2.3 Systematic listing strategies — Learn

Prerequisites: multiplication, addition and reading ordered pairs.

Objectives: list possibilities without repetition or omission; use a table or organised list to solve a counting problem.

Covers: N5 (systematic listing strategies).

Organised lists

A systematic list follows a fixed order. You choose one part, record every possible partner, then move to the next part. This makes omissions easier to spot.

Worked example. A spinner has red, blue and green sections. A coin shows heads or tails. List all outcomes in a table.

Start with red: red-heads, red-tails.

Then blue: blue-heads, blue-tails.

Then green: green-heads, green-tails.

There are six outcomes. Each colour appears with both coin results, so the list is complete.

Worked example. Make two-digit numbers from 1, 2 and 3 without repeating a digit.

Starting with 1 gives 12 and 13.

Starting with 2 gives 21 and 23.

Starting with 3 gives 31 and 32.

There are six numbers. The first digit groups make the list straightforward to check.

Watch out. A list such as 12, 13, 21, 31 misses 23 and 32. Check each starting choice and then each allowed partner.

Progress check

Before using a shortcut to count outcomes, make a small organised list for two choices from three colours and two coin results. The list gives evidence that nothing was missed.

You should now be able to

• make an organised list in a fixed order;
• avoid repeating an outcome;
• explain how your structure shows the list is complete;
• use a table when several choices must be paired.