right triangle are 3 cm and 6 cm long. What is the hypotenuse?” the teacher can ask “The answer is √45. What could the question be?”
There are many possible questions. For example,
Determine the length of the hypotenuse.
A square has an area of 45 cm². What is the side length?
What is an example of a square root that has a value between 6 and 7?
Which number is the greatest: √37, 6, 6½, √45?
Students will come up with a variety of questions. However, at first, I imagine the response to open questions such as “The answer is √45. What could the question be?” will be silence. Students are used to being asked questions where there is one correct answer. In math, you either get it or you don’t. It’s not just questions that need turning around. This black and white view of mathematics also needs turning around. With time and practice, class discussions about open questions can help change this attitude.