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Multiplication as groups and arrays
Years 3 to 6
Multiplication means equal groups, and a grid of dots shows why the order does not matter.
For learners
4 × 6 means 4 groups of 6. Draw 4 rows with 6 dots in each row. Count them: 24.
Turn the picture on its side. Now there are 6 rows of 4. It is still 24. That is why 4 × 6 = 6 × 4.
Division is the other way round. 24 ÷ 4 asks: if I share 24 dots into 4 equal rows, how many are in each row?
A worked example
Use an array to work out 7 × 8.
- Draw 7 rows of 8 dots.
- Split it into 5 rows and 2 rows: 5 × 8 = 40 and 2 × 8 = 16.
- 40 + 16 = 56.
For grown-ups
Seeing multiplication as an array builds the idea of area, factors and the link between multiplying and dividing. If a child knows 4 × 6 = 24, they also know 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
How to help
- Learn the tables in short daily bursts, and use the commutative trick to halve what you must learn.
- Use the quiet-speed idea: quick recall is the aim, not rushing.
- Link tables to patterns: the 9s digits add to 9, the 5s end in 0 or 5.
Why it matters
Arrays lead straight to area, to long multiplication and to algebra, where is also a rectangle split into parts.
Topics in quarter that use this
- Times tables
- Multiplying
- Dividing
- Area by counting squares