ACARA v9 CONTENT DESCRIPTION “multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies”
Multiplication begins as a change of unit: stop counting biscuits and start counting rows. In 3 rows of 4, the two numbers do different jobs — one counts groups, the other says how big each group is — and Year 2 keeps both jobs visible through concrete models: repeated addition, arrays, and fair shares. No tables are memorised here. A child who can build, turn and split these pictures will meet the tables next year as old friends rather than a chant to survive.
Groups or a jumble
Multiplication is fussy. It counts groups, but only if every group matches.
One bench is 3 groups of 4; the other is a jumble. Which is which?
The equal-groups law
Multiplication is fussy on exactly one point: equal groups or it is just adding. Bags of 3, 4 and 5 lollies hold twelve, but no multiplication sentence can say so — only 4 + 3 + 5 can. The fussiness is the power: the moment every group matches, a long count collapses into two numbers. Children should test the law by breaking it — let them build a jumble, feel the skip count stumble, then equalise the groups and feel it run. The sentence 3 × 4 is compressed counting, and compression only works on pattern.
The Anzac tray
Nobody counts biscuits one by one. Bake a row, say the new total, repeat.
An empty tray. Bake equal rows and count by the row, not the biscuit.
Say the rows, not the biscuits
Repeated addition is multiplication still wearing its training wheels, and the chant is the skill: 4, 8, 12 said aloud while rows appear. This is skip counting from Year 1 promoted to a tool. Insist on the reading three fours rather than three times four at first — the words keep the meaning attached, where times can become noise. When the tray fills, both sentences sit together: the long one with plus signs and the short one with the new symbol, the same fact at two compressions.
The array turner
Turn the tray on its side. Rows become columns; the biscuits never notice.
3 rows of 4 — read straight off as 3 × 4 = 12.
The array is the argument
Arrays are the central picture of this whole topic, and they prove things words cannot. Turn a 3 by 4 tray on its side: nothing was added, nothing eaten, yet the sentence reads 4 by 3 — so the two products must be equal, biscuit for biscuit. That is commutativity discovered, not decreed, and a child who has turned the tray owns a fact that halves every table they will ever learn. The same picture grows up later into area, so time spent staring at arrays is never wasted.
Share it out or bag it up
One pile of lollies, two different questions. Division answers both.
12 lollies, 3 mates. Deal fairly — one each per round.
Division asks two questions
One pile, two stories: share it out or bag it up. Sharing deals 12 lollies to 3 mates and asks how many each; grouping ties the same 12 into bags of 4 and asks how many bags. Both end in a division sentence, and children need both, because real life refuses to pick one. Notice the quiet fact-family at work too — the plates showing 3 fours and the bags showing 4 threes are the array from the previous activity read backwards, the triangle idea from the addition unit returning with new clothes.
The friendly five
Big times tables can wait. Split at five and the pieces are easy.
6 × 4 in one bite is a mouthful. Five is friendlier.
Split the hard ones
Partitioning is the strategy half of the descriptor: a hard times splits at the friendly five into two easy pieces, 6 fours becoming 5 fours and 1 more. This is the distributive law in short pants, and it matters more than any memorised answer, because it turns unknown facts into known ones on demand. From here the strand walks into mathematical modelling next — money problems that mix all four operations — while doubling and halving wait in Algebra to give the twos their own engine. The pictures built here drive all of it.
Quick self-check
1. Which is the same as 3 × 5?
2. A tray has 4 rows of 6 Anzac biscuits. How many biscuits?
3. 20 lollies shared equally among 5 mates — each mate gets...