Key takeaways
- Division is the inverse of multiplication, secure times tables make division facts almost free.
- Both division and fractions are really about sharing and grouping into equal parts.
- The word 'equal' is where children most often go wrong with fractions.
- Concrete objects (pizza, counters) build understanding before any symbols.
- Long division breaks down when the underlying facts aren't fluent.
Division is just times tables in reverse
Every division fact is a multiplication fact wearing a different hat. Because 6 × 4 = 24, we also know 24 ÷ 4 = 6 and 24 ÷ 6 = 4. Children who know their times tables already know their division facts, they simply need to see the connection. Two questions keep it grounded: "how many groups?" (24 ÷ 6 = how many sixes in 24) and "how much each?" (24 shared between 6).
From sharing to fractions
A fraction is what you get when you divide something into equal parts: a half is one of two equal parts, a quarter one of four. Start with real objects, a pizza, a chocolate bar, a strip of paper, so children see that 3/4 is bigger than 1/2 before they ever handle the symbols. The numerator (top) counts the parts you have; the denominator (bottom) says how many equal parts make the whole.
Skipping the word 'equal'. "Cut it in half" must mean two equal parts, unequal parts are the root of most fraction confusion.
Where children get stuck, and why
Two misconceptions dominate. First, that a bigger denominator means a bigger fraction, children reason 1/8 > 1/4 because 8 > 4. Cutting a cake into 8 versus 4 pieces fixes it instantly: more pieces means smaller pieces. Second, treating numerator and denominator as two unrelated whole numbers. Both are cured by returning to concrete, equal parts. Long division stalls for a different reason, it's a multi-step chain, and a wobble in times-table recall snaps the whole chain.
Worked example, a fraction of an amount
To find 3/4 of 20, use the link to division: the denominator divides, the numerator multiplies. First 20 ÷ 4 = 5 (one quarter), then 5 × 3 = 15 (three quarters). Saying it as "divide by the bottom, times by the top" gives children a reliable, understandable procedure.
Practise division facts the moment a times table is secure. They cost almost nothing extra and unlock fractions and sharing.
When children learn this, a Year-by-Year guide
Roughly where each idea sits in the England primary maths curriculum. Every child is different, use it as a map, not a deadline.
| Stage | What children work on |
|---|---|
| Year 1–2 (ages 5–7) | Share objects equally; recognise a half and a quarter of shapes and amounts. |
| Year 3 (age 8) | Recall division facts for the 3, 4 and 8 tables; count in fractions. |
| Year 4 (age 9) | Divide using known tables; find fractions of quantities; equivalent fractions. |
| Year 5–6 (ages 10–11) | Long division; add, subtract and compare fractions with different denominators. |
Two meanings of division
| Model | Question it answers | Example |
|---|---|---|
| Sharing (partitive) | How much does each get? | 12 sweets shared between 3 → 4 each |
| Grouping (quotitive) | How many groups can I make? | 12 sweets in bags of 3 → 4 bags |
How to introduce fractions with a pizza
A concrete first lesson that builds the right mental model.
- Take a real (or paper) pizza and agree it is one whole.
- Cut it into two equal parts, name each a half. Stress 'equal'.
- Cut into four equal parts, name each a quarter; compare sizes with the halves.
- Show that two quarters cover the same space as one half (equivalence).
- Only now write the symbols 1/2 and 1/4 next to the real pieces.
Troubleshooting
| Problem | What to try |
|---|---|
| My child thinks 1/8 is bigger than 1/4 | Cut something into 8 pieces and into 4. More pieces = smaller pieces. Seeing beats telling. |
| They can't get started on long division | Check times-table fluency first, long division is a chain of facts, and a gap breaks it. |
| Fractions of amounts confuse them | Anchor it to division: divide by the denominator, multiply by the numerator, with objects to show why. |
Free printable: Division Facts Practice Sheet
A branded, print-ready worksheet to practise offline.
Frequently asked questions
How are division and times tables connected?
Division is the inverse of multiplication. Knowing 7 × 8 = 56 means you also know 56 ÷ 8 = 7 and 56 ÷ 7 = 8, so secure times-table recall makes division facts almost automatic.
Why do children find fractions difficult?
The most common stumbling block is thinking a larger denominator means a larger fraction, and treating the top and bottom numbers as unrelated. Using real, equal parts, pizza slices or paper strips, resolves both quickly.
What should children learn before long division?
Secure recall of times tables and related division facts, plus confidence with place value. Long division is a multi-step chain, so a gap in the underlying facts is usually what causes it to break down.