Add and Subtract Within 20
Two sides of one picture
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.
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
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.
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.
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.
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.