rate and proportion

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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]

Rate and Rate and ProportionProportion

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Friday, April 21, 2023Friday, April 21, 2023 11

Finding the Rate

Using the Rate

Best Buys

In Proportion

Scales and models

Graphs in Proportion

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Starter QuestionsStarter Questionsw

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S4

72 of 81

4.

pay. weekly total my is What hour. per £8 is

pay of rate my and week a hours 20 work I 3.

2.35 (b) 1.24 (a)

place decimal 1 to Round 2.

140 of 5% Find 1.


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1.1. To understand the term To understand the term rate and unit value.rate and unit value.

2.2. Solve problems including Solve problems including rate and unit value.rate and unit value.

1. To explain the term rate and unit value.

S4


RatesRates

Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]

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Per means for each. A phrase that contains the word ‘per’

is called a RATE.

Example : Sean walks at 5 km per hour (km/hr)

This means that if Sean walked at this speed forone hour he would travel 5km.

RatesRatesS4


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Example : Sean walks at 5 km per hour (km/hr)

How far would he walk in :

(a) 4 hours (b) Half an hour

(a) 4 x 5 =

(b) 5 x 0.5 =

20km

2.5 km

RatesRatesS4


Now try Ex 2.1

Ch 2 (page 21)

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66

RatesRatesS4

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S4

246 of 61

4.

pay. weekly total my is What hour. per £9 is

pay of rate my and week a hours 40 work I 3.

0.85 (b) 17.55 (a)


360 of 5% Find 1.


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1.1. To be able to find the term To be able to find the term rate from information rate from information given.given.

1. To explain how to find the rate.

Proportion

S4



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Finding the Rate

Example : For 5 hours’ work Darius is paid £30.Calculate his rate of pay per hour.

Answer :

5 hours £30

1 hour £30 ÷ 5 =£6


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Finding the Rate

Example : 3 litres of paint covers a fence area of 36 m2 How much will 1 litre cover.

Answer :

3 litres 36

1 litre 36 ÷ 3 = 12m2


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1111

Finding the Rate

Example : I get paid £48 000 pounds a year. What is my monthly rate of pay.

Answer :

12 months £48 000

1 month £48 000 ÷ 12 =£4 000


Now try Ex 3.1

Ch 2 (page 22)

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Finding the Rate

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S4

210 of 71

4.

pay. of rate daily my is What

work. days7 for £364 paid got I 3.

2.78 (b) 172.66 (a)


650 of 20% Find 1.


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1.1. To be able to find the term To be able to find the term rate from information rate from information given.given.

1. To explain how to use the rate to solve problems.

S4


Using the Rate


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Using the Rate

Example : A pipeline delivers 15 litres of water in 5 secs.

(a) Calculate the rate of flow per second.

(b) How many litres will the pipeline deliver in 8 secs

Answer : (a) 5 secs 15 litres

1 secs 15 ÷ 5 = 3 litres

Answer : (b) 1 secs 3 litres

8 secs 8 x 3 = 24 litres


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Using the Rate

Example : A pupil can type 20 words in 10 seconds.

(a) Calculate how many words typed per second.

(b) How many words typed in 14 seconds.

Answer : (a) 10 secs 20 words

1 secs 20 ÷ 10 =2 words

Answer : (b) 1 secs 2 words

14 secs 14 x 2 = 28 words


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Using the Rate

Example : To hire a car for 5 days costs £200.

(a) Calculate the cost to hire for 1 day.

(b) Calculate the cost for 8 days.

Answer : (a) 5 days £200

1 day 200 ÷ 5 = £40

Answer : (b) 1 day £40

8 days 40 x 8 = £320


Now try Ex 4.1

Ch 2 (page 23)

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1818

Using the Rate

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S4

450 of 91

4.

pay. of rate hourly my is What

work. hours 9 for £54 paid got I 3.

72.38 (b) 163.82 (a)


640 of 25% Find 1.


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1.1. To be able tTo be able to work out harder type rate problems.

1. To work out harder type rate problems.

S4


Using the Rate


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Using the Rate

Example : Nicola exchanges £10 into Euros.She receives 16 Euros.

How many Euros will she get for £200.

Answer : £10 € 16

£1 16 ÷ 10 =€ 1.60

£200 200 x 1.60 =€ 320


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2222

Using the Rate

Example : Joseph’s library book is 4 days overdue.He pays a fine for each day.In total he pays 28p.

Alana’s book is 5 days overdue how muchdid she have to pay.

Answer : 4 days 28p

1 day 28 ÷ 4 =7p

5 days 5 x 7 =35p


Now try Ex 4.2

Ch 2 (page 24)

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2323

Using the Rate

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S4

1. Find 75% of 180

2. I f 3 pints of milk cost £ 9. How much f or 2 pints.

3. I got paid £ 63 f or 7 hours work.

What is my hourly rate of pay.

14. of 280

7


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1.1. To be able tTo be able to find the price of one product.

1. Calculating the Best Buys for household goods.

S4


Best Buys

2.2. Decide which is the best Decide which is the best buy.buy.


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We often see lots of special offers at varioussupermarkets.

Answer : 1 bulb 90 ÷ 2 = 45p

1 bulb 2.00 ÷ 5 =40p or £0.40

Best buy is 5 bulbs at 40p

Best BuysS4

2 for 150% off

Example : Which is the better buy?

2 light bulbs for 90p or 5 light bulbs for £2.00

(i)

(ii)


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Answer : 1 balloon 1.20 ÷ 5 = 24p or £0.24

1 balloon 1.50 ÷ 6 =25p or £0.25

Best buy is 5 balloons at 24p

Best BuysS4


5 balloons for £1.20 or 6 balloons for £1.50

(i)

(ii)


Now try Ex 5.1

Ch 2 (page 26)

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2828

Using the Rate

S4

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S4

1. Find 40% of 200

2. I f 3 pints of milk cost £ 1.20. How much f or 2 pints.

3. I get paid £ 5.50 an hour. How will i get paid

f or 10 hours work.

14. of 360

8



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Answer : Box A £2.88 ÷ 160 = 1.8p per bag

Box B £3.84 ÷ 240 = 1.6p per bag

Best buy is Box B since it costs only 1.6p per bag

Best BuysS4


Tea box A costs £2.88 and holds 160 tea bags.Tea box B costs £3.84 and holds 240 tea bags.

(i)

(ii)

Harder example


Now try Ex 5.1

Ch 2 (page 25)

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3131

Using the Rate

S4

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S4

1. Find 50% of 95

2. fi nd the time diff erence between

08.30 and 16.39

3. What is the better deal

3 bars of soap f or 99p

or 4 bars of £ 1.40

14. of 240

5Friday, April 21, 2023Friday, April 21, 2023 3232

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1.1. Understand the term Understand the term proportion.proportion.

1. To be able to identify simple connections between two quantities.

S4


In Proportion

2.2. Solve problems using Solve problems using proportion.proportion.


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If two quantities are in proportion then there is a connection between them.

In ProportionS4

Example : Jake mixes sand and cement to make a patio.He uses 1 part sand and 3 parts cement.

This means for every shovel of sand he must use 3 shovels of cement

For every 1kg of sand he must use 3 kg of cement.OR

How much cement for 5kg of sand : 5 x 3 = 15 kg


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In ProportionS4

Example : To make a healthy fruit drink Darius uses4 parts apple and 1 part water.

Part Water Part Apple

1 4

2

12

4

10

Complete the table

8

3

16

40


Now try Ex 6.1

Ch 2 (page 29)

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S4

In Proportion

Example : Scott makes an almond mobile cake which makes 4 portions. The ingredients are:


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In ProportionS4

Makes 4 Portions

Flour 220g

Sugar 150g

Butter Almond

80g

Complete the table

Harder Example

How much ingredients

for 2 portions

Half the ingredients Flour 110gSugar 75g

Butter Almond 40g

How much ingredients

for 6 portions

Multiply 2 portions by 3

Flour 330gSugar 225g

Butter Almond 120g


Now try Ex 6.2

Ch 2 (page 30)

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S4

In Proportion

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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Starter QuestionsStarter Questions

2. Calculate 70% of 84

(a) 2.67 (b) 3.23 (c) 2.91

1. 99.6 + 7.27

3. 25% of 160p

4. Round to 1 decimal place

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Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To be able to To be able to understand the term understand the term scales.scales.

1. To understand the term scale and how

they are used in real life.2. Interpret scales into

real-life measurements.

Scales and Scales and ModelsModels

S4


A scale of A scale of

1 cm = 2m1 cm = 2mThis simply means for every 1cm measured on a

drawing this represents 2m in real-life.

Definition


S4

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4cm

2cm

The scale of this drawing is 1cm = 25cmThe scale of this drawing is 1cm = 25cm

What is the actual length and breadth of the TV ?

4x25= 4x25= 100cm100cm

2x25 = 2x25 = 50cm50cm


S4

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12cm

8cm

The scale of this drawing living room is 1cm = 50cmThe scale of this drawing living room is 1cm = 50cmWhat is the actual length and breadth of the room ?

12x50 = 12x50 = 600cm = 600cm =

6m6m

8x50 = 8x50 = 400cm 400cm =4m=4m

Living room


S4

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Now try Ex 7.1

Ch 2 (page 31)

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4444

S4


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3 cans of beans for 57p

or 4 cans 72p

Explain your answer.

1. 13.6 + 7.9

3. What is the best buy

S4

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1.1. To be able to calculate To be able to calculate the scale of a model.the scale of a model.

1. To explain how to calculate the scale of a model.


S4


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Example : A model bicycle is 30cm long.The real length of the bicycle is 150cm.What is the scale of the model.

Answer : 150 ÷ 30 =5

Scale is 1 to 5


S4


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Example : A model car is 10cm long.The real length of the car is 300cm.What is the scale of the model.

Answer : 300 ÷ 10 =30

Scale is 1 to 30


S4


Now try Ex 7.2

Ch 2 (page 32)

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4949

S4


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5 bottles of water for £3.50

or 4 cans £2.88

Explain your answer.

1. 18.7 + 12.9

3. What is the best buy

S4

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1.1. To be able to identify a To be able to identify a proportion graph.proportion graph.

1. To explain the main features of a proportion graph and used it to solve problems.

S4

Proportion Proportion graphsgraphs

2.2. Use graph to solve Use graph to solve problems.problems.

Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected] 5252


S4 A proportion graph is always a straight line graph through the origin

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7 8 9 10

Dis

tanc

e (K

m)

Petrol Litres

1 minuteto come up with a question

How far can I travel with 6

litres of petrol

120km

How much petrol do I

need to travel 80 km.

4 litres

S4



0

20

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60

80

100

120

140

0 20 40 60 80 100

Eur

os €

Pounds £

How Euros for £80

5353

100 €

How many Pounds for 25

€

£20


Now try Ex 8.1

Ch 2 (page 34)

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S4


rate and proportion

Documents

b1 secs

litres1 secs

a5 secs

words1 secs

a10 secs

litres8 secs

words14 secs

term rate