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Lesson 5: �Percentage change and best buys

Objectives

Become fluent at working with percentage change
Determine the best deal following a percentage change
Understand different approaches to solving multi-step percentage problems
Use representations to provide insight when solving problems

1

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Packing tape

2

How many metres of tape are on the rolls of brown tape?

120 �metres

50% �longer

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Different approaches

3

DISCUSS

Nel

Reuben

Saskia

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Nel’s approach

4

REVIEW

What has Nel done?
Why has Nel multiplied by 15?

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Reuben’s approach

5

REVIEW

What has Reuben done?
Why has Reuben multiplied by 1.5?

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Saskia’s approach

6

REVIEW

What has Saskia done?
Why has Saskia divided by 2?

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Increasing by 50%

7

DISCUSS

What does an increase of 50% mean?

120 �metres

50% �longer

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Diagrams

8

DISCUSS

Handout�available

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Whose diagram? (1)

9

REVIEW

Nel’s approach

Reuben’s approach

Saskia’s approach

0%

0 m

120 m

100%

180 m

150%

×1.5

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Whose diagram? (2)

10

REVIEW

Nel’s approach

Reuben’s approach

Saskia’s approach

Clear tape

Brown tape

60 m	60 m

60 m	60 m	60 m

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Whose diagram? (3)

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REVIEW

Clear

tape

Brown

tape

12 m

12 m × 15 = 180 m

120 m

12 m

10%

Nel’s approach

Reuben’s approach

Saskia’s approach

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Brown packing tape offers

12

20% increase in length of tape

Offer 1:

DISCUSS

20% decrease in price of tape

Offer 2:

180 m

£2.70

Tell students that a 180-metre roll of brown tape is currently priced at £2.70. The packing tape company are investigating two possible special offers: increasing the length of tape by 20%, or decreasing the price of the tape by 20%.

Ask students to spend a few minutes working individually to find the new length of tape in Offer 1 and the new price in Offer 2. Encourage them to draw a diagram to help to explain their thinking. Once students have had some time to work alone, ask them to discuss their thinking with their partner. Avoid intervening as they work: it is important that they have enough time to think before you explain. Make a note of the different approaches adopted by students, as you may want to call on students who used different approaches in the next section of the lesson.

Deepening understanding If students have calculated the new length and new price (216-metre roll for £2.70 and 180-metre roll for £2.16), ask them which of the two offers will be best for the manufacturer.

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Original length: 180 metres

13

REVIEW

Additive�approach:

Multiplicative�approach:

216 m

£2.70

Offer 1: �Now 20% longer

	20%

20%

36 m

180 m

36 m

216 m

0%

0 m

180 m

100%

216 m

120%

×1.2

Current price: 180 m, £2.70

Click to reveal

Hold a class discussion, asking a couple of different students to share their thinking for the two percentage problems. Many students are likely to use an additive approach for both problems. Use the representations of the additive approaches on these two slides to support a discussion of students’ additive approaches. Use the representations of the multiplicative approaches on these two slides to support students’ understanding that multiplying by 1.2 gives an increase of 20% and multiplying by 0.8 gives a decrease of 20%.

For Offer 1,it is likely that students will have found 20% of 180 m (36 m) and added it on to get 216 m (additive approach). Check whether anyone used a multiplicative approach, using a calculator to multiply 180 by 1.2. Whilst an additive approach is easier to complete numerically without access to a calculator, the double number line representation of a multiplicative approach can be used to support students’ understanding that multiplying by 1.2 gives an increase of 20%, regardless of whether students used a multiplicative approach or not.

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Original price: £2.70

14

REVIEW

Additive�approach:

Multiplicative�approach:

180 m

£2.16

Offer 2: �20% OFF

100%

0%

£0

£2.70

100%

£2.16

80%

×0.8

80%	20%

£2.70

£2.16

54p

Current price: 180 m, £2.70

Click to reveal

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Price per metre

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YOUR TURN

Find the price per metre
If the price per metre is increased, who benefits?

120 m

£2.40

Tell students that a 120-metre roll of clear tape is currently priced at £2.40. Ask them to calculate the price per metre.

After a minute or so, ask students to explain their thinking when finding the price (2 pence per metre). Use formative assessment approaches to check that students know which number to divide by, and why; if any students are confused, you may want to spend some time with them to establish what they do, and do not, understand.

Discuss how the price per metre affects the company and the customer. (The greater the price per metre, the more money the company get per metre, but the more expensive it is for the customer to buy, so it is better for the company. The smaller the price per metre, the less money the company get per metre and the cheaper it is for the customer to buy, so it is better for the customer).

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Clear packing tape offers

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YOUR TURN

Increase the length, keep the price the same

Decrease the price, keep the length the same.

Nel

Reuben

Same price per metre

___ m

£2.40

120 m

£ ___

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Comparing offers

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YOUR TURN

Handout�available

Write down everything you know about the offers.
Do calculations.
Take turns to make a contribution.
Discuss your reasoning with your partner.

Give each pair of students a large sheet of paper and scissors and a copy of the ‘Clear tape offers’ handout (or the ‘Clear tape offers landscape’ handout photocopied onto A3 paper).

Explain that Nel and Reuben have come up with some suggestions of offers for the students to explore. Before setting students off on the task, you may like to spend a couple of minutes discussing with students some of the things that might be helpful to consider. These might include things like:

the new length of tape
the new discounted price
similarities and differences between Nel’s and Reuben’s suggestions
a comparison of the price per metre of tape in pence
which offer is best for the company/customer

Ask students to work in pairs to explore Nel’s and Reuben’s suggestions. They should write information about the offers and any calculations next to the relevant suggestion. Emphasise that there is no one correct response; there are many different, valid things they could write down. Students may prefer to use a pencil to record their thinking, so they can make any necessary amendments as they work. They could also use post-it notes.

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Offer A

18

0%

0 m

120 m

100%

192 m

160%

×1.6

REVIEW

DISCUSS

REVIEW

120 metres

Increase length by 60%

£2.40

A

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Offer B

19

0%

£0

£2.40

100%

£1.44

60%

×0.6

REVIEW

DISCUSS

REVIEW

Decrease price by 40%

120 metres

£2.40

B

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Price per metre

20

REVIEW

Price per metre

= ……… p

Price per metre

= ……… p

REVIEW

192 m

£2.40

Offer A:

120 m

£1.44

Offer B:

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Offer C

21

0%

0 m

120 m

100%

192 m

160%

×1.6

REVIEW

DISCUSS

REVIEW

120 metres

Increase length by 60%

£2.40

C

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Offer D

22

0%

£0

£2.40

100%

£1.56

65%

×0.65

REVIEW

DISCUSS

REVIEW

Decrease price by 35%

120 metres

£2.40

D

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Price per metre

23

REVIEW

DISCUSS

Price per metre

= 1.25p

Price per metre

= ……… p

192 m

£2.40

Offer C:

120 m

£1.56

Offer D:

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Comparing offers

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REVIEW

Price per metre: 1.25p

REVIEW

192 m

£2.40

Price per metre: 1.2p

120 m

£1.44

Price per metre: 1.25p

192 m

£2.40

Price per metre: 1.3p

120 m

£1.56

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Practice questions

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……………….. (5)

Q15 from Pearson Edexcel Practice Tests: Set 4 Regular (1F)

(From mathsemporium.com)

Tom wants to buy the plants as cheaply as possible.

Should Tom buy the plants from Kirsty’s Plants or Hedge World?

You must show all your working.

Food Mart and Jan’s Store sell boxes of the same type of breakfast cereal.

Each shop has a special offer.

Food Mart Jan’s Store

……………….. (4)

Q18 from November 2018, 1MA1/1F

YOUR TURN

Handout�available

Which box of cereal is the better value for money?

You must show your working

Tom is going to buy 25 plants to make a hedge.

Here is information about the cost of buying the plants.

Kirsty’s Plants

£2.39 each

Hedge World

Pack of 25

£52.50 plus VAT at 20%

400 g

20% off the normal price of £5

400 g

plus 30% extra

£5

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Practice question (1)

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Which box of cereal is the better value for money?

Food Mart Jan’s Store

……………….. (4)

Q18 from November 2018, 1MA1/1F

DISCUSS

20% off:

0%

£0

£5

100%

£4

80%

×0.8

400 g

20% off the normal price of £5

400 g

plus 30% extra

£5

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Practice question (1)

27

0%

0 g

400 g

100%

520 g

130%

×1.3

Which box of cereal is the better value for money?

Food Mart Jan’s Store

……………….. (4)

Q18 from November 2018, 1MA1/1F

DISCUSS

30% extra:

400 g

20% off the normal price of £5

400 g

plus 30% extra

£5

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Practice question (2)

28

0%

0 g

£52.50

100%

£63

120%

×1.2

DISCUSS

20% VAT:

……………….. (5)

Q15 from Pearson Edexcel Practice Tests: Set 4 Regular (1F)

(From mathsemporium.com)

Tom wants to buy the plants as cheaply as possible.

Should Tom buy the plants from Kirsty’s Plants or Hedge World?

Kirsty’s Plants

£2.39 each

Hedge World

Pack of 25

£52.50 plus VAT at 20%

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Lesson review: �Percentage change and best buys

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Suggested further steps/areas to work on

Calculate percentage change given original and new amounts

Objectives

Become fluent at working with percentage change
Determine the best deal following a percentage change
Understand different approaches to solving multi-step percentage problems
Use representations to provide insight when solving problems

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Lesson 5: �Credits

Photo acknowledgements

Shutterstock.com: Kitch Bain, Vectorfair.com; joom seeda

Text acknowledgements

Pearson Education Ltd: Pearson Edexcel GCSE (9 – 1) In Mathematics (1MA1) Foundation (Non-Calculator) Paper 1F

Pearson Education Ltd: Pearson Edexcel Practice Tests: Set 4 Regular (1F) (From mathsemporium.com)

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