What do I mean by "good" questions?

1. Write fifteen numbers between 5.1 and 5.2
2. *Suppose you can weigh all integer masses (that's just code for weights like 1, 2, 3, 4...) from 1 to 60 using just six weights, putting the weights into one pan of the scale and the object into the other. (So each weight is a number, like 1, 2, 5, etc.) 
1. Which weights are used?
2. What about weighing all integer massess from 1 to 1000, or 1 to n?
3. How many weights are needed if you put the weights on both pans?
3. A number is rounded to 5.8. What might the number be?
1. What is the largest possible answer?
2. What is the smallest possible answer?
3. Describe all numbers that round to 5.8
4. What do you think this graph might represent?
5. Find a fraction between 1/2 and 3/4
6. If your calculator's 5 and 7 keys are broken, how can you calculate 732 + 577?
7. In how many different ways could you design a box-shaped building using exactly 24 cubes?

Features of "Good" Questions

• Students are required to do more than remember a strategy.
• Students can learn in the process of answering the question.
• Questions have several acceptable answers.

Features of "Good" Tasks

• All students are able to start the tasks.
• Individuals or groups need to be able to work productively with minimal assistance.
• Explanations and reviews are given to the whole class (despite mixed ability - all hear language appropriate to the task, others' ideas and alerts individuals to a range of possibilities).
• Tasks should be easily extended, student who complete the work should be given extensions of the original task (not something unrelated).
• Tasks should require minimal teacher direction. The teacher does not tell the students how to do the tasks.
• More than one solution and more than one path to a solution should be possible.

Sullivan, P. & Clarke, D. (1991). Catering to all abilities through "good" questions. Arithmetic Teacher, October 14-18.

*Averill & Harvey (2009), p. 19. Wellington: NCER press.