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Rate and Proportion
Rates and Unit Value
Finding the Rate
Using the Rate
Best Buys
In Proportion
Scales and models
Graphs in Proportion
Monday, July 20, 2015
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1
Starter Questions
S4
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1.
Find 5% of 140
2. Round to 1 decimalplace
(a) 1.24
(b)
2.35
3. I work 20 hours a week and my rate of pay
is £8 per hour. What is my total weekly pay.
4.
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Rates
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Learning Intention
Success Criteria
1. To explain the term rate
and unit value.
1. To understand the term rate
and unit value.
2. Solve problems including rate
and unit value.
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Rates
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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 for
one hour he would travel 5km.
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Rates
S4
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Example :
Sean walks at 5 km per hour (km/hr)
How far would he walk in :
(a)
4 hours
(a)
4 x 5 = 20km
(b)
5 x 0.5 = 2.5 km
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(b)
Half an hour
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Rates
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Now try
Ex 2.1
Ch 2 (page 21)
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Starter Questions
S4
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1.
Find 5% of 360
2. Round to 1 decimalplace
(a) 17.55
(b)
0.85
3. I work 40 hours a week and my rate of pay
is £9 per hour. What is my total weekly pay.
4.
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of 246
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Proportion
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Learning Intention
Success Criteria
1. To explain how to find the
rate.
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1. To be able to find the term
rate from information given.
8
Finding the Rate
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Example :
For 5 hours’ work Darius is paid £30.
Calculate his rate of pay per hour.
Answer :
5 hours  £30
1 hour 
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£30 ÷ 5 = £6
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Finding the Rate
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Example :
3 litres of paint covers a fence area of 36 m2
How much will 1 litre cover.
Answer :
3 litres  36
1 litre 
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36 ÷ 3 =
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12m2
10
Finding the Rate
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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
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Finding the Rate
Now try
Ex 3.1
Ch 2 (page 22)
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Starter Questions
S4
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1.
Find 20% of 650
2. Round to 1 decimalplace
(a) 172.66
(b)
2.78
3. I got paid £364 for 7 days work.
What is my daily rate of pay.
4.
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Using the Rate
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Learning Intention
Success Criteria
1. To explain how to use the
rate to solve problems.
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1. To be able to find the term
rate from information given.
14
Using the Rate
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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)
Answer : (b)
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5 secs 
15 litres
1 secs 
15 ÷ 5 =
1 secs 
3 litres
8 secs 
8x3=
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3 litres
24 litres
15
Using the Rate
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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)
Answer : (b)
10 secs  20 words
1 secs 
20 ÷ 10 = 2 words
1 secs 
2 words
14 secs  14 x 2 =
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28 words
16
Using the Rate
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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)
Answer : (b)
Monday, July 20, 2015
5 days 
£200
1 day 
200 ÷ 5 = £40
1 day 
£40
8 days 
40 x 8 =
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£320
17
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Using the Rate
Now try
Ex 4.1
Ch 2 (page 23)
Monday, July 20, 2015
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18
Starter Questions
S4
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1.
Find 25% of 640
2. Round to 1 decimalplace
(a) 163.82
(b)
72.38
3. I got paid £54 for 9 hours work.
What is my hourly rate of pay.
4.
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Using the Rate
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Learning Intention
Success Criteria
1. To work out harder type
rate problems.
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1. To be able to work out
harder type rate problems.
20
Using the Rate
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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 
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200 x 1.60 = € 320
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Using the Rate
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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 much
did she have to pay.
Answer :
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4 days
 28p
1 day
28 ÷ 4 = 7p
5 days
 5 x 7 = 35p
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Using the Rate
Now try
Ex 4.2
Ch 2 (page 24)
Monday, July 20, 2015
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23
Starter Questions
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S4
1.
Find 75% of 180
2. If 3 pints of milk cost £9. How much for 2 pints.
3. I got paid £63 for 7 hours work.
What is my hourly rate of pay.
4.
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of 280
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Best Buys
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S4
Learning Intention
Success Criteria
1. Calculating the Best Buys
for household goods.
1. To be able to find the price
of one product.
2. Decide which is the best buy.
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2 for 1 Best Buys
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50%
We often see lots of special offers at various
off
supermarkets.
Example :
Which is the better buy?
2 light bulbs for 90p or 5 light bulbs for £2.00
Answer : (i)
(ii)
1 bulb
1 bulb
 90 ÷ 2 = 45p
 2.00 ÷ 5 = 40p or £0.40
Best buy is 5 bulbs at 40p
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Best Buys
S4
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Example :
Which is the better buy?
5 balloons for £1.20 or 6 balloons for £1.50
Answer : (i)
(ii)
1 balloon
1 balloon
 1.20 ÷ 5 = 24p or £0.24
1.50 ÷ 6 = 25p or £0.25
Best buy is 5 balloons at 24p
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Using the Rate
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S4
Now try
Ex 5.1
Ch 2 (page 26)
Monday, July 20, 2015
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Starter Questions
S4
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1.
Find 40% of 200
2. If 3 pints of milk cost £1.20. How much for 2 pints.
3. I get paid £5.50 an hour. How will i get paid
for 10 hours work.
1
4.
of 360
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Best Buys
Harder example
S4
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Example :
Which is the better buy?
Tea box A costs £2.88 and holds 160 tea bags.
Tea box B costs £3.84 and holds 240 tea bags.
Answer : (i)
(ii)
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
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Using the Rate
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S4
Now try
Ex 5.1
Ch 2 (page 25)
Monday, July 20, 2015
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31
Starter Questions
S4
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1.
Find 50% of 95
2. find the time difference between
08.30 and 16.39
3. What is the better deal
3 bars of soap for 99p
or 4 bars of £1.40
4.
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1
of 240
5
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In Proportion
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S4
Learning Intention
Success Criteria
1. To be able to identify
simple connections between
two quantities.
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1. Understand the term
proportion.
2. Solve problems using
proportion.
33
In Proportion
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S4
If two quantities are in proportion then there is a
connection between them.
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
OR
For every 1kg of sand he must use 3 kg of cement.
How much cement for 5kg of sand :
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5 x 3 = 15 kg
34
In Proportion
S4
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Example :
To make a healthy fruit drink Darius uses
4 parts apple and 1 part water.
Complete the table
Part Water
1
2
Part Apple
4
8
12
3
4
16
40
10
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In Proportion
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S4
Now try
Ex 6.1
Ch 2 (page 29)
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How much
ingredients
S4for 2 portions
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Example :
Half the ingredients
Flour 110g
Sugar 75g
Harder Example
Butter Almond 40g
Scott makes an almond mobile cake which
makes 4 portions. The ingredients are:
In Proportion
Complete the table
Makes 4 Portions
How much
Flour
220g Multiply 2 portions
ingredients
by 3
for 6 portions
Sugar
150g
Flour 330g
Butter Almond
80g
Sugar 225g
Butter Almond 120g
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In Proportion
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S4
Now try
Ex 6.2
Ch 2 (page 30)
Monday, July 20, 2015
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38
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Starter Questions
1.
99.6 + 7.27
2. Calculate 70% of 84
3.
25% of 160p
4.
Round to 1 decimal place
(a) 2.67
20-Jul-15
(b) 3.23
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(c) 2.91
Scales and Models
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S4
Learning Intention
1.
20-Jul-15
To understand the term
scale and how they are
used in real life.
Success Criteria
1. To be able to understand
the term scales.
2. Interpret scales into reallife measurements.
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Scales and Models
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S4
Definition
A scale of
1 cm = 2m
This simply means for every 1cm measured on a
drawing this represents 2m in real-life.
20-Jul-15
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Scales and Models
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S4
4x25= 100cm
4cm
2cm
2x25 = 50cm
The scale of this drawing is 1cm = 25cm
What is the actual length and breadth of the TV ?
20-Jul-15
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Scales and Models
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S4
12cm
12x50 =
600cm = 6m
Living room 8cm
8x50 =
400cm =4m
The scale of this drawing living room is 1cm = 50cm
What is the actual length and breadth of the room ?
20-Jul-15
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Scales and Models
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S4
Now try
Ex 7.1
Ch 2 (page 31)
Monday, July 20, 2015
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44
Starter Questions
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S4
1.
13.6 + 7.9
2. Calculate 20% of 64
3.
What is the best buy
3 cans of beans for 57p
or
4 cans 72p
Explain your answer.
20-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales and Models
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S4
Learning Intention
1.
20-Jul-15
To explain how to
calculate the scale of a
model.
Success Criteria
1. To be able to calculate
the scale of a model.
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Scales and Models
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S4
Example :
Answer :
A model bicycle is 30cm long.
The real length of the bicycle is 150cm.
What is the scale of the model.
150 ÷ 30 = 5
Scale is 1 to 5
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Scales and Models
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S4
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
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Scales and Models
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S4
Now try
Ex 7.2
Ch 2 (page 32)
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49
Starter Questions
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S4
1. 18.7 + 12.9
2. Calculate 30% of 40
3.
What is the best buy
5 bottles of water for £3.50
or
4 cans £2.88
Explain your answer.
20-Jul-15
Created by Mr. Lafferty Maths Dept.
Proportion graphs
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S4
Learning Intention
1.
20-Jul-15
To explain the main
features of a proportion
graph and used it to solve
problems.
Success Criteria
1. To be able to identify a
proportion graph.
2. Use graph to solve
problems.
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How much
How far can I
petrol do I
travel with 6
need to travel
litres
of petrol
A proportion
graph is always a straight line graph through the origin
80 km.
Proportion graphs
200
Distance (Km)
S4
180
160
120km
140
1 minute
to come up
with a
question
120
100
80
60
40
4 litres
20
0
0
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1
2
3
4
5
6
7
Petrol Litres
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8
9
10
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Proportion graphs
How Euros
How£80
many
for
S4 Pounds for 25 €
140
Euros €
120
100
100 €
80
60
40
20
£20
0
0
20
40
60
80
100
Pounds £
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53
Proportion graphs
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S4
Now try
Ex 8.1
Ch 2 (page 34)
Monday, July 20, 2015
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54