Fractions
KS1MA-Y2-D004
Pupils recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of lengths, shapes, sets and quantities, write simple fractions, and recognise the equivalence of 2/4 and 1/2.
National Curriculum context
In Year 2, fractions extend beyond the halves and quarters of Year 1 to include thirds and three-quarters, and pupils begin to write fraction notation. Pupils use fractions as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities, connecting unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. Pupils meet 3/4 as the first example of a non-unit fraction — a fraction where the numerator is greater than 1. A significant conceptual milestone is the recognition that 2/4 and 1/2 are equivalent — the same quantity expressed in two different ways — which establishes the fundamental idea of fraction equivalence that will be central to mathematics through Key Stage 2 and beyond. Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (for example, 1 1/4, 1 2/4 (or 1 1/2), 1 3/4, 2), reinforcing the concept of fractions as numbers that can add up to more than one.
2
Concepts
1
Clusters
2
Prerequisites
2
With difficulty levels
Lesson Clusters
Find and compare fractions of shapes and sets, including equivalent fractions
practice CuratedRecognising fractions of quantities and identifying the first equivalence (2/4 = 1/2) naturally co-occur — equivalence arises directly from partitioning work. Only two concepts; a single cluster is appropriate.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Fractions: Halves, Quarters, and Thirds
Mathematics Worked Example SetPedagogical rationale
Y2 extends fraction understanding from halves and quarters to include thirds, and from unit fractions to non-unit fractions (2/4, 3/4). The critical new idea is that 2/4 is equivalent to 1/2 -- this is the first encounter with fraction equivalence. Fractions of quantities (1/3 of 12) connect fractions to division. Concrete folding and sharing remain essential, but pupils now also work with fraction notation and begin to reason about the relationship between fractions.
Access and Inclusion
1 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)
Fractions as 'fractions of': 1/3, 1/4, 2/4, 3/4
knowledge AI FacilitatedMA-Y2-C012
Year 2 extends the set of fractions pupils can find and name from halves and quarters (Year 1) to include thirds and three-quarters. Pupils use fractions to describe a part of a discrete quantity (e.g. 1/3 of 12 = 4) or a continuous quantity (e.g. 1/3 of a length). A quarter of a quantity is one of four equal parts; two quarters (2/4) is two of those four equal parts; three quarters (3/4) is three of those four equal parts. Three-quarters is explicitly the first non-unit fraction pupils encounter. Mastery means pupils can find any of these fractions of given quantities and lengths, and write the fraction notation correctly.
Teaching guidance
Use sharing as the primary concrete approach: to find 1/3 of 12, share 12 equally among 3 (each person gets 4). To find 3/4 of 12, first find 1/4 (share among 4 = 3), then multiply by 3 (three-quarters = 3 groups of the unit fraction = 9). Use fraction strips and number lines to show fractions of continuous quantities. The curriculum specifies that pupils should count in fractions up to 10 on the number line (1 1/4, 1 2/4, 1 3/4, 2...) to understand fractions as numbers in their own right. Write fraction notation clearly: the vinculum (fraction bar) separates numerator and denominator.
Common misconceptions
Pupils frequently confuse the denominator with the number of shaded parts, rather than the total number of equal parts. When finding fractions of quantities by sharing, pupils may share unequally and not recognise the error. For three-quarters, pupils often do not connect this to 3 × (1/4) — they see it as a new fraction to memorise rather than as three unit fractions combined. Writing fraction notation is confused: some pupils write the numerator below the line.
Difficulty levels
Finding one half and one quarter of a small quantity by physically sharing objects equally.
Example task
Find half of 10 by sharing 10 counters equally between 2 plates. Find a quarter of 8 by sharing between 4 plates.
Model response: Half of 10 is 5 (each plate gets 5). A quarter of 8 is 2 (each plate gets 2).
Finding 1/3, 1/4, 2/4 and 3/4 of quantities using sharing or by finding the unit fraction first then multiplying.
Example task
Find 3/4 of 12.
Model response: First find 1/4 of 12 = 3. Then 3/4 = 3 × 3 = 9. So 3/4 of 12 is 9.
Finding unit and non-unit fractions of quantities and lengths, and counting in fractions on a number line.
Example task
Count in quarters from 0 to 2 on the number line: 0, 1/4, 2/4, 3/4, 1, ... What is 1/3 of 18?
Model response: 0, 1/4, 2/4, 3/4, 1, 1 1/4, 1 2/4, 1 3/4, 2. One third of 18 is 6.
CPA Stages
concrete
Children find fractions of quantities by sharing objects equally between the denominator number of plates or cups. For 1/3 of 12: share 12 counters between 3 plates (4 each). For 3/4 of 12: share 12 between 4 plates (3 each), then count 3 of the 4 plates (9).
Transition: Child shares objects equally between the correct number of groups to find unit fractions (1/3, 1/4) and then counts the appropriate number of groups for non-unit fractions (2/4, 3/4).
pictorial
Children use fraction strips, fraction walls and number lines to find fractions of quantities and lengths. They draw sharing diagrams for 1/3, 1/4, 2/4 and 3/4 of given quantities, and count in fractions on number lines (0, 1/4, 2/4, 3/4, 1, 1 1/4...).
Transition: Child uses fraction strips and drawn diagrams to find any of the required fractions (1/3, 1/4, 2/4, 3/4) of quantities up to 30, and counts in fractions along a number line beyond 1.
abstract
Children find fractions of quantities mentally by dividing by the denominator and multiplying by the numerator. They write fraction notation correctly and count in fractions on a number line, understanding fractions as numbers that can exceed 1.
Transition: Child finds fractions of quantities mentally by dividing then multiplying, writes the fraction notation correctly (numerator above vinculum, denominator below), and explains the method in their own words.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Counters, Plates or cups for sharing (2, 3 and 4)). AI delivers instruction; facilitator sets up materials.
Access barriers (2)
Fractions as 'fractions of' (1/3, 1/4, 2/4, 3/4) require understanding part-whole relationships with multiple different denominators. Each denominator represents a different equal-sharing scenario. Without extensive concrete partitioning experience, the notation is meaningless.
Fraction vocabulary introduces 'numerator', 'denominator', 'third', 'quarter', 'equal parts', and 'fraction of' — all new mathematical terms that describe relationships rather than objects.
Fraction equivalence: 2/4 = 1/2
knowledge AI FacilitatedMA-Y2-C013
The recognition that 2/4 and 1/2 name the same quantity — the same point on the number line, the same part of a whole — is the first exposure to fraction equivalence in the national curriculum. This is conceptually significant: two fractions with different numerators and denominators can have the same value. Mastery means pupils understand why 2/4 = 1/2 (because two of four equal parts is the same as one of two equal parts), and can identify this equivalence in different contexts.
Teaching guidance
Demonstrate equivalence concretely by folding: fold a strip of paper into halves, shade one half; fold a congruent strip into quarters, shade two quarters — the shaded regions are the same size. Use fraction walls and number lines where both 1/2 and 2/4 appear at the same point. The non-statutory guidance specifies counting in fractions on the number line using both 1 2/4 and 1 1/2 as equivalent names for the same point. Avoid purely symbolic demonstration at this stage; always ground equivalence in a visual or concrete model that shows the equality of the quantities.
Common misconceptions
Pupils initially resist the idea that fractions with different numerators and denominators can be equal — they interpret 2/4 and 1/2 as different fractions because 2 is not the same as 1 and 4 is not the same as 2. They may know that 2/4 = 1/2 as a rote fact without understanding why. Some pupils think larger denominators always mean larger fractions.
Difficulty levels
Comparing folded paper strips to see that 1/2 and 2/4 cover the same area.
Example task
Fold one strip in half and shade one part. Fold another strip in quarters and shade two parts. Compare them — are they the same?
Model response: Yes, the shaded parts are the same size. 1/2 and 2/4 are the same amount.
Recognising 2/4 = 1/2 on a number line and using fraction walls to verify the equivalence.
Example task
On the fraction wall, which fraction is the same as 1/2? Point to where 1/2 and 2/4 are on the number line.
Model response: 2/4 is the same as 1/2. They are both at the same point on the number line, exactly halfway between 0 and 1.
Explaining why 2/4 = 1/2 and recognising that equivalent fractions name the same value.
Example task
Explain to a friend why 2/4 and 1/2 are the same.
Model response: If you cut something into 4 equal parts and take 2, you have taken exactly half. 2 out of 4 is the same proportion as 1 out of 2.
CPA Stages
concrete
Children fold identical paper strips: one into 2 equal parts (halves), the other into 4 equal parts (quarters). They shade 1/2 of one strip and 2/4 of the other, then place them side by side to see the shaded regions are the same size. This physical comparison makes equivalence visible.
Transition: Child folds and compares strips accurately, stating: '1/2 and 2/4 are the same because 2 out of 4 equal parts covers the same area as 1 out of 2 equal parts.'
pictorial
Children use fraction walls and number lines to verify that 1/2 and 2/4 occupy the same position. They shade diagrams to show the equivalence and count in fractions on number lines using both names for the same point (e.g. 1 2/4 = 1 1/2).
Transition: Child identifies 2/4 and 1/2 as the same point on a fraction wall and number line, and uses both names interchangeably when counting in fractions.
abstract
Children explain why 2/4 = 1/2 as a mathematical equivalence: two of four equal parts is the same proportion as one of two equal parts. They recognise that equivalent fractions name the same value and apply this in context.
Transition: Child explains the equivalence of 2/4 and 1/2 in their own words using the concept of equal parts, without needing to fold or draw, and applies the equivalence to solve problems.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Paper strips for folding, Crayons for shading). AI delivers instruction; facilitator sets up materials.