← BlogOct 1, 20263 min read

The 3 times table: the number plus its double

I'm Heron. I help people do math in their heads, and the 3s taught me that counting out loud has a leak in it.

For years I got to 3 × 9 by saying 3, 6, 9, 12 and on up, and I lost my place every time. Let's learn it the way that worked.

The 3 times table from 1 to 12

Here is the whole chart. Twelve facts from the multiplication table for 3, and the next section turns each into two easy steps.

• 3 ×1=3
• 3 ×2=6
• 3 ×3=9
• 3 ×4=12
• 3 ×5=15
• 3 ×6=18
• 3 ×7=21
• 3 ×8=24
• 3 ×9=27
• 3 ×10=30
• 3 ×11=33
• 3 ×12=36

The table climbs in jumps of three, from 3 up to 36.

Now read the last digit of the first ten answers: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. That is every digit there is, so the ending tells you nothing here.

Why the number plus its double works

Three is 2 plus 1. That is the whole trick: multiplying by 3 is doubling, then adding the number once more.

Why one more add? Every tricycle has three wheels, and doubling counts only two of them on each one. The third wheel on all nine is the 9 you add back.

Tap through and the steps are 7, 14, and 21: one double, one add, and the fact turns up.

Double 11 to get 22, add 11 back, and there is 3 × 11 = 33.

The digit check that catches a wrong answer

Add up the digits of any answer on the chart, and you land on 3, 6, or 9. Every time, all twelve of them.

• 3→3
• 6→6
• 9→9
• 12→3
• 15→6
• 18→9
• 21→3
• 24→6
• 27→9
• 30→3
• 33→6
• 36→9

Read the number after each arrow: 3, 6, 9, then 3, 6, 9 again. The same three numbers, four times over, all the way to 36.

So the check is yours to run. Answer 23 and the digits give 2 + 3 = 5, and no answer on this chart comes to 5.

One honest warning: the check works one way only. It catches a wrong answer and cannot promise a right one: a child who answers 3 × 8 = 21 passes the check (2 + 1 = 3) and is still wrong.

Practice the 3 times table

Ten questions, friendly ones first. Type an answer, and if it is wrong, the box doubles it for you.

The next five are where the double earns its keep. Say both steps out loud: the saying makes it stick.

3 × 12 can be cut the other way, so we split the 12 into 10 and 2: three tens make 30, three twos make 6, and that is 36.

The 3s in England's tables check

England does not count the 3s among its hardest. Year 4 there takes a multiplication tables check, 25 questions at six seconds each, and the tables it names as most difficult are the 6, 7, 8, 9, and 12 times tables.

The questions come from the 121 facts in the 2 to 12 tables, and every version asks between one and three of them from the 3s.

The 3s are the lowest table the check never skips. A version can leave out the 2s and the 10s completely, and the 3s always get at least one.

Four of them sit close together, one jump apart.

• 3 ×6=18
• 3 ×7=21
• 3 ×8=24
• 3 ×9=27

With only six seconds, it is easy to answer 21 when the question asked for 24. The digit check cannot separate those two, so practice these four until they arrive on their own.

England's year 4 gets there: in 2025 the most common result was full marks, and 37% of eligible pupils scored 25 out of 25.

Doubling outlasts this table: the habit behind grown-up mental arithmetic, with a question a day in our mental math practice. The 4 times table, the 7 times table, and the 8 times table sit next door.

What to remember

• Three is a double plus one more. Double the number, add it back, and the table looks after itself.
• Add the digits to catch yourself. Every answer on the chart comes to 3, 6, or 9, so anything else is wrong.
• The last digit is no help here. All ten turn up in the 3s, so the digit check does the work instead.

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