Step by step
- 2 digits by 1. Multiply the ones, carry, then multiply the tens.
- 3 and 4 digits by 1. The same steps across more columns.
- 2 digits by 2. Two partial products, one for the ones and one for the tens, then add them.
- 3 digits by 2. Bigger numbers, the same method.
Times tables first
Long multiplication goes smoothly once the facts are automatic. If they are not yet, practise with the times tables worksheets alongside.In the Australian Curriculum
- Year 3Solving single-digit multiplication problems and recalling facts for twos, threes, fours, fives and tens.
- Year 4Multiplying by multiples of 10, and choosing efficient strategies for multiplication (AC9M4N06).
- Year 5Multiplying large numbers by one- and two-digit numbers, and checking answers with estimates.
In the Australian Curriculum the two-digit by two-digit problems on this page belong to Year 5. Year 4 work on multiplying by multiples of ten is what makes the second partial product make sense: 47 × 30 is 47 × 3, then times 10.
The curriculum describes efficient strategies rather than one method, so some schools use an area model before the vertical layout. The partial products on these answer keys line up with the two parts of an area model, which helps children connect the two.
Summarised in our own words from the Australian Curriculum: Mathematics, Version 9.0 (ACARA).
