ACARA v9 CONTENT DESCRIPTION “add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies”
Everything in Year 1 number work has been leading here: adding and subtracting within 20. This is the workshop where number facts are made — not memorised in a rush, but built from one sturdy picture. The picture is part-part-whole: a whole splits into two parts, and the parts snap back into the whole. Read it forwards and you have addition; read it backwards and you have subtraction. Two operations, one idea. Around that picture sit the strategies the curriculum asks for — counting on, making ten, finding the missing part — and the quiet star of them all is ten, the stepping stone our number system hands every child.
The part-part-whole bar
Slide the split. The parts trade with each other while the whole stands still.
Read the bar forwards for addition and backwards for subtraction — same picture, two directions.
Parts and wholes
Take any whole up to 20 and slide a split through it. Ten can be 4 and 6, or 3 and 7, or 1 and 9 — the parts trade with each other while the whole stands perfectly still. Knowing the parts of numbers to 10 by heart is what the curriculum calls part-part-whole knowledge, and it is the raw material every strategy on this page is built from. A child who owns the parts of ten already owns half of this unit.
Count on, not over
The slow way recounts everything. The strong way trusts the first number.
The bag already holds 8. Start there and count on.
Count on, not over
When children first add 8 and 5, many tip everything out and count all thirteen from one. It works, but it is slow and fragile. The stronger move is to trust the first number: keep the 8 whole, say it once, then count on — 9, 10, 11, 12, 13. Five steps instead of thirteen. And since order never changes a total, always start from the larger number, whichever way the sum happens to be written.
Bridge through ten
Crossing ten by ones loses count. Cross it in one planned move instead.
8 sits in the first ten-frame; 5 wait outside. What does 8 need to reach ten?
Ten is the bridge
Crossing ten by ones is where counts go wrong, so we cross it in one planned step instead. To add 8 and 5, ask what 8 needs to reach ten: two. Take 2 from the 5, land on 10, and the leftover 3 rides along — 10 and 3 is 13. The sum has not changed; it has been regrouped around ten, the friendliest number in the system. This make-ten move will carry students all the way into the two-digit work ahead.
The missing part
Subtraction is a whole with one part hiding. Find it by counting up.
A whole of 13 with a part of 8 — the other part is hiding. Count up to find it.
Subtraction without tears
Subtraction often arrives looking like a brand-new operation, but the part-part-whole picture says otherwise. Thirteen take away eight is just a whole with one part known and one part hiding — so find the missing part. Count up from 8: two to reach ten, three more to reach 13, five altogether. Children who think addition to subtract stop fearing the minus sign, because it asks a question they already know how to answer.
Birds on the wire
Thirteen birds, one scene — and a whole family of facts living in it.
13 birds on the wire: 8 magpies and 5 rainbow lorikeets. One scene, four facts.
One scene, four facts
Look at thirteen birds on a powerline — eight magpies, five rainbow lorikeets — and you are looking at four facts at once: 8 + 5, 5 + 8, 13 − 5 and 13 − 8. One scene, one family. Learning facts in families more than halves the memorising, and it keeps addition and subtraction living where they belong: in the very same picture.
Quick self-check
1. To work out 9 + 4, the fastest start is...
2. 8 + 6 = ? Using ten: 8 + 2 + 4 = ...
3. The whole is 12. One part is 5. The other part is...
4. 13 − 9 = ? Think: 9 + ? = 13.
5. Which fact belongs to the family of 8, 5 and 13?