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Systematic Listing

Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)

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What a learner can do afterwards

  • List all possible meal combinations from 3 starters and 4 mains
  • Organise combinations into a systematic table to ensure none are missed
  • Explain why the total number of combinations equals the product of the options in each category

The lesson

A combination is one choice from each group, put together. If you have 3 T-shirt colours and 2 trouser colours, each outfit combines one shirt colour with one trouser colour. To list every combination without missing any, go through the colours in order instead of guessing.

Tap to fill the grid, one at a time: 3 rows of 2.
Each row is a shirt colour. Each column is a trouser colour. Every cell in the grid is one outfit, so there are 3 x 2 = 6 outfits in total.
Try it together

A cafe offers 3 starters and 4 mains. Pick the first starter and pair it with each of the 4 mains. Then move to the second starter and pair it with each main again. Keep going until every starter has been paired with every main. This gives 3 x 4 = 12 meal combinations.

Tap to fill the grid, one at a time: 3 rows of 4.
Good to know

Work through one group in order, pairing each item with every item in the other group before moving on. This systematic method stops you skipping a pair or writing the same one twice.

List combinations one group at a time, and the total always equals the two group sizes multiplied together.

Watch it

Where it sits

Learn first

This opens up

Nothing builds on it yet.

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.

Systematic Listing · Mathematics, ages 10 to 11 · LightMySky