Most fraction trouble comes from one thing: children are shown symbols like ¾ before they have a feel for what three quarters looks like. The symbol is a shorthand for an idea, and if the idea isn't there yet, the shorthand is just two numbers and a line.
Teachers often use a three-stage approach called concrete, pictorial, abstract (CPA). It's central to the "maths mastery" teaching used in many UK and Singapore classrooms, and it works just as well at the kitchen table.
- Concrete: real objects you can cut, fold and share.
- Pictorial: drawings and diagrams of those same objects.
- Abstract: numbers and symbols, once the first two make sense.
Here's how to walk through it, step by step.
Step 1: Start with "fair shares"
Before any fraction words, play at sharing. Cut a sandwich for two people and ask: "Is that fair?" Children have a strong sense of fairness from a very young age, and fractions are fair sharing given a name.
The key idea to land is that the parts have to be equal. A sandwich cut into one big piece and one small piece has two pieces, but they aren't halves. Children who skip this step often think any shape cut into four pieces shows quarters.
Try this: fold a paper square in half three different ways (side to side, corner to corner, top to bottom). Each way gives two pieces that look different, and each piece is still exactly one half.
Step 2: Name the parts: halves, quarters, thirds
Once "equal parts" makes sense, give them names. Start with halves and quarters, since folding in half twice makes quarters, which children can check for themselves. Bring in thirds later. You can't fold your way to thirds as easily, so they feel less obvious.
Use the language often and casually:
- "You've eaten half of your apple."
- "A quarter of the pizza is left. That's one of the four pieces."
- "Fill the jug about a third of the way."
Step 3: Discover the big surprise: more pieces means smaller pieces
This is the idea that trips up nearly every child, and plenty of adults too. Because 4 is bigger than 2, it seems natural that ¼ should be bigger than ½. It isn't, and no rule will convince a child of that as well as seeing it.
Cut two identical cakes (or circles of paper). Share one between 2 people and one between 4. Put a half next to a quarter. The point makes itself: the more people sharing, the smaller each slice. The bottom number tells you how many pieces the whole is cut into, and more pieces means smaller pieces.
Why circles work so well: a circle cut from the centre, like a pie or a pizza, shows every fraction as a slice of the same whole. You can lay a half-slice over a quarter-slice and see the difference at once. That's the idea behind our game Slice, where every fraction is a coloured wedge of one circle.
Step 4: Draw it (the pictorial stage)
Once children can show fractions with objects, move to drawings. Three kinds of picture are worth using:
- Circles (pie models): best for seeing "part of a whole" and comparing sizes.
- Bars (fraction strips): rectangles split into equal parts. Brilliant for lining fractions up and spotting equivalents, like ½ being the same length as 2/4.
- Number lines: show that fractions are numbers that sit between whole numbers. This one is harder, so save it for later.
A useful exercise: draw a bar, split it into quarters and shade three. Ask your child to say what they see: "Three out of four equal parts are shaded." Now they're ready for the symbol.
Step 5: Introduce the symbols (the abstract stage)
Now write ¾ and connect it straight back to the picture:
- The bottom number (denominator) is how many equal parts the whole is cut into.
- The top number (numerator) is how many of those parts we're talking about.
A handy way to remember it: the denominator is down below. Keep drawing pictures next to the symbols for a while. Dropping the pictures too early is the most common way fractions fall apart.
Step 6: Equivalent fractions: same amount, different name
Equivalent fractions (½ = 2/4 = 4/8) are where the visual approach really pays off. Lay strips or pie slices on top of each other and let your child find matches for themselves. Then ask them to explain the pattern in their own words: "If you cut every piece in half, you get twice as many pieces, but each one is half as big."
Only after that should you show the shortcut of multiplying the top and bottom by the same number. A child who has discovered the pattern will remember the rule. A child who was only told the rule will often mix it up.
Step 7: Add fractions that make a whole
A satisfying next challenge is to make exactly one whole from different pieces. ½ + ¼ + ¼ works. So does ½ + ⅓ + ⅙. With physical pieces, children can test combinations, see when they overshoot, and swap pieces around, which is the reasoning that formal addition of fractions builds on later.
Common mistakes and how to fix them
| Mistake | What's going on | What helps |
|---|---|---|
| Thinks ¼ is bigger than ½ | Treating the bottom number like a normal number | Compare real slices of the same whole, side by side |
| Calls unequal pieces "quarters" | Counting pieces without checking they're equal | Ask "is it fair?" every time; fold paper to check |
| Adds ½ + ½ to get 2/4 | Adding tops and bottoms like separate numbers | Draw it: two halves fill the whole circle, so the answer is 1 |
| Can't place fractions on a number line | Sees fractions as "pieces", not numbers | Use a measuring tape or ruler: ½ m sits halfway to 1 m |
What to expect at each age
Every child is different, but as a rough guide based on the English national curriculum:
- Ages 5 to 7: recognising halves and quarters of shapes and small sets ("half of 8 sweets").
- Ages 7 to 9: thirds, tenths and simple equivalent fractions; comparing fractions with the same denominator.
- Ages 9 to 11: adding and subtracting fractions, linking fractions to decimals and percentages.
If your child is ready to connect fractions to decimals and percentages, our guide Fractions, decimals and percentages: how they connect picks up from here.
Keep it playful
The best fraction practice rarely looks like a worksheet. Cooking (half a cup, a quarter teaspoon), sharing snacks, folding paper, reading a clock ("quarter past") and puzzle games all build the same understanding with much less resistance. A few minutes a day of noticing fractions in everyday life beats an hour of drills once a week.