Measurement

1
Measurement
2
Note 1 Measurement Systems

• In NZ the measurement system used is the metric
  system. The units relate directly to each other.

3
Capacity Basic Unit Symbol
Distance
Mass (weight)
Capacity
Temperature
Time
Area
Land Area
Volume
metre
m
gram
g
litre
L
C
degrees celsius
s/min
seconds/minutes
square metres
m²
ha
hectares
m³
cubic metres
4

• To change within a unit from one prefix to
  another prefix, we either multiply or divide by a
  power of 10.

smaller to larger unit divide by a power of
10 larger to smaller unit multiply by a power
of 10
Examples convert the following 5.76m to
cm 489mL to L 3789600cm to km
5
Homework Book Page 159-160
6
STARTERS

• Convert the following
• 59mL to L
• 4200kg to tonne
• 11m465mm to cm
• A dairy stores milk in 5 litre containers. How
  many 350mL milkshakes can be made from one of
  these containers?

7

• Note 2 Derived Units

Derived units show comparisons between two
related measures. For example, speed is a measure
of how much distance changes over time. The
units for speed are m/s or km/h.
Distance
Speed
Time
8

• Examples
• A cyclist travels at a steady speed of 24km/h for
  40 minutes. How far did the cyclist travel?
• 40 minutes 2/3hour
• Distance speed x time
• 24 x 2/3
• 16 km

9
Changing from one speed unit to another

• Note 1km 1000m
• 1 hour 3600sec

Examples Change 45km/h into m/s 45km/h 45 x
1000m/h 45000m/h 45000m/3600s 12.5 m/s
10
Examples Change 74m/s into km/h 74m/s
3600x74m/h 266400m/h 266.4km/h
11
Homework Book Page 162-163
12
STARTERS

• Convert the following
• 19m/s to km/h
• A truck travels at an average speed of 75km/h for
  a distance of 300km. What time does the journey
  take?
• A Boeing 747 has a cruising speed of 910km/h.
  Change this into m/s?

13

• Note 3 Perimeter

The perimeter is the distance around the outside
of a shape. Start at one corner and work around
the shape calculating any missing sides.
5 cm
6 cm
5 cm
2 cm
Perimeter 5cm 3cm 6cm 2cm 11cm
5cm 32cm
14
Homework Book Page 164 - 166
15
STARTERS

• Calculate the perimeter of

The plan shows an L-shaped paddock. Calculate
the total cost of fencing it at 24/m
16

• Note 4 Circumference

The perimeter of a circle is called the
circumference. The formula for the circumference
is C pd or C 2pr where d
diameter r radius.
Example Find the circumference of
C 2pr 2 x p x 8cm 50.3cm (1dp)
17
If a sector has an angle at the centre equal to
x, then the arc length is x/360 of the
circumference.
Example Find the perimeter of the sector
Angle of sector 360 - 120 240 Arc
Length x/360 x 2pr 240/360 x 2 x p x
6m 25.1m (1dp) Perimeter 2 x 6m
25.1m 37.1m
18
Homework Book Page 167 - 169
19
STARTERS

• Calculate the perimeter of

Paul goes for a short cycle ride. Each wheel on
his bike has a radius of 27cm. His distance
counter tells him the wheel has rotated 650
times. Find how far he has travelled in metres.
20
Note 5 Area
Area is measured in square units.
21
Examples converting units
22
Examples of converting units
5.6cm2 to mm2 Big Small x 5.6cm2 5.6 x
100 560mm2 396000cm2 to m2 Small
Big 396000cm2 39600010000 39.6m2
23
Examples Calculate the area of these shapes

Area ½ ? base ? height ½ ? 17 ? 10 85
m2
½ ? 12 ? 7 42 m2
24
Radius 7 2 3.5 cm Area x/360 x p x
r² 180/360 x p x 3.5² 19.2 m² (1dp)
Area ½ (sum of bases) x height ½(9 12) x
7 73.5 m² (1dp)
25
Homework Book Page 170 171
26
STARTERS

• Find the area of

A chocolate bar is wrapped in a rectangular piece
of foil measuring 10cm by 15cm. Calculate the
area of the piece of foil. How many pieces could
be cut out from a larger sheet of foil measuring
120cm by 75cm?
27
Note 6 Compound Area

• Compound shapes are made up of more than one
  mathematical shape.
• To find the area of a compound shape, find the
  areas of each individual shapes and either add or
  subtract as you need to.

28
Examples find the area of
Area splits into a rectangle and a triangle
Area Area rectangle area triangle b ? h
½ b ? h 4 ? 5 ½ ? 4 ? 2 24cm2
29
Area splits into a rectangle with another
rectangle taken away
Area area big rectangle area small
rectangle b ? h -
b ? h 6 ? 4 3 ? 2 18m2
30
Homework Book Page 172 174
31
STARTERS

• Find the area of

Trapezium 750 Rectangle 1000 Half Circle
628.3 Area 750 1000 - 628.3 1121.7
cm2
32
Note 7 Finding missing parts of shapes
To find missing sides of shapes, rearrange the
formulas .
Example 1 The area of the triangle is 135m2.
Calculate the height of the triangle.

Area ½ ? base ? height 135 ½ ? 18
? x 135 9x x 15m
33
Example 2 Calculate the radius of a circle
with an area of 65cm2.
Area p ? r2 65 p ? r2 r2
65/p r v65/p 4.5 cm
34
EXERCISES Each of these shapes has an area of
60cm2. Calculate the lengths marked x.
10cm
15cm
2.5cm
v60 7.7cm
35
EXERCISES Calculate the radii of these circles
with the given areas.
18.7 cm
3.87 m
1.38 cm
0.798 km
36
EXERCISES A circle has an area of 39.47m2.
Calculate

• Radius
• Diameter
• circumference

3.55 m
7.09 m
22.27 m