What to notice
Every starting number on the list is in the 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36. The quick test for whether a number divides by 3 with nothing left over is to add its digits: 2 + 7 = 9, so 27 divides by 3; 2 + 5 = 7, so 25 does not.
The answers count up by one while the starting numbers go up by three. Covering the answers with a strip of paper and revealing them one at a time is a simple self-check.
A fact family links four facts: 3 × 8 = 24, 8 × 3 = 24, 24 ÷ 3 = 8 and 24 ÷ 8 = 3. Learning 24 ÷ 3 also gives your child 24 ÷ 8, which belongs on the divide-by-8 page.
How to practise at home
- Share real things among three: three plates, three teddies. Deal them out one at a time, then count one plate.
- Ask the multiplication question first, “three times what makes 18?”, and then the division fact, “18 ÷ 3 is?” Over time the multiplication step goes quiet.
- Play “in the 3s or not?” with the digit-sum test: you say a number, your child adds the digits and decides. It builds a feel for which numbers belong.
- Use the drill on this page, and when a fact is slow, have your child say the matching multiplication fact aloud.
- Use the 3s chant backwards: count 3, 6, 9, 12, 15 on fingers, and the number of fingers up when you reach the starting number is the answer. 15 ÷ 3 = 5, five fingers. As the multiplication becomes known, the counting fades.
Slips to watch for
- Landing on a neighbour, such as 6 or 8 for 21 ÷ 3. Ask what 3 × 7 is, then check.
- Confusing 18 ÷ 3 with 18 ÷ 6. They are fact-family partners and their answers swap: 6 and 3.
- Trying to divide a number that is not on the list, such as 20 by 3. It does not come out even. That is fine to notice, and it is the start of remainders, which come later.