We came up with the following rules for question generation:

Do

Don’t

Ask “How” questions

Have an end goal in mind

Look at interaction between two variables

Make links to other topics

Examine the scenario from multiple viewpoints

Ensure your question is comprehensible to a stranger

Be trivial

Be vague

Ask questions with a yes/no answer

Make assumptions in your questions – include them as sub-questions instead

Examples of good questions:

What are the conditions required to create a 45 degree angle from the lines going through a square’s vertices? What would the collection of possible “45 degree points” look like?

Suppose the squares have side length 1 – what is the largest possible perimeter for the triangles formed from the straight lines and the square (with the 90 degree angle still assumed)

Examples of poor questions:

Is it drawn to scale?

How can I link this to trigonometry?

Are those squares?

7. After all of this warm-up, when the students saw the original question they were remarkably quick at finding the answer (once they had parsed the word-heavy question). Great recall of circle theorems. I made a toy on Geogebra to illustrate the problem