Halves and Quarters
Halves and Quarters is the Year 1 introduction to fractions: splitting a single shape, object or small group of objects into 2 equal parts (halves, written 1/2) or 4 equal parts (quarters, written 1/4), and naming what one of those equal parts is called.
Method
- Start with a real object that can be physically cut or folded, not a worksheet picture: fold a paper square, or (with supervision) cut a real piece of fruit, into 2 pieces, then place one piece on top of the other to check they match exactly before calling them halves - this physical checking step is what teaches 'equal' as a size comparison, not just a count of pieces.
- Extend to quarters by folding the same shape in half a second time: this shows quarters as halving the halves rather than as an unrelated new idea, and lets the child count that 4 quarters make one whole and that 2 quarters together make the same amount as 1 half.
- Move to the pictorial stage with shapes already split into equal and unequal parts side by side, and ask the child to sort them into 'these are split fairly' and 'these are not', before ever asking them to name a fraction - spotting unequal parts is the skill that prevents wrong answers later.
- Once a child can reliably spot equal parts, ask them to name the shaded fraction of a correctly-split shape, always starting with 'how many equal parts is the whole shape split into' before 'how many of those parts are shaded'.
- Apply the same idea to a small group of objects rather than a shape, since this is where many children who understand shape-fractions get stuck: to find half of 8 counters, physically deal them one at a time into 2 equal groups (like dealing cards) and count how many end up in one group; to find a quarter, deal into 4 equal groups the same way.
- Connect halving a group of objects to the idea of sharing between 2 people, and quartering to sharing between 4 people, since 'sharing fairly' is language the child already has from everyday life, well before the word 'fraction' is introduced.
- Introduce the written forms 1/2 and 1/4 only once the physical and pictorial stages are solid, always saying the words 'a half' and 'a quarter' alongside the symbols so the two representations are linked.
- Directly challenge the bigger-number-means-bigger-piece misconception with a side-by-side physical comparison: fold two identical paper strips, one into halves and one into quarters, and lay a half-piece next to a quarter-piece so the child sees directly that the quarter piece is smaller, despite 4 being a bigger number than 2.
Worked example
Noah has 12 toy cars. He wants to find a quarter of them. How many toy cars is that?
- Line up all 12 toy cars so they are ready to be shared out fairly.
- A quarter means sharing into 4 equal groups, so deal the cars one at a time into 4 groups.
- Sharing 12 cars equally into 4 groups gives 3 cars in each group.
- So a quarter of 12 toy cars is 3 toy cars.
Practice questions
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Q1Priya folds a rectangular flag in half so both parts match exactly. What fraction is each part of the flag?Show answer
Answer: One half (1/2)
Q2A square biscuit is broken into 4 equal pieces. What fraction is each piece of the whole biscuit?Show answer
Answer: One quarter (1/4)
Q3Look at these two circles, both cut into 2 pieces. Circle A's pieces are the same size. Circle B's pieces are different sizes. Which circle shows true halves?Show answer
Answer: Circle A (the pieces must be equal to be halves)
Q4Jamal has 16 building blocks. He gives half of them to his sister. How many blocks does his sister get?Show answer
Answer: 8 blocks (half of 16 is 8)
Q5Aisha has 20 conkers. She shares a quarter of them with her friend. How many conkers does her friend get?Show answer
Answer: 5 conkers (a quarter of 20 is 5)
Q6A chocolate bar is broken into 4 equal pieces. How many pieces make up the whole bar?Show answer
Answer: 4 pieces
Q7Which is smaller: a quarter of a sandwich, or a half of the same sandwich?Show answer
Answer: A quarter is smaller
Q8A ribbon is cut into 2 equal pieces. What fraction is 1 piece of the ribbon?Show answer
Answer: One half (1/2)
Exam-style questions
Written in the style of a KS1 Maths exam paper, with a full mark scheme.
Kian has 24 marbles. He gives a quarter of them to his cousin. How many marbles does his cousin get? Show your working.
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A rectangular garden is split into 2 equal parts. One part is used for vegetables and the other for flowers. What fraction of the garden is used for vegetables? Explain how you know the two parts must be equal for this to be a true half.
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Two identical strips of ribbon are the same length. Ravi cuts his strip into 2 equal pieces. Deepa cuts her strip into 4 equal pieces. Whose single piece of ribbon is longer, and why?
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Free printable worksheet
Want more practice on paper? Download the halves and quarters worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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