These are the facts people find hardest, but you already have the tools. Breaking apart and doubling handle every one of them.
| To find | Think | Example |
|---|---|---|
| $9 \times n$ | $10 \times n$, take away one $n$ | $9 \times 6 = 60 - 6 = 54$ |
| $8 \times n$ | double $4 \times n$ | $8 \times 7 = 28 + 28 = 56$ |
| $7 \times n$ | $5 \times n + 2 \times n$ | $7 \times 7 = 35 + 14 = 49$ |
Why it works
9 groups is one group less than 10 groups, so take one group away from the 10s fact. 8 groups is two sets of 4 groups, so double the 4s fact. 7 groups is 5 groups and 2 groups. Each strategy just splits or adjusts the groups, so the total is right.
Key idea
Nines: ten groups minus one. Eights: double the fours. Sevens: five groups plus two groups.
Worked example: Nines
Find $9 \times 6$.
- $10 \times 6 = 60$.
- Take away one 6: $60 - 6 = 54$.
- Check: $5 + 4 = 9$.
Answer: $54$
Worked example: Eights
Find $8 \times 7$.
- $4 \times 7 = 28$.
- Double: $28 + 28 = 56$.
Answer: $56$
Worked example: Sevens
Find $7 \times 8$.
- $5 \times 8 = 40$ and $2 \times 8 = 16$.
- $40 + 16 = 56$. (The same as $8 \times 7$: a turn-around fact.)
Answer: $56$
Common mistake
Taking away the wrong number in the 9s. $9 \times 6$ is ten 6s minus one 6: $60 - 6 = 54$. Taking away 9 gives 51, which is wrong. The digit check catches it: $5 + 1 = 6$, not 9.