Transcript Chapter 17 - Scaled Drawings

Scaled Drawings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Working with Scales
Making Simple Scale Drawings
Harder Scale Drawings
Compass Points
Bearings
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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MTH 2-17c
MTH 2-17d
MTH 3-17b
1.
99.6 + 7.27
2. Calculate 70% of 84
3.
25% of 160p
4.
Round to 1 decimal place
(a) 2.67
5.
8-Jul-15
(b) 3.23
(c) 2.99
Find the value of x
4x +25 = 69
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Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Learning Intention
1. We are learning the term
scale drawing.
Success Criteria
1. Understand the term
scale drawings.
2. Interpret scale drawing into
real-life measurements.
8-Jul-15
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Scales
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MTH 2-17c
MTH 2-17d
S1
Level
E
MTH
3-17b
Definition
A scale of
1 cm = 2m
This simply means for every 1cm measured on a
drawing this represents 2m in real-life.
8-Jul-15
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Scales
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MTH 2-17c
MTH 2-17d
MTH 3-17b
In order to make sense of a map or scale diagram
the scale must be known.
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.
8-Jul-15
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Scales
MTH 2-17c
MTH 2-17d
MTH 3-17b
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The scale of this drawing is
1cm = 5m
6cm
What is the actual length
of the tree ?
6 x 5 = 30m
8-Jul-15
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Scales
MTH 2-17c
MTH 2-17d
MTH 3-17b
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The scale of this drawing is
1cm = 90cm
What is the actual length
of the bus in metres ?
5cm
5 x 90 = 450cm
4.5m
8-Jul-15
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Scales
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Now try Ex 1
Ch17 (page 194)
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
MTH 2-17c
MTH 2-17d
MTH 3-17b
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1.
Write in litres
(a) 100ml
(b) 500ml (c) 2500ml
2. Calculate 75% of 240
3. If the area and perimeter of
the shape.
4.
8-Jul-15
Find the mean of
6, 9, 15, 10, 5
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7cm
14cm
10cm
Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Learning Intention
1
8-Jul-15
We are learning to draw a
scale drawing given
suitable information.
Success Criteria
1. Interpret information in a
problem and create a
suitable scale drawing.
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Scaled Drawings
Problem
A garden is rectangular in shape and
has length 12m and breadth 8m.
Make rough sketch of the garden.
12m
Draw an accurate
scaled drawing of the garden
Use a scale of
1cm represents 2m
8-Jul-15
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8m
Scaled Drawings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Use a scale of
1cm represents 2m
12m
8m
12m
8m
8-Jul-15
Created by Mr. Lafferty Maths Dept.
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Scaled Drawings
Problem
A road junction is triangular in shape.
A rough sketch is given below.
Draw an accurate
scaled drawing of the junction
Use a scale of
1cm represents 2m
20m
12m
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Scaled Drawings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Use a scale of
1cm represents 2m
Find the real
life length of
the 3rd side
20m
20m
2 x 11.6 = 23.2m
12m
8-Jul-15
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12m
Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Now try Exercise 2
Ch17 (page 197)
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
MTH 2-17c
MTH 2-17d
MTH 3-17b
85.7 - 7.8
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1.
2. Calculate
60% of 120
3.
75% of 360p
4.
Round to 1 decimal place
(a) 15.673
5.
8-Jul-15
(b) 13.55
(c) 23.49
Find the value of x
5x +35 = 90
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Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Learning Intention
1. We are learning to solve
real-life problems using
scale drawings.
Success Criteria
1. Interpret information in a
problem to create a suitable
scale drawing.
2. Apply a scale drawing methods
to solve a given problem.
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Problem
The sketch shows a flag-pole YT supported by
a wire. The distance from X to Y is 6m and
o
angle TXY = 55 .
T
Make a scale drawing and work
Out the real height of the pole.
Use a scale of 1cm = 2m
8-Jul-15
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X
o
55
6m
Y
T
Scale Drawings & Bearings
X
55
o
Y
6m
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Solution
Using a scale of 1cm = 2m
Step 1: Draw line XY=3cm
T
Step 2: Draw a line straight up from Y.
o
Step 3: Measure angle 55 from X.
Step 4: Draw line from X to vertical line
and mark T at crossover point.
Step 5: Measure length YT.
Step 6: Multiply length YT.
by scale factor.
4.3cm
4.3 x 2 = 8.6m
Flag pole is 8.6m high
8-Jul-15
X
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Y
Harder Scale Drawings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Now try Exercise 3
Ch17 (page 199)
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
MTH 2-17c
MTH 2-17d
MTH 3-17b
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1.
13 + (- 20)
2. If I am facing SE and turn 90o
clockwise. Which direction am I facing now.
3.
5% of £120
4.
A square has length 3m.
Find the perimeter and area.
8-Jul-15
Created by Mr. Lafferty Maths Dept.
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Directions & Scale Drawings
Learning Intention
1. We are learning how to
write down directions
using a map.
2. We are learning how to
construct a scale drawing
using bearings.
8-Jul-15
Success Criteria
1. Be able to make sense of a
map.
2. Write down accurate
directions from a map.
3. Construct and interpret
an accurate scale drawing.
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Compass Points
360/000o
Half way between
North and West
270o
N
NW
NE
W
E
SW
Half way between
South and West
8-Jul-15
Half way between
North and East
090o
SE
S
180o
Created by Mr. Lafferty Maths Dept.
Half way between
South and East
Gary
walks
John
If If
Anne
Julie
Daniel
is to
facing
If
If Daniel
Amy isisfacing
facingPaul
North
and
then
to
Barry
and
then
then
to is
Amy
and
then
Frances
and
turns
Who
South
West
Who
is
North
East
and
turns
turns
anti-clockwise
clockwise
to
to
Who
is
North
of
Daniel
Who
is
East
of
John
back
to
where
he
back
to
where
she
clockwise
to
face
Amy.
of
of Barry
Gary
MTH 2-17c
face
Anne.
Daniel.
How
Howmany
many
MTH 2-17d started. Write down all
How
many
degrees
is
MTH 3-17b
degrees
degreesisisthis.
this.
the directions
directions
he
took.
the
she
took.
this.
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Compass Points
John
Frances
Barry
N
8-Jul-15
Julie
Daniel
Anne
Gary
Amy
Paul
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MTH 2-17c
MTH 2-17d
MTH 3-17b
After
going
toof
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go
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and
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my
car
which
is
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town
library.
Right
down
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catch
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bus.
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directions
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the building.
Map Directions
N
8-Jul-15
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Compass points
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Now try Ex 4
Ch17 orally (page 202)
do
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
MTH 2-17c
MTH 2-17d
MTH 3-17b
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1.
- 3 + 14
2. If I am facing SE and turn 90o
clockwise. Which direction am I facing now.
3.
15% of £120
4.
A rectangle has length 4m breadth 5m
Find the perimeter and area.
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Scale Drawings & Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Learning Intention
1
8-Jul-15
We are learning how to
work out a bearing..
Success Criteria
1. Calculate a bearing.
2. Remember to give a
bearing in the correct
format (three figure
reference).
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Bearings
360/000o
N
1. Measured from North.
060o
2. In a clockwise direction.
270o
60o
W
090o
E
3. Written as 3 figures.
S
180o
N
145o
W
S
8-Jul-15
N
N
E
145o
W
230o
230o
S
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315o
E
W
315o
S
E
A 360o
protractor is
used to measure
bearings.
315o
Bearings
Use your protractor to
measure the bearing
of each point from the
centre of the circle.
360/000o
350o
N
020o
NW
(Worksheet 1)
045o
NE
290o
270o
080o
W
E
250o
110o
SW
225o
Worksheet 1
8-Jul-15
SE
210o
S
160o
180o
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135o
090o
N
360/000o
030o
330o
045o
315o
290o
075o
090o E
W 270o
Control
Tower
110o
250o
135o
225o
170o
200o
8-Jul-15
Estimate the
bearing of
each aircraft
from the
centre of the
radar screen.
180o
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S
Air Traffic
Controller
N
360/000o
7
325o
010o
8
310o
040o
1
ACE
060o
Controller
11
contest
12
4
280o
2
Estimate the
bearing of
each aircraft
from the
centre of the
radar screen.
090o E
W 270o
3
Control
Tower
250o
235o
10
9
120o
6
195o
8-Jul-15
5
155o
180o Worksheet 2
Created by Mr. Lafferty Maths Dept.
S
Air Traffic
Controller
Bearings
Measuring the bearing of one point from another.
N
To Find the bearing of Q from P.
P
1. Draw a straight line between both points.
118o
Q
2. Draw a North line at P.
3. Measure angle between.
8-Jul-15
Worksheet 3
Created by Mr. Lafferty Maths Dept.
Bearings
Measuring the bearing of one point from another.
To Find the bearing of P from Q.
N
298o
P
1. Draw a straight line between both points.
Q
2. Draw a North line at Q.
3. Measure angle between.
8-Jul-15
Worksheet 3
Created by Mr. Lafferty Maths Dept.
Bearings: Fixing Position
Trainee pilots have to to learn to be cope when the unexpected
happens. If their navigation equipment fails they can quickly find
their position by calling controllers at two different airfields for
a bearing. The two bearings will tell the pilot where he is. The
initial call on the controllers radio frequency will trigger a line on
the radar screen showing the bearing of the calling aircraft.
Airfield (A)
283.2 MHZ UHF
170o
255o
Airfield (B)
306.7 MHZ UHF
Thankyou
8-Jul-15
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Bearings
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MTH 2-17c
MTH 2-17d
MTH 3-17b
Now try Ex 5
Ch17 (page 203)
8-Jul-15
Created by Mr. Lafferty Maths Dept.
Bearings
000/360o
N
270o
W
E
S
Worksheet 1
8-Jul-15
180o
Created by Mr. Lafferty Maths Dept.
090o
My
Estimated
Bearing
True
Bearing
Error
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
True
Bearing
Total
Error
Total
Error
Average
Error
Average
Error
Worksheet 2 (Radar)
8-Jul-15
My
Estimated
Bearing
Created by Mr. Lafferty Maths Dept.
Error