Negative Numbers
Includes:
 Read and understand straightforward mathematical
information
 Specify and describe practical activities and tasks using
mathematical information
 Generate results to a given level of accuracy
 Present and explain results
Reviewed Feb 2014/SW
Welcome
Welcome to your workbook on negative numbers.
This workbook contains a mixture of information and exercises to make sure you
understand key points. The workbook is easy to use and totally flexible. It is
designed to help you identify negative numbers that are used in practical
contexts. When you have completed this workbook you will be able to
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Read and understand straightforward mathematical information
Specify and describe practical activities and tasks using mathematical
information
Generate results to a given level of accuracy using methods, measures and
checking procedures
Present and explain results which meet given levels of accuracy
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Negative numbers
In this section we will be looking at negative numbers. To recognise negative
numbers in practical contexts you need to understand
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The words positive and negative
That 0°C is the temperature at which water freezes
That a negative temperature is below zero
An example of how you would be able to use this is to understand the storage
temperature on frozen food packets.
Think about what you do at work or when you are out and about
When would you look need to identify negative numbers?
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What are negative numbers?
It's time for the next space shuttle
launch. The countdown starts:
But what happens after lift off, after
zero?
Let's look at another example, the weather. On a cold December night you can
watch the thermometer as the temperature drops, as the numbers go down:
2 degrees, 1 degree, zero degrees
But what happens to the numbers if it
gets even colder? The temperature and
the numbers keep going down!
These numbers below zero are called negative numbers
A negative number is less than zero.
We write negative numbers like this:
negative 2 is the same as -2
The dash is the negative sign. It is usually written slightly shorter and a little
higher up than a normal minus signs. But on the internet and in newspapers you
will see it written using a minus sign.
Sometimes negative numbers are called minus numbers, careful you don't
confuse these with subtraction.
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Positive numbers
You already use positive numbers all the time! But, unlike negative numbers you
don't have to put a + sign in front of them. Here are some examples of positive
numbers:
3, 46, 689, 1 982
A positive number is more than zero.
Why do negative numbers 'get bigger'?
As you extend a number line showing negative numbers, they seem to get
'bigger'.
The numbers seem to increase in value as they go down the number line.
But as the negative number gets bigger, the value gets lower. -10 is a larger
number than -5, so it is further below zero. If you look at the number line you can
see that -10 is less than -5.
If it helps you remember, think about the weather. As the temperature gets lower
the negative numbers seem to get bigger.
Compare the temperatures during spring, autumn and winter:
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Negative numbers - practical examples
You use negative numbers in lots of different situations.
Temperature
You read about negative numbers in weather reports and on food packaging.
The temperature -5°C is 'negative five degrees' and it means 5 degrees below
zero.
Buildings
Have you ever been in the lift of a building that goes underground?
Watch the floors as you go down. Starting on the third floor you would see:
3, 2, 1, 0, -1, -2
In the building -2 is the second floor underground.
Bank statements
Many of us will recognise negative numbers on a bank statement. If you spend
more money than you have in the account it will show up as a negative number.
Sometimes these numbers are written in red, with a negative sign in front of them
or you will see the letters DR. These all mean that the account is overdrawn - oh
no!
Here's a section from Anna's statement. It shows she is £135 overdrawn. This is
the same as saying -£135; she has negative one hundred and thirty five pounds
in the bank.
Date
17
Feb
19
Feb
22
Feb
24
Feb
Description
Details
ATM (withdrawal) Stoke
1030
Misc deposit
Money
out
20.00
Money
in
Balance
40.00
50.00
90.00
Cheque
100629 150.00
DR -60.00
Cheque
End balance
100630
DR -135.00
DR -135.00
75.00
Take a look around to see if you can find other examples where negative
numbers are used to show less than zero.
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Freezing point of water
On a weather forecast temperatures are given in degrees Celsius. Sometimes
temperatures are called degrees centigrade, which is the same scale.
You can use a short hand for writing temperatures. You use the degree sign °
and C for Celsius. For example you write the temperature 8 degrees Celsius as
8°C.
When water turns to ice it freezes. The temperature water freezes at is zero
degrees Celsius, that's 0°C. Here are some other common temperatures:
Water freezes at 0°C
Below and above freezing
Negative temperatures are called below freezing
and positive temperatures are above freezing.
On the weather map it shows that:
In Newcastle it is 1 which is 1 degree Celsius, 1°C
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1 degree above freezing
In Glasgow it is -4 which is negative 4 degrees Celsius, -4°C
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4 degrees below freezing
On this map it's colder in Glasgow than in Newcastle.
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Reading a thermometer
A thermometer is something that is used to measure temperature. When you've
been to the doctors they might have taken your temperature with a thermometer.
Or you might have one at home showing how hot, or cold, it is inside your house.
Thermometers come in all
shapes and sizes. The digital
ones give the temperature in
numbers, such as 5°C.
With other thermometers you
have to read off the scale - the
numbers along the side. Look at
where the liquid inside the
thermometer is against the scale.
Have a look at these
thermometers and their readings.
What do you notice about the scales?
Did you notice that the scales on the thermometers are different?
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On the first thermometer the scale is between -3°C and 24°C and goes up in
lots of 1°C.
On the second thermometer the scale is between -6°C and 20°C and shows
only even numbers.
On the third thermometer the scale is between -25°C and 40°C and goes up
in lots of 5°C.
Temperature increase and decrease
When the weather changes the temperature can go up or down. If a temperature
goes up, gets warmer, it is a temperature increase. If a temperature goes down,
gets colder, it is a temperature decrease.
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During the summer when you wake up the
morning temperature could be 3°C. By
lunchtime it is up to 10°C.
In the early afternoon the temperature is 15°C. By early
evening the temperature goes down to 12°C.
But what happens if we have negative temperatures?
During winter the early morning temperature
could be -3°C. By lunchtime it is up to 6°C.
From -3°C to 0°C is 3°C.
From 0°C to 6°C is a further 6°C.
The total of 3°C + 6°C makes 9°C.
In the early afternoon the temperature is 3°C. By early
evening the temperature goes down to -5°C.
From 3°C to 0°C is 3°C.
From 0°C to -5°C is a further 5°C.
The total of 3°C + 5°C makes 8°C.
Storing frozen food
Using storage temperatures on packed food.
When food is frozen it is kept at a negative temperature. We keep food cold,
chilled or frozen because it keeps it for longer. But it makes a big difference what
temperature we store it at.
When you buy food that you want to put in the freezer you have to read the
storage instructions. These tell you what temperatures to store the food at. The
colder your freezer, the longer you can store the food for. They show negative
numbers and * symbols which mean different temperatures.
Have a look at these storage instructions from a bag of frozen vegetables. They
show that at different temperatures you can store the food for different lengths of
time:
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Food freezer
Star Marked Frozen Food
Compartment
Ice Making Compartment
Refrigerator
No cold storage
Until best before date (at -18°C)* * *
Until best before date (at -18°C)* * *
1 month at (-12°C)* *
1 week at (-6°C)*
3 days at (-6°C)*
24 hours (at 5°C)
Eat on day of purchase if not kept
frozen.
Star ratings
On the bag for the vegetables * symbols were used beside temperatures. Many
freezers have these star ratings. The stars mean the freezer, of parts of the
freezer, is at a certain temperature.
Number of stars Temperature Degrees below freezing
4****
-18°C
18 degrees below freezing
Suitable for long term storage
3***
-18°C
18 degrees below freezing
2**
-12°C
12 degrees below freezing
1*
-6°C
6 degrees below freezing
none, a fridge
5°C
5 degrees above freezing
Now try the BBC skillswise fact sheets!
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Summary
Having completed this work book you should now be able to:




Read and understand straightforward mathematical information
Specify and describe practical activities and tasks using mathematical
information
Generate results to a given level of accuracy using methods, measures and
checking procedures
Present and explain results which meet given levels of accuracy
What are your thoughts?
Further learning
We hope that you have enjoyed your workbook on negative numbers. You can
access other interactive resources from Ask ELLE .
Or the BBC skills wise website where you can find
 Worksheets
 Quick quizzes
www.bbc.co.uk/skillswise
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