Percentages GCSE lesson: multipliers, percentage change and reverse percentages

Percentages: practice

A calculator is allowed. Write new = multiplier × original first. The stretch is optional.

Diagnostic question: choose and explain

1. In a sale, prices are cut by 20%. A jacket now costs £48. What did it cost before the sale?
   1. £57.60
   2. £60
   3. £38.40
   4. £68

Practice questions

1. Find 35% of £80.
2. Sort each change onto its multiplier.They sort 8 items into × 1.05 and × 1.5 and × 0.95 and × 0.5 and × 0.05.
3. Increase £240 by 12.5%.
4. A plant grows from 40 cm to 50 cm. Drag the marker to its percentage increase.They drag a marker on a number line from 0 to 50.
5. A bill went up by 15% and is now £92. Call the bill before x, so 1.15x = 92. Solve it a line at a time to find the bill before.They solve 1.15x = 92 line by line, each line checked as they write it.
6. A price goes up by 10%. Then the new price goes down by 10%. Compared with the start, the price is now:
   1. the same
   2. 1% higher
   3. 1% lower
   4. 10% lower
7. A car bought for £12,500 is sold for £9,750. The percentage loss is ___ %.
8. In a sale, everything is 40% off. Trainers cost £51 in the sale. What did they cost before the sale?
9. A price of £186 includes VAT at 20%. How much of the £186 is VAT?
10. Stretch: a price goes up by 25%. To get back to where it started, the new price must go down by ___ %.

Support: For reverse questions: write new = multiplier × original, put in what you know, and divide by the multiplier. Then check by going forwards.

Percentages: exit

Show the equation, the answer and one or two sentences.

1. A sale price is £84 after 30% off. Find the price before the sale, and explain why adding 30% of £84 back on gives the wrong answer.

Exit check

One reverse percentage, explained, shows who divides by the multiplier.

Students write the equation, 0.7 × original = 84, and solve it.

Percentages: multipliers and reverse

A calculator is allowed. For each, write new = multiplier × original first, then answer. Check reverse answers by going forwards.