25-May-15Created by Mr. Lafferty Maths Dept. Measuring & Scales Working with Scales Scaled Drawings Scaled Drawings Making Simple

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Measuring & Scales

Working with Scales

Scaled DrawingsScaled Drawingsw

ww

.math

srevis

ion

.com

Making Simple Scale Drawings

Harder Scale Drawings

Compass Points & Scale Drawings

Enlarging and Reducing Drawing

Similar Shapes & Scale Factor

National 4 REL 1.2b


Starter QuestionsStarter Questionsw

ww

.math

srevis

ion

.com (a) 500cm (b) 380cm (c) 157cm

(a) 4m (b) 2.6m (c) 1.92m

(a)

1. Convert these distance to metres

2. Convert these distance to centimetres

3. Convert these distances to metres. 7km (b) 2.6km (c) 1.045km

(a) 8000m (b) 6390m (c) 360m

4. Convert these distances to kilometres.

National 4 REL 1.2b

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

w.m

ath

srevis

ion

.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. To explain how to enlarge or reduce a given shape by a factor.

1. Be able to enlarge a shape by a factor.

Enlarging & Enlarging & ReducingReducing

2. Be able to reduce a shape by a factor.

National 4 REL 1.2b



w.m

ath

srevis

ion

.com

Double the size of

the shape.

Half the size of the

shape.National 4 REL 1.2b


Now try Ex 1Q1 (e)(g)(i) (j)

Q2 (c)(d)((g)(h) Ch5 (page 50)

ww

w.m

ath

srevis

ion

.com


National 4 REL 1.2b



ww

.math

srevis

ion

.com

o2. I f I am f acing NW and turn 180

clockwise. Which direction am I f acing now.

1. 99.6 + 7.27

3. 25% of £2.60

4. Round to 1 decimal place

(a) 2.67 (b) 3.23 (c) 2.99

National 4 REL 1.2b


w.m

ath

srevis

ion


1.1. To understand the term To understand the term scale.scale.

1. To explain the term scale on a map.

2. Calculate the real life distances using a scaled.

ScalesScalesNational 4 REL 1.2b


w.m

ath

srevis

ion

.com In order to make sense of a map or scale diagram

the scale must be known.



w.m

ath

srevis

ion

.com In order to make sense of a map or scale diagram

the scale must be known.

ScalesScales

4 cm

For this scale model1 cm represents 1m

This means for every 1 metre of the actual car, 1cm is drawn on the map.

National 4 REL 1.2b


w.m

ath

srevis

ion

.com

6cm

The scale of this drawing is 1cm = 5m

What is the actual length of the tree ?

ScalesScales

6 x 5 =30m

National 4 REL 1.2b


w.m

ath

srevis

ion

.com

5cm

The scale of this drawing is 1cm = 90cm

What is the actual length of the bus in metres ?

ScalesScales

5 x 90 = 450cm

4.5m

National 4 REL 1.2b


Now try Ex 2Ch5 (page 52)

ww

w.m

ath

srevis

ion

.com




ww

.math

srevis

ion

.com

o2. I f I am f acing North and turn 45

anti - clockwise. Which direction am I f acing now.

1. 17.6 - 13.9

3. 4% of £20

4. A cuboid has length 5m breadth 3m

and height 5m. Find the volume.

National 4 REL 1.2b


w.m

ath

srevis

ion


1. To draw a scale drawing given suitable information.

1. From information given make a scaled drawing.

Scaled DrawingsScaled DrawingsNational 4 REL 1.2b


w.m

ath

srevis

ion

.com

Problem

A garden is rectangular in shape and has length 12m and breadth 8m. Make rough sketch of the garden.

12m

8m

Scaled DrawingsScaled Drawings

Draw an accurate scaled drawing of the garden

Use a scale of 1cm represents 2m

National 4 REL 1.2b


w.m

ath

srevis

ion

.com

12m

8m



12m

8m

1cm represents 2m

National 4 REL 1.2b


w.m

ath

srevis

ion

.com

Problem

A road junction is triangular in shape. A rough sketch is given below.

20m


Draw an accurate scaled drawing of the junction


12m

National 4 REL 1.2b



w.m

ath

srevis

ion

.com


20m

12m

1cm represents 2m

20m12m

Find the real life length of the 3rd side

2 x 11.6 = 23.2m

National 4 REL 1.2b


Now try Ex3Ch5 (page 55)

ww

w.m

ath

srevis

ion

.com

Scaled DrawingsScaled DrawingsNational 4 REL 1.2b



ww

.math

srevis

ion

.com

1. 8.7 - 7.8

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.

National 4 REL 1.2b

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 2121

‘‘To construct a triangle given To construct a triangle given the length of two sides the length of two sides and the and the includedincluded angle’ angle’

Aim of the LessonAim of the Lesson

Drawing SAS TrianglesDrawing SAS Triangles



SAS TrianglesSAS Triangles

AngleAngle SideSideSideSide



Toolkit required

1.1.RulerRuler

2.2.ProtractorProtractor

3.3.Pencil & PaperPencil & Paper



Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30o and AC = 5cm

Step 1 Draw line AB=6cm

A B

CStep 2 Measure

angle CAB from A

Step 3 Draw the line AC = 5cm

through X. Label it C.

Step 4 Join C to B.

Check angles add to 180o

A B

C

30o

X



ww

w.m

ath

srevis

ion

.com

Scale DrawingsScale DrawingsNational 4 REL 1.2b



ww

.math

srevis

ion

.com

o2. I f I am f acing SE and turn 90

clockwise. Which direction am I f acing now.

1. 84.6 - 26.8

3. 5% of £120

4. A cuboid has length 4m breadth 5m

and height 6m. Find the volume.

National 4 REL 1.2b


w.m

ath

srevis

ion


1. To show how to write down directions using a map.

2. To explain how to construct a scale drawing using bearings.

1. Be able to make sense of a map.

Directions & Scale Directions & Scale DrawingsDrawings

2. Write down accurate directions from a map.

3. Construct and interpret an accurate scale drawing.

National 4 REL 1.2b

18 Apr 2023 Created by Mr. Lafferty Maths Dept.

Compass Points

N

S

EW 090o

360/000o

270o

180o

SE

Half way between South and East

SW

Half way between South and West

Half way between North

and WestNW NE

Half way between North and East

Compass PointsCompass PointsIf Anne walks to Julie then to Amy and then

back to where she started. Write down all

the directions she took.

If Daniel is facing North and turns

clockwise to face Anne. How many degrees is this.

If Daniel is facing Frances and turns

clockwise to face Amy. How many degrees is

this.

If Amy is facing Paul and turns anti-

clockwise to face Daniel. How many

degrees is this.


w.m

ath

srevis

ion

.com John

Julie

Gary

Frances

Daniel

Amy

Barry

Anne

Paul

N

Who is North of DanielWho is East of JohnWho is South West of Barry

Who is North East of Gary

National 4 REL 1.2b

If Gary walks to John then to Barry and then

back to where he started. Write down all the directions he took.

National 4 REL 1.2b

Map DirectionsMap DirectionsI leave the zoo to go back to my car which is in the

town car park. Write down the directions I should

take.

There’s a fire at the library. Right down the

directions the fire engine should take.

I come out of the swimming pool and turn

right then left. I go into the building second on my the

right. Name the building.

After going to the park I want to go to the cinema.

Tea Lane is closed. Write down the directions

I should take.

I come out of school and go to the Park.

Write down the directions I must take.

I come out of the charity shop and need to catch a bus. Write

down the directions to the bus station.


w.m

ath

srevis

ion

.com

N

N

18 Apr 2023 Created by Mr. Lafferty Maths Dept.ww

w.m

ath

srevis

ion

.com

Make an accurate scale drawing of this sketch.

1cm represents 3km

Scaled Drawings using Bearings

N

50o15km

50o

1cm represents 3km

15km

12km

N

120o

1cm represents 2km

N

18 Apr 2023 Created by Mr. Lafferty Maths Dept.ww

w.m

ath

srevis

ion

.com

Make an accurate drawing of the plane journey

1cm represents 2km

Scaled Drawings using Bearings

N

120o

12km45o

8km

N

45o

8km



ww

w.m

ath

srevis

ion

.com

Compass points & Scale Compass points & Scale DrawingsDrawings

National 4 REL 1.2b



ww

.math

srevis

ion

.com

2.

1. 55.27 + 56.4

Calculate 2

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

% of 90

National 4 REL 1.2b


w.m

ath

srevis

ion


1. To explain the connection between measuring and scale.

1. Understand the connection between measuring and scale.

2. Be able to do solve problems in context.

Measuring & ScalesNational 4 REL 1.2b


w.m

ath

srevis

ion

.com

Given that the scale of this drawing is 1cm = 35cm

What is the actual length of the car in metres ?

10 x 35 =350 cm

Measuring & Scales

? m

metres(m)

centimetres(cm)

· 100

3.5 m

National 4 REL 1.2b

? m


w.m

ath

srevis

ion

.com

Given that the scale of this drawing is

1cm = 700cm

What is the actual height of the wind turbine in metres ?

9 x 700 =6300 cm

Measuring & Scales metres(m)

centimetres(cm)

· 100

63 m

National 4 REL 1.2b


Now try Extension Booklet Ex 6E

Ch5 (page 19)

ww

w.m

ath

srevis

ion

.com

Measuring & ScalesNational 4 REL 1.2b



ww

.math

srevis

ion

.com

2.

1. 6.2 - 5.4

Calculate 3

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

% of 120

National 4 REL 1.2b


w.m

ath

srevis

ion


1. To explain the meaning of the word ‘similar’ and ‘factor’ in mathematics. Enlarge and reduce similar shapes by a given factor.

1. Understand the words similar and factor.

Similar ShapesSimilar Shapes

2. Be able to enlarge / reduce a shape by a given factor .

National 4 REL 1.2b



w.m

ath

srevis

ion

.com These two photos are of the same view

1.5cm

2cm

3cm

4cm

The second is double the size of the first.

The first could be ENLARGED to make the second.

Enlarged by a Scale Factor

of two (Double)

National 4 REL 1.2b



w.m

ath

srevis

ion

.com These two photos are of the same view

1.5cm

2cm

3cm

4cm

The first is half the size of the second.

The second could be REDUCED to make the first.

Reduced by a Scale Factor

of a half

National 4 REL 1.2b


w.m

ath

srevis

ion

.com These two rectangles are similar.

2cm

4cm

4cm

8cm

The first has been ENLARGED by a factor (ESF) of 2

Similar ShapesSimilar ShapesNational 4 REL 1.2b


w.m

ath

srevis

ion


2cm

4cm

?cm

12cm


Similar RectanglesSimilar RectanglesFind the enlargemen

t factor

Find the missing

length ? cm

? = 2 x 3 = 6cm

National 4 REL 1.2b


w.m

ath

srevis

ion


8cm

16cm

?cm

4cm


Similar RectanglesSimilar RectanglesFind the reduction

factor

Find the missing

length ? cm

? = 8 ÷ 4 = 2cm

National 4 REL 1.2b

Given the shapes are similar, find the values y and z ?

Scale Factor applies to ANY SHAPES that are mathematically similar.

15 cm

3 cm

7 cm2cm

yz

6 cm

Scale factor = ESF = 3

15= 5

is 2 x 5 = 10

1.4 cm

Scale factor = RSF = 5

1

is 6 x 0.2 = 1.2

= 0.2

y z

Given the shapes are similar, find the values a and b ?

Scale Factor applies to ANY SHAPES that are mathematically similar.

8 cm

7.5 cmb

10 cm

Scale factor = RSF = 10

4= 0.4

is 8 x 0.4 = 3.2

Scale factor = ESF = 4

10

is 2 x 2.5 = 5

= 2.5

a b

4 cm

2cm

a

3 cm

Scale factors Scale factors

8cm12cm

Enlargement Scale factor?

Reduction Scale factor?

5cm

7.5cm

ESF =

RSF =

Can you see the relationship between the two scale factors?w

ww

.math

srevis

ion

.com

1288

12

32

=

23

=

National 4 REL 1.2b

9cm a

Find a given ESF = 3

b

15cm

By finding the RSF Find the value of b.

ESF = 3

a9

=

Scale factors Scale factors w

ww

.math

srevis

ion

.com

27cm

5cm

13

RSF =

b15

= = 515

National 4 REL 1.2b


Now try Extension Booklet Ex 7E

Ch5 (page 21)

ww

w.m

ath

srevis

ion

.com

Scale factors Scale factors National 4 REL 1.2b

Documents

25-May-15Created by Mr. Lafferty Maths Dept. Measuring & Scales Working with Scales Scaled Drawings Scaled Drawings Making Simple