ACARA v9 CONTENT DESCRIPTION “recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts”
This unit lives in the Algebra strand for a reason: facts to 20 are not a list to chant but a web of relationships, and proficiency means travelling that web fast. The toolbox is small and complete — pairs that make ten, doubles and their neighbours, and the bridge through ten for everything awkward. A child who can reach any fact in one short hop has it; speed then arrives on its own with use. Drill without the web produces fast forgetting; the web without drill stays slow. The unit builds the web first.
Rainbow facts
Ten is the home base of our whole number system. These pairs are the keys to it.
Every number under ten has one best mate on the rainbow. Who pairs with 7?
Ten is home base
Australian classrooms call them rainbow facts: the pairs 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, arched over the number line like a rainbow landing on 10. They matter more than any other handful of facts because our whole number system is built in tens — every bridge, every renaming, every column a child will ever carry leans on knowing instantly what a number needs to reach ten. Five arcs. Worth knowing the way a name is known.
The doubles engine
Children adore doubles and remember them first. Everything one step away comes free.
Double 6: two matching stacks, 12 in a single breath.
Doubles first, neighbours free
Doubles are the facts children learn without being asked — two hands, two boots, the symmetry sticks. The strategy is to spend that gift: once 6 + 6 is instant, 6 + 7 is not a new fact but a nudge, one more than a known thing. This is the first taste of deriving — using a fact you own to mint a fact you need — and deriving is the actual skill this descriptor wants. Ask for the double hiding inside any near-double and the answer usually arrives mid-sentence.
Bridge through ten
Awkward sums stop being awkward the moment the tray of ten is full.
8 in the tray of ten, 5 waiting outside. The tray wants 2.
The bridge through ten
For sums that cross ten — 8 + 5, 9 + 6 — the move is always the same: feed the ten first. The second number splits, the frame fills, and the sum becomes ten-and-something, which is no sum at all. This is where the rainbow pairs earn their keep, because knowing 8 needs 2 is the whole trick. Notice the special ease of adding 9: it only ever wants 1. Children who bridge stop crossing ten on their fingers, and the habit scales straight into the two-digit work they have already met.
The fact family triangle
Whole on top, parts below. Read it down for subtraction, up for addition.
Three numbers, one triangle: 8, 5 and 13. How many true sentences live inside?
One triangle, four sentences
Put the whole on top and the parts below, and every addition fact turns out to be four sentences wearing one shape — two additions and two subtractions, all true together. The double family with its two overlapping twins is the delightful exception that proves children are really looking. This triangle is the same part-part-whole picture from the addition unit, now used as a fact press: learn 8 + 5 = 13 once, and 13 - 5 and 13 - 8 are not new burdens but the same knowledge read in a different direction.
Subtraction you already know
Every subtraction to 20 is an addition fact wearing a disguise.
Do not count back — ask the addition you already know.
Subtraction is remembering, not removing
The descriptor asks for subtraction facts to be developed from addition, and the final activity makes the move explicit: faced with 14 - 6, do not count backwards into the fog — ask which addition already answers it. Subtraction is remembering, not removing. A child who reaches for the family instead of the fingers has finished this unit in the deepest sense. Next in the strand, the twos get an engine of their own — doubling and halving — and the doubles practised here become multiplication facts overnight.
Quick self-check
1. Which pair are friends of ten?
2. Double 7 is 14. So 7 + 8 is...
3. 8 + 5: fill the ten first. Which line shows it?
4. 9 + 7 = 16. Which subtraction belongs to the same family?
5. Mia knows 6 + 9 = 15. Without counting, she also knows...