1. Multiplication facts: look at products
Paul Broadbent
@broadbentmaths

2. Multiples of 10
100 90 80 70 60 50 40 30 20 10
List all the multiples of 10 up to 10x10 = 100 – these usually cause few problems for children to learn.

3. The products > 80
100 90 80 81 70 60 50 40 30 20 10
Start at the top. If we think about all the products of the multiplication facts up to 10x10, there are no products in the 90s and only one in the 80s and that is 9x9=81.

4. The products > 70
100 90 80 81 70 72 60 50 40 30 20 10
How many products in the 70s? Only one – 8x9=72

5. The products > 60
100 90 80 81 70 72 60 63 64 50 40 30 20 10
There are two products in the 60s: 63 and 64

6. The products > 50
100 90 80 81 70 72 60 63 64 50 54 56 40 30 20 10
… and amazingly only two products in the 50s: 54 and 56. So, if we focus on the facts up to 10x10 (and ignore multiples of 10), there are only 6 products to learn and remember.

7. The products > 40
100 90 80 81 70 72 60 63 64 50 54 56 40 42 45 48 49 30 20 10
If we carry on down, the numbers increase: 4 products in the 40s: 42, 45, 48 and 49

8. The products > 30
100 90 80 81 70 72 60 63 64 50 54 56 40 42 45 48 49 30 32 35 36 20 10
Three products in the 30s: 32, 35, 36

9. The products > 20
100 90 80 81 70 72 60 63 64 50 54 56 40 42 45 48 49 30 32 35 36 20 21 24 25 27 28 10
…and 5 products in the 20s: 21, 24, 25, 27, 28. A number like 24 has several multiplication facts, but that’s OK – just highlight it’s importance.

10. Multiplication facts: products up to 10x10
100 90 80 81 70 72 60 63 64 50 54 56 40 42 45 48 49 30 32 35 36 20 21 24 25 27 28 10 12 14 15 16 18
There are 5 more numbers in the teens. The ones missing are just as interesting: 11, 13, 17 and 19 are all prime numbers.

11. 100 square 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
So let’s look at all those products on a 100 square.

12. Products on 100 square 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
These are the 23 numbers between 10 and 100 that are the products of all the multiplication facts up to 10x10. Spot the interesting diagonal pattern?

13. Products and patterns 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
The red numbers are all multiples of 9

14. Elevens and twelves 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100
The green numbers are highlighted to show multiples of 11 and the blue numbers are the only two extra for products of 12.