Math // Ratio & Proportion

Calculating Percentages

Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison

Ages
10 to 11
Type
Method
Builds on
4 topics
Leads to
4 topics
Standards
1 code

Quick check

If a jumper originally costs £40 and is 15% off, can the learner work out how much the discount is and what the sale price would be?

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.
  • Calculate 15% of 360 by finding 10% and 5% and combining
  • Compare two discounts given as percentages of different original prices
  • Explain a strategy for finding any percentage of an amount using known percentage facts

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

4 topics
  • Percentages (age 9+)Required

    Ratio & Proportion // Ages 9 to 11

    Calculating percentages of amounts requires 'percentage', 'proportion', and 'out of' vocabulary

  • Decimals and fractions (age 10+)Required

    Fractions // Ages 10 to 11

    Calculating percentages requires fraction-decimal-percentage equivalence

  • Bar Models for RatiosHelpful

    Ratio & Proportion // Ages 9 to 12

    Percentage-of-amount problems can be set up as bar models showing 100% divided into parts

  • Decimal place valueHelpful

    Multiplication & Division // Ages 10 to 11

    Finding percentages often involves decimal multiplication

You are here

Calculating Percentages

Ages 10 to 11 // Method

Leads to

4 topics
  • Pie chartsRequired

    Data & Statistics // Ages 10 to 11

    Calculating pie chart sector angles requires computing percentages of 360; interpreting sectors requires proportional reasoning

  • Percentages as FractionsRequired

    Ratio & Proportion // Ages 11 to 13

    Percentages as fractions/decimals extends Y6 percentage calculations

  • Percentages (age 12+)Required

    Ratio & Proportion // Ages 12 to 14

    Percentage increase/decrease extends KS2 percentage calculations

  • Efficiency, Sankey diagrams, and work doneHelpful

    Science // Energy // Ages 12 to 13

    Calculating energy efficiency as a percentage requires percentage calculation skills from Math

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 6 pupils learn to find a percentage of an amount (e.g. 15% of 360) by building from benchmark facts — 10% (÷10), 5% (half of 10%), 1% (÷100) — and combining them (15% = 10% + 5%), keeping the calculation grounded in 'parts per hundred'. The subtler skill is comparison: because a percentage is always relative to its base, comparing two percentages of DIFFERENT amounts requires computing the actual amounts, not just comparing the percentages. Anchoring to a 100-grid or bar, drilling the benchmark building blocks, and forcing explicit attention to 'percent of WHAT' when comparing are the core moves.

Common misconceptions

  • Compares two percentages while ignoring their different bases (assumes 30% off always saves more than 25% off, whatever the prices)
  • Misplaces the decimal when converting: treats 15% as 1.5 (or 6% as 0.6), giving a tenfold error
  • Cannot assemble a percentage from benchmarks, or takes 5% as 10% ÷ 5 instead of 10% ÷ 2
  • Treats a percentage as a fixed absolute amount rather than a proportion of the given whole

Useful representations

  • 100-square (each cell = 1%) and a bar split into ten 10% chunks
  • Benchmark fact ladder: 10%, 5%, 1%, 25%, 50% and how to combine them
  • Percentage bar model (whole = 100%, shade the required part)
  • The equivalence triple 15% = 15/100 = 0.15
  • Two labelled bars of different totals for comparison (percent of WHICH base)

Teaching practices

  • Build percentages from benchmark facts: 10% (÷10), 1% (÷100), 5% (half of 10%), 25% (÷4), 50% (÷2), then combine (15% = 10% + 5%; 35% = 25% + 10%).
  • Anchor to a 100-square or a bar split into ten 10% chunks so 'parts per hundred' stays visible and 10% of 360 = 36 is seen, not just computed.
  • Make 'percent of what?' explicit in every comparison problem: a bigger percentage of a smaller amount can be less than a smaller percentage of a bigger amount — always compute the actual amounts to compare.
  • Connect the three forms fluently — 15% = 15/100 = 0.15 — and check the decimal is placed correctly (15% = 0.15, not 1.5), since misplacing it is a common source of tenfold errors.
  • Use bar models for percentage-of-amount: the whole bar is 100%, partition and shade to read off the required percentage.
  • Progress from friendly percentages (multiples of 5) to any percentage, and to a single-multiplier method (×0.15) once the benchmark method is secure.

Activities to try

  1. 1

    Build a percentage from benchmark chunks

    Why it works: Finding a percentage of an amount is assembling friendly known pieces, not recalling an opaque rule; 'parts per hundred' stays visible on the bar.

    1. Treat a bar as the whole amount (e.g. £360 = 100%) and partition it into ten equal 10% chunks.
    2. Find 15% of £360 by taking one 10% chunk (£36) and half of another (5% = £18), then combining them to read £54.
    3. Say aloud how each benchmark is found: 10% = ÷10, 1% = ÷100, 5% = half of 10%, 25% = ÷4, 50% = ÷2, and combine (e.g. 35% = 25% + 10%).
    4. Record the matching equivalence each time: 15% = 15/100 = 0.15, and check the decimal point is in the right place (0.15, not 1.5).
    5. Progress from friendly multiples of 5 to any percentage, and later to a single multiplier (×0.15) once the benchmark method is secure.
  2. 2

    Compare mode: percent of WHICH base?

    Why it works: A percentage is relative to its own base; to compare two percentages of different amounts you must compute the actual amounts, not compare the percentages.

    1. Look at two bars of different totals side by side, e.g. an £80 coat at 25% off and a £60 jacket at 30% off.
    2. First predict which deal saves more, then compute both actual savings: 25% of £80 = £20 and 30% of £60 = £18.
    3. State the result: the COAT saves more (£20 > £18) even though its percentage is smaller, because the two percentages are taken of different prices.
    4. Test the base explicitly: if the jacket had cost £100 instead of £60, recompute — 30% of £100 = £30 would now win — to show that the base matters.
    5. Finish by writing a one-sentence explanation of why a smaller percentage can give a larger amount.
  3. 3

    Scored practice set with a base-ignoring distractor

    Why it works: Fluency with benchmark build-up and correct decimal conversion, plus recognising when a percentage-only comparison is wrong.

    1. Complete fill-in build-ups: 10% of 360 = ☐, 5% of 360 = ☐, so 15% of 360 = ☐.
    2. Answer a multiple-choice comparison of two discounts on differently-priced items, where one option is the 'bigger percentage must win' answer.
    3. Use a slider to estimate a percentage on a 0-to-amount scale as a proportional sanity check before computing exactly.
    4. Convert between forms in short items: write 15% as a fraction and a decimal and check decimal placement.

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
Ma6/2.4b

Math // Ratio & Proportion

More in Ratio & Proportion

All 18 topics