Many children can chant "three fours are twelve" and still freeze at a word problem like "There are 4 bags with 3 apples in each. How many apples?" They've learned the sound of the fact without the idea behind it.
So we start with the idea: multiplication is counting equal groups. Recall comes later, and it lasts longer because there is something underneath it.
The order we teach it in
- Equal groups. Make 4 groups of 2 with counters. Count them. Then make groups that aren't equal and talk about why that's different.
- Repeated addition. 2 + 2 + 2 + 2 = 8. The same groups, written as a number sentence.
- Arrays. Line the groups up in rows. An array of 4 rows of 2 shows the same 8, and turning it around shows 2 rows of 4.
- Twos, then doubles. The two times table comes first, then doubling as a strategy for other facts.
- Tens, then halving, then fives. Ten is easy to see with bundles. Half of ten gives five, so the fives grow out of the tens.
- Division alongside. Every multiplication fact has division partners. 8 shared between 4 is 2. 8 put into groups of 2 makes 4 groups.
Use more than one way of saying it
We say "4 groups of 2", "4 twos", "4 times 2" and "4 multiplied by 2" from the first day. Children who only hear one phrasing often don't recognise the same idea when a teacher or a test words it differently.
For division, we keep two meanings apart: sharing ("12 shared between 3") and grouping ("12 put into groups of 3"). They give the same answer, but they're different pictures, and word problems use both.
When does speed come in?
Fluency matters. The Victorian Curriculum expects children to recall their two times table facts quickly by the end of Level 2, and to know the 3, 4, 5 and 10 facts in Level 3. We build that with a few minutes of warm-up practice every session, always on facts the child has already understood.
Understanding first, then speed. A child who knows what 4 × 3 means can work it out when memory fails. A child who only memorised it can't.
Try this at home
- Use real objects: pasta pieces, coins or Lego bricks. Ask "How many groups? How many in each group? How many altogether?"
- Spot arrays around the house: egg cartons, muffin trays, window panes.
- Ask your child to explain, not just answer: "How do you know?"