Here is the strategy behind the last topic, building facts: a hard fact can be broken apart into two easy ones. Look at 7 rows of 6.
Why it works
Splitting the array does not add or remove any squares. The top part is 5 rows of 6 and the bottom part is 2 rows of 6. Every row in both parts still has 6, so both parts are multiplied by 6. Then the two parts add back to the whole.
Key idea
Break one factor into two parts. Multiply each part by the other factor, then add: $7 \times 6 = 5 \times 6 + 2 \times 6$.
Worked example: Break the 7
Find $7 \times 6$.
- $7 = 5 + 2$.
- $5 \times 6 = 30$ and $2 \times 6 = 12$.
- $30 + 12 = 42$.
Answer: $42$
Worked example: Break the 8
Find $8 \times 7$.
- $8 = 5 + 3$.
- $5 \times 7 = 35$ and $3 \times 7 = 21$.
- $35 + 21 = 56$.
Answer: $56$
Worked example: Bigger numbers
Find $6 \times 12$.
- $12 = 10 + 2$.
- $6 \times 10 = 60$ and $6 \times 2 = 12$.
- $60 + 12 = 72$.
Answer: $72$
Common mistake
Multiplying only one part. Some people write $7 \times 6 = 5 \times 6 + 2 = 32$. But the 2 is 2 rows of 6, so it must be $2 \times 6$. Check with the array: the bottom part has 12 squares, not 2.