Week 13 · Nines, place value puzzles and three-digit sums · 3 lessons
1
The finger trick for nines
Discover Mathematics P3: Term 1, Lessons 51–60
GoalUse the finger trick and the patterns in the nines facts to find the products of 9.
New words
nines facts · multiplication facts that have 9 as a factordigit · one of the symbols 0 to 9 used to write numberspattern · something that repeats in a way you can predict
Explanation
The nines facts have helpful patterns. For the finger trick, hold up all 10 fingers. To find 9 × 4, fold down your 4th finger from the left. The 3 fingers on the left of the folded finger are the tens, and the 6 fingers on its right are the ones. So 9 × 4 = 36. Look at the products 9, 18, 27, 36, 45, and so on. The tens digit goes up by 1 and the ones digit goes down by 1, and the two digits always add up to 9. Another way: 9 × 6 is one group of 6 less than 10 × 6, so 9 × 6 = 60 − 6 = 54.
Fact
Product
Tens + ones
9 × 1
9
0 + 9
9 × 2
18
1 + 8
9 × 3
27
2 + 7
9 × 4
36
3 + 6
9 × 5
45
4 + 5
9 × 6
54
5 + 4
9 × 7
63
6 + 3
9 × 8
72
7 + 2
9 × 9
81
8 + 1
9 × 10
90
9 + 0
Worked examples
Folded finger
Left (tens)
Right (ones)
Product
7
6
3
63
Find 9 × 7. Fold down the 7th finger. There are 6 fingers on its left and 3 fingers on its right. So 9 × 7 = 63.
Find 9 × 6 from 10 × 6. The tape shows 10 groups of 6, which is 60. Take away the dashed group of 6: 60 − 6 = 54. So 9 × 6 = 54.
Answer
Digits added
Right?
56
5 + 6 = 11
no
54
5 + 4 = 9
yes
Use the digit pattern to check. Salma says 9 × 6 = 56. The digits 5 and 6 add up to 11, not 9, so the answer is wrong. The right answer is 54, and 5 + 4 = 9.
Class activity
Nines speed game. Work with a partner and a timer. In 2 minutes, one player calls out nines facts in a mixed order, such as 7 × 9, 9 × 3, 9 × 10 and 4 × 9, and the other player answers using the finger trick or a pattern. Count the correct answers, then swap roles and try to beat your score.
Practice
1
Use the finger trick to find 9 × 5.
Fold the 5th finger: 4 fingers on the left and 5 on the right. 9 × 5 = 45.
2
Find 9 × 8.
Fold the 8th finger: 7 on the left and 2 on the right. 9 × 8 = 72. The digits add up: 7 + 2 = 9.
