“But you must… But you can’t…” Simple ways of adding complexity to challenging tasks

Sometimes it seems like we make maths teaching more difficult than it needs to be, but make the maths itself easier than it should be.  Challenging tasks are not only good for the brain, but also very engaging and fun for kids.  Here are a few simple phrases that I find useful when designing extending prompts.

To design a great challenging task, start with any normal question and try adding, “But you must…”, or “But you can’t…” to the end of it.  Let’s have a go together.

Basic question 1:

The perimeter of a shape is 24 – draw it.

Now, let’s add some challenge!

But you must…

• Use more than 4 right angles
• Have angles that sum to 540^o
• Have three sets of parallel lines
• Use a triangle and draw it to check
• Use a decimal number on at least one side
• Use a curved line

But you can’t…

• Have any side the same length
• Have any angle smaller than… or larger than…
• Use four or less sides
• Use any side length bigger than 3cm

Worked pretty well hey?  Let’s try it again…

Basic question 2:

Roll two dice 20 times and record the results.  Highest score wins.

But you must…

• Only count scores that total less than nine
• Double the score of any rolls less than or equal to 4
• Choose to either multiply or add the two numbers on the dice, then add it to your total
• Choose to either add both amounts to your total, or subtract them from one other player’s total

But you can’t…

• Roll a total of 10 – that deletes your total score so far and you start again with your remaining rolls
• Roll any double – that subtracts the total from your score instead of adding it

What can you think of to try?  Remember to email them through so that we can share them with others!

Want more?  Check out these articles.

• Serious extension for gifted kids
• Connecting and generalising questions
• Differentiation without going nuts
• The time crunch: making an extra hour every week (without cutting anything out)
• Improving student reasoning