ACARA v9 CONTENT DESCRIPTION “add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies”
Year 2 does not stack numbers in columns; it grows a toolbox. The descriptor asks for a variety of calculation strategies on purpose, because good arithmetic at this age is choosing a route, not running a procedure. A number sentence states the problem — 38 + 25 = ? or 28 + ? = 60 — and then the child picks: bound along the line, split into tens and ones, lean on a round number, or chase the gap. Every visualisation below is one route over the same terrain, and the right question after each is simply: which road suits these numbers?
Parts and the whole
Morning runs, afternoon runs, match total. Hide any one of the three and the other two will tell on it.
Two parts on the scoreboard — the whole is waiting. Add to find it.
One triangle, three sentences
Part, part, whole — a fact family lives in one triangle. Hide the whole and the parts add; hide a part and the whole subtracts; the numbers never change, only the question does. This is the deepest idea in the unit: subtraction is not a new operation to fear but the same triangle read backwards, which is why 38 + 25 = 63 quietly guarantees both 63 - 25 = 38 and 63 - 38 = 25. Children who see the triangle stop treating every missing-number problem as a fresh emergency.
The kangaroo line
A kangaroo never counts by ones if a big bound will do. Land on the target exactly.
Start at 38. Bound by tens, bridge to a round number, hop the rest.
Bound, bridge, hop
The kangaroo line is the jump strategy: travel by tens, bridge to a friendly round number, finish with ones — the tens did the heavy lifting. Bridging matters most: from 38, two small hops reach 40, and the rest of the journey runs on round rails. Encourage the commentary out loud — 38, 48, 58, 60, 63 — because the saying is the strategy. A child who bounds in tens has stopped counting and started calculating; a child still hopping by ones needs more time here, not a faster method.
Split and stack
Take both numbers apart, add the easy piles, and let renaming sweep up the spill.
Too big to swallow whole? Split both numbers first.
Split, add, rename
The split strategy takes both numbers apart: tens with tens, ones with ones, then reassemble. The interesting moment is the spill — 8 and 5 make 13, which is not a digit but a ten and 3. Renaming under deadline, exactly as promised: the skill from two units ago now earns its keep, boxing ten loose ones into a fresh ten on the spot. This is also where the classic error of gluing digits — 70 and 13 becoming 713 — gets prevented for good, because the child has watched the 13 get renamed instead of written.
The round-number trick
Nobody pays 29 in coins. Hand over a round 30, settle the 1 after.
29 is awkward — but it lives next door to 30.
Borrow a round number
Compensation is the strategy of the corner shop: nobody counts out 29; you hand over a round 30 and take 1 back. Numbers ending in 9 or 1 are begging for it, and the ledger keeps the conscience — overshoot by one, refund one; fall short by one, pay one. This is also the first taste of a powerful mathematical habit: deforming a problem into an easier one and repairing the deformation afterwards. Children who learn the repair step here will later trust it with far bigger machinery.
The run chase
Every chase is a subtraction wearing whites. Count up, not back.
Three claims in the sheds — how many runs are still to get?
The chase and the road ahead
Subtraction can be a chase: when two numbers are close, counting up beats counting back — 80 take away 58 is just 2 to 60 and 20 more, gathered on the run. Choosing between chasing, splitting and borrowing is the whole art, and the choosing is worth praising more than the answer. Next in the strand, equal groups arrive — multiplying and dividing — and after that the modelling unit will throw real money at all of these routes at once. The toolbox built here gets used for years.
Quick self-check
1. Mia had 34 shells and found 18 more. Which sentence matches?