Math // Fractions

Percentage and decimal equivalents

Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

If the learner knows that 1/4 = 25% = 0.25, can they use that to work out 25% of £80 — and also find 4/5 of 60 sweets?

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 1/5 = 20% = 0.2 and use this to find 20% of 60
  • Convert 3/4 to 75% and to 0.75
  • A shop offers 25% off a £40 item — what is the sale price?

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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Percentage and decimal equivalents

Ages 9 to 10 // Method

Leads to

2 topics

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 build fluent, usable knowledge that landmark fractions (1/2, 1/4, 3/4, 1/5, 2/5, 4/5 and tenths/hundredths) have partner percentage and decimal forms, and — crucially — deploy those equivalences to solve problems (25% off £40; 20% of 60). The core is procedural: recognise which landmark applies, convert to the handiest form, and compute. Ground every equivalent on a hundred-grid or bar so 'per cent = per hundred' stays concrete, and build a benchmark toolkit (50% = halve, 10% = ÷10, 1% = ÷100, 25% = ÷4) that children combine to reach any whole-number target percentage rather than memorising isolated facts. Always require interpreting the answer in context (discount vs sale price).

Common misconceptions

  • Base-neglect: treats a percentage as a fixed amount independent of the whole — '25% off means £25 off' or '20% of 60 is 20'.
  • Denominator-as-decimal / faulty equivalent: converts 1/5 to 0.5 (copies the 5) or thinks 1/5 = 15%.
  • Rote 'divide by 100' with no meaning: divides by 100 and stops, or divides by the wrong number (e.g. by 20 for 20%).
  • Solves '25% off' by finding 25% and forgetting to subtract, giving the discount as the sale price.

Useful representations

  • Hundred-grid (10×10) with a fraction shaded, read simultaneously as fraction, hundredths-decimal and percentage
  • Bar model / percentage bar marked at 0, 25, 50, 75, 100% aligned with the whole amount
  • Double number line: amount on top, percentage on the bottom, for scaling to any percentage
  • Benchmark toolkit table: 50% = ÷2, 25% = ÷4, 10% = ÷10, 1% = ÷100 with worked combinations

Teaching practices

  • Teach percentages of amounts via landmark benchmarks — 50% (halve), 10% (divide by 10), 1% (divide by 100), 25% (quarter) — and combine them (e.g. 20% = double 10%), so the child reasons rather than recalls a rule.
  • Ground every equivalent on a hundred-grid or bar model: 1/5 shaded is 20 of 100 squares = 20% = 0.2, keeping 'per cent means per hundred' visible.
  • Rehearse the recall set (1/2, 1/4, 3/4, 1/5, 2/5, 4/5 and /10, /25 denominators) as a connected web, deriving 2/5 and 4/5 from 1/5 rather than as separate facts.
  • Always require the child to interpret the answer in context — '25% off £40' means find the DISCOUNT (£10) then the SALE PRICE (£30), not just compute 25% of 40.
  • Move between all three forms in problems so the child chooses the easiest tool: 1/5 of 60 is fastest as 60 ÷ 5, while 20% of 60 might be found as double-10%.

Activities to try

  1. 1

    Live percentage bar over a settable amount

    Why it works: A percentage is a proportion of the whole, not a fixed amount: changing the whole changes the pounds answer. Benchmark percentages (50%, 10%, 1%, 25%) can be combined to reach any whole-number target percentage, and the discount is a different quantity from the sale price.

    1. Set the whole amount to £40 on a percentage bar and move a marker to 25%; read off the shaded amount (£10) and a separate sale-price readout (£30), so discount and remaining stay distinct.
    2. Build 20% of 60 by stacking two 10% benchmark blocks (10% of 60 = 6, so 20% = 12), watching the arithmetic appear as you combine them.
    3. Keep the marker at 25% but change the whole from £40 to £80 and observe the pounds answer change from £10 to £20 — the same percentage, a different amount.
    4. Try each target percentage two ways where possible (e.g. 1/5 of 60 as 60 ÷ 5, and 20% of 60 as double 10%) and compare.
  2. 2

    Hundred-grid reference for landmark equivalents

    Why it works: 'Per cent means per hundred': the fraction, hundredths-decimal and percentage are three readings of the same shaded quantity on a hundred-grid, and related fractions (2/5, 4/5) derive from 1/5.

    1. Shade 1/5 of a 10×10 hundred-grid and count the squares (20 of 100), then read it simultaneously as 1/5 = 20 hundredths = 0.2 = 20%.
    2. Shade 1/4 to reveal 25 squares = 25% = 0.25, and 3/4 to reveal 75 squares = 75% = 0.75.
    3. Contrast 1/5 (20 squares) with 1/2 (50 squares) to check against the 'copy the denominator digit' habit (1/5 is not 0.5 or 15%).
    4. Derive 2/5 and 4/5 from 1/5 by counting 40 and 80 squares, building the recall set as a connected web rather than separate facts.
  3. 3

    Fluency and context-step rehearsal

    Why it works: Fluent recall of the equivalents must combine with the context subtract-step: finding the discount is not the same as finding the sale price.

    1. Match the three equivalent forms: 1/5 ↔ 20% ↔ 0.2 and 3/4 ↔ 75% ↔ 0.75.
    2. Complete fill-in-the-blank computations such as '20% of 60 = __' and '1/5 of 60 = __'.
    3. Answer a contextual item: a shop offers 25% off a £40 item — what is the sale price? Watch for the trap of £10 (that is the discount, not the price) and £25 (base-neglect, '25% off = £25').
    4. Explain, for at least one item, a second route to the same answer (e.g. 20% of 60 via 10% of 60 doubled).

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
Ma5/2.4l

Math // Fractions

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