Percentages

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Preliminary work on percentages

Find a percentage of an amount (the basics)
My Maths percentage of an amount 1
CB: answer questions on slides 5, 7 and 8 online

Find a percentage of an amount (more difficult)
My Maths percentage of an amount 2
CB: work through all slides, answering questions online






 1 Starter: finding percentages of quantities with and without a calculatorCalculator method (change the % to a decimal and multiply)
·    36% of 120 = 0.36 x 12

Main: increasing/decreasing a quantity by a percentage using multiplicative methods (use of a percentage multiplier is expected):Calculator method (change the % to a decimal and multiply)
·    Increase 60 by 15% = 115% of 60 = 1.15 x 60
·    Decrease 60 by 15% = 85% of 60 = 0.85 x 60
·    Using the % key on a calculator

My Maths lesson
Increase or decrease an amount by a % CB
           
 2 Starter: compound interest without a calculator e.g. £550 is invested at 10% per annum compound interest, how much will there be after 2 years?

Main: compound interest with a calculator (using multipliers)

My Maths lesson - Slides 1-6
Teachers TV on Calculating Interest
Worksheet to complete whilst watching Teachers TV

Note that problems involving simple interest for more than one year will not be set but that compound interests on investments up to 20 years could be assessed.
           
 3 Starter: In the last 2 weeks of a sale prices are reduces first by 30% and then by a further 40% of the new price. What is the final sale price of a shirt which originally cost £15. Want pupils to appreciate that this is not the same as working out 70% of £15 and subtracting it from £15.

Calculator method: 15 x 0.7 x 0.6. Want pupils to appreciate that this is the same as 15 x 0.42 i.e. the shirt has actually been reduced by 58% overall.
Example Questions JEE
Successive Percentage Change CB

Main: repeated percentage change including compound interest

Plenary:  solving problems

E.g. a seal colony is decreasing at 12% per annum. If the original population is 2000, after how many years will the population have fallen to half its original number? (Calculator)
           
4
Starter: expressing one quantity as a fraction or percentage of another (non-calculator)

Main: expressing one quantity as a percentage of another including percentage change (calculator)
Easiteach lesson ck
Teachers TV on Percentage Change
Worksheet to complete whilst watching Percentage Change

Method: write change/original as a fraction then multiply by 100






5
Starter: To increase sales the price of a magazine is reduced by 5%. Find the original price if the new price is £1.90. Want pupils to appreciate that you can’t just add 5% onto £1.90 because its 5% of the original price.

Main: reverse percentages
My Maths - Slides 7, 8, 9

Plenary: After a 7% decrease the cost of a TV is £232.50. What was the original price? A meal in a restaurant costs £36 with VAT at 17.5%. What was the price before the VAT was added?






6
Starter: Ben buys a car. In the first year it loses 32% of its value and during the second year it loses another 17% of its value. By what percentage has the value of the car decreased in the 2 years?Method: value x 0.68 x 0.83 = value x 0.5644 = 43.6% decrease

Main: more complicated percentage questions – see past papers

Mymaths link: Booster pack – A 2 A* - Percentage and exponentials – revise it (problems 1, 2, 3 and 5) and online worksheet (problems 1, 2 and 3)