MNU 3-08a 7-Dec-15Created by Mr. Lafferty Maths Dept. Proportion Proportion Direct Proportion Graph of Direct Proportion Proportional

MNU 3-08a

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

ProportionProportionw

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Direct Proportion

Graph of Direct Proportion

Proportional Division

Proportion per item

MNU 3-08a


Starter QuestionsStarter Questionsw

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2. Calculate the area of the shape.

5 1+2 4

(a) 0.853 (b) 0.356 (c) 1.995

1. 6x + 5 = 59

3. Round to 2 decimal places.

4.

9

6

8

MNU 3-08a

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

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1. We are learning to calculate proportional division by using shares.

1. Be able to find total shares.

ProportionProportionProportional Division

2. Find fractional share.

3. Solve problems using appropriate working.

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ProportionProportion

Example : Jack and Victor share a raffle win of £500 in the ratio 2:3. How much does each get ?


Total number of shares :2 + 3 = 5 shares

No. of shares £5 → 5002 → Jack

Are we expecting more or

less

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2

5500 £200

Make smaller fraction

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No. of shares £5 → 5003 → Victor


less

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3

5500 £300

£200 + £300 = £500Check :


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Ex : Ryan, Ross and Ben share 24 cakes in the ratio1 : 2 : 3. How many cakes does each get ?


Total number of shares :3 + 1 = 4 shares

No. of shares Cakes6 → 241 → Ryan


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6 24 4


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No. of shares Cakes6 → 242 → Ross


less

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2

6 24 8

18 + 6 = 24Check :


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No. of shares Cakes6 → 243 → Ben


less

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3

6 24 12

4 + 8 + 12 = 24Check :


MNU 3-08a


Now try TJ3bEx 1

Ch10 (page 96)

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Are you on Target ?I can ?

MNU 3-08a



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1. Simplfy the ratio 13 : 52

Calculate 2.5

3. I got $650 for £100. How much would I get for £2.

4. Put in order, smallest first.

0.25, 0.19, 0.01, 0.026

5. Find the value

% of 4002.

of x 7x +2.5 = 20

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1 We are learning the value of one item using proportion.

1. Understand the term per item.


2. Solve simple proportional problems.

Proportion

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Example : The cost of 5 chocolate bars is £8.00. Find the cost of one.

If you know the total cost of several items, you caneasily find the cost per item ( cost for 1 ).

Proportion

No. of Bars £5 → 8.001 → Per item


less

1

5 8.00 £1.60


MNU 3-08a


Now try TJ3bEx 2 Orally

Ch10 (page 98)

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MNU 3-08a



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2.

4. Calculate 4 5×5 8


Calculate 6.5% of 300

3. Find the mean, median and mode for

25, 20, 55, 20

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1. We are learning the term Direct Proportion.

1. Understand the idea of Direct Proportion.


2. Solve simple proportional problems.

Direct Proportion

MNU 3-08a

Example : The cost of 6 cakes is £4.20. Find the cost of 5 cakes.


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“ .. When you double the number of cakes you double the cost.”

Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT PROPORTION, if :

Direct Proportion

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No. of cakes £6 → 4.205 →


less

5

6 4.20 £3.50


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ProportionProportionDirect Proportion

Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.

£ $30 → 4550 →


less

50

30 45 $75

Make bigger fraction

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ProportionProportionDirect Proportion

Example : 300 pencils cost £6. How much will 200 cost.

Pencil £300 → 6200 →


less

200

300 6 £4


MNU 3-08a


Now try TJ3bEx 3

Ch10 (page 99)

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2.

4. Calculate 31 1 × 12 2


Calculate 2.5% of 500

3. Find the mean, median and mode for

5, 2, 5, 8

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1. We are learning about Direct Proportion Graphs.

1. Understand that Direct Proportion Graph is a straight line.


2. Construct Direct Proportion Graphs.

Direct Proportion Graphs

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The table below shows the cost of packets of “Pencilss”.


No. of Pkts 1 2 3 4 5 6

Cost (p) 20 40 60 80 100 120

We can construct a graph to represent this data.

What type of graph do we expect ?

MNU 3-08a


Direct Proportion

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

No. of Packets

Cos

t (p

)

Direct Proportion GraphsNotice that the points lie on a straight line

passing through the origin

This is true for any two quantities

which are in Direct Proportion.

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ProportionProportionDirect Proportion Graphs

KeyPoint

Two quantities which are in DIRECT PROPORTION

always lie on a straight linepassing through the origin.

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Example : Plot the points in the table below. Are they in direct proportion?


We plot the points (1,3) , (2,6) , (3,19) , (4,12)

xx 11 22 33 44

yy 33 66 99 1212

Linear Patterns !Can you find a

formula connecting y and x

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Plotting the points

(1,3) , (2,6) , (3,9) , (4,12)


0 1 2 3 4

101112

23456789

Since we have a straight linepassing through the origin

x and y are in direct proportion.

x

y

MNU 3-08a


Now try TJ3bEx 4

Ch10 (page 101)

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ProportionProportionDirect Proportion Graphs

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Log ?


Documents

MNU 3-08a 7-Dec-15Created by Mr. Lafferty Maths Dept. Proportion Proportion Direct Proportion Graph of Direct Proportion Proportional