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Maths · Ages 10–11 · 55 minutes

Percentages of amounts

Pupils find percentages of amounts by building from 50%, 10% and 1%, and explain why per cent means parts per hundred.

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Success criteria

  • I can find 50% 10% and 1% of an amount
  • I can build other percentages from these
  • I can check my answer is sensible

Key vocabulary

  • per cent
  • percentage
  • hundredth
  • of
  • equivalent
  • discount
  • build up

You will need

  • 100-square grids
  • mini whiteboards
  • a shop "sale" poster with prices
  • calculators for checking only

Curriculum links

  • Year 6· England
  • Grade 5· United States
  • Primary 6· Nigeria
  • Class 6· India

Practice sheets

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The lesson at a glance

55 minutes in all. Timings are a guide: follow your class.

  1. Step 1: Starter

    Show a 100-square with 30 squares shaded.
    8 minutes

  2. Step 2: Teach

    "Per cent means per hundred, out of every hundred.
    14 minutes

  3. Step 3: Guided practice

    On whiteboards, show the building blocks you used: 10% of 450 30% of 450 25% of 64 75% of 64 12% of 300 99% of 200 (pupils who spot "100% minus 1%" deserve credit) Then ask: "Is 40% of 50 the same as
    10 minutes

  4. Step 4: Independent practice

    Use the practice buttons above.
    18 minutes

  5. Step 5: Plenary

    Return to 40% of 50 and 50% of 40.
    5 minutes

  6. Step 6: Assessment for learning

    Look for pupils who: find 10% by dividing by 10, not by subtracting 10; choose efficient building blocks; check that an answer is sensible (a percentage under 100% must give less than the whole).

  7. Step 7: Differentiation

    Pupils who need support should stick to 50%, 25%, 10% and multiples of 10% with a 100-square for reference.

  8. Step 8: Common misconceptions

    Finding 10% by subtracting 10.

  9. Step 9: Home link

    In a shop or online, find a sale price and work out the discount together using 10% and 50%.

1.Starter

8 minutes

Show a 100-square with 30 squares shaded. "What fraction is shaded? As a decimal? As a percentage?" (30/100, 0.3, 30%.) Repeat with 75 and 5 squares.

Then a quick fire on whiteboards: "Half of 80. A tenth of 80. A hundredth of 800." These three are the whole lesson in disguise.

2.Teach

14 minutes

"Per cent means per hundred, out of every hundred. 100% is the whole amount."

Write 360 in a bar at the top of the board. "Let's find some percentages of 360."

  • "50% is half: 180."
  • "10% is one tenth, so divide by 10: 36."
  • "1% is one hundredth, so divide by 100: 3.6."

"Now I can build almost anything. 20% is 10% doubled: 72. 5% is half of 10%: 18. 15% is 10% + 5%: 54. 25% is half of 50%: 90."

Step by step

  1. Find the building blocks50% (halve), 10% (÷ 10), 1% (÷ 100).
  2. Build the percentage you need35% = 10% + 10% + 10% + 5%, or 50% − 15%.
  3. Check it makes sense35% is a bit more than a third, so the answer should be a bit more than a third of the amount.

Model one more in context: "A coat costs $80. It's 15% off. How much is the discount? 10% is $8, 5% is $4, so 15% is $12. The coat now costs $68."

The rest of the plan

Guided and independent practice, the plenary, assessment for learning, differentiation, common misconceptions and the home link are free with a Crayonbird account.

  1. Guided practice10 minutes
  2. Independent practice18 minutes
  3. Plenary5 minutes
  4. Assessment for learning
  5. Differentiation
  6. Common misconceptions
  7. Home link
See the whole plan, free

Learning Wiki

Percentages

A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.

Direct proportion

Two quantities are in direct proportion when one is always the same multiple of the other, so doubling one doubles the other. The rule is y = kx, where k is the constant of proportionality.

Profit and loss

Profit = selling price − cost price; loss = cost price − selling price. Profit percentage = profit ÷ cost price × 100. Buy at $20, sell at $25: profit $5, which is 25%.

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