Fractions
KS1MA-Y1-D004
Pupils recognise, find and name halves and quarters as equal parts of objects, shapes and quantities.
National Curriculum context
In Year 1, fractions are introduced through the practical concept of equal sharing and fair division, rather than as abstract notation. Pupils are taught half and quarter as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities — for example, recognising and finding half a length, a quantity, a set of objects or a shape. The curriculum emphasises that pupils should connect halves and quarters to equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole. This conceptual grounding — built entirely on equality and physical partitioning — is critical because it establishes the meaning of the fraction before any notation is introduced. Pupils use language such as 'one half' and 'one quarter' to describe what they find, preparing them for the written fraction notation and equivalences that follow in Year 2.
2
Concepts
1
Clusters
1
Prerequisites
2
With difficulty levels
Lesson Clusters
Recognise and find halves and quarters of shapes and quantities
practice CuratedOne half and one quarter are introduced together as the first fraction pair; C014 and C015 are mutually co-taught and together complete the Year 1 fractions curriculum. Only two concepts; a single cluster is appropriate.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Halves and Quarters of Shapes and Quantities
Mathematics Worked Example SetPedagogical rationale
Fractions begin with the physical experience of equal sharing and folding. A half means two equal parts -- the word 'equal' is critical and must be emphasised. Pupils who fold paper, cut playdough, and share counters into two equal groups develop an intuitive understanding that transfers to the symbolic notation 1/2. Quarters extend this to four equal parts. The emphasis at Y1 is on the concrete action of equal partitioning, not on the fraction notation.
Access and Inclusion
2 of 2 concepts have identified access barriers.
Barrier types in this domain
Recommended support strategies
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (2)
Recognising one half
knowledge AI FacilitatedMA-Y1-C014
One half is the first fraction pupils encounter formally and is defined as one of two equal parts. The critical understanding is that the two parts must be equal — not merely two parts. Pupils must be able to find one half of a shape, object, quantity or set of objects, recognising that halving means dividing into two equal parts. Mastery at Year 1 level means pupils can identify whether a shape or quantity has been halved correctly (both parts equal) and can find half of small even numbers.
Teaching guidance
Begin with concrete folding: fold paper shapes in half and show that the two parts match exactly when overlaid. Extend to physical sharing: share 8 counters equally between 2 people and establish that each gets 4 — one half of 8 is 4. Use fraction language from the start: 'one whole divided into two equal parts; each part is one half.' Include examples of incorrect halving (two unequal parts) and ask pupils to judge whether it shows 'a half'. Connect to the fraction notation 1/2 when pupils are ready, but the statutory requirement is recognition and naming without formal notation.
Common misconceptions
Pupils frequently think any partition into two parts constitutes a half, regardless of whether the parts are equal. They may accept an asymmetric fold as 'a half' if it looks roughly similar. Some pupils confuse 'half' as an adjective describing a size ('half-size') with 'one half' as a fraction of a specific whole.
Difficulty levels
Folding a shape in half and checking that the two parts are the same size by overlaying them.
Example task
Fold this paper circle in half. Are the two parts the same size? How do you know?
Model response: Yes, the two parts are the same size. I can see they match exactly when I fold them on top of each other.
Finding one half of a small quantity by sharing equally between 2.
Example task
Find half of 8 counters by sharing them equally between 2 plates.
Model response: Half of 8 is 4. Each plate gets 4 counters.
Finding one half of shapes, objects and quantities up to 20, identifying when something has or has not been halved correctly.
Example task
Is this shape cut in half? [Shows a rectangle with an unequal cut] Find half of 18.
Model response: No, the shape is not cut in half because the two parts are different sizes. Half of 18 is 9.
CPA Stages
concrete
Children fold paper shapes in half and overlay the two parts to check they are exactly equal. They split real objects (playdough, fruit, ribbon) into two equal pieces. Sharing objects between 2 plates connects halving a quantity to the concept of one half.
Transition: Child folds shapes in half accurately so both parts match when overlaid, and shares small even quantities between 2 to find a half, stating 'Half of [number] is [answer]' with confidence.
pictorial
Children shade one of two equal parts in drawn shapes and draw lines to divide shapes in half. They draw sharing diagrams to find half of quantities, and identify correct and incorrect halvings in pictures.
Transition: Child correctly identifies whether pictured shapes have been halved (both parts equal) or not, rejecting unequal partitions, and shades exactly half of drawn shapes.
abstract
Children use the language 'one half' to describe equal division into two parts. They find half of even numbers up to 20 mentally, connecting halving to division by 2 and to the fraction notation 1/2 when ready.
Transition: Child finds half of any even number up to 20 mentally without concrete support, and explains that 'half' means two equal parts using complete sentences.
Delivery rationale
Primary maths (Y1) with concrete stage requiring physical manipulatives (Paper circles, squares and rectangles for folding, Playdough). AI delivers instruction; facilitator sets up materials.
Access barriers (1)
Recognising one half requires understanding that a whole must be divided into two EQUAL parts. The concept of equal division is abstract — children with learning difficulties need extensive concrete experience with folding, cutting, and sharing before the fraction notation becomes meaningful.
Recognising one quarter
knowledge AI FacilitatedMA-Y1-C015
One quarter is the second fraction pupils encounter and is defined as one of four equal parts. Pupils must recognise that a whole can be divided into four equal parts and that each part is called a quarter. Mastery at Year 1 level means pupils can identify and find one quarter of shapes, objects and quantities (particularly sets of objects with a number divisible by 4), and can describe what they have done in appropriate fraction language.
Teaching guidance
Connect to halving: a quarter is half of a half — establish this by folding paper in half, then in half again, and counting the four equal parts. Use physical sharing between 4: share 12 objects equally among 4 and find that each gets 3 — one quarter of 12 is 3. Extend the range of representations: quarter of a shape (fold), quarter of a length (mark the quarter point on a strip of paper), quarter of a set (12 counters shared among 4). Connect explicitly to the language of turns: a quarter turn is a rotation of one right angle.
Common misconceptions
Similar to halving, pupils may accept any division into four parts as 'quarters' without checking equality. They may confuse the spoken word 'quarter' with 'four' (misremembering 'quarter past' on a clock as 'four past'). Pupils who understand half but not quarter may guess that a quarter is bigger than a half because the number 4 is bigger than 2.
Difficulty levels
Folding a shape into four equal parts by folding in half and then in half again.
Example task
Fold this paper square in half, then in half again. How many parts are there? Are they all the same size?
Model response: There are 4 parts. Yes, they are all the same size. Each part is a quarter.
Finding one quarter of a quantity by sharing equally between 4.
Example task
Find a quarter of 12 by sharing 12 counters equally between 4 plates.
Model response: A quarter of 12 is 3. Each plate gets 3 counters.
Finding one quarter of shapes, objects and quantities up to 20, and connecting a quarter to half of a half.
Example task
Find a quarter of 20. Explain how a quarter relates to a half.
Model response: A quarter of 20 is 5. A quarter is half of a half: half of 20 is 10, half of 10 is 5.
CPA Stages
concrete
Children fold paper in half, then in half again, to make four equal parts — each part is one quarter. They share objects equally between 4 teddies or plates to find one quarter of a quantity. Cutting fruit (an apple) into quarters provides a real-world, tactile experience.
Transition: Child folds paper into four equal parts by halving twice, names each part 'one quarter', and shares objects equally between 4 to find one quarter of a quantity correctly.
pictorial
Children shade one of four equal parts in drawn shapes and use fraction strips showing one quarter. They draw diagrams to find one quarter of quantities and identify correct and incorrect partitions into quarters.
Transition: Child shades exactly one quarter of drawn shapes divided into four equal parts, and finds one quarter of multiples of 4 up to 20 using drawn sharing diagrams.
abstract
Children use the language 'one quarter' to describe four equal parts. They find one quarter of small multiples of 4 mentally, connecting a quarter to 'half of a half' and to the fraction turn vocabulary (quarter turn = one right angle).
Transition: Child finds one quarter of multiples of 4 up to 20 mentally by halving twice, and connects the fraction quarter to quarter turns without prompting.
Delivery rationale
Primary maths (Y1) with concrete stage requiring physical manipulatives (Paper squares and circles for double-folding, 4 plates or teddies for sharing between). AI delivers instruction; facilitator sets up materials.
Access barriers (1)
One quarter is more abstract than one half because four equal parts are harder to visualise and verify than two. Children with dyscalculia often struggle to confirm that four parts are truly equal, particularly with irregular shapes or sets of objects.