Measures of distance
This document aims to give KS3 students an understanding of imperial and
metric measures of distance and speed. By the end of this worksheet students
should be able to convert distances and speed between a variety of different
units.
An satellite view of the 12 mile track
(19km) which will be used for the world
record attempt of BLOODHOUND SSC.
Key Vocabulary
Mile
Foot
Inch
Kilometre
Meter
Centimetre
Unit
Measures of length
Length (or distance) measurements are everywhere.
Why are there 2 different ways of measuring length?
Before travel and communication between different countries was easy every
county had their own way of measuring things. In the UK and USA this system
was called the imperial system. This system had units such as miles, feet and
inches but, because it was a system that was sort of invented as it went along,
it was very difficult to work with.
Miles
Feet
Inches
1
= 5280
= 63360
0.0002
=1
= 12
0.00006
= 0.08
=1
In 1668, English bishop John Wilkins, invented a system which was much
easier to understand, called the metric system.
Kilometres
Meters
Centimetres
1
= 1,000
= 100,000
0.001
=1
= 100
0.00001
= 0.01
=1
Nowadays the metric system is officially used in 192 of the 196 countries and
used worldwide in lots of important areas such as medicine and science.
Although most the world now uses the metric system the imperial system is
still used, at least partially, in the UK and the USA.
Because both systems are still in use it is important that you can use both, and
can convert numbers between each system.
It is very important that you know which units you are measuring in! In 1999
NASA lost a spaceship on a trip to Mars because the English scientists involved
in the mission were using imperial units and the NASA team thought the units
were metric. They completely lost the spaceship (it is suspected to have
crashed) and the project had cost $125 million in total!
Starter – Converting Distances
Find an object in the room (e.g. pencil case, desk, poster etc) and measure its
size in both centimetres and inches. Record this data in a table such as the one
below.
Note: Your table will need space to record data for 11 objects.
Size
Object
Cm
Inches
Desk (length)
Desk (width)
Pen
Now find 5 different objects around the room and measure their size in
centimetres only. Without performing any more measurements, find the size
of each of the objects in inches.
Hint: Use information from the object which was measured in both cm and
inches to perform this conversion.
Complete the sentence below to describe how you did each conversion.
Size in inches = size in cm...
Now find 5 more objects and measure their size in inches. Again, record this
data in the table. Next convert the sizes measured in inches into centimetres
and complete the sentence below to describe how you did the conversion.
Size in centimetres = size in inches...
1 meter is equal to 3.3 feet. Using this information, complete the sentences
below to describe the calculation necessary when converting between meters
and feet.
Size in feet = size in meters...
Size in meters = size in feet...
To convert a distance from units of kilometres to miles, the number must be
divided by 1.61. Fill in the correct units to the equation below.
1
= 1.61
Distance conversions – Check your understanding
Work in pairs to put the following lengths in order from shortest to longest.
Colour the ones which are metric units in red and the ones which are imperial
units in blue.
It may be easiest for students to do this activity if the table below is printed
and cut out so that they can physically move the measurements into the
correct order. The activity could also be performed on an interactive
whiteboard.
1m
10cm
2km
6ft
20in
1mi
1cm
1in
1ft
50mi
150cm
1km
Calculating and converting speed
By now you should have had some practice at converting distances between
metric and imperial units, but can we do the same with speed?
Speed can also be measured in either imperial units (miles per hour for
example) or metric units (meters per second is a very common example). So
how can we convert between these units?
Converting between units with the same time factor is exactly the same
principle as converting distances e.g. a mph to kmph conversion would be a
multiplication of 1.61, just the same as a miles to kilometres conversion.
Using this information complete the following calculations:
1. 70kmph in mph
2. 10ft/s in meters/s
3. 5cm/min in inches/min
4. 100 meters/min in ft/min
Converting between speeds with a different time factor requires a little more
thought.
Lets take the example of BLOODHOUND SSC travelling at 1000mph, how fast
is that in meters/s?
It is easiest to perform this calculation in stages. Firstly we can convert the
distance from miles to kilometres:
1000 miles/hour = 1610 kilometres/hour
Next we can convert kilometres into meters:
1610 kilometres/hour = 1,610,000 meters/hour.
The final part of the calculation is to convert the time factor of the speed.
Currently we are measuring how many meters is travelled in 1 hour, but we
want to know how many meters are travelled in 1 second. In order to calculate
this we need to know how many seconds there are in 1 hour.
1 hour = 60 minutes
1 minute = 60 seconds
60 x 60 = 3600 seconds in 1 hour.
Currently we know that the car travels 1,610,000 meters in 1 hour so to find
how many meters are travelled in 1 second that number must be divided by
3600 (i.e. the number of seconds in 1 hour).
1,610,000 / 3600 = 447 meters/s
Hint: Whenever you perform conversion calculations, especially complicated
ones like this, it is a good idea to perform a 'reality check' at each stage. For
example does it sound sensible that 1,610,000 meters/hour is the same as 447
meters/s? Given that we are measuring over a much shorter time period (a
second rather than an hour) this answer does sound plausible. Doing this sort
of check can highlight any silly errors, such as multiplying instead of dividing,
which are easy to make when doing this type of calculation.
Fill in the blanks
This table is quite challenging. You will need a separate piece of paper to write
down your working as you try to convert between each of the units (its always
a good idea to show your working, even if you don't think you need to, just in
case you make a mistake).
Note: Mach 1 is the speed of sound, 340 meters/s.
mph
meters/s
Snail
0.001
Walking pace
1.4
Cheetah
Car on a
motorway
kmph
Mach
110
70
Jet plane
(Boeing 747)
Bullet
988
1.2
BLOODHOUND 1000
SSC
Game - Quick-fire questions
Very often when converting between imperial and metric units it is not
important that you are completely accurate, you may just need a rough idea.
For this activity you should work in groups of 3. 1 person will be the host whilst
the other two are the competitors. The host asks a question from the selection
below and the competitors try to answer as quickly as they can, the first to
answer correctly wins the point. Once one competitor reaches 3 points that
game is won and people should switch roles.
The correct answer for each question is not an exact answer but is within a
range. For example:
Question: A mobile phone screen may be 3.5 inches diagonally, what size is
that in cm?
Answer: The correct answer for this activity is any number between 8 and
10cm (actual answer is 8.89cm).
Questions:
If you can run 10 kilometres in an hour, how long will you take to run 10
miles?
The speed limit in French villages is 50kmph, how fast is that in mph?
The average height of a woman in the UK is 5ft 3in, how tall is that in cm?
A large television may be 55in across, how big is it in cm?
The average length of a football pitch is 340ft, how long is that in meters?
You are flying from London to New York, a journey of about 3500 miles, how
far is that in Km?
The current land speed record is 1228kmph, how fast is that in mph?
The drive from Southampton to Edinburgh takes roughly 7 hours when you
average 60mph, how long would it take if you were travelling at 60kmph?
The long jump world record is 8.95m, how far is that in feet?
BLOODHOUND SSC will cover a mile in 3.6 seconds, how long will it take to do
1 kilometre?
The fastest swimmers in the world swim at a top speed of 2.2m/s, how fast is
that in ft/s?
An A4 piece of paper is 21cm tall, how tall is it in inches?
Run out of questions? Think of your own to challenge your friends to answer!
Remember you need to work out the correct answer before you can use the
question.