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Metric units
The metric system of measurement is based on powers of
ten and uses the following prefixes:
These prefixes are then followed by a base unit.
The base unit for length is metre.
The base unit for mass is gram.
The base unit for capacity is litre.
Kilo-
Centi-
Milli-
Micro-
meaning 1000
meaning one hundredth
meaning one thousandth
meaning one millionth
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Metric units of length
Metric units used for length are kilometres, metres,
centimetres and millimetres.
1 kilometre (km) = 1000 metres (m)
1 metre (m) = 100 centimetres (cm)
1 metre (m) = 1000 millimetres (cm)
1 centimetre (cm) = 10 millimetres (cm)
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Metric units of length
A race track measures 400 m. An athlete runs
2.6 km around the track. How many laps is this?
400 m = 0.4 km
Number of laps = 2.6 ÷ 0.4
= 6.5 laps
The following day the athlete completes 8 laps.
How many km is this?
8 laps = 8 × 0.4 km
= 3.2 km
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Metric units of mass
Metric units used for mass are tonnes, kilograms and
grams and milligrams.
1 tonne = 1000 kilograms (kg)
1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
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Metric units of mass
60 tea bags weigh 150 g.
How much would 2000 tea bags weigh in kg?
We can solve this problem using a unitary method.
60 tea bags weigh 150 g
So, 1 tea bag weighs (150 ÷ 60) g = 2.5 g
Therefore, 2000 tea bags weigh (2.5 × 2000) g = 5000 g
= 5 kg
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Metric units of capacity
Capacity is a measure of the amount of liquid that a 3-D
object (for example a glass) can hold.
Metric units of capacity are litres (l), centilitres (cl) and
millilitres (ml).
1 litre (l) = 100 centilitres (cl)
1 litre (l) = 1000 millilitres (ml)
1 centilitre (cl) = 10 millilitres (ml)
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Metric units of capacity
A bottle contains 750 ml of orange squash.
The label says: Dilute 1 part squash with 4 parts water.
How many of litres of drink can be made with one bottle?
If the whole bottle was made up we would have
750 ml of squash + (4 × 750) ml of water
= 750 ml of squash + 3000 ml of water
= 3750 ml of drink
= 3.75 l of drink
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Converting metric units
Complete the following:
34 cm = mm
54.8 cl = ml
0.0471 km = m
0.4 l = ml 0.3428 m = mm
7.3 kg = g 23.51 g = mg
0.085 m = mm
To convert from a larger metric unit to a smaller
one we need to _______ by 10, 100, or 1000.multiply
340
548
47.1
400 342.8
7300 23 510
85
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Converting metric units
To convert from a smaller metric unit to a larger
one we need to ______ by 10, 100, or 1000.
Complete the following
920 mm = cm
43.1 cm = m
65800 m = km
530 g = kg 526 mg = g
3460 ml = l 4539 cl = l
87 kg = tonnes
divide
92
0.431
65.8
0.53 0.526
3.46 45.39
0.087
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Units of area
How many cm2
are
there in a m2
?
= 100 cm
= 100 cm
1 m × 1 m = 1 m2
100 cm × 100 cm = 10000 m2
So,
1 m2
= 10 000 cm21 m2
= 10 000 cm2
1 m
1 m
Area is measured in square units.
Here is a square metre or 1 m2
.
10 000 cm2
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Units of area
We can use the following to convert between units of area.
1 km2
= m2
1 000 000
1 m2
= cm2
1 m2
= mm2
1 cm2
= mm2
100
1 hectare = m2
10 000
10 000
1 000 000
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Units of area
A rectangular field measures 150 m by 250m.
What is the area of the field in hectares?
150 m
250 m
The area of the field is
150 m × 250 m = 37 500 m2
1 hectare = 100 m × 100 m
= 10 000 m2
37 500 m2
= 3.75 hectares
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1 cm
1 cm
1 cm
Units of volume
Volume is measured in cubic units.
Here is a cubic centimetre or 1 cm3
.
How many mm3
are
there in a cm3
?
= 10 mm
= 10 mm 1 cm × 1 cm × 1 cm = 1 cm3
10 mm × 10 mm × 10 mm
So, 1 cm3
= 1000 mm31 cm3
= 1000 mm3
= 10 mm
= 1000 mm3
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1 m
1 m
1 m
Units of volume
Volume is measured in cubic units.
Here is a cubic metre or 1 m3
.
How many cm3
are
there in a m3
?
= 100 cm
= 100 cm 1 m × 1 m × 1 m = 1 m3
100 cm × 100 cm × 100 cm
So, 1 m3
= 1 000 000 cm31 m3
= 1 000 000 cm3
= 100 cm
= 1 000 000 cm3
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Units of volume
We can use the following to convert between units of volume.
1 km3
= m3
1 000 000 000
1 m3
= cm3
1 m3
= mm3
1 cm3
= mm3
1000
1 000 000
1 000 000 000
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Units of volume
Dice are packed into boxes measuring 20 cm
by 12 cm by 10 cm.
If the dice are 2 cm cubes, how many of them
fit into a box?
The volume of the box = (20 × 12 × 10) cm3
=
The volume of one dice = (2 × 2 × 2) cm3
= 8 cm3
Number of dice that fit in the box = 2400 ÷ 8
= 300 dice
2400 cm3
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Volume and capacity
Capacity is a measure of the amount of liquid that a 3-D
object can hold.
A litre of water, for example, would fill a container
measuring 10 cm by 10 cm by 10 cm (or 1000 cm3
)
1 l = 1000 cm3
1 ml = 1 cm3
1000 l = 1 m3
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Volume and capacity
Which holds more juice when full; a litre bottle or
a carton measuring 6 cm by 10 cm by 20 cm?
The volume of the carton is (6 × 10 × 20) cm3
= 1200 cm3
1 litre = 1000 cm3
The carton holds more juice.
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Converting units of area, volume and capacity
Complete the following
3 ha = m2
4000 m2
= ha
2.8 m3
= l 6 200 cm2
= m2
4.35 cm2
= mm2
9.6 cl = cm3
0.07 cm3
= mm3
38 000 cm3
= m3
0.72 l = cm3
5630 cm3
= l
30 000 0.4
2800 0.62
435 96
70 0.038
720 5.63
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Units of time
Time does not use the metric system.
1 minute (min) = 60 seconds (s)
1 hour (h) = 60 minutes (min)
1 day = 24 hours (h)
1 week = 7 days
Units of time include years, months, weeks, days, hours (h),
minutes (min) and seconds (s).
1 year = 365 days = 52 weeks
1 leap year = 366 days
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Units of time
A machine takes 4 minutes and 10 seconds to make a
toy car. How long would it take to make 18 toy cars?
4 minutes × 18 = 72 minutes
10 seconds × 18 = 180 seconds = 3 minutes
72 minutes + 3 minutes = 75 minutes
= 1 hour 15 minutes
Hinweis der Redaktion
Ask pupils why they think powers of ten are used for the metric system of measurement. Discuss the fact that it is easy to convert between units by multiplying or dividing by a power of ten. Link: N1 Place value ordering and rounding – powers of ten.
Pupils should know these conversions and the abbreviation for each unit. Ask pupils to give you an example of something that measures about 1 mm. For example, the width of a grain of rice. Ask pupils to give you an example of something that measures about 1 cm. For example, the width of a little finger. Ask pupils to give you an example of something that measures about 1 m. For example, the width of a desk. Ask pupils to give you an example of a distance of about 1 km. For example, the distance from the school to a well-known local landmark.
For the first part of the problem we can either convert both measurements to m or both measurements to km before dividing. Link: N8 Ratio and proportion – direct proportion.
Pupils should know these conversions and the abbreviation for each unit. Distinguish between mass and weight. We often use the word weight to mean mass. However, weight is actually a force due to gravity and can change depending on gravity. Mass, on the other hand, is a measure of the amount of matter contained in an object and is constant throughout space. (The imperial system refers to weights; the metric system refers to mass. So to convert between them using the common conversion formulae we assume them to refer to objects here on earth!) The tonne is also used in the imperial system to describe a similar weight spelt ton. Point out that when the metric system system of measurement was devised in France more than 200 years ago, 1 gram was defined as the weight of 1 cm 3 of pure water. 1000 cm 3 (that ’ s a cube 10 cm by 10 cm by 10 cm) of water weighs 1 kg, and 1 m 3 (or 1 000 000 cm³) weighs 1 tonne. A mm 3 of water weighs 1 mg. Ask pupils to give you an example of something that has a mass of about 1 tonne. For example, the mass of a small car. Ask pupils to give you an example of something that has a mass of about 1 kg. For example, a bag of sugar. Ask pupils to give you an example of something that has a mass of about 1 g. For example, an aspirin tablet (a 1p coin weighs about 3.5 g). Ask pupils to give you an example of something that has a mass of about 1 mg. For example, the mass of 1 mm 3 of water.
Link: N8 Ratio and proportion – direct proportion.
Link: N8 Ratio and proportion – direct proportion.
Pupils often believe that to convert from a larger unit to a smaller unit we should divide to make it smaller. Explain that we actually have to multiply because there are more smaller units in each larger unit. For each problem ask pupils what we have to multiply by to complete the conversion before asking for the solution. Change the numbers to make a new set of problems. Link: N1 Place value, ordering and rounding – Multiplying by 10, 100 and 1000.
Pupils often believe that to convert from a smaller unit to a larger unit we should multiply to make it larger. Stress that we actually have to divide because there are fewer large units for each smaller unit. For each problem ask pupils what we have to divide by to complete the conversion before asking for the solution. Link: N1 Place value, ordering and rounding – Dividing by 10, 100 and 1000.
Practice matching metric units of length.
A square metre is 1 m × 1 m. 1 m is equivalent to 100 cm. Ask pupils to imagine that the square is divided into 100 cm across the length and 100 cm across the width. We can conclude that 1 m 2 is equivalent to 100 cm × 100 cm = 10000 cm 2 .
As each unit appears remind pupils verbally that: 1 km 2 = 1000 m × 1000 m = 1 000 000 m 2 A hectare = 100 m × 100 m = 10 000 m 2 1 m 2 = 100 cm × 100 cm = 10 000 cm 2 1 m 2 = 1000 mm × 1000 mm = 1 000 000 mm 2 1 cm 2 = 10 mm × 10 mm = 100 mm 2
Link: S8 Perimeter, area and volume – area.
Ask pupils to imagine filling a cubic centimetre with cubic millimetres.
Ask pupils to imagine filling a cubic metre with cubic centimetres.
As each unit appears remind pupils verbally that: 1 km ³ = 1000 m × 1000 m × 1000 m = 1 000 000 000 m ³ 1 m ³ = 100 cm × 100 cm × 100 cm = 1 000 000 cm ³ 1 m ³ = 1000 mm × 1000 mm × 1000 mm = 1 000 000 000 mm ³ 1 cm ³ = 10 mm × 10 mm × 10 mm = 1000 mm ³
An alternative method would be to work out how many dice would fit along each length of the box and multiply these together. This would be 10 × 6 × 5 = 300.
Use this activity to demonstrate that we can find the volume of the cuboids by observing the change in the height of the water in the beaker. Each centimetre cube displaces 1 ml of water.
The problems on the left involve converting larger units to smaller units. The problems on the right involve converting smaller units to larger units.
