Math Core

The 3s, 4s and 6s can feel harder than the 2s, 5s and 10s. The good news: you can build every one of them from facts you already know. You never have to start from zero.

Multiplying by 3: double, then one more group

3 groups is 2 groups plus 1 more group. So find the double, then add one more.

What is $3 \times 7$ ?

2 groups of 7: $2 \times 7 = 14$ .
1 more group of 7: $14 + 7 = 21$ .

$3 \times 7 = 21$ .

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You can also count by threes on a number line: 3, 6, 9, 12, 15, 18, 21.

Multiplying by 4: double, then double again

4 is $2 + 2$ . So 4 groups is a double of a double.

What is $4 \times 8$ ?

Double 8: 16.
Double 16: 32.

$4 \times 8 = 32$ .

Multiplying by 6: double the 3s

6 groups is two sets of 3 groups. So find the 3s fact, then double it.

What is $6 \times 7$ ?

$3 \times 7 = 21$ .
Double 21: 42.

$6 \times 7 = 42$ .

Another way: 6 groups is 5 groups plus 1 more. $5 \times 7 = 35$ , and $35 + 7 = 42$ . Same answer!

Build from facts you know

× 3: find × 2, then add one more group.
× 4: double, then double again.
× 6: find × 3, then double. (Or find × 5, then add one more group.)

$n$	1	2	3	4	5	6	7	8	9	10
$3 \times n$	3	6	9	12	15	18	21	24	27	30
$4 \times n$	4	8	12	16	20	24	28	32	36	40
$6 \times n$	6	12	18	24	30	36	42	48	54	60

Look down each column. The 6s row is always double the 3s row.

Worked example: A 4s fact

What is $4 \times 9$ ?

Double 9: 18. Double 18: 36.

$4 \times 9 = 36$ .

Worked example: A 6s fact two ways

What is $6 \times 8$ ?

Way 1: $3 \times 8 = 24$ . Double 24: 48.

Way 2: $5 \times 8 = 40$ . One more group of 8: $40 + 8 = 48$ .

$6 \times 8 = 48$ .

Worked example: A division fact

What is $24 \div 3$ ?

Think: $3 \times ? = 24$ . Count by threes: 3, 6, 9, 12, 15, 18, 21, 24. That is 8 threes.

$24 \div 3 = 8$ .

Common mistake

When you use "5 groups plus 1 more group," add a whole group, not 1. For $6 \times 8$ , add 8 to 40 to get 48. Adding 1 would give 41, which is wrong.

Tip

Every answer in the 4s and 6s is even. If you get an odd answer for a 4s or 6s fact, check again.

Practice

Practice 1

What is $3 \times 6$ ?

Type a number.

Practice 2

What is $4 \times 7$ ?

Type a number.

Practice 3

What is $6 \times 6$ ?

Type a number.

Practice 4

What is $36 \div 4$ ?

Type a number.

Practice 5

Lee knows $5 \times 9 = 45$ . Which way helps him find $6 \times 9$ ?

Practice 6

What is $42 \div 6$ ?

Type a number.

Practice 7

A pack has 4 juice boxes. Dan buys 8 packs. How many juice boxes does he buy?

Type a number.