The fraction symbol 1/2 is not where they should start. It's abstract. They should start with a pizza cut into two equal pieces. Then they learn what the symbol 1/2 means. Skipping the concrete step is the commonest reason kids hate fractions.
This article shows the path from concrete fractions to symbolic fractions, step by step. At Kluriko there are fraction games in the Learning Games — but at home with real food the deep understanding happens.
What is a fraction?
A fraction is a part of a whole.
- 1/2 = a half
- 1/4 = a quarter
- 3/4 = three quarters (= three of four parts)
They need to understand two concepts:
- The whole is something — pizza, biscuits, apple, paper.
- The fraction is how many parts of the whole.
Step 1: Halves
Start at 5-6. They learn:
- Pizza cut into 2 equal pieces. They get half. You get half.
- Apple cut into 2 equal pieces. They get half.
- A piece of paper folded in the middle. Half.
They learn the word "half" and link it to physical division.
Step 2: Quarters
At 6-7.
- Pizza cut into 4 equal pieces. They get a quarter.
- Apple cut into 4 equal pieces.
- Paper folded in the middle twice. Four squares.
They learn the word "quarter".
Step 3: Other fractions
At 7-8.
- Third: pizza cut into 3.
- Sixth: pizza cut into 6.
- Eighth: pizza cut into 8.
They see the pattern: the fraction name matches the number of parts.
Step 4: The fraction symbol
At 8 introduce the symbol.
"A half" = 1/2. "A quarter" = 1/4. "Three quarters" = 3/4.
Explain:
- Below the line: how many parts the whole is divided into (denominator).
- Above the line: how many parts you take (numerator).
They don't need the terms "numerator" and "denominator" yet. Just link the digits to the number of parts.
Concrete materials
Pizza template
Buy a large round paper pizza. Cut into 8. They play with:
- Half = 4 pieces
- Quarter = 2 pieces
- An eighth = 1 piece
They physically see: 4/8 = 1/2. Equivalent fractions!
Cuisenaire rods
Coloured maths rods. They see 1/2 of a 4-rod = 2-rod.
Paper folding
They fold paper in the middle. One fold = half. Two folds = quarter. Three folds = eighth. Concrete and tactile.
Fraction fridge magnets
Stick magnetic cards with 1/2, 1/4, 3/4 on the fridge. They see them daily.
How fractions show up in daily life
- Kitchen: "Half cup of milk." "Quarter-teaspoon of salt." Recipes are full of fractions.
- Pizza night: "You get two sixths." They count.
- Clock: "Half past 3." "Quarter past 3." Fractions of an hour.
- Money: "Half price!" 50% off.
Games and exercises
The fraction-pizza game
You say a fraction. They pick that many pieces. "Give me 3/8." They take 3 of 8 pieces.
Halving game
"What's half of 8?" 4. "Half of 12?" 6. "Half of 50?" 25. Trains fractions + division at once.
Equivalent fractions
Show: 1/2 = 2/4 = 4/8. They see equivalents. Advanced but important.
Fraction bingo
A board with various fractions. You say a fraction, they mark it.
When they grasp the basics
By 8-9 they can:
- Identify half, quarter, third
- Read 1/2, 1/4, 3/4
- Spot fractions in everyday life
By 9-10 they can:
- Equivalents (1/2 = 2/4)
- Add simple fractions (1/4 + 1/4 = 2/4)
- Fractions larger and smaller than 1 (3/2 = 1 whole + 1/2)
Common problems
They think bigger digits = bigger fraction. "1/2 is bigger than 1/4 — but 4 is bigger than 2!" Explain: the denominator is how many parts, so more parts = smaller each part.
They mix fractions and decimals. "1/2 and 0.5 are the same." Wait until 9-10 for the decimal link.
They think 1/2 + 1/4 = 2/6. Classic trap. Solve: concrete with pizza. 1/2 (4 of 8) + 1/4 (2 of 8) = 6/8 = 3/4.
Fractions as percent
At 10: they learn 1/2 = 50%. 1/4 = 25%. 3/4 = 75%.
They meet this at the store ("50% off!"). Foreshadow from 7: "Half price = 50% off = half".
Fraction size
Show them:
- 1/2 > 1/3 > 1/4 > 1/8
Big denominators = small fractions. Counter-intuitive. Solve: concrete with pizza cutting.
How Kluriko helps
Kluriko Learning Games have fraction games that progress from concrete-visual (pizza pictures) to symbolic (1/2, 1/4). It matches the pedagogy: visualisation first, symbols later.