Math // Fractions

What Is a Half?

Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity

Ages: 5 to 6
Type: Concept
Builds on: 1 topic
Leads to: 5 topics
Standards: 1 code

Quick check

If the learner is helping share a sandwich equally between two people, can they cut it so both pieces are the same size — and tell you each piece is called a half?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.

Fold a shape into two equal parts and identify each as 'a half'
Find half of 8 objects by sharing into 2 equal groups
Identify whether a shape has been divided into halves or not (equal vs unequal parts)

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.

RequiredMust come first
HelpfulHelps, but not essential

Before this

1 topic

Division as equal sharingRequired
Multiplication & Division // Ages 4 to 6
Finding a half requires equal sharing into 2 groups — a division concept

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What Is a Half?

Ages 5 to 6 // Concept

Leads to

5 topics

Finding halves and quarters (age 5+)Required
Fractions // Ages 5 to 6
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
Fractions of amountsRequired
Fractions // Ages 6 to 7
Working with fractions extends from Y1 understanding of halves
Halves & Quarters of ShapesRequired
Fractions // Ages 6 to 7
Partitioning shapes into halves extends from Y1 understanding of halves
Turns & DirectionsHelpful
Geometry // Ages 5 to 6
Understanding half and quarter turns benefits from the concept of halves and quarters
Telling Time: Hours and Half HoursHelpful
Measurement // Ages 5 to 6
Understanding 'half past' benefits from the concept of halves

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Teach 'a half' as ONE OF TWO EQUAL parts of a whole, where the equality — not merely having two pieces — is the defining idea. Build on children's informal fair-sharing intuition, starting by sharing a set of objects evenly between two before partitioning a single object. Cover halving of single objects (fold/cut a shape), lengths (split a strip at the midpoint), and quantities/sets (share counters into two equal groups). Reinforce that two halves recompose the whole, and that 'half of' a quantity is found by sharing equally into two. For ages 5–6.

Common misconceptions

Any two pieces count as 'halves' regardless of size — the equal-parts requirement is missing
A half is only the one piece you take, not seeing that both parts are halves and together make the whole
Calling any fractional part 'a half' (a documented early error — IES)
Sharing a set by equal NUMBER of items rather than equal AMOUNT when items differ in size (number-vs-quantity confusion)

Useful representations

Folded/cut shapes (circle, rectangle, strip) into two matching parts
A bar or length split at the midpoint
A set of counters shared into two equal groups
Two halves clicking back together to make the whole

Teaching practices

Build on the informal halving/fair-share strategy children already bring; begin by sharing a SET of objects evenly between two before partitioning a single object (IES progression)
Make 'equal' the explicit criterion — use fair-sharing language ('would that be fair?') and check by matching/overlaying the parts
Accept approximately-drawn parts as long as the child treats them as equal (IES roadblock guidance)
Name the parts and the whole: 'a half', 'the other half', 'two halves make one whole'
Use both continuous (folded shapes, strips) and discrete (sharing counters) models so 'half' is not tied to one picture

Activities to try

1
The halving bench: make it fair
Why it works: A half requires two EQUAL parts; the count of two pieces alone does not make halves. Both parts are halves, and together they rebuild the whole.
1. Drag a cutting line across a rectangular chocolate bar (cutting straight across its length); when the cut is off-centre, note that the two parts are unequal (e.g. they glow red / are labelled 'not halves – not fair') and when at the midpoint the two parts are equal (snap green / labelled 'two equal halves').
2. Slide the two equal halves back together to remake the whole bar, saying 'two halves make one whole'.
3. Switch to a set mode: share a plate of biscuits (or counters) into two hoops, and only accept it as 'done' when the two amounts match.
4. Check equality by matching or overlaying the parts, and describe each as 'a half' and 'the other half'.
2
Share the set first
Why it works: 'Half of' a quantity is found by sharing equally into two groups; fairness means equal amount, which may differ from equal number when items vary in size.
1. Share a set of objects (for example, 8 counters, or 6 sweets) evenly between two people, giving one each in turn until the pile is gone.
2. State how many each person gets and, when all the objects are the same size, that each group is 'half of' the set.
3. With objects of different sizes (big and small sweets), check whether equal COUNT gives equal AMOUNT, and discuss which sharing is fair.
3
Halved or not? Sort and choose
Why it works: Recognising halves means checking for two EQUAL parts, so an unequal split is not halves even though it has two pieces.
1. Sort pictures of shapes and sets into 'halved' (two equal parts) versus 'not halved' (unequal parts).
2. Choose which picture shows a half when one option has an unequal cut as a tempting wrong choice.
3. For each 'not halved' example, say what is wrong and what would make it a half.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.

The national curriculum in England: Key stages 1 and 2 framework document: Maths/Y1/F/1

Math // Fractions