Scaled Drawings
General
Enlarging and Reducing Drawing
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Working with Scales
Making Simple Scale Drawings
Harder Scale Drawings
Compass Points & Scale Drawings
Measuring & Scales
Similar Shapes & Scale Factor
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. Convert these distance to metres
(a) 500cm (b) 380cm (c) 157cm
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2. Convert these distance to centimetres
(a) 4m (b) 2.6m (c) 1.92m
3. Convert these distances to metres.
(a) 7km (b) 2.6km (c) 1.045km
4. Convert these distances to kilometres.
(a) 8000m (b) 6390m (c) 360m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
General
Learning Intention Success Criteria
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1. Be able to enlarge a shape
1. To explain how to enlarge
by a factor.
or reduce a given shape by
a factor. 2. Be able to reduce a shape
by a factor.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
Half the
size of the
Double the
size of the
General shape. shape.
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10-Nov-11 Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
General
Now try Ex 1
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Q1 (e)(g)(i) (j)
Q2 (c)(d)((g)(h)
Ch5 (page 50)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 99.6 + 7.27
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2. If I am facing NW and turn 180o
clockwise. Which direction am I facing now.
3. 25% of £2.60
4. Round to 1 decimal place
(a) 2.67 (b) 3.23 (c) 2.99
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
Learning Intention Success Criteria
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1. To explain the term scale 1. To understand the term
on a map. scale.
2. Calculate the real life
distances using a scaled.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
In order to make sense of a map or scale diagram
the scale must be known.
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10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
In order to make sense of a map or scale diagram
the scale must be known.
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For this scale model
1 cm represents 1m
4 cm
This means for every 1 metre of the actual car,
1cm is drawn on the map.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
The scale of this drawing is
1cm = 5m
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6cm
What is the actual length
of the tree ?
6 x 5 = 30m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
The scale of this drawing is
1cm = 90cm
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What is the actual length
of the bus in metres ?
5cm 5 x 90 = 450cm
4.5m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scales
General
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Now try Ex 2
Ch5 (page 52)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 17.6 - 13.9
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2. If I am facing North and turn 45o
anti - clockwise. Which direction am I facing now.
3. 4% of £20
4. A cuboid has length 5m breadth 3m
and height 5m. Find the volume.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
Learning Intention Success Criteria
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1. From information given
1. To draw a scale drawing
make a scaled drawing.
given suitable information.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
Problem
A garden is rectangular in shape and
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has length 12m and breadth 8m.
Make rough sketch of the garden.
Draw an accurate 12m
scaled drawing of the garden
8m
Use a scale of
1cm represents 2m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
Use a scale of
1cm represents 2m
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12m
8m 12m
8m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
Problem
A road junction is triangular in shape.
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A rough sketch is given below.
Draw an accurate
scaled drawing of the junction
20m
Use a scale of
1cm represents 2m
12m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
Use a scale of
1cm represents 2m
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Find the real
life length of
20m the 3rd side
20m
12m
2 x 11.6 = 23.2m
12m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings
General
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Now try Ex3
Ch5 (page 55)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 8.7 - 7.8
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2. Calculate 7% of 120
3. A model boat has scale of 1cm to 2m
The model length of the boat is 5.5cm.
What is the real life length of the boat.
4. I get paid £80 for 5 hour work.
What is my hourly rate.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Drawing SAS Triangles
Aim of the Lesson
‘To construct a triangle given
the length of two sides
and the included angle’
10-Nov-11 Created by Mr. Lafferty 21
Drawing SAS Triangles
SAS Triangles
Side
Angle Side
10-Nov-11 Created by Mr. Lafferty 22
Drawing SAS Triangles
Toolkit required
1.Ruler
2.Protractor
3.Pencil & Paper
10-Nov-11 Created by Mr. Lafferty 23
Drawing SAS Triangles
C
o
30 B
Example : Draw to scale the triangle ABC A
with AB = 6cm and angle CAB = 30o and AC = 5cm
Step 1 Draw line AB=6cm
Step 2 Measure
C
angle CAB
from A X
Step 3 Draw the line
AC = 5cm
through X. Label it C. A B
Step 4 Join C to B.
Check angles add to 180o
10-Nov-11 Created by Mr. Lafferty 24
Scale Drawings
General
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Now try Ex 4
Ch5 (page 58)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 84.6 - 26.8
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2. If I am facing SE and turn 90o
clockwise. Which direction am I facing now.
3. 5% of £120
4. A cuboid has length 4m breadth 5m
and height 6m. Find the volume.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Directions & Scale Drawings
General
Learning Intention Success Criteria
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1. Be able to make sense of a
1. To show how to write down
map.
directions using a map.
2. Write down accurate
2. To explain how to directions from a map.
construct a scale drawing
using bearings. 3. Construct and interpret
an accurate scale drawing.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Compass Points
360/000o
N
Half way between Half way between
North and West NW North and East
NE
270o W E 090o
SW SE
Half way between Half way between
S
South and West South and East
180o
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Anne walks facing
Gary
If If Daniel is to John
Julie
If Amy is facing Paul and
If Daniel is facing North
then to Barryand West
Who Amy and East
Frances North then
then to is South then
and turns
Who isclockwise to
and turns East of John
Who anti-clockwise to
turns isis
Who to where Daniel
North of
back of Barry Amy.
back to to facehe
clockwise where she
Compass Points
of How
face Anne. Gary many
Daniel. How many
How many degrees all
General started. Write down is
degrees is this.
degrees is this.
the directions he took.
the directions she took.
this.
John Frances Barry
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N
Julie Daniel Anne
Gary Amy Paul
10-Nov-11 Created by Mr. Lafferty Maths Dept.
come out to the park I want
After going ofof the
I I come out the swimming
I leave the a school and
There’s zoo to go back
I come out offire at the to
Map Directions
pool and go and need to
to turn the cinema.
charity shopto right then left.
my carto Right down the
library. the Park.the town
go which is in
I go aTea Lane is closed.
bus. Write down
catch into the building second
Write Write down the
car park. the the
directions downfire engine
on my the directions
theWrite downto the bus
directionsthe right.
General should should
directions I take. take.
directions I must take.
I the
Nameshould take.
station. building.
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N
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings using Bearings
Make an accurate scale drawing of this sketch.
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N N
50o 50o 15km
15km
1cm represents 3km
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scaled Drawings using Bearings
Make an accurate drawing of the plane journey
N
N
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N
N
120o 120o
45o
45o 12km 8km 12km
8km
1cm represents 2km
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Compass points & Scale Drawings
General
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Now try Ex 5
Ch5 (page 61)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 55.27 + 56.4
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2. Calculate 2% of 90
3. Find the rule x 1 2 3 4
y 5 8 11 14
4. What is the area of a rectangle
with length 6cm and breadth 7cm
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Measuring & Scales
General
Learning Intention Success Criteria
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1. Understand the connection
1. To explain the connection
between measuring and
between measuring and
scale.
scale.
2. Be able to do solve
problems in context.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Measuring & Scales metres
(m)
100
General
Given that the scale of this drawing is
centimetres
(cm)
1cm = 35cm
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What is the actual length
of the car in metres ?
10 x 35 = 350 cm
3.5 m
?m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Measuring & Scales metres
(m)
100
General
Given that the scale of this drawing is
centimetres
(cm)
1cm = 700cm
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What is the actual height
of the wind turbine in metres ?
?m
9 x 700 = 6300 cm
63 m
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Measuring & Scales
General
Now try
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Extension Booklet Ex 6E
Ch5 (page 19)
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
General
1. 6.2 - 5.4
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2. Calculate 3% of 120
3. Find the rule x 1 2 3 4
y 12 18 24 30
4. What is the perimeter of a rectangle
with length 4cm and breadth 10cm
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Similar Shapes
General
Learning Intention Success Criteria
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1. Understand the words
1. To explain the meaning of
similar and factor.
the word ‘similar’ and
‘factor’ in mathematics. 2. Be able to enlarge / reduce
Enlarge and reduce similar a shape by a given factor
shapes by a given factor. .
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
General
photos by a
These twoEnlarged are of the same view
Scale Factor
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of two (Double)
3cm
1.5cm
2cm 4cm
The second is double the size of the first.
The first could be ENLARGED to make the second.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
General
These two Reduced by a of the same view
photos are
Scale Factor
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of a half
3cm
1.5cm
2cm 4cm
The first is half the size of the second.
The second could be REDUCED to make the first.
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Similar Shapes
General
These two rectangles are similar.
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4cm
2cm
4cm 8cm
The first has been ENLARGED by a factor (ESF) of 2
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Similar
Find the Rectangles length
Find the
missing
enlargement
General
factor ? cm
These two rectangles are similar.
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?cm
2cm
4cm 12cm
The first has been ENLARGED by a factor (ESF) of 3
? = 2 x 3 = 6cm
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Similar
Find the Rectangleslength
Find the
missing
reduction
General
factor ? cm
These two rectangles are similar.
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8cm
?cm
16cm 4cm
The first has been ENLARGED by a factor (ESF) of 4
?=8 4 = 2cm
10-Nov-11 Created by Mr. Lafferty Maths Dept.
Scale Factor applies to ANY SHAPES that are
mathematically similar.
1.4 cm 7 cm
2cm
y
z 3 cm
15 cm
6 cm
Given the shapes are similar, find the values y and z ?
15 1
Scale factor = ESF = =5 Scale factor = RSF = = 0.2
3 5
y is 2 x 5 = 10 z is 6 x 0.2 = 1.2
Scale Factor applies to ANY SHAPES that are
mathematically similar.
b 7.5 cm a 4 cm
3 cm
8 cm 2cm
10 cm
Given the shapes are similar, find the values a and b ?
4 10
Scale factor = RSF = = 0.4 Scale factor = ESF = = 2.5
10 4
a is 8 x 0.4 = 3.2 b is 2 x 2.5 = 5
Scale factors
General
Enlargement Scale factor?
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3
ESF = =
8cm
8 2
12
12cm
Reduction Scale factor?
5cm 2
RSF = =
3
7.5cm
Can you see the relationship
between the two scale factors?
Scale factors
General
Find a given ESF = 3
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a
ESF = 3 =
9cm 9
a
27cm
By finding the RSF
b
5cm Find the value of b.
1 b 5
RSF = = = 15cm
3 15 15
Scale factors
General
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Now try
Extension Booklet Ex 7E
Ch5 (page 21)
10-Nov-11 Created by Mr. Lafferty Maths Dept.