Transcript Slide 1

Scaled Drawings
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National 4
REL 1.2b
Enlarging and Reducing Drawing
Working with Scales
Making Simple Scale Drawings
Harder Scale Drawings
Compass Points & Scale Drawings
Measuring & Scales
Similar Shapes & Scale Factor
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
REL 1.2b
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1.
Convert these distance to metres
(a) 500cm
2.
(b) 380cm (c) 157cm
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
18-Jul-15
(b) 6390m (c) 360m
Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
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National 4
REL 1.2b
Learning Intention
1.
18-Jul-15
To explain how to enlarge
or reduce a given shape by
a factor.
Success Criteria
1. Be able to enlarge a shape
by a factor.
2. Be able to reduce a shape
by a factor.
Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
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National 4
REL 1.2b
Half the
size of the
shape.
18-Jul-15
Double the
size of the
shape.
Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
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National 4
REL 1.2b
Now try Ex 1
Q1 (e)(g)(i) (j)
Q2 (c)(d)((g)(h)
Ch5 (page 50)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
REL 1.2b
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1.
99.6 + 7.27
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
18-Jul-15
(b) 3.23
(c) 2.99
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Scales
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National 4
REL 1.2b
Learning Intention
1.
To explain the term scale
on a map.
Success Criteria
1. To understand the term
scale.
2. Calculate the real life
distances using a scaled.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales
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National 4
REL 1.2b
In order to make sense of a map or scale diagram
the scale must be known.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales
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National 4
REL 1.2b
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.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales
National 4
REL 1.2b
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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
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales
National 4
REL 1.2b
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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
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scales
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National 4
REL 1.2b
Now try Ex 2
Ch5 (page 52)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
REL 1.2b
1.
17.6 - 13.9
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.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scaled Drawings
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National 4
REL 1.2b
Learning Intention
1.
18-Jul-15
To draw a scale drawing
given suitable information.
Success Criteria
1. From information given
make a scaled drawing.
Created by Mr. Lafferty Maths Dept.
Scaled Drawings
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National 4
REL 1.2b
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
18-Jul-15
Created by Mr. Lafferty Maths Dept.
8m
Scaled Drawings
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National 4
REL 1.2b
Use a scale of
1cm represents 2m
12m
8m
12m
8m
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scaled Drawings
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National 4
REL 1.2b
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
18-Jul-15
20m
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12m
Scaled Drawings
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National 4
REL 1.2b
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
18-Jul-15
Created by Mr. Lafferty Maths Dept.
12m
Scaled Drawings
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National 4
REL 1.2b
Now try Ex3
Ch5 (page 55)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
REL 1.2b
1.
8.7 - 7.8
2.
Calculate
3.
A model boat has scale of 1cm to 2m
7% of 120
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.
18-Jul-15
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’
18-Jul-15
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21
Drawing SAS Triangles
SAS Triangles
Side
Angle
18-Jul-15
Side
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22
Drawing SAS Triangles
Toolkit required
1.Ruler
2.Protractor
3.Pencil & Paper
18-Jul-15
Created by Mr. Lafferty
23
Drawing SAS Triangles
C
Example :
30
o
B
A
Draw to scale the triangle ABC
with AB = 6cm and angle CAB = 30o and AC = 5cm
Step 1 Draw line AB=6cm
Step 2 Measure
angle CAB
from A
C
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
18-Jul-15
Created by Mr. Lafferty
24
Scale Drawings
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National 4
REL 1.2b
Now try Ex 4
Ch5 (page 58)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
REL 1.2b
1.
84.6 - 26.8
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.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Directions & Scale Drawings
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National 4
REL 1.2b
Learning Intention
1. To show how to write down
directions using a map.
2. To explain how to
construct a scale drawing
using bearings.
18-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.
Created by Mr. Lafferty Maths Dept.
Compass Points
360/000o
Half way between
North and West
270o
N
NW
NE
W
E
SW
Half way between
South and West
18-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
to
where
he
back
where
she
clockwise
to
face
Amy.
of
of Barry
Gary
face
Anne.
Daniel.
How
Howmany
many
National 4 started. Write down all
How
many
degrees
is
REL 1.2b
degrees
degreesisisthis.
this.
the directions
directions
he
took.
the
she
took.
this.
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Compass Points
John
Frances
Barry
N
18-Jul-15
Julie
Daniel
Anne
Gary
Amy
Paul
Created by Mr. Lafferty Maths Dept.
After
going
toof
the
park I want
I Icome
come
outout
of
the
the
swimming
leave
theof
toat
gothe
back to
There’s
azoo
fire
II come
out
school
and
toshop
go
to
the
cinema.
charity
pool and
turn
and
right
need
then
to left.
my
car
which
is
in
the
town
library.
Right
down
the
go to the Park.
Lane
is closed.
catch
I go into
aTea
bus.
the
Write
building
down
second
car
park.
Write
down
the
directions
the
fire
engine
Write down the
National 4
the
directions
theWrite
directions
on down
my the
to
the
right.
bus
REL 1.2b
directions
I
should
take.
should
take.take.
directions
I must
I should
take.
Name
station.
the building.
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Map Directions
N
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Scaled Drawings using Bearings
www.mathsrevision.com
Make an accurate scale drawing of this sketch.
18-Jul-15
N
N
50o
15km
50o 15km
1cm represents 3km
Created by Mr. Lafferty Maths Dept.
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Scaled Drawings using Bearings
Make an accurate drawing of the plane journey
N
N
N
N
18-Jul-15
120o
45o
8km
120o
12km
45o
8km
12km
1cm represents 2km
Created by Mr. Lafferty Maths Dept.
Compass points & Scale Drawings
www.mathsrevision.com
National 4
REL 1.2b
Now try Ex 5
Ch5 (page 61)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
REL 1.2b
www.mathsrevision.com
1.
55.27 + 56.4
2. Calculate
2% of 90
3.
Find the rule
4.
What is the area of a rectangle
with length 6cm and breadth 7cm
18-Jul-15
x
y
1 2 3 4
5 8 11 14
Created by Mr. Lafferty Maths Dept.
Measuring & Scales
www.mathsrevision.com
National 4
REL 1.2b
Learning Intention
1.
18-Jul-15
To explain the connection
between measuring and
scale.
Success Criteria
1. Understand the connection
between measuring and
scale.
2. Be able to do solve
problems in context.
Created by Mr. Lafferty Maths Dept.
Measuring & Scales
metres
(m)
100
National 4
REL 1.2b
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centimetres
Given that the scale of this drawing
is
(cm)
1cm = 35cm
What is the actual length
of the car in metres ?
10 x 35 = 350 cm
3.5 m
?m
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Measuring & Scales
metres
(m)
100
National 4
REL 1.2b
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Given that the scale of thiscentimetres
drawing
is
(cm)
1cm = 700cm
?m
What is the actual height
of the wind turbine in metres ?
9 x 700 = 6300 cm
63 m
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Measuring & Scales
www.mathsrevision.com
National 4
REL 1.2b
Now try
Extension Booklet Ex 6E
Ch5 (page 19)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
REL 1.2b
www.mathsrevision.com
1.
6.2 - 5.4
2. Calculate
3% of 120
3.
Find the rule
4.
What is the perimeter of a rectangle
with length 4cm and breadth 10cm
18-Jul-15
x 1
2 3 4
y 12 18 24 30
Created by Mr. Lafferty Maths Dept.
Similar Shapes
www.mathsrevision.com
National 4
REL 1.2b
Learning Intention
1.
18-Jul-15
To explain the meaning of
the word ‘similar’ and
‘factor’ in mathematics.
Enlarge and reduce similar
shapes by a given factor.
Success Criteria
1. Understand the words
similar and factor.
2. Be able to enlarge / reduce
a shape by a given factor
.
Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
www.mathsrevision.com
National 4
REL 1.2b
by a of the same view
These twoEnlarged
photos are
Scale Factor
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.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Enlarging & Reducing
www.mathsrevision.com
National 4
REL 1.2b
These two Reduced
photos by
area of the same view
Scale Factor
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.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Similar Shapes
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National 4
REL 1.2b
These two rectangles are similar.
4cm
2cm
4cm
8cm
The first has been ENLARGED by a factor (ESF) of 2
18-Jul-15
Created by Mr. Lafferty Maths Dept.
www.mathsrevision.com
National 4
REL 1.2b
Find
the
Rectangles
missing length
? cm
Find
the
Similar
enlargement
factor
These two rectangles are similar.
?cm
2cm
4cm
12cm
The first has been ENLARGED by a factor (ESF) of 3
? = 2 x 3 = 6cm
18-Jul-15
Created by Mr. Lafferty Maths Dept.
www.mathsrevision.com
National 4
REL 1.2b
Find
the
Rectangles
missing length
? cm
Find
the
Similar
reduction
factor
These two rectangles are similar.
8cm
?cm
4cm
16cm
The first has been ENLARGED by a factor (ESF) of 4
?=8
18-Jul-15
4 = 2cm
Created by Mr. Lafferty Maths Dept.
Scale Factor applies to ANY SHAPES that are
mathematically similar.
2cm
z
1.4 cm
7 cm
y
3 cm
15 cm
6 cm
Given the shapes are similar, find the values y and z ?
15
Scale factor = ESF =
=5
3
y is 2 x 5 = 10
1
Scale factor = RSF =
= 0.2
5
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
Scale factor = RSF =
= 0.4
10
a is 8 x 0.4 = 3.2
10
Scale factor = ESF =
= 2.5
4
b is 2 x 2.5 = 5
Scale factors
National 4
REL 1.2b
www.mathsrevision.com
Enlargement Scale factor?
ESF =
8
8cm
3
=
2
Reduction Scale factor?
5cm
RSF =
12
12cm
2
=
3
Can you see the relationship
between the two scale factors?
7.5cm
Scale factors
National 4
REL 1.2b
www.mathsrevision.com
Find a given ESF = 3
ESF = 3 =
9cm
b
5cm
a
9
27cm
a
By finding the RSF
Find the value of b.
1
b
5
RSF =
=
=
3
15 15
15cm
Scale factors
www.mathsrevision.com
National 4
REL 1.2b
Now try
Extension Booklet Ex 7E
Ch5 (page 21)
18-Jul-15
Created by Mr. Lafferty Maths Dept.