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Year 10
Higher

Advanced problem solving with percentages

I can use my knowledge of percentages to solve problems.

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New
New
Year 10
Higher

Advanced problem solving with percentages

I can use my knowledge of percentages to solve problems.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A context can be evaluated to determine what sort of percentage calculation is involved.
  2. As percentages can be written as fractions and decimals, they are very versatile.
  3. Percentage change is not just connected to money.

Common misconception

Assuming that an increase of 10% followed by a decrease of 10% takes you back to 100%, etc.

Provide plenty of examples to illustrate the structure of what happens. If you increase a number by a percentage the number will increase meaning that you will be finding 10% of a larger number and hence decrease by more.

Keywords

  • Simple interest - Simple interest is always calculated on the original amount.

  • Compound interest - Compound interest is the interest calculated on the original amount and the interest accumulated over the previous period.

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

Use MWB to revisit double number lines as they are used in this lesson. Share a problem on the board and ask pupils to draw a double number line to represent the problem. Pupils needing more help with this could find missing multipliers to review this skill.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Increase 400 by 3.2%.
Correct Answer: 412.8
Q2.
If a number increases by 22% and is now 34.16, what was it originally?
Correct Answer: 28
Q3.
A mathematician celebrates their shares increasing by 18% which are now worth £649. How much did they originally invest?
Correct Answer: £550, 550
Q4.
Find 156% of 800
Correct Answer: 1248
Q5.
If I decrease £105 to £21, what is the percentage loss?
Correct Answer: 80%, 80, -80, -80%
Q6.
A good investment gains value by 9% each year. If the investment was worth £20 000 when purchased how much is it worth after 3 years?
Correct Answer: 25900.58, £25900.58, £25 900.58, 25 900.58

Exit quiz

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6 Questions

Q1.
A bank offers compound interest of 3% for the first 2 years, followed by 2% for the final year. If I invest £5000 at the start, how much money will I have at the end?
Correct Answer: £5410.59, 5410.59
Q2.
A square (A) has an area of $$36cm^2$$ and a second square (B) has an area of $$144cm^2$$. What is the percentage difference in side length between square A and square B?
Square A has sides 50% larger than square B.
Square B has sides 50% larger than square A.
Square A has sides 75% larger than square B.
Correct answer: Square B has sides 100% larger than square A.
Q3.
A toy is reduced in price by 10%, then a further 10% on the new price a week later. What is the percentage decrease overall from the original price?
Correct Answer: 19%, 19, -19, -19%
Q4.
A bank offers compound interest of 5% for the first 2 years, followed by 2% for the final year. If I invest £10 000 at the start, how much money will I have at the end?
Correct Answer: 11245.50, £11245.50
Q5.
Aisha declares that "40% of 26 is the same as 26% of 40". Which statement below is correct?
This is a coincidence and is only true for this example.
This is not true.
Correct answer: Reversing percentages in this way always works.
Q6.
A 500g box of cereal (A) costs £2.60. A larger 1300g box (B) costs £6.76. Which is the best value for money?
Box A
Box B
Correct answer: They're the same value for money.