ACARA v9 CONTENT DESCRIPTION “find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation; count and represent fractions on a number line including mixed numerals”
A fraction is built from equal parts of a single whole: split a bar into four equal pieces and three of them is three quarters, written 3/4. The number underneath, the denominator, says how many equal parts the whole is cut into; the number on top, the numerator, says how many are taken. Year 3 met unit fractions like one quarter; Year 4 works with any number of those parts and, crucially, discovers that the same amount can be written in more than one way. Everything in this unit rests on that first picture of equal parts of one whole.
Build a fraction
A fraction is equal parts of one whole. Shade parts to make it.
The whole bar is 1, split into 4 equal parts. Shade parts to make a fraction.
Different names, same amount
The central idea of Year 4 fractions is equivalence: different fractions can name exactly the same amount. Lay bars on top of each other and one half covers the same length as two quarters, three sixths and four eighths — 1/2 = 2/4 = 3/6 = 4/8. The fraction looks different each time because the whole is cut more finely, but the shaded length never changes. This is why a fraction can be simplified: 4/8 and 1/2 are the same number written two ways. Seeing equivalence as the same length, not just a rule about multiplying top and bottom, is what makes it stick.
The equivalence wall
The same amount can be written as different fractions. The shaded length stays equal.
Each row splits the same whole more finely. Reveal the next row and compare the shaded length.
Fractions live on the number line
Fractions are not only parts of a shape; they are numbers with a place on the number line, and counting by a unit fraction steps along it. Counting in quarters goes 1/4, 2/4, 3/4, and the next step, 4/4, lands exactly on one. Keep going and you pass one into 5/4, 6/4 and beyond. This counting shows two things at once: that fractions sit between whole numbers, and that enough of them add up to whole numbers and past them. Placing and counting fractions on the line connects them to the counting of whole numbers children already know.
Count by fractions
Counting in unit fractions moves along the number line and passes whole numbers.
Start at 0 and count up in quarters: 1/4, 2/4, 3/4, then 4/4 which is one whole.
More than one whole
Once counting passes one, a fraction can be bigger than a whole, like 5/3 or 7/4. There are two ways to write such an amount. The improper fraction 5/3 keeps counting thirds: five of them. The mixed number says the same thing as wholes plus a part: 5/3 is one whole (three thirds) with two thirds left over, written 1 2/3. Both describe the identical quantity; the mixed number simply separates the whole bars from the leftover part. Moving between the two forms is a key Year 4 skill, and the bars make plain that nothing about the amount changes.
Make a mixed number
A fraction bigger than one whole is so many wholes plus a fraction left over.
5/3 is more than one whole. How many wholes and what is left over?
Recognising equal fractions
With equivalence understood, a child can recognise when two fractions are the same and pick the simplest name for an amount. Two quarters is one half; three sixths is one half; four eighths is one half. The test is whether the parts cover the same length, which is the same as dividing the top and bottom by the same number: 6/8 becomes 3/4 by dividing both by two. Simplifying is not a separate trick but the equivalence wall read in reverse — finding the fraction with the fewest, largest parts that still names the amount. This skill makes fractions easier to compare and, later, to add.
Find the same value
An equivalent fraction names the same amount. Pick the one that matches.
Which of the choices is the same value as 2/4?
Two ways to write one amount
The unit closes by putting the two forms side by side. Every improper fraction over one equals a mixed number: 3/2 is 1 1/2, 5/4 is 1 1/4, 7/3 is 2 1/3. Choosing which form to use depends on the situation — mixed numbers are easier to picture and place on a line, while improper fractions are often easier to calculate with. What matters at Year 4 is knowing they are equal and moving between them confidently. With fractions built from equal parts, equivalence seen as equal length, counting along the number line, and amounts over one written both ways, a child has the foundation for adding, subtracting and comparing fractions in the years ahead, and for linking fractions to the decimals of the last unit.
Improper and mixed
A fraction over one can be written two ways, as improper or as a mixed number.
Each improper fraction equals a mixed number. Reveal each row to pair them.
Quick self-check
1. Which fraction is equivalent to 1/2?
2. Counting up in quarters: 1/4, 2/4, 3/4, then the next is...
3. The improper fraction 5/3 written as a mixed number is...