ACARA v9 CONTENT DESCRIPTION “recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5 and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole”
A fraction begins with a fair cut. Take one whole — a round of damper, a bar, a length — and divide it into equal parts. One of those parts is the unit fraction, and the bottom number names how many equal parts the whole was cut into: halves come in twos, fifths in fives, tenths in tens. The word equal carries the whole idea. Three uneven lumps of damper are not thirds; thirds are three parts of exactly the same size. This unit names five unit fractions — 1/2, 1/3, 1/4, 1/5 and 1/10 — builds their multiples, places them on a line, and shows how same-size pieces add back up to one whole.
The damper split
One round of damper, cut into equal parts. The shaded piece is the unit fraction.
The shaded piece is one of 4 equal parts — one quarter, written 1/4. It takes 4 of them to rebuild the whole damper.
The bottom number is a job, not a count
The most useful idea here is that the denominator does not count anything you can see; it tells you the size of the cut. In 1/10 the 10 does not mean ten pieces are present; it means the whole was shared into ten equal parts and you are holding one of them. That is why a tenth is small and a half is large: the bigger the bottom number, the more ways the same whole has been shared, so the thinner each share. Children who grasp this stop thinking 1/10 is bigger than 1/2 because ten beats two. The damper makes it visible — more cuts, thinner slices.
Count the unit
A fraction like 3/4 is just three copies of the unit fraction 1/4. Count them up.
1/4 means 1 copy of the unit fraction 1/4. Add one more piece each time.
A fraction is a count of unit fractions
Once the unit fraction is named, every other fraction with that bottom number is just a count of it. Three quarters is three copies of one quarter; seven tenths is seven copies of one tenth. This is exactly the counting of whole numbers, carried into the space between 0 and 1 — instead of counting ones we count quarters or fifths. It also explains the top number, the numerator: it simply says how many of the unit-fraction pieces you have collected. Counting in unit fractions is the bridge from whole-number thinking into fractions, and it is why adding fourths to fourths feels no harder than adding apples to apples.
Complete the whole
Pieces of the same size add up. Top the bar up to exactly one whole.
You have 3/4. Add 4-piece thirds, fifths or tenths until the bar is full.
Same-size pieces add up
When pieces are the same size, they combine without any fuss: 3/4 and 1/4 make 4/4, and 4/4 is the whole bar back again. This is the heart of the descriptor — combining fractions with the same denominator to complete the whole. The denominator stays put because the size of the piece has not changed; only the count of pieces grows. A child who can see that two fifths plus three fifths is five fifths, and that five fifths is one, has met the rule that later makes all same-denominator addition obvious. The whole is always the moment the count of pieces reaches the bottom number.
The fraction number line
Between 0 and 1, every unit fraction is an equal step. Walk it.
The line from 0 to 1 is split into 5 equal steps, each one 1/5. Step along it.
Fractions live on the number line too
Whole numbers were positions on a line in earlier units, and fractions are no different — they fill in the gaps between 0 and 1. Split the unit step into equal parts and each mark is a unit fraction: fifths put four marks between 0 and 1, tenths put nine. Reading 3/5 as three steps of one fifth along from zero ties the count of unit fractions to a place, and a place makes order easy to see — 3/5 sits further along than 2/5, so it is larger. The line will carry these same fractions into measurement and into the fractions beyond one whole that come in later years.
Same piece, different cut
The same amount of bar can wear two names. Reveal the finer cut.
1/2 of the bar is shaded. Is there another way to name that same piece?
One piece can wear two names
Cut a bar in half and shade one part; now cut the same bar into quarters and you find the same shaded amount is two quarters. Half and two quarters are different names for the same piece, because a finer cut does not change how much is shaded, only how it is counted. The same is true of one half and five tenths, or one fifth and two tenths. This is the first taste of equivalent fractions, kept deliberately simple here: same amount, finer cut. It rewards the child who checks by eye rather than trusting the digits, and it sets up the renaming of fractions that arrives in Year 4.
How much more?
Part of the bar is filled. Choose the fraction that tops it up to one whole.
You have 1/4 of the bar. How much more makes one whole?
Finding the missing piece
The last move turns the whole idea into a question worth asking at any table: how much more makes one whole? With 3/5 eaten, the empty parts answer it — two fifths are left, and 3/5 plus 2/5 is 5/5, the whole pie. Seeing the gap as a fraction in its own right is the same completing-the-whole skill, read backwards, and it is genuinely useful: it is how you know how much of a recipe is left, or how much of a journey remains. With unit fractions named, counted, placed, combined and completed, the rest of Year 3 Number can lean on them — and the addition and subtraction of larger whole numbers comes next.
Quick self-check
1. Which fraction shows one quarter?
2. What is 3/5 + 2/5?
3. A damper is cut into 10 equal pieces. One piece is...
4. What is 1/4 + 1/4 + 1/4?
5. You have eaten 2/3 of a pie. How much is left to make the whole?