The idea, step by step
Rows and columns
An array arranges items in straight rows and columns. In the picture there are 3 rows of 5 dots. Each row must have the same number. The total is 3 × 5 = 15.
Turn the array and it has 5 rows of 3. The total does not change. This shows why 3 × 5 and 5 × 3 have the same answer.
Split an array to calculate
You can split 4 rows of 6 into 4 rows of 5 and 4 rows of 1. The totals are 20 and 4, making 24. The parts must cover the array once, with no missing dots or overlaps.
An array also shows division. If 24 dots make four equal rows, each row has six dots. If each row must have six, there are four rows.
A common trap
Calling any scattered collection of dots an array.
Instead: An array needs equal rows and columns. Check that each row and each column is straight and contains a consistent number.
See the thinking
Read an array
The picture has 4 equal rows. Write its multiplication and division facts.
- There are 5 dots in each of the 4 rows.
- 4 × 5 = 20 and 5 × 4 = 20.
- The division facts are 20 ÷ 4 = 5 and 20 ÷ 5 = 4.
Split a larger array
Use 3 × 10 and 3 × 2 to work out 3 × 12.
- Split each row of 12 into 10 and 2.
- 3 × 10 = 30 and 3 × 2 = 6.
- Combine the two parts: 30 + 6 = 36.
Check your understanding
An array has 5 rows of 4. How many dots are there?
Show answer
20 dots.
5 × 4 = 20.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Draw 2 rows of 6 dots. Write the total.
- Write a multiplication fact for the supplied array.
- Eighteen dots are arranged in 3 equal rows. How many are in each row?
- Use an array split to calculate 4 × 12.
- Draw two different rectangular arrays with exactly 20 dots.
- An array has 4 rows of 7. Another whole row is added. How many dots are there now?
Read the worked solutions
- Draw 2 rows of 6 dots. Write the total.
2 × 6 = 12. The drawing should have exactly two equal rows.
12 dots. - Write a multiplication fact for the supplied array.
The array has 3 rows and 4 columns.
3 × 4 = 12 or 4 × 3 = 12. - Eighteen dots are arranged in 3 equal rows. How many are in each row?
18 ÷ 3 = 6.
6 dots. - Use an array split to calculate 4 × 12.
4 × 10 = 40 and 4 × 2 = 8; 40 + 8 = 48.
48 - Draw two different rectangular arrays with exactly 20 dots.
Both products are 20. Rotated versions are also valid arrays; accept any two different row counts that divide 20.
For example, 4 rows of 5 and 2 rows of 10. - An array has 4 rows of 7. Another whole row is added. How many dots are there now?
The new array has 5 rows of 7: 5 × 7 = 35.
35 dots.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Tables 2, 3, 4, 5 and 10; linked division; arrays; one-/two-digit problems.
Official curriculum source ↗