Build a picture before recalling a fact
Put counters into 3 equal rows of 4. There are 12 counters altogether, so 3 × 4 = 12. This rectangular arrangement is called an array.
Turn the array to see 4 rows of 3. It still has 12 counters. That is why switching the order of the two factors gives the same product: 3 × 4 = 4 × 3.
Worked example: use a known fact to find 6 × 7
Split 6 groups of 7 into 5 groups of 7 and 1 more group of 7. If you know 5 × 7 = 35, add another 7: 35 + 7 = 42.
Written as one chain, 6 × 7 = (5 × 7) + (1 × 7) = 35 + 7 = 42. Draw an array with 5 rows and then add a sixth row to see why it works.
This is the distributive property in action. Later, the same idea helps with 16 × 7: split 16 into 10 and 6, calculate 70 + 42, and get 112.
Useful times-table strategies
- Twos: double the other factor. For example, 2 × 9 is 9 + 9 = 18.
- Fours: double twice. To find 4 × 6, double 6 to get 12, then double 12 to get 24.
- Fives and tens: use a familiar 10-times fact and take half when working with fives.
- Nines: start with ten groups and subtract one group. For 9 × 8, calculate 80 − 8 = 72.
Practice division alongside multiplication
Use the same array to connect related facts. If 6 × 7 = 42, then 42 ÷ 6 = 7 and 42 ÷ 7 = 6. Ask whether you are finding the number of groups or the number in each group.
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