B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and DividingMultiplication Facts to 10 × 10
B2.2 B2.1 A1About 40 minutes
Learning goals- I can recall multiplication facts up to 10 × 10.
- I can use a fact I know to find a fact I don't know yet.
- I can use doubling, adding a group and taking away a group.
Words to know
factor
A number you multiply. In 6 × 7 = 42, the factors are 6 and 7.
product
The answer when you multiply. In 6 × 7 = 42, the product is 42.
double
Multiply by 2, or add a number to itself.
square number
The product of a number times itself, like 6 × 6 = 36.
recall
Remember a fact quickly without counting.
Remember from Grade 3
In Grade 3 you learned your facts of 2, 5 and 10 by heart. In Grade 4 you will learn all the facts from 1 × 1 to 10 × 10. That sounds like a lot, but you already know many of them, and there are smart tricks for the rest.
Why learn facts by heart?
Imagine reading a book if you had to sound out every word. Slow! Knowing your facts is like knowing words by sight. It makes bigger math fast and easy, like 6 × 40 or 7 × 38, which you will do later in this unit.
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
Good news: there are fewer facts than you think
Because of the any order rule, 6 × 8 and 8 × 6 are the same fact. You already know the facts of 1 (the number stays the same), 2, 5 and 10. That leaves only a few fact groups to learn: the 3s, 4s, 6s, 7s, 8s and 9s. Use these strategies.
Strategy 1: Doubling (for 4s and 8s)
- × 4 = double, then double again. 4 × 7: double 7 is 14, double 14 is 28.
- × 8 = double three times. 8 × 6: 6 → 12 → 24 → 48.
Strategy 2: Add a group (for 3s and 6s)
- × 3 = × 2, plus one more group. 3 × 8: 2 × 8 = 16, plus 8 more = 24.
- × 6 = × 5, plus one more group. 6 × 8: 5 × 8 = 40, plus 8 more = 48.
Worked exampleExample 1: Add a group
- Start with a fact you know: 5 × 7 = 35.
- 6 × 7 is one more group of 7.
- 35 + 7 = 42.
Strategy 3: Take away a group (for 9s)
× 9 = × 10, minus one group.
9 × 7: 10 × 7 = 70, minus one 7 = 63.
A pattern to check your 9s: the digits of the product add up to 9. 63 → 6 + 3 = 9. 72 → 7 + 2 = 9.
Worked exampleExample 2: Take away a group
- 10 × 8 = 80.
- 9 × 8 is one group of 8 less.
- 80 − 8 = 72.
- Check the pattern: 7 + 2 = 9. ✓
Strategy 4: Split into two facts you know (great for 7s)
Split 7 into 5 + 2.
7 × 8 = 5 × 8 + 2 × 8 = 40 + 16 = 56.
This is the splitting rule from the last lesson.
Worked exampleExample 3: Split a 7s fact
- Split 7 into 5 + 2.
- 5 × 6 = 30 and 2 × 6 = 12.
- 30 + 12 = 42.
7 × 6 = 42. (It's the same as 6 × 7 from Example 1!)
Strategy 5: Square numbers
The facts where a number is multiplied by itself are called square numbers, because the array makes a square. Learn them as a set: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
A trick: 6 × 6 = 36, 7 × 7 = 49, 8 × 8 = 64.
Be kind to your brain
Learning facts takes practice, and everyone learns at their own speed. Make a list of facts you know for sure and a list of "working on it" facts. Practise only 3 or 4 "working on it" facts at a time. Move them to your "know it" list when you can say them quickly. Notice how your list grows!
Just for funYour hands know the 9s! Hold up 10 fingers. For 9 × 4, fold down your 4th finger from the left. There are 3 fingers before the fold and 6 after: 36. A calculator you can never lose!
Hands-on activityMultiplication war (card game)
You need: a deck of playing cards with the face cards (jacks, queens, kings) taken out. Ace = 1. A partner.
- Split the cards between the two players, face down.
- Each player flips two cards and multiplies them. For a 7 and a 6, say "7 × 6 = 42".
- The bigger product wins all four cards. If you tie, flip again.
- If you are not sure of a fact, say the strategy out loud: "5 × 6 is 30, plus one more 6 is 36."
- Play for 10 minutes. Write down any facts that were tricky and practise them tomorrow.
Math talk: "Which strategy helped you most today?"
Your turn
18. 2 × 6 = 12, plus one more 6 = 18.
32. Double 8 is 16, double 16 is 32.
42. 5 × 7 = 35, plus 7 = 42.
54. 10 × 6 = 60, minus 6 = 54.
64. It's a square number. Or: 8 → 16 → 32 → 64.
63. 10 × 7 = 70, minus 7 = 63.
28. Double 7 is 14, double 14 is 28.
21. 2 × 7 = 14, plus 7 = 21.
More practice: on your own
49. 5 × 7 = 35 and 2 × 7 = 14. 35 + 14 = 49.
72. 10 × 8 = 80, minus one 8 = 72.
36. 5 × 6 = 30, plus 6 = 36.
36. Double 9 is 18, double 18 is 36.
56. 5 × 7 = 35 and 3 × 7 = 21. 35 + 21 = 56.
Challenge
1Find all the facts up to 10 × 10 that have a product of 24.
3 × 8, 8 × 3, 4 × 6 and 6 × 4. (2 × 12 also makes 24, but 12 is bigger than 10.)
2You know 6 × 7 = 42. How can you use it to find 6 × 8?
6 × 8 is one more group of 6. 42 + 6 = 48.
3Show how to find 8 × 6 by doubling three times.
Start with 6. Double: 12 (2 × 6). Double: 24 (4 × 6). Double: 48 (8 × 6). So 8 × 6 = 48.
Quiz
4. To find 6 × 7, start with 5 × 7 = 35. What next?
6. Which fact has a product of 36?
Big idea: By the end of Grade 4, the Ontario curriculum (B2.2) expects children to recall multiplication facts from 1 × 1 to 10 × 10 and the related division facts. Recall grows from understanding: strategies first, speed later.
Common difficulties:
- Skip-counting from the beginning every time (6, 12, 18...). That's a good start; next, show how to start from a known fact (5 × 6) and add or take away a group.
- The 6s, 7s and 8s are the hardest for many children. Focus on a few at a time.
- Mixing up 6 × 8 = 48 and 7 × 8 = 56. Practise them side by side: "56 is one more 8 than 48."
How to help: Short and often beats long and rare: 5 minutes a day in the car or at dinner. Keep it low-stress; timed tests can cause anxiety for some children. Celebrate the growing "know it" list.