Fractions: maths lessons by year

What's taught, year by year

The steps in fractions, in the order children usually meet them. Years are named as in Australia; the ages are a guide.

Share things fairly between two. Share a small collection so that two people get the same amount.

Equal and unequal parts. Tell whether a shape or object has been cut into equal parts or not.
Find half of a shape or object. Split a shape or object into two equal parts and name each part a half.
Find half of a set of objects. Find half of a small group by sharing it into two equal groups.
Find a quarter of a shape or object. Split a shape into four equal parts and name each part a quarter.
Find a quarter of a set of objects. Find a quarter of a small group by sharing it into four equal groups.

Halves, quarters and eighths by halving again. Fold or cut a whole in half, then half again, to make quarters and eighths.
Thirds of shapes and sets. Split a shape or a group into three equal parts and name each part a third.
Read and write fractions with numbers. Write a fraction as a numerator over a denominator and say what each part means.
Two-quarters and three-quarters. Show 2/4 and 3/4 of a shape or set by shading more than one part.
A half is the same as two quarters. Show with shapes and strips that 1/2 and 2/4 cover the same amount.
Fraction parts that make a whole. Recognise that two halves, three thirds or four quarters make one whole.

Unit fractions with denominators up to 10. Name and show unit fractions such as 1/5, 1/6, 1/8 and 1/10 of a whole.
Non-unit fractions as groups of unit fractions. See 3/5 as three lots of 1/5 and shade it on a shape or strip.
Fractions on a number line from 0 to 1. Mark unit and non-unit fractions on a number line split into equal parts.
Compare unit fractions. Explain why 1/8 is smaller than 1/4: more equal parts means smaller parts.
Compare and order fractions with the same denominator. Order fractions like 2/7, 5/7 and 3/7 by comparing numerators.
Whole numbers written as fractions. Recognise that 4/4 = 1 and 6/2 = 3 and show them on a number line.
Equivalent fractions with a fraction wall. Use a fraction wall to find fractions that are the same size, like 2/6 and 1/3.
Unit fraction of an amount. Find 1/3 of 12 or 1/5 of 40 by dividing by the denominator.
Add and subtract fractions with the same denominator. Add or take away fractions like 2/5 + 1/5 within one whole.

Count in fractions past one. Count forwards and backwards in halves, quarters or thirds beyond one whole.
Mixed numbers and improper fractions. Convert between improper fractions like 7/4 and mixed numbers like 1 3/4.
Make equivalent fractions by multiplying. Multiply or divide the numerator and denominator by the same number.
Compare fractions with related denominators. Compare fractions such as 3/4 and 5/8 by renaming one of them.
Split a fraction into a sum of fractions. Write 5/6 as 1/6 + 4/6 or 2/6 + 3/6 in several ways.
Add and subtract like fractions beyond one whole. Add or subtract fractions with the same denominator, including mixed numbers.
Non-unit fraction of an amount. Find 2/3 of 24 or 3/8 of 48 by finding one part first.
Find the whole from a fraction. Work out the whole set when a fraction of it is known, using a bar model.

Multiply a fraction by a whole number. Work out 3 x 2/5 as repeated addition of a fraction.
Compare fractions with unlike denominators. Compare fractions using a common denominator or the benchmark of one half.
Simplify fractions. Write a fraction in its simplest form by dividing by a common factor.
Add and subtract fractions with related denominators. Add fractions like 1/2 + 3/8 by renaming one fraction first.
Add and subtract fractions with different denominators. Use a common denominator to add or subtract fractions like 2/3 + 1/4.
Add and subtract mixed numbers. Add or subtract mixed numbers, regrouping wholes when needed.
A fraction is a division. Read 3/4 as 3 divided by 4 and share 3 things among 4 people.
Multiply a fraction by a fraction. Find 2/3 of 3/4 using an area model and multiply numerators and denominators.
Multiplying by a fraction makes it smaller or bigger. Predict whether a product grows or shrinks when multiplying by a fraction.

Divide a fraction by a whole number. Share a fraction like 1/3 equally into 2 parts and write 1/6.
Divide a whole number by a unit fraction. Find how many quarters are in 3 wholes and write 3 / (1/4) = 12.
Divide a fraction by a fraction. Use diagrams and common denominators to divide one fraction by another.
Fraction of a remainder problems with bar models. Solve two-step problems where a fraction is taken from what is left over.