Math // Fractions

Fraction-Decimal Equivalents

Recognise and write decimal equivalents of 1/4, 1/2, and 3/4

Ages
8 to 9
Type
Concept
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

If a recipe calls for 3/4 of a cup of flour, can the learner tell you what that is as a decimal — without looking it up?

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.
  • State that 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75
  • Match fractions to decimals in a sorting activity
  • Explain why 1/4 = 25/100 = 0.25 using a hundredths grid

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

2 topics

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Fraction-Decimal Equivalents

Ages 8 to 9 // Concept

Leads to

1 topic

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

Children should learn the benchmark decimal names for 1/2, 1/4 and 3/4 (0.5, 0.25, 0.75) by understanding WHY they hold, not just memorising them. The reliable route is through hundredths: 1/4 = 25/100 = 0.25 because a quarter of a hundred squares is 25 of them. Grounding this on a 10×10 grid (and a number line where 1/4 and 0.25 mark the same point) helps counter the digit-copying error (1/4 → '0.14' or '0.4') and the denominator-as-count error (shading 4 squares). These three equivalents are high-utility landmarks across the fraction–decimal–percentage web, so children should be able to both recall them and justify them.

Common misconceptions

  • Digit-copying: writing 1/4 as 0.14 or 0.4 (treating numerator/denominator digits as decimal digits).
  • Denominator-as-count on the grid: shading 4 squares for 1/4 (reading 1/4 as 4/100 = 0.04).
  • Believing 0.25 > 0.5 because '25 > 5' (whole-number bias across the decimal).
  • Treating the fraction and its decimal as different, unrelated values.
  • Recalling the facts with no grounding, so errors cannot be self-checked.

Useful representations

  • 10×10 hundred grid with a quarter (25 squares), half (50), three-quarters (75) shaded
  • Number line where 1/4 and 0.25 share a point (also 1/2 = 0.5, 3/4 = 0.75)
  • Equivalent-fraction chain 1/4 = 25/100 = 0.25
  • Money model (£1 = 100p; a quarter = 25p = £0.25)
  • Fraction↔decimal matching cards for the three landmarks

Teaching practices

  • Derive each equivalent through hundredths on a 10×10 grid: 1/4 of 100 squares = 25 squares = 25/100 = 0.25; 1/2 = 50/100 = 0.5; 3/4 = 75/100 = 0.75.
  • Use a number line to show 1/4 and 0.25 landing on the SAME point, reinforcing that the fraction and decimal name one value.
  • Contrast the correct route with the digit-copying trap: 1/4 is NOT 0.14 or 0.4 — check by shading a quarter of the grid (25 squares, not 4).
  • Build the three as a connected family (1/4, 1/2, 3/4 ↔ 0.25, 0.5, 0.75) and connect to money (£ and quarters) and measures for familiar anchors.
  • Move both directions — fraction to decimal and decimal to fraction — and ask children to justify with the grid, so recall is backed by reasoning.

Activities to try

  1. 1

    Shade a quarter: finding 0.25 on the hundred grid

    Why it works: A quarter of 100 is 25 squares, so 1/4 and 0.25 name one and the same value — a fact the child can rebuild for 1/2 and 3/4 rather than recall blindly.

    1. On a 10×10 grid of 100 squares, split the whole into four equal groups and shade one group to make a quarter.
    2. Count the shaded squares (25) and write the result as 25/100, then as the decimal 0.25.
    3. Repeat for one half (50 squares = 50/100 = 0.5) and three-quarters (75 squares = 75/100 = 0.75), building the three as a connected family.
    4. Mark 1/4 and 0.25 on a number line and check they land on the SAME point; do the same for 1/2 = 0.5 and 3/4 = 0.75.
    5. Work in both directions: given a fraction, find the decimal; given the decimal, shade the grid and name the fraction, justifying each with the grid.
  2. 2

    Predict, then check: why isn't a quarter 4 squares?

    Why it works: Making the prediction explicit surfaces the denominator-as-count error ('4, because of the 4 in 1/4') so the child confronts and corrects it against the actual 25 squares.

    1. Before shading anything, predict how many of the 100 squares you will shade for 1/4, and say WHY.
    2. Then shade a quarter by splitting into four equal groups and taking one; count the squares.
    3. Reconcile the count (25) with your prediction: if you predicted 4, explain what went wrong.
    4. Read off 25/100 = 0.25 and state whether 1/4 and 0.25 are the same value or different.
  3. 3

    Which is bigger: 0.25 or 0.5?

    Why it works: Comparing decimals means comparing by highest place value (tenths first), not by treating the digits after the point as whole numbers; a quarter is clearly less than a half on the grid.

    1. Shade a quarter (25 squares) and a half (50 squares) on separate hundred grids and compare the shaded areas.
    2. Decide which decimal is larger, 0.25 or 0.5, and explain the choice using the grids rather than the digit strings.
    3. State why '25 is more than 5' does not make 0.25 bigger, referring to tenths and hundredths place value.
    4. Order 0.25, 0.5 and 0.75 and check the order against the grids and the number line.

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
Ma/KS2/Y4/F/6

Math // Fractions

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