Post on 20-Jan-2016
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
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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.
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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ProportionProportion
Example : Jack and Victor share a raffle win of £500 in the ratio 2:3. How much does each get ?
Proportional Division
Total number of shares :2 + 3 = 5 shares
No. of shares £5 → 5002 → Jack
Are we expecting more or
less
21 Apr 202321 Apr 2023
2
5500 £200
Make smaller fraction
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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ProportionProportionProportional Division
No. of shares £5 → 5003 → Victor
Are we expecting more or
less
21 Apr 202321 Apr 2023
3
5500 £300
£200 + £300 = £500Check :
Make smaller fraction
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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ProportionProportion
Ex : Ryan, Ross and Ben share 24 cakes in the ratio1 : 2 : 3. How many cakes does each get ?
Proportional Division
Total number of shares :3 + 1 = 4 shares
No. of shares Cakes6 → 241 → Ryan
Are we expecting more or
less
21 Apr 202321 Apr 2023
1
6 24 4
Make smaller fraction
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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ProportionProportionProportional Division
No. of shares Cakes6 → 242 → Ross
Are we expecting more or
less
21 Apr 202321 Apr 2023
2
6 24 8
18 + 6 = 24Check :
Make smaller fraction
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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ProportionProportionProportional Division
No. of shares Cakes6 → 243 → Ben
Are we expecting more or
less
21 Apr 202321 Apr 2023
3
6 24 12
4 + 8 + 12 = 24Check :
Make smaller fraction
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3bEx 1
Ch10 (page 96)
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ProportionProportion
Are you on Target ?I can ?
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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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
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 the value of one item using proportion.
1. Understand the term per item.
ProportionProportion
2. Solve simple proportional problems.
Proportion
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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ProportionProportion
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
Are we expecting more or
less
1
5 8.00 £1.60
Make smaller fraction
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3bEx 2 Orally
Ch10 (page 98)
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ProportionProportion
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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2.
4. Calculate 4 5×5 8
1. Simplfy the ratio 85 : 25
Calculate 6.5% of 300
3. Find the mean, median and mode for
25, 20, 55, 20
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 the term Direct Proportion.
1. Understand the idea of Direct Proportion.
ProportionProportion
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.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
“ .. 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
21 Apr 202321 Apr 2023
No. of cakes £6 → 4.205 →
Are we expecting more or
less
5
6 4.20 £3.50
Make smaller fraction
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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ProportionProportionDirect Proportion
Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.
£ $30 → 4550 →
Are we expecting more or
less
50
30 45 $75
Make bigger fraction
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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ProportionProportionDirect Proportion
Example : 300 pencils cost £6. How much will 200 cost.
Pencil £300 → 6200 →
Are we expecting more or
less
200
300 6 £4
Make smaller fraction
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3bEx 3
Ch10 (page 99)
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ProportionProportion
Are you on Target ?I can ?
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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2.
4. Calculate 31 1 × 12 2
1. Simplfy the ratio 95 : 35
Calculate 2.5% of 500
3. Find the mean, median and mode for
5, 2, 5, 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 about Direct Proportion Graphs.
1. Understand that Direct Proportion Graph is a straight line.
ProportionProportion
2. Construct Direct Proportion Graphs.
Direct Proportion Graphs
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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ProportionProportion
The table below shows the cost of packets of “Pencilss”.
Direct Proportion Graphs
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
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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.
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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ProportionProportionDirect Proportion Graphs
KeyPoint
Two quantities which are in DIRECT PROPORTION
always lie on a straight linepassing through the origin.
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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ProportionProportion
Example : Plot the points in the table below. Are they in direct proportion?
Direct Proportion Graphs
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
MNU 3-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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ProportionProportion
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12)
Direct Proportion Graphs
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
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3bEx 4
Ch10 (page 101)
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ProportionProportionDirect Proportion Graphs
Have you updated your Learning
Log ?
Are you on Target ?I can ?