Math // Fractions

Understanding fractions

Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2

Ages
6 to 7
Type
Concept
Builds on
3 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner has 6 strawberries and eats half of them, can they write that as "1/2 of 6 = 3" — and explain why 2/4 and 1/2 are the same amount?

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.
  • Write 1/2 of 10 = 5
  • Explain that 2/4 is the same as 1/2 using a diagram
  • Calculate simple unit fractions of quantities and write the result

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

3 topics
  • Fractions of amountsRequired

    Fractions // Ages 6 to 7

    Writing fractions and recognising equivalence requires knowing what the fractions mean

  • Fraction NotationRequired

    Fractions // Ages 6 to 9

    Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary

  • Reading +, −, and = symbolsHelpful

    Addition & Subtraction // Ages 5 to 6

    Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign

You are here

Understanding fractions

Ages 6 to 7 // Concept

Leads to

1 topic
  • Equivalent fractionsRequired

    Fractions // Ages 7 to 8

    Extends equivalence of 2/4 and 1/2 to broader equivalent fractions

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

Year 2 children (ages 6-7) write simple fractions of quantities (e.g. 1/2 of 6 = 3) and meet their first fraction equivalence: 2/4 = 1/2. Equivalence means two differently-written fractions name the same amount - the same-sized piece, cut into a different number of parts. This is the natural place to confront the whole-number bias that '2/4 must be more than 1/2 because the numbers are bigger'. The core teaching move is predict-then-check: the child predicts a comparison, then overlays two quarters onto one half to see them coincide exactly.

Common misconceptions

  • 2/4 is more than 1/2 because the numbers are bigger (whole-number bias)
  • Two fractions written with different numbers cannot name the same amount (no concept of equivalence)
  • Errors computing a unit fraction of a quantity (1/2 of 6) by not sharing equally

Useful representations

  • Two identical bars, one halved and one quartered, with two quarters overlaid on one half
  • A fraction wall aligning 1/2 with 2/4
  • A set of 6 shared into two equal groups (1/2 of 6 = 3)
  • Number line with 1/2 and 2/4 landing on the same point

Teaching practices

  • Establish equivalence by overlaying identical wholes cut two ways (two quarters exactly cover one half)
  • Derive equivalence from sharing (four pizzas among eight children = 4/8 = 2/4 = 1/2 - IES)
  • Write the fraction sentence alongside the model (1/2 of 6 = 3) so notation records a known amount
  • Confront the 'bigger numbers = more' intuition head-on with a predict-then-check comparison
  • Ask for more than one name for the same amount to normalise many-names-one-value

Activities to try

  1. 1

    Overlay check: proving 1/2 = 2/4 by covering

    Why it works: Two quarters cover exactly one half, so 2/4 and 1/2 name the same amount even though 2/4 uses bigger numbers. A fraction has many names for one value. The prediction step surfaces the 'bigger numbers = more' intuition so the overlay can confront it directly.

    1. Take two identical chocolate bars (or paper strips of the same length). Cut one into 2 equal pieces and the other into 4 equal pieces.
    2. Before moving anything, predict and say aloud: are 2 pieces from the four-piece bar MORE, LESS, or the SAME as 1 piece from the two-piece bar? Give your reason.
    3. Place the two quarter-pieces exactly on top of the one half-piece and check whether they cover it with nothing left over and no overlap.
    4. Write the result as a fraction sentence: 1/2 = 2/4, and say in words 'the same amount, cut into a different number of parts'.
    5. Find at least one more name for the same amount (for example cut another identical bar into 6 and check that 3/6 also covers one half).
  2. 2

    Equal sharing: deriving equivalent fractions

    Why it works: Equivalent fractions arise naturally from equal sharing: the same real share can be written with different numbers, and these names are equal.

    1. Share 4 pizzas equally among 8 children by drawing or using counters; work out how much each child gets.
    2. Write the share each child receives as a fraction (4/8), then show by grouping that this is also 2/4 and 1/2.
    3. Explain in your own words why 4/8, 2/4 and 1/2 all describe the same share.
  3. 3

    Finding a fraction of a quantity by equal sharing

    Why it works: A unit fraction of a quantity is found by sharing equally into the number of parts named by the denominator and taking one group. Because 2/4 = 1/2, taking 2/4 of a quantity gives the same result as taking 1/2 of it.

    1. Take a set of 6 counters. Share them into 2 equal groups and count one group to find 1/2 of 6.
    2. Write the sentence 1/2 of 6 = 3 next to your groups.
    3. Try 1/2 of 10 by sharing 10 into 2 equal groups, and write 1/2 of 10 = 5.
    4. Now find 2/4 of 6. Sharing 6 counters into 4 equal groups does not give whole counters (each group would be one and a half), so use the equivalence 2/4 = 1/2: since 1/2 of 6 = 3, we know 2/4 of 6 is also 3.

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/Y2/F/2

Math // Fractions

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