At a glance
- Year 1
- Half and quarter of a shape or quantity
- Year 3
- Fractions of amounts; same-denominator addition
- Year 5
- Mixed numbers and improper fractions
- Year 6
- Different denominators; multiply and divide
- Key idea
- Equivalent fractions
Fractions year by year (national curriculum for England)
| Year | What pupils should be taught |
|---|---|
| Year 1 | Recognise, find and name a half and a quarter of an object, shape or quantity |
| Year 2 | Find and write 1/3, 1/4, 2/4 and 3/4 of a length, shape, set or quantity; see that 2/4 equals 1/2 |
| Year 3 | Unit and non-unit fractions of a set; fractions on a number line; equivalent fractions with small denominators; add and subtract with the same denominator within one whole; compare and order |
| Year 4 | Families of equivalent fractions; hundredths; fractions of quantities; decimal equivalents of tenths, hundredths, 1/4, 1/2 and 3/4 |
| Year 5 | Compare fractions with related denominators; mixed numbers and improper fractions; add and subtract where denominators are multiples of the same number; multiply fractions by whole numbers |
| Year 6 | Simplify using common factors; add and subtract with different denominators and mixed numbers; multiply simple pairs of proper fractions; divide proper fractions by whole numbers; fraction to decimal, such as 3/8 = 0.375 |
Source: Department for Education, mathematics programmes of study for key stages 1 and 2.
The two ideas that matter most
First, the denominator (bottom number) says how many equal parts the whole is split into, and the numerator (top number) says how many of those parts you have. So 3/4 means 'split into 4 equal parts, take 3'. Children who are secure on this can work out most questions by drawing a bar.
Second, equivalent fractions name the same amount: 1/2 = 2/4 = 4/8 = 6/12. You make an equivalent fraction by multiplying or dividing the top and bottom by the same number. This is the key to comparing fractions, simplifying them, and adding fractions with different denominators.
Worked example 1 (Year 3 to 4): find 3/4 of 20
- Find one quarter first: 20 ÷ 4 = 5.
- Three quarters is three of those: 5 × 3 = 15.
- Draw it to check: a bar of 20 split into 4 boxes of 5, with 3 boxes shaded, is 15.
- The same method works for any fraction of an amount: divide by the bottom, multiply by the top. So 2/3 of 18 is 18 ÷ 3 × 2 = 12.
Worked example 2 (Year 5): 3/4 + 5/8
- The denominators are 4 and 8, and 8 is a multiple of 4, so change quarters into eighths.
- 3/4 = 6/8, because both top and bottom are multiplied by 2.
- Now add eighths: 6/8 + 5/8 = 11/8. Only the tops are added; the size of the parts does not change.
- 11/8 is an improper fraction. Eight eighths make one whole, so 11/8 = 1 and 3/8.
Worked example 3 (Year 6): 2/3 - 1/4, and 2/3 × 3/4
- For subtraction, find a common denominator. The smallest number that both 3 and 4 divide into is 12.
- 2/3 = 8/12 and 1/4 = 3/12, so 2/3 - 1/4 = 8/12 - 3/12 = 5/12.
- For multiplication, multiply the tops and multiply the bottoms: 2/3 × 3/4 = 6/12.
- Simplify by dividing top and bottom by 6: 6/12 = 1/2. Check with a picture: three quarters of a bar, and then two thirds of that, is half the bar.
- Dividing by a whole number: 1/3 ÷ 2 means half of one third, which is 1/6.
Common mistakes
- Adding tops and bottoms: 1/2 + 1/4 is not 2/6. Make the denominators the same first: 2/4 + 1/4 = 3/4.
- Thinking a bigger denominator means a bigger fraction: 1/8 is smaller than 1/4, because the whole is cut into more pieces.
- Unequal parts: a shape cut into 4 pieces of different sizes does not show quarters.
- Forgetting to simplify when the question asks for the simplest form.
- Finding a fraction of an amount by multiplying first and then losing track: divide by the denominator first, then multiply.
- Treating 1 and 3/8 as 1 × 3/8 rather than 1 + 3/8.
Fractions in Year 6 tests, and how lessons help
In England's end of key stage 2 maths tests, fractions, decimals and percentages sit inside the 'number, ratio and algebra' area, which carries 75% to 85% of the marks across three papers: an arithmetic paper and two reasoning papers. Fractions appear as straight calculations in the arithmetic paper and inside word problems in the reasoning papers. British-curriculum schools in the Gulf often use similar end-of-year tests.
In one-to-one lessons a tutor uses the shared whiteboard to draw bars and number lines with your child, so the rules make sense rather than being memorised. The tutor listens to how your child explains a step, which shows quickly whether the problem is understanding (what a denominator means) or procedure (finding a common denominator). Short daily practice between lessons keeps the method fresh.
Self-check
- Which is bigger, 2/3 or 3/4? (3/4, because 8/12 < 9/12)
- Find 3/8 of 40. (15)
- Write 17/4 as a mixed number. (4 and 1/4)
- Work out 1/2 + 1/3. (5/6)
- Work out 3/4 × 2/3 in its simplest form. (1/2)
- Write 3/4 as a decimal. (0.75)
Common questions
Why does my child find fractions so hard?
Usually because they learned rules without the picture behind them. If a child cannot draw 3/4 as a bar or place it on a number line, the rules for adding or comparing feel random. Going back to diagrams nearly always helps.
When do children learn to add fractions with different denominators?
In the national curriculum for England, Year 5 covers denominators that are multiples of the same number (such as quarters and eighths), and Year 6 covers any different denominators and mixed numbers.
Should my child use a calculator for fractions?
Not while learning them. The national curriculum for England says calculators should not be used as a substitute for good written and mental arithmetic, and the equipment list for its key stage 2 maths tests does not include one. Fraction sense needs to be built by hand.
My child is in an American school. Is this the same?
The ideas are the same but the order and grade levels differ. The year-by-year table here follows the national curriculum for England, which British-curriculum schools use.
How do LiveTutor primary maths lessons work and what do they cost?
Lessons are one to one, online and 60 minutes, with a tutor using a shared whiteboard to draw and explain. Every lesson costs $15, on a weekly plan of 1 to 5 lessons billed monthly, and the first lesson is a free trial.
Sources
Dates and figures on this page come from these official and published sources. Always confirm deadlines on the official page before acting on them.