The idea, step by step
Facts describe equal groups
Six rows of seven objects gives 6 × 7 = 42. An array shows all the equal rows at once. Turning the array swaps rows and columns, so 7 × 6 has the same total. This is why multiplication can be done in either order.
A multiplication table is a way to organise these facts. Learn the patterns and check uncertain facts with an array or a known fact. Multiplying by 1 keeps the amount; multiplying by 0 gives no objects.
Build a fact rather than guess
If 5 × 7 = 35, one more group of seven gives 6 × 7 = 42. If 10 × 8 = 80, one group of eight fewer gives 9 × 8 = 72. These methods explain why the facts are true.
Some facts can be doubled. Knowing 4 × 6 = 24 lets you find 8 × 6 = 48. Practise facts in different orders so you recognise the relationship, not just a counting song. Say the complete fact, including the total.
A common trap
Treating 6 × 7 as 6 + 7.
Instead: 6 × 7 means six equal groups of seven. The total is 42, not 13.
See the thinking
Use a fives fact
Find 6 × 7 using 5 × 7.
- 5 × 7 = 35.
- Six groups is one more group: add 7.
- 35 + 7 = 42.
Use a tens fact
Find 9 × 8 using 10 × 8.
- 10 × 8 = 80.
- Nine groups is one group fewer: subtract 8.
- 80 − 8 = 72.
Check your understanding
If 7 × 4 = 28, what is 4 × 7?
Show answer
28.
Turning the array changes its arrangement but not its number of objects.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Find 7 × 8.1 mark
- Find 9 × 6.1 mark
- Complete: 4 × 9 = 9 × ____.1 mark
- Use 5 × 8 = 40 to find 6 × 8.2 marks
- A tray has 7 equal rows with 7 muffins in each. How many muffins are there?1 mark
- A learner says 8 × 4 is 28. Show a known fact that helps correct the answer.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find 7 × 8.1 mark
7 × 4 = 28, so doubling gives 7 × 8 = 56.
56. - Find 9 × 6.1 mark
10 × 6 − 6 = 60 − 6 = 54.
54. - Complete: 4 × 9 = 9 × ____.1 mark
Swapping the factors leaves the product unchanged.
4. - Use 5 × 8 = 40 to find 6 × 8.2 marks
Add one more group of eight: 40 + 8 = 48.
48. - A tray has 7 equal rows with 7 muffins in each. How many muffins are there?1 mark
7 × 7 = 49.
49 muffins. - A learner says 8 × 4 is 28. Show a known fact that helps correct the answer.2 marks
For example, 4 × 4 = 16 and doubling gives 8 × 4 = 32.
Alternatively 8 × 2 = 16, then double again.
8 × 4 = 32.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.
Official curriculum source ↗