What to notice
Add the digits of any answer in the 3 times table and you get 3, 6 or 9. For 27 it is 2 + 7 = 9, for 18 it is 1 + 8 = 9, and for 24 it is 2 + 4 = 6. That makes a handy check: if your child says 23 for 3 × 8, the digits add to 5, so something is off.
The answers alternate odd and even: 3 is odd, 6 is even, 9 is odd, 12 is even. Adding an odd number to an even one gives an odd number, and adding two odd numbers gives an even one, so the pattern can never break. It is another quick check on a guess.
Some of these facts are also in the 6s and 9s, seen from the other side: 3 × 6 = 18 is the same fact as 6 × 3, and 3 × 9 = 27 is 9 × 3. If your child knows those already, they come free.
How to practise at home
- Practise “double and one more” out loud. You say 3 × 6; your child says “double 6 is 12, and 6 more is 18.” Over a week or two the middle step drops away and the answer arrives on its own.
- Use things that come in threes: wheels on a tricycle, sides of a triangle, leaves on a clover. “Five tricycles, how many wheels?” is a real reason to work out 3 × 5.
- Chant the 3s to a beat while walking or bouncing a ball, then start in the middle: “begin at 18 and keep going.” Starting partway through breaks the habit of always counting from 3.
- Once the chant is solid, switch to single facts in a random order with the drill on this page. It shows which ones are still being counted up.
Slips to watch for
- Answers one step off, such as 18 or 24 for 3 × 7. They come from counting up and landing in the wrong place. The digit check will not catch these, since 18 and 24 are both in the table, so go back to the double: 2 × 7 = 14, and 14 + 7 = 21.
- Adding instead of multiplying, and answering 7 for 3 × 4. Saying “three fours” instead of “three times four” brings the meaning back.
- Mixing up the last few facts, 27, 30, 33 and 36. Ask your child to say the chant up to that point, then check with “double and one more.”