Understand the idea.
Facts describe equal groups
Multiplication counts equal groups. Six rows with seven objects in every row give . Turn the array and it becomes seven rows of six, with the same objects. This explains why swapping the factors keeps the product unchanged.
Read each factor and the total when practising a fact. One group of an amount is that same amount; zero groups contain no objects. An array or multiplication table can help you check an uncertain fact without guessing.
Build a fact rather than guess
Build a new fact from one you know. If five groups of seven total , a sixth group adds another . If ten groups of eight total , nine groups contain one group of eight less. Think about the group being added or removed.
Doubling the number of equal groups doubles the total. Knowing gives . Choose a nearby fact you can recall quickly, then explain the change in groups so your calculation has a reason.
See the method in action.
Use a fives fact
Find 6 × 7 using 5 × 7.
Worked solution
- 1
Start with five groups of seven.
The known fives fact counts all objects in the first five groups.
- 2
Add one more group.
Six groups contain one more group of seven than five groups do.
- 3
State the complete multiplication fact.
The total 42 now includes all six equal groups.
42.
Use a tens fact
Find 9 × 8 using 10 × 8.
Worked solution
- 1
Start with ten groups of eight.
The tens fact gives a nearby total.
- 2
Remove one group of eight.
Nine groups have exactly one fewer group than ten groups.
- 3
State the fact for nine groups.
The remaining total counts nine complete groups of eight.
72.
Try it yourself.
Check your understanding
If 7 × 4 = 28, what is 4 × 7?
Show answer & reasoning
28.
The answer is . Rotating a seven-by-four array gives a four-by-seven array without adding or removing any objects, so .
Keep practising
6 worksheet questions · 8 marks
Read the questions online
- Find .1 mark
- Find .1 mark
- Complete: .1 mark
- Use to find .2 marks
- A tray has 7 equal rows with 7 muffins in each. How many muffins are there?1 mark
- A learner says 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 .1 mark
, so doubling gives .
56. - Find .1 mark
.
54. - Complete: .1 mark
Swapping the factors leaves the product unchanged.
4. - Use to find .2 marks
Add one more group of eight: .
48. - A tray has 7 equal rows with 7 muffins in each. How many muffins are there?1 mark
.
49 muffins. - A learner says is 28. Show a known fact that helps correct the answer.2 marks
For example, and doubling gives .
Alternatively , then double again.
.
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 ↗