3 times table: chart, tricks and practice

The 3 times table chart

Here's the whole table. The third column adds up the digits of each answer. Watch the pattern: 3, 6, 9, then 3, 6, 9 again, all the way down.

The double-plus-one trick

Three groups is two groups plus one more group. Your child already knows the 2s (doubles), so every 3s fact becomes “double it, then add one more”:

• 3 × 6: double 6 is 12, plus 6 more is 18
• 3 × 7: double 7 is 14, plus 7 more is 21
• 3 × 8: double 8 is 16, plus 8 more is 24
• 3 × 9: double 9 is 18, plus 9 more is 27

A second route is to step from a fact your child knows. 3 × 5 = 15, so 3 × 6 is one more 3: 15 + 3 = 18. Stepping works well for the facts right after 3 × 5 and 3 × 10.

The 3, 6, 9 digit pattern

Add the digits of any answer in the 3s: 2 + 1 = 3 for 21, 2 + 4 = 6 for 24, 2 + 7 = 9 for 27. The digit sums go 3, 6, 9 and repeat. It isn't a coincidence, and it doesn't stop at 36: a whole number is a multiple of 3 exactly when its digits add up to a multiple of 3. That lets kids test numbers far beyond the table:

• 51: 5 + 1 = 6, so 51 is a multiple of 3. Check: 3 × 17 = 51.
• 74: 7 + 4 = 11, and 11 isn't a multiple of 3, so 74 isn't either. (3 × 24 = 72 and 3 × 25 = 75, so 74 falls in between.)
• 123: 1 + 2 + 3 = 6, so it's a multiple of 3: 3 × 41 = 123.

Older kids love using this as a party trick, and it's a useful check when they start dividing bigger numbers.

Hidden patterns in the ones digits

Look at just the last digit of each answer from 3 × 1 to 3 × 10: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. Every digit from 0 to 9 shows up exactly once. On a phone keypad (with 1, 2, 3 on the top row), the first three run down the right-hand column, the next three down the middle, the next three down the left, and then you land on 0.

The answers also take turns being odd and even: 3, 6, 9, 12… An odd number of 3s is odd, and an even number of 3s is even.

Print or draw a hundred chart, color every third number, and let your child discover the stripes for themselves.

Facts your child already knows from easier tables

Thanks to the turn-around rule, 3 × 5 is the same fact as 5 × 3, so every table your child learned earlier already covers part of the 3s. In our recommended order, the 3s come after the 1s, 2s, 10s and 5s, so 4 of the 12 facts are already known.

• 3 × 1 = 3from the 1s
• 3 × 2 = 6from the 2s
• 3 × 3 = 9new · square
• 3 × 4 = 12new
• 3 × 5 = 15from the 5s
• 3 × 6 = 18new
• 3 × 7 = 21new
• 3 × 8 = 24new
• 3 × 9 = 27new
• 3 × 10 = 30from the 10s
• 3 × 11 = 33with the 11s
• 3 × 12 = 36with the 12s

already knownnewonly if your school teaches the 11s and 12s

New in the 3s: 3 × 3, 3 × 4 and 3 × 6 through 3 × 9, plus 3 × 11 = 33 and 3 × 12 = 36 if your child's school teaches the 11s and 12s.

From here on, the 3s keep paying off: 3 × 4 = 12 is also 4 × 3 = 12, and the same goes for the 6s, 7s, 8s and 9s. Every 3s fact your child learns now is one less fact to learn later.

Common mistakes with the 3s (and quick fixes)

• Mixing up neighbors. Answering 24 for 3 × 7, or 21 for 3 × 8. Use the ladder: 3 × 6 = 18, then 21, then 24, adding 3 each time.
• Adding instead of multiplying. Answering 7 for 3 × 4. Go back to 3 groups of 4 and count.
• Doubling instead of tripling. Answering 16 for 3 × 8, forgetting the extra group. Say the trick out loud: “double it, then one more 8.”
• Losing the skip count. “18, 21, 23…” Use the digit check: 2 + 3 is 5, not 3, 6 or 9, so 23 can't be in the 3s.

The 3 times table in real life

Look for threes: holes in a pretzel, wheels on a tricycle, sides of a triangle, feet in a yard. Here are four stories to solve together.

Tap a story to see the answer. Ask your child to draw a quick picture first: groups, an array or a number line.

3 times table practice

Ten questions, mixed on purpose: some are turned around, and some have a missing number, like 3 × ? = 18. Tap a question to check the answer, and ask your child which trick they used. Finding a missing factor is how third graders start to think about division (3.OA.A.4).

1. 3 × 4 = ?Check

   3 × 4 = 12

2. 3 × 7 = ?Check

   3 × 7 = 21

3. 8 × 3 = ?Check

   8 × 3 = 24

4. 3 × ? = 18Check

   3 × 6 = 18

5. ? × 3 = 27Check

   9 × 3 = 27

6. 3 × 12 = ?Check

   3 × 12 = 36

7. 3 × 3 = ?Check

   3 × 3 = 9

8. 3 × ? = 33Check

   3 × 11 = 33

9. ? × 3 = 15Check

   5 × 3 = 15

10. 3 × 10 = ?Check

    3 × 10 = 30

Division facts for the 3s

Dividing by 3 means sharing into 3 equal groups. Use the 3s backward: to find 27 ÷ 3, ask “3 times what is 27?” Since 3 × 9 = 27, the answer is 9.

1. 21 ÷ 3 = ?Check

   21 ÷ 3 = 7

2. 27 ÷ 3 = ?Check

   27 ÷ 3 = 9

3. 12 ÷ 3 = ?Check

   12 ÷ 3 = 4

4. 24 ÷ 8 = ?Check

   24 ÷ 8 = 3

5. 36 ÷ 3 = ?Check

   36 ÷ 3 = 12

6. 18 ÷ ? = 6Check

   18 ÷ 3 = 6

Want a printed set? Our times tables worksheets and division facts worksheets come with answer keys.