B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates

Multiplication Facts to 12 × 12

B2.2 B2.1About 40 minutes

Learning goals

I can recall multiplication facts from 0 × 0 to 12 × 12.
I can use facts I know (like the 10s and 2s) to find the 11s and 12s.
I can explain a strategy for a fact I'm not sure of.

Words to know

factor
A number you multiply. In 12 × 7 = 84, the factors are 12 and 7.

product
The answer when you multiply. In 12 × 7 = 84, the product is 84.

dozen
A group of 12. Eggs often come in cartons of a dozen.

square number
The product of a number times itself, like 11 × 11 = 121 or 12 × 12 = 144.

Remember from Grade 4

In Grade 4 you learned all your multiplication facts from 1 × 1 to 10 × 10, using strategies like doubling, adding a group and taking away a group. In Grade 5 you will add the 11s and 12s, so you know every fact up to 12 × 12. You will also remember that 0 times any number is 0, even 0 × 0.

Let's start with a question

Eggs come in cartons of 12 (a dozen). Your family buys 7 cartons for a Thanksgiving baking day. How many eggs is that?

You need 7 × 12. You may not know it yet, but you know 7 × 10 = 70 and 7 × 2 = 14. So 7 × 12 = 70 + 14 = 84 eggs.

That is the secret to the 12s: 12 = 10 + 2.

7 rows of 12 dots. The dashed line splits each row into 10 and 2. 7 × 10 = 70 and 7 × 2 = 14, so 7 × 12 = 84.

The 11s: ten groups plus one more group

11 = 10 + 1. So 11 × a number = 10 × the number + the number.

11 × 6 = 60 + 6 = 66
11 × 11 = 110 + 11 = 121
11 × 12 = 120 + 12 = 132

From 11 × 1 to 11 × 9, the product is the digit written twice: 11, 22, 33 ... 99. After that, use 10 groups plus one more group.

Fact	Product	How to think of it
11 × 10	110	10 × 10 + 10
11 × 11	121	110 + 11
11 × 12	132	120 + 12
12 × 3	36	30 + 6
12 × 4	48	40 + 8
12 × 6	72	60 + 12
12 × 7	84	70 + 14
12 × 8	96	80 + 16
12 × 9	108	90 + 18
12 × 12	144	120 + 24

Facts with 11 and 12, built from the 10s and 2s (or the 10s and 1s).

The 12s: ten groups plus two groups

12 × a number = 10 × the number + 2 × the number.

Another way: 12 is double 6. So 12 × 8 is double 6 × 8. 6 × 8 = 48, and double 48 is 96.

12 rows of 8 squares split into two halves of 6 × 8 = 48. Two 48s make 96, so 12 × 8 = 96. Doubling a 6s fact gives the 12s fact.

Worked example

Example 1: Use 10s and 2s

Solve 12 × 9.

Split 12 into 10 + 2.
10 × 9 = 90.
2 × 9 = 18.
90 + 18 = 108.

12 × 9 = 108

Worked example

Example 2: Use doubling

Solve 12 × 6.

12 is double 6.
Find 6 × 6 = 36.
Double it: 36 + 36 = 72.

12 × 6 = 72

Worked example

Example 3: A story problem

A hockey team has 11 players on the ice and bench for a practice game. 12 teams come to a tournament. How many players is that?

That's 12 groups of 11, or 12 × 11. Any order works, so think 11 × 12.
10 × 12 = 120.
One more group of 12: 120 + 12 = 132.

132 players

Fact reminders

0 × any number = 0 (even 0 × 0 = 0).
1 × any number = that number.
Any order: if you know 12 × 7, you know 7 × 12.
Practise a few facts each day. Short, regular practice works better than one long session.

Just for fun

A baker's dozen is 13, not 12! So 12 cartons of eggs hold 12 × 12 = 144 eggs, but 12 baker's dozens of muffins would be 12 × 13 = 156. Lucky muffin fans!

Hands-on activity

Multiplication war to 12 × 12

You need: a deck of playing cards with the kings removed. Ace = 1, Jack = 11, Queen = 12, number cards are their numbers.

Split the deck between two players.
Each player turns over two cards and multiplies them. Say the fact out loud, like "Queen and 7: 12 × 7 = 84".
The bigger product wins all four cards. If you're not sure of a fact, explain a strategy (like 10s plus 2s) before checking.
Play for 10 minutes.

Extra: Use an egg carton (12 cups). Fill some cups with a small item like dry beans to show 12 × 3 or 12 × 5. Keep beans away from small children.

Your turn

11 × 6 = ?

12 × 4 = ?

11 × 11 = ?

12 × 6 = ?

0 × 12 = ?

12 × 11 = ?

9 × 12 = ?

12 × 12 = ?

More practice: warm-up

11 × 3 = ?

12 × 2 = ?

11 × 10 = ?

12 × 5 = ?

12 × 1 = ?

More practice: on your own

12 × 7 = ? Show your strategy.

12 × 8 = ? Use doubling.

11 × 12 = ?

A carton holds 12 eggs. How many eggs are in 9 cartons?

12 × 3 = ? and 3 × 12 = ?

Challenge

Find the missing factor: 12 × □ = 132.

Explain why 12 × 12 = 144 using a fact you know well.

Ellie says 11 × 12 = 1212. What mistake did she make? What is the right answer?

Check your understanding

Quiz

What is 12 × 6?

What is 11 × 9?

What is 12 × 9?

Which helps you find 12 × 7?

How many eggs are in 4 dozen?

What is 11 × 11?

For parents and teachers

Big idea: By the end of Grade 5, the Ontario curriculum (B2.2) expects students to recall multiplication facts from 0 × 0 to 12 × 12 and the related division facts. Facts to 10 × 10 were the Grade 4 goal, so the 11s and 12s are the main new learning.

Common difficulties:

Mixing up 11 × 11 and 11 × 12, or 12 × 8 and 12 × 9. Have your child say the strategy ("10 × 8 plus 2 × 8") until the fact becomes automatic.
Weak facts from earlier grades (often 6s, 7s and 8s). The 12s depend on them; spend a few minutes reviewing those too.
Forgetting that 0 × a number is 0.

How to help: Practise a few facts for 5 minutes most days: in the car, while cooking ("we need 3 dozen eggs"), or with the card game. Praise strategies, not only speed. Recall should become quick, but understanding comes first.