How To Turn 1 Short Maths Problem Into An Entire Lesson

Wish you could spend less time finding good tasks to use for lessons?

Here's how you can turn one short maths problem into an entire lesson.

(It's a method I use for every problem I create.)

1. Choose a problem that matters

The problem you choose doesn’t need to be interesting, or even particularly difficult. In fact, the more mundane the better.

(Textbooks and worksheets are a great source.)

What’s important is that it’s a skill/concept you want your students to focus on.

2. Open it up

Opening up the problem gives you FAR more insight about what your students know.

All it takes is a small tweak.

For example, instead of asking ‘What's halfway between 1/2 and 3/4?', this question asks for ANY fraction between the other two-

What's a fraction that lies between these two numbers?
1/2, 3/4

3. Focus on the reasons

Maths is way more interesting when we focus on reasons – not just answers.

It also helps students make sense of ideas and understand different approaches.


  • How do you know?
  • Can you explain it a different way?
  • How are these solutions similar? different?

4. Follow up with similar problems

The power of a problem comes when you follow with a similar one.

It allows students to take existing and known strategies into a different context or to look at an idea in a new way.

A similar problem also feels safer – it gives students an entry point that’s familiar.

Here are 2 examples:

Example 1. After identifying any fraction, between two others, students are asked this question-

Are these fractions in size order?
15/16, 16/17, 17/18

Example 2. This next follow up problem starts to draw out a general principle-

Does this always work?  The fractions in this triple are all in size order:  1/2, 2/3, 3/4.  Does this work for all fraction triples with the same structure?


How to turn one short maths problem into an entire lesson:

  1. Choose a problem that matters
  2. Open it up
  3. Focus on the reasons
  4. Follow up with similar problems.

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