ACARA v9 CONTENT DESCRIPTION “use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem”
No one has to teach a Year 1 child to care about fairness; the playground does that. This unit puts that instinct to work. Two jobs share the spotlight: equal sharing, where a collection is dealt out so everyone gets the same, and equal grouping, where a collection is packed into same-sized bundles. Both are solved by hand — real strawberries, real bags, real sausages — because at this age the materials are the mathematics. And both are the first quiet steps towards division, years before the word appears.
Deal them out
One for you, one for you, one for you — around and around until the pile is gone.
Sharing 12 strawberries among 3 plates. Keep dealing in turn.
One for you, one for you
Dealing out, one at a time, around and around, is the great strategy of sharing — the same move every card game uses. It guarantees fairness by construction: nobody can end up ahead, because the rotation never skips anyone. Children should say the round aloud as they deal, and notice the moment the pile runs out: that is when the answer appears on every plate at once.
Fill the bags
Same-sized bags, filled one at a time — the pile decides when to stop.
Putting 12 lollies into bags of 3. How many bags will it take?
Bags of the same size
Grouping flips the job: the size of each bundle is fixed, and the question becomes how many bundles the pile will make. Filling a bag of three, then another, then another, the pile itself announces the answer by running out. This is the kind of equal-group thinking children met when counting in groups — now driven by a practical problem instead of a counting one.
Same lollies, two questions
Twelve lollies never change — but the question changes everything.
Sharing among 3: four each. The question was how many each. Two different questions about the same collection — listen for which one the story asks.
Listen for the question
Here is the distinction worth a whole lesson: twelve lollies shared among three children, and twelve lollies packed in bags of three, use the same twelve lollies and land on the same numbers — yet they are two different questions about the same collection. One asks how many each; the other asks how many bags. Children who learn to listen for the question, before touching a single lolly, are doing the real work of mathematical modelling.
The leftovers
Sometimes the pile does not come out even. Year 1 maths is allowed to say so.
13 shared among 4 — keep going and watch the pile.
Leftovers are allowed
Real piles rarely come out even, and that is not a flaw in the problem — it is the problem. Eleven pies among three players is three each and two left over, said plainly and proudly. Naming the remainder keeps children honest with the materials in front of them, and it spares them the later shock of discovering that division does not always end tidily. The leftover is part of the answer, not a failure to find one.
Sausage sizzle Saturday
One real Saturday job, solved with the whole modelling cycle.
16 snags, and the barbie grills 4 at a time. How many rounds of cooking?
There is the pile. What is the story really asking — each, or groups?
Saturday at the sizzle
The sausage sizzle is the perfect Year 1 capstone: a real Saturday job, a pile of sixteen snags, a barbie that takes four at a time. The story names a group size, so it is a grouping question; the rings make the groups visible; and skip counting by fours — 4, 8, 12, 16 — counts the rounds the fast way. Next year these same groups will earn a grander name, multiplication. The thinking, though, is already here, smelling faintly of onions. Keep the sharing going at home as well: dealing out cutlery for dinner, packing tomatoes into bags of four at the market, splitting a punnet of strawberries between cousins — fair shares and equal groups hide in every ordinary Saturday.
Quick self-check
1. Share 10 strawberries fairly between 2 plates. Each plate gets...
2. 12 lollies go into bags of 4. How many bags?
3. The question how many does EACH child get belongs to...
4. Share 11 pies among 3 players. The answer is...
5. 16 snags cook 4 at a time. Skip count the rounds — 4, 8, 12, 16 — that is...