NQF Level:
1
US No:
7449
Learner Guide
Primary Agriculture
T h e u s e of
M a t h e m a t ic s in S oc ia l,
P olit ic a l a n d E c on o m ic
R e la t ion s
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The availability of this product is due to the financial support of the National
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
2
Unit Standard No: 7449
Before we start…
Dear Learner - This Learner Guide contains all the information to acquire all the
knowledge and skills leading to the unit standard:
Title:
US No:
Critically analyse how mathematics is used in social, political and economic
relations
7449
NQF Level: 1
Credits: 2
Your facilitator will hand the full unit standard to you. Please read the unit standard
at your own time. Whilst reading the unit standard, make a note of your questions
and aspects that you do not understand, and discuss it with your facilitator.
This unit standard is one of the building blocks in the qualifications listed below.
Please mark the qualification you are currently doing:
Title
ID Number
NQF Level
Credits
National Certificate in Animal Production
48970
1
120
National Certificate in Mixed Farming Systems
48971
1
120
National Certificate in Plant Production
48972
1
120
Please mark the learning program you
are enrolled in:
Your facilitator should explain the above
concepts to you.
Are you enrolled in a:
Mark
Y
N
Learnership?
Skills Program?
Short Course?
You will also be handed a Learner Workbook. This Learner Workbook should be used
in conjunction with this Learner Guide. The Learner Workbook contains the activities
that you will be expected to do during the course of your study. Please keep the
activities that you have completed as part of your Portfolio of Evidence, which will be
required during your final assessment.
You will be assessed during the course of your study. This is called formative
assessment. You will also be assessed on completion of this unit standard. This is
called summative assessment. Before your assessment, your assessor will discuss
the unit standard with you.
Enjoy this learning experience!
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
3
How to use this guide …
Throughout this guide, you will come across certain re-occurring “boxes”. These
boxes each represent a certain aspect of the learning process, containing
information, which would help you with the identification and understanding of these
aspects. The following is a list of these boxes and what they represent:
What does it mean? Each learning field is characterized by unique terms and
definitions – it is important to know and use these terms and definitions correctly. These
terms and definitions are highlighted throughout the guide in this manner.
You will be requested to complete activities, which could be group activities, or individual
activities. Please remember to complete the activities, as the facilitator will assess it and
these will become part of your portfolio of evidence. Activities, whether group or individual
activities, will be described in this box.
Examples of certain
concepts or principles to
help you contextualise
them easier, will be
shown in this box.
The following box indicates a summary of
concepts that we have covered, and offers
you an opportunity to ask questions to your
facilitator if you are still feeling unsure of the
concepts listed.
My Notes …
You can use this box to jot down questions you might have, words that you do not understand,
instructions given by the facilitator or explanations given by the facilitator or any other remarks that
will help you to understand the work better.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
4
What are we going to learn?
What will I be able to do? ...................................................................................
5
Learning Assumed to be in Place ........................................................................
5
Learning Outcomes .............................................................................................
5
An Introduction ...................................................................................................
6
Session 1:
Critically analyse the use of mathematical language and
relationships in the workplace ....................................................
8
Session 2:
Critically analyse the use of mathematical language and
relationships in the economy ......................................................
28
Session 3:
Critically analyse the use of mathematics in social relations .....
32
Session 4:
Critically analyse use of mathematics & mathematical
language & relationships in political relations ............................
38
Bibliography ................................................................................
40
Terms & Conditions .....................................................................
41
Acknowledgements .....................................................................
41
SAQA Unit Standards
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
5
What will I be able to do?
When you have achieved this unit standard, you will be able to:
Analyse critically the use of mathematical language and relationships in the work
place and in the economy.
Analyse critically the use of mathematics in social relations.
Analyse critically the use of mathematics and mathematical language and
relationships in political relations.
Learning Assumed to be in Place
The following competencies at ABET Numeracy level 4 are assumed to be in place:
The ability to work with numbers in various contexts.
The ability to work with patterns in various contexts.
Learning Outcomes
When you have achieved this unit standard, you will have a basic
knowledge and understanding of:
Critically analyse the use of mathematical language and relationships in the
workplace.
Critically analyse the use of mathematical language and relationships in the
economy.
Critically analyse the use of mathematics in social relations.
Critically analyse use of mathematics & mathematical language & relationships in
political relations.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
6
An Introduction
Is math important?
Knowing math is more than being able to balance
your chequebook. Math skills are needed to shop
wisely, buy the best insurance, build your house, buy
furniture, and follow a recipe and, especially critical
today, in the world of work.
How would one be able to make sure you earned the correct salary, you
measured correctly or that an items cost you the correct price without math?
Let’s take a bit of time to examine this in more detail:
Attitudes and misconceptions
Do your experiences in mathematics cause you anxiety? Have you been left with
the impression that mathematics is difficult and only some people are 'good' at
mathematics? Are you one of those people who believe that you 'can't do math',
that you're missing that 'math gene'? Do you have the dreaded disease called
Math Anxiety? Read on, sometimes our school experiences leave us with the
wrong impression about mathematics. There are many misconceptions that lead
one to believe that only some individuals can do mathematics. It's time to dispel
those common myths…
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
7
Tick off true or false:
Statement
True
False
Answer
1. There is one way to
solve a problem…
There are a variety of ways to
solve math problems and variety
of tools to assist with the process.
2. You need a 'math
gene' or dominance
of your left-brain to
be successful at
math…
Like reading, the majority of
people are born with the ability to
do mathematics.
Children and adults need to
maintain a positive attitude and
the belief that they can do
mathematics.
This self-belief has often been
scarred somewhere in the past…
today is the day to make a fresh
start and begin from scratch!
3. People don't learn the
basics anymore
because of a reliance
on calculators and
computers….
Research at this time indicates
that calculators do not have a
negative impact on achievement.
The calculator is a powerful
teaching tool when used
appropriately. Most facilitators
now help you to learn how to use
any technological tool to your
advantage!
4. You need to
memorize a lot of
facts, rules and
formulas to be good
at math…
As stated earlier, there's more
than one way to solve a problem.
Memorizing procedures is not as
effective as conceptually
understanding concepts!
The question to ask yourself is: Do I really understand how, why, when this will
work?
Positive attitudes towards mathematics are the first step to success!
When does the most powerful learning usually occur?
When one makes a mistake!
If you take the time to analyse where you go wrong, you can't help but
learn. Never feel badly about making mistakes in mathematics!
Mathematics has never been more important, technology demands that we
work smarter and have stronger problem solving skills!
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Session
1
NQF Level 1
Unit Standard No: 7449
8
Ma t h e ma t i c a l l a n gu a ge a n d
r e l a t i on s h i p s i n t h e
w or k p l a c e
After completing this session, you should be able to:
SO 1: Critically analyse the use of mathematical language
and relationships in the workplace.
In this session we explore the following concepts:
How mathematics is used in the workplace; wage negotiations,
productivity ratios and salary increases.
Mathematical relationships and language that represent a particular
perspective.
Different forms of comparisons; differences, ratio and versus.
Manipulation of graphs through choice of graph, scale of axes and nature
of axes.
Use of different averages: mean, median, mode.
1.1
How mathematics is used in the
workplace?
Please complete Activity
1 in your learner
workbook
Version: 01
My Notes …
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
1.2
NQF Level 1
Unit Standard No: 7449
9
Salaries and wages
Once we know how mathematics is used in the calculation of salaries and wages, we
can more easily negotiate our salary or wage to ensure that we have the correct
amount of money to pay our bills every week or month! Let’s take a detailed look at
some of the types of mathematical calculations.
Salaries and wages are paid to staff or personnel employed in any business and
organisation for the services they render to the business or organisation. In some
businesses or organisations, this may be one of the biggest expenses that a business
incurs to make a profit or to render services or to sell goods.
When employing a person, you will normally need a contract or an agreement
defining the duties, remuneration, benefits, etc. with each of the employees. Should
you pay or calculate any amount not defined in such agreement, you may overpay
the employee. On the other hand, if you do not pay any amounts defined in such
contract or agreement, you may underpay the employee, which could possibly result
in a dispute, or an unhappy employee.
Salaries
Salaries are usually paid on a monthly basis at a fixed rate for the month.
There is usually no direct relationship between the hours worked or the number
of units produced, as is the case with wages.
Salary = Fixed hourly rate x 22 days x 9 hours
R 1980 = R 10 x 22 x 9
Wages
Wages are normally paid on a weekly, fortnightly and in some cases on a daily
basis. Wages normally has a direct relationship with the amount of hours worked
or the number of units produced in the case of piecework. In some cases, wages
can be charged to the trading account, where it is a component of the cost of
the goods sold. However, when it is not directly related to the cost of goods
sold, it may be charged to the profit and loss account as normal business
expenses.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
10
Wage = Fixed hourly rate x 7 days x 9 hours
R 630 = R 10 x 7 x 9
Gross Pay
In the case of wages, gross pay is the total of the basic hourly rate
multiplied by the number of hours worked, plus any other remuneration
such as overtime, allowances, etc. paid to an employee or worker before any
deductions is taken into consideration.
In the case of salaries, gross pay is the total of the basic monthly salary plus any
allowances, such as commissions, travel allowances, etc. before any deductions
is taken into consideration.
Gross pay = (Fixed hourly rate x 7 days x 9 hours) + (number of hours overtime x 1.5 x
fixed hourly rate)
R 705 = (R 10 x 7 x 9) + (5 x 1.5 x R10)
Deductions
Deductions are any amounts that you must deduct (in accordance with any
legislation or any agreement) from an employee or worker’s salary or wages.
The following are some examples of deductions:
Unemployment Insurance Fund is currently calculated at a rate of 1
percent of the gross earnings.
UIF deduction = Gross pay x 1%
UIF deduction = R 630 x 1/100 = R 6.30
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
11
Employee’s Tax must be calculated and deducted from the employee’s
salary or wages in accordance with the Income Tax Act, as amended from
time to time. However, if an employee or worker earns less than a certain
threshold, which is determined from time to time, no income tax is to be
deducted from that employee or worker’s salary or wage. The tax is
calculated from the income tax tables or IRP 10 tables on the taxable
income.
Pension scheme or provident fund of which the employee is a member.
Medical aid or medical scheme of which the employee is a member.
Insurance - Life and/or short term insurance for which an employee has a
valid debit order to deduct the premiums from his or her salary or wage.
Trade Union or any other agreed deductions.
Garnishee orders issued by a court of law (in order to recover bad debts or
maintenance from an employee’s salary or wages).
Deductions are actually money that is deducted on behalf of an employee. It is
normally paid over to the relevant institution or statutory body.
Net Pay
This is the amount that an employee will take home after any deductions are
made from his gross pay. The net pay is usually paid in cash or cheque to the
employee or worker or by bank transfer directly from your bank account into the
employee’s bank account.
Net pay = Gross pay – UIF – Medical aid
R 560.70 = R 630 – R 6.30 – R 63
Employer’s Contributions
Employer’s contributions are the amount that the employer must contribute
towards certain deductions deducted from an employee’s salary or wages. In
some cases levies must also be paid to the relevant authorities, calculated on the
payroll. The employer must pay the employer’s contributions to the relevant
institution or organisation together with the amount deducted from an
employee’s salary or wage (if applicable).
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
12
The following is a few examples of employer’s contributions:
Unemployment Insurance Fund calculated at a rate of 1 percent of the
gross earnings.
Pension or provident fund.
Medical aid or Medical scheme.
Skills Development Levy (SDL) – 1 percent of the payroll must also be paid
to the South African Revenue Services. In the case of the Skills
Development Levy, no amount is deducted from an employee’s salary or
wages.
1.3 Salary increases
When we receive an increase in salary or wage the increase will normally be
expressed as a percentage. Our boss or union representative might say: You will
receive a 5% increase in wages from the 1st of July 2006. But how will you know
how much that is?
New Gross pay = Old gross pay + (Old Gross pay x 5%)
R 661.50 = R 630 + (R630 x 5 / 100)
Sometimes you might hear that the union has negotiated an “across the board”
increase of R 50.00. That means that every one will then receive R50 more than
they did previously. There is then a difference in how much the percentage increase
would be per person, because every worker might have a different rate of gross pay
to start off with.
Worker A
New Gross pay = Old gross pay + R 50
R 680 = R 630 + R50
Worker B
New Gross pay = Old gross pay + R 50
R 650 = R 600 + R50
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Please complete
Activity 2 in your
learner workbook
NQF Level 1
Unit Standard No: 7449
13
My Notes …
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1.4 Productivity ratios
In order to make sure that an agribusiness is profitable and that all the workers are
working at the best possible speed to produce a high quality crop that can be sold
for a high price at a profit, we need to measure “productivity” of our workers.
But what is productivity and how can we use mathematics to work out that each
worker is measured in the same way?
Productivity:
A measurement of output per hours worked.
Let’s look at a practical example:
Worker A - John manages to prune 50 trees per 9 hour day
Productivity ratio = 50/9
Productivity ratio = 5.555 trees per hour
Worker B - Sipho manages to prune 60 trees per 9 hour day
Productivity ratio = 60/9
Productivity ratio = 6.666 trees per hour
Can you see that Sipho has a better productivity ratio than John?
Please complete
Activity 3 in your
learner workbook
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
14
1.5 Mathematical relationships and language
that represent a particular perspective
Mathematics in the workplace has a language on its own. It is important that we
understand the words and their meanings before we can understand the
mathematical steps to solve problems. We are going to review a list of mathematical
words, some that you may already know and some that may be new to you. Have
fun and remember what you learn!
1.6 Different forms of comparisons
is for
Compare and Comparison
Compare (Verb): To look at two or more things together
and consider them
Susie worked fast compared to Alfred because she weeded 15 more rows than he did.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
1.7
NQF Level 1
Unit Standard No: 7449
15
Differences
Differences:
The difference is what is found when one number is
subtracted from another. Finding the difference in a number
requires the use of subtraction.
Let’s look at a practical example:
Worker A
John manages to prune 50 trees per 9 hour day
Productivity ratio = 50/9
Productivity ratio = 5.555 trees per hour
Worker B
Sipho manages to prune 60 trees per 9 hour day
Productivity ratio = 60/9
Productivity ratio = 6.666 trees per hour
The comparrisson in productivity rate is:
• Worker A: 5.555 < then Worker B: 6.666
The difference in productivity rate is
• Worker A has a 1.111 lower productivity ratio than worker B.
My Notes …
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
1.8
NQF Level 1
Unit Standard No: 7449
16
Versus
Versus:
Means "against" or "opposed to".
Let’s look at a practical example:
Worker A has a 6.66 productivity ratio versus Worker B’s ratio of 5.55
Worker A earns R630 per week versus worker B who earns R650
My Notes …
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
17
1.9 Manipulation of graphs through choice
of graph, scale of axes and nature of
axes
In some of the other modules we have learnt about drawing graphs, and what types
of information we might express on a graph. Let’s take a brief look at how we can
express data differently through applying different types of graph or adjusting the
scale of the graph’s axis:
Pie charts
Information in reports, agri-business meetings, newspapers, magazines and
leaflets may be displayed as pie charts.
A pie chart is a good way of displaying data as it is easy to compare the
segments. Look at this pie chart that shows why people are in debt.
Yield of Oranges / in tones per Block
Yield of Oranges per
ton
Block 6
Block 7
Block 8
Block 9
Note:
• A pie chart is difficult to read if it has more than six slices.
• It may be difficult to compare slices when they are very similar in size.
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
18
Line graphs
Here is an example of a line graph.
What temperature was it on
Wednesday?
Find Wednesday on the horizontal axis.
Lay a ruler up from this point and note
where it crosses the line. Then lay a ruler
across to the vertical axis. Read off the
answer. You should get 19°C. The value
is halfway between the marks for 18°
and 20°.
What are the temperatures for
Monday and Sunday?
The temperature for Monday is 18°C and
the temperature for Sunday is 26°C.
Note:
• A line graph shows how the temperature varies.
• By joining the points together, you can see that the temperature doesn't
just 'jump' from one degree to the next.
In the graph above the temperature difference look very small don’t they?
But let’s see what happens if we change the scale on the y-axis:
28
26
24
22
20
18
16
14
12
10
Fr
id
ay
Tu
es
da
y
W
ed
ne
sd
ay
Th
ur
sd
ay
M
on
da
y
Series1
Let’s discover why the change looks so different…
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
19
1.10 Use of different averages: mean,
median, mode
What is an average?
The average value is a number that is typical for a set of figures. The average is
like the middle point of the numbers. Finding the average helps you do
calculations and also makes it possible to compare sets of numbers.
For example you might spend between R20 and R100 a week on shopping.
Finding the average amount you've spent per week will help you plan your
month's spending. The average weekly spend gives you an idea of whether
you're spending more or less than you plan to.
There is more than one type of average you can have. The type used most often
is the mean value. When people talk about the average of something, like
average price, average wage or average height, they are usually talking about
the mean value.
The mean value of the weekly spending shown in the graph is R46. Can you see
that this is about in the middle of the five different amounts shown?
The mean value can be useful for comparing things. For example you can find
the goal average for a football team by finding the mean value of the goals
scored per match. When you compare goal averages of two teams you are
comparing mean values.
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
20
Mean values can be worked out for the weather too. If the mean winter
temperature increases every year then you might think that global warming is a
serious problem (see the chart below).
How do you calculate the mean?
The mean value of a set of figures is calculated like this: add up the figures to
find the total and then divide by the number of figures in the set.
mean value = total amount ÷ number of figures
So to find the mean value of 5 numbers add them then divide the answer by 5.
To find the mean of 20 numbers add them then divide by 20.
Here are some examples:
Let’s look at a practical example:
Calculate the mean value of 2, 3, and 7.
The total of these numbers is 2+3+7=12
There are 3 figures, so divide by 3, 12÷3=4
The mean value is 4.
Calculate the mean value of 16, 13, 21 and 14.
The total of these numbers is 16+13+21+14=64
There are 4 figures, so divide the total by 4, 64÷4=16
The mean value is 16.
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
21
What about real life averages?
This method works for 'real problems' as well as for just figures. Here's an
example:
The shoe sizes of a group of
6 students are
5, 6, 8, 8, 9 and 12.
How do you find the mean shoe size of the six students?
The total of the students' shoe sizes is 5+6+8+8+9+12=48
There are 6 students, thus the mean shoe size is 48÷6=8.
(We might guess from this that most of the students are male as
the majority of females have feet smaller than size 8!)
Decimal answers (impossible answers)
The mean value is sometimes an 'impossible' number.
Let’s look at a practical example:
A football team has a mean score of 2.4 goals
in a
month.
You can't have 0.4 of a goal!
The mean family size in a town is 4.5
But we can't have 0.5 of a person!
These real-life mean value averages often don't make sense as the answer is not
a whole number. Let's look at an example:
Example In a college there are four classes of numeracy students. The number of
students in each class is 11, 13, 14 and 16. What is the mean number of students in a
class?
To work out the mean number of students in a class find the total number of students and
divide by the number of classes.
The total number of students is 11 + 13 + 14 + 16 = 54
There are 4 classes, so divide the total by 4, 54 ÷ 4 = 13.5
The mean number of students in a class is 13.5
You can't have 0.5 of a student, but this is still the mean value. You could call it an
impossible number in this case.
But, you could still use this number to make calculations. For example, if you know that
the mean class size is 13.5 students then you could estimate that in 10 classes there
would be 10 x 13.5 = 135 students
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
22
Distorted averages
Sometimes the mean value may give a false impression of the figures. In that
case the mean value is said to be distorted.
The mean salary earned in a company is R42 200. You might like the idea of working for
the company! But let's look at the figures:
Employee 1 earns R8 000
Employee 2 earns R12 000
Employee 3 earns R8 000
Employee 4 earns R8 000
The Director of the company earns R175 000
Because the Director earns much more than the employees his/her salary raises the mean
salary. Let's do the sum:
To work out the mean first find the total of the wages:
8 000 + 12 000 + 8 000 + 8 000 + 175 000 = 211 000
Then divide by 5, the number of people:
211 000 ÷ 5 = 42 200
The mean salary is R42 200. But most of the staff earns a lot less than this. Most
employees earn less than the mean salary. For this reason we say that the mean is
distorted.
The average price of a house in an area seems reasonable.
But be careful, the average could be distorted.
The mean price could be distorted if one or two houses are selling for much less
than the others, perhaps because they need lots of work doing to them. It may
seem like a cheap area to buy a house in, but if you look at all of the prices they
may be more expensive than the mean (or 'average') price suggested!
Notice that people say 'average' price of houses when usually what they are
talking about is the mean price.
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
23
Range
Range is the difference between the highest and lowest values in a set of data.
Let’s look at a practical example:
Find the range of these numbers: 6, 4, 6, 5, 3
Put them in order first as this makes it easier to see the lowest and highest
3, 4, 5, 6, 6
The lowest number is 3 and the highest is 6.
Find the difference. Subtract 3 from 6
6-3=3
The range of this set of data is 3.
Compare the range of temperatures for Johannesburg and Cape Town for a week in
January. Temperatures are given in the table in degrees centigrade.
Sun
Mon
Tue
Wed
Thu
Fri
Sat
Johannesburg
19°
19°
20°
20°
20°
18°
18°
Cape Town
20°
22°
22°
21°
20°
21°
19°
Find the range for Johannesburg and put the data into order;
Johannesburg: 18, 18, 19, 19, 20, 20, 20; thus the lowest temperature was 18°C, and the
highest was 20°C.
The difference between the highest and lowest is: 20 – 18 = 2. The range for
temperatures of Johannesburg is therefore 2°C.
Find the range for Cape Town and put the data into order;
Cape Town: 19, 20, 20 , 21, 21, 22, 22; The range is the difference between the highest
and the lowest: 22 – 19 = 3. The range for the temperatures of Cape Town is therefore
3°C
We can compare the temperature ranges for Johannesburg and Cape Town.
Cape Town has a slightly larger range of 3, compared to a range of 2 in
Johannesburg. This means that during this week the temperature in Cape Town
was more variable than in Johannesburg.
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
24
The median
Median is the middle value of a set of data. It is the mid-point when the
numbers are written out in order.
Find the median of these numbers
6, 4, 6, 5, 3
First put the numbers in order. This makes it easier to find the median
3, 4, 5, 6, 6,
You can now see that 5 is the middle number. It is half way along the list.
The median value of this set of data is therefore 5.
Find the median value of these numbers
9, 3, 5, 7, 10, 5
First put the numbers in order. This makes it easier to find the median
3, 5, 5, 7, 9, 10
You can now see that 5 and 7 are in the middle of the list. The median is the exact
middle. So here we need a number half way between 5 and 7. That is 6.
The median value of this set of numbers is therefore 6.
Notice that you can have a median value, which isn't in the list of data itself. In
the example above, 6 is the median value, but 6 isn't in the list of numbers given
in the question.
Why do we use the median?
The median is not so easily distorted as the mean value. It is therefore a better
type of average to use.
Example : Look again at the wages example:
The wages in order are
R8 000, R8 000, R8 000, R12 000, R175 000
The mean is R42 200. This is misleading as it much higher than most of the wages.
The median value is the middle one in the list. The median wage is R8 000. This is a good
indication of the general level of pay.
For this example you could argue that the median is more useful than the mean for giving
an impression of the wages at the company.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
25
The mode
The mode is the name of another type of average. The mode is the most
common item in a set of data. It's the number or thing that appears most often.
For example in a list of peoples' favourite films the mode would be the most
popular choice - the one with most votes.
Find the mode of 6, 4, 6, 5, 3, 7, 6
First put the numbers in order. This makes it easier to find the mode
3, 4, 5, 6, 6, 6, 7
You can see that 6 is the most common number in the list. There are three of them.
We say that 6 is the mode of this set of data.
Find the mode of the shoe sizes for a group of students. Their shoe sizes are:
5, 6, 7, 4, 3, 9, 7, 6, 7, 8, 9
It's easier to see what's going on if you put them in number order
3, 4, 5, 6, 6, 7, 7, 7, 8, 9, 9
It is now easier to see which number appears most often in the list. The most common
number is 7.
So the mode of these shoe sizes is 7.
Find the mode of the sick days taken by employees from the 'Acme Ltd.' company.
Sick days for each employee: 0, 0, 1, 3, 2, 0, 0, 2, 14, 1, 0, 0, 1, 2, 0, 0, 3, 1
First sort them into order
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 14
There are eight people who took no sick days, that's eight 0's. There five 1's, three 2's,
two 3's and one person who took 14 days off sick. So the most common number is 0.
So 0 is the mode of this data.
Mean, median and mode together
Mean = total ÷ number of figures.
Median = middle value when the figures are written in order.
Mode = most common figure in the data.
Comparing mean, median and mode
Let’s look at the figures for sick days in the farm 'Acme Ltd'. The number of days
taken by the employees was:
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 14.
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Critically analyse how mathematics is used in social, political and economic relations
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NQF Level 1
26
Unit Standard No: 7449
Now let's compare those figures with the figures from another farm, 'Corn
Supplies'.
The number of sick days taken by employees at Data Supplies are:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4
For this farm there are two people with no days off sick, ten with 1 day sick,
three 2's, three 3's and one 4. So the mode is 1.
If we compare sick days for these farms we could choose to compare using the
mean, the median or the mode. Let's look at the difference between them.
We need to know the mean, median and mode for both farms. You can work
these out yourself if you want to, but to save time here they are:
Mean
Median
Mode
Acme Ltd
1.6
1
0
Corn Supplies
1.5
1
1
In both companies the mean is higher than the number of sick days most people
have taken. The one person who took 14 days off distorts For Acme Ltd the
mean.
The median is 1 for both companies. So we'd expect the sick days to be more or
less the same in both companies if we used the median values to compare them.
We can also use the mode to compare them. Acme Ltd has a mode of 0 and
Data Supplies a higher value of 1. Going by the mode, we expect sick days to be
more common in Data Supplies.
Which measure do you think is most useful for comparing the companies in this
case? You could say that the mode is best as there does seem to be a higher
level of sick days taken in Data Supplies - only two people there weren't sick at
all!
Please complete
Activity 4 in your
learner workbook
My Notes …
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Concept
NQF Level 1
I understand
this concept
Unit Standard No: 7449
27
Questions that I still would
like to ask
• The ways in which mathematics is
used in the workplace are described.
• Ways in which mathematical
relationships and language can be
used to represent particular
perspectives are described.
• Different forms of comparisons such
as differences versus ratio.
• Manipulation of graphs through
choice of graph, scale of axes and
nature of axes.
• Use of different averages: mean,
median, mode.
• More than one perspective is to be
described
My Notes …
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Session
NQF Level 1
Unit Standard No: 7449
28
Ma t h e ma t i c a l l a n gu a ge a n d
r e l a t i on s h i p s i n t h e
e c o n om y
2
After completing this session, you should be able to:
SO 2: Critically analyse the use of mathematical language
and relationships in the economy.
In this session we explore the following concepts:
Defining mathematical language and relationships in the economy.
•
Budgeting.
•
Mortgage.
•
Fuel prices.
•
Inflation.
•
Exchange rates.
•
Interest rates.
•
Service charges.
•
Pensions.
•
Value of the rand.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
29
Let’s define and understand each of the terms and concepts above
Term
Definition
Example
We budget to spend our weekly wage of R600 as
follows:
R 120 for food
+ R 50 for water and electricity
Budgeting
Budget generally refers
to a list of all planned
expenses
+ R 130 for transport
+ R 100 for clothes
+ R 100 for payment of accounts
+ R 50 for entertainment
+ R 50 for saving
R 600 total
Interest
rates
The cost of borrowing
money, expressed as a
percentage, usually
over a period of one
year.
•
We could buy a television set for R 500.00 cash.
•
But we choose to pay it off over 12 months at an
interest rate of 10%.
•
This means we would calculate our monthly
payment as follows:
o
Capital R 500 / 12 months = R41.66 per
month
o
Interest (R500 x 10%) / 12 months = R4.16
per month
o
This means that we must pay a total
instalment of R45.83 per month.
o
At the end we would have paid R550.00.
We take a mortgage of R 180 000.00 + interest of 10%
over a 20 year period to buy a house.
Mortgage
A loan to purchase a
home, where the
property is used to
guarantee repayment of
the loan
Version: 01
The interest and repayments would work in the same
way as that of account payments.
The difference is that the interest rate will be calculated
differently – this is called compound interest.
The interest rates are also not always fixed and may
change accordingly to decisions made by the bank
when the economy of the country changes.
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Term
Service
charges
NQF Level 1
Definition
The price that we pay
for a public service.
Unit Standard No: 7449
30
Example
When you establish or re-establish an electric service,
water service or telephone service account for
residential or general service, one of the following
service charges will be applied to your first bill
When you connect to Telkom, you will normally pay
services charges of R45.00 per month.
Fuel prices
The price that we pay
for Petrol, Diesel and Oil
varies a from month to
month.
The largest component of the basic fuels price is the
price that one would be paying on international markets
when physically importing product to South Africa. The
FOB (Free on ship’s board) product prices from different
locations in the world, based on international product
availability and product quality, are used. The petrol
FOB price is calculated as 50% of the Mediterranean
spot price for Premium unleaded petrol and 50% of the
Singapore spot price for 95 Octane unleaded petrol. For
the FOB price of Diesel, the new BFP formula use spot
prices calculated as 50% of the Mediterranean price for
Gas oil and 50% of the Arab Gulf price for Gas oil, plus
the quoted spot price market premiums applicable.
The amount of the old age grant changes every year. In 2005 it is R780 per
month.
Pensions
Inflation
If you cannot look after yourself and need full-time care from someone else, you
may also apply for a Grant-In-Aid which you can get in addition to your old age
grant. Also remember that people who get an old age pension have special housing
subsidies available to them
Consumer inflation is calculated as the annual percentage change of the prices of a
collection of some 1 500 different goods and services bought by South African
households – much more than just a shopping basket-full. This is what is called the
Consumer Price Index (CPI). Other definitions of inflation are really nothing more
than a form of shorthand for explaining which goods and services are either
included in, or excluded from, the "basket" for different purposes.
The value of the rand influences the quantity of goods South Africa can export and
import.
Value of the
rand
Exchange
rates.
The dramatic fall in the value of the rand at the end of 2001 had a dramatic
influence on the value of goods that South Africa exported and imported last year.
This affected the trade balance of the balance of payments. This balance measures
the relationship between the value of goods that a country exports and imports. If
the value of goods exported is more than that of the imported goods, the balance
is in surplus, i.e. more foreign money flows into the country than flows out as
payment for goods produced in the rest of the world. If the value of imports is
more than exports, the balance is in a deficit.
The price of a unit of foreign currency in terms of domestic currency. Alternatively
the number of units of domestic currency required purchasing one unit of foreign
currency. The higher this price, the weaker is the domestic currency's exchange
rate. In 2000 the price of exchange rate of the rand to the dollar was $1= R12. By
early 2005 one dollar cost significantly less at around $1 = R 6.
Version: 01
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Please complete
Activity 5 in your
learner workbook
NQF Level 1
Unit Standard No: 7449
31
My Notes …
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.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concept
I understand
this concept
Questions that I still would
like to ask
• The ways in which mathematics is
used is described.
• Ways in which mathematical
relationships and language can be
used to represent particular
perspectives are described.
• The impact of economic changes on
the individual is described.
My Notes …
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Session
3
NQF Level 1
Unit Standard No: 7449
32
Ma t h e ma t i c s i n s oc i a l
r e l a t i on s
After completing this session, you should be able to:
SO 3: Critically analyse the use of mathematics in social
relations.
In this session we explore the following concepts:
Mathematics in social relations.
•
Ways in which mathematics can be used as a filter for social
differentiation.
•
The significance attached to number by different societies.
•
The use of mathematics in the media.
3.1 Ways in which mathematics can be used
as a filter for social differentiation
Statistics:
Interpreting and constructing graphs, mean, median
and mode, frequency distribution, and histograms.
Social differentiation
Mathematics is a human activity. All peoples of the world have contributed
to the development of mathematics.
Mathematics is used as an instrument to express ideas from a wide range
of other fields. The use of mathematics in these fields often creates
problems. This outcome aims to foster a critical outlook to enable learners
to engage with issues that concern their lives individually, in their
communities and beyond.
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
33
Statistical information of all our social resources and
markets
A few statistics about our country:
Population:
Age structure:
44,187,637
Note: estimates for this country explicitly take into account the
effects of excess mortality due to AIDS; this can result in lower life
expectancy, higher infant mortality and death rates, lower
population and growth rates, and changes in the distribution of
population by age and sex than would otherwise be expected (July
2006 est.)
0-14 years: 29.7% (male 6,603,220/female 6,525,810)
15-64 years: 65% (male 13,955,950/female 14,766,843)
65 years and over: 5.3% (male 905,870/female 1,429,944) (2006
est.)
Median age:
Total: 24.1 years
Male: 23.3 years
Female: 25 years (2006 est.)
Population
growth rate:
-0.4% (2006 est.)
Birth rate:
18.2 births/1,000 population (2006 est.)
Death rate:
22 deaths/1,000 population (2006 est.)
Net migration
rate:
-0.16 migrant(s)/1,000 population
Note: there is an increasing flow of Zimbabweans into South Africa
and Botswana in search of better economic opportunities (2006
est.)
Sex ratio:
At birth: 1.02 male(s)/female
Under 15 years: 1.01 male(s)/female
15-64 years: 0.95 male(s)/female
65 years and over: 0.63 male(s)/female
Total population: 0.95 male(s)/female (2006 est.)
Infant mortality
rate:
Total: 60.66 deaths/1,000 live births
Male: 64.31 deaths/1,000 live births
Female: 56.92 deaths/1,000 live births (2006 est.)
Life expectancy
at birth:
Total population: 42.73 years
Male: 43.25 years
Female: 42.19 years (2006 est.)
Total fertility
rate:
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2.2 children born/woman (2006 est.)
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Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
HIV/AIDS - adult
prevalence rate:
HIV/AIDS people living
with HIV/AIDS:
HIV/AIDS deaths:
Ethnic groups:
NQF Level 1
Unit Standard No: 7449
34
21.5% (2003 est.)
5.3 million (2003 est.)
370,000 (2003 est.)
Black African 79%, white 9.6%, coloured 8.9%, Indian/Asian 2.5%
(2001 census)
Religions:
Zion Christian 11.1%, Pentecostal/Charismatic 8.2%, Catholic
7.1%, Methodist 6.8%, Dutch Reformed 6.7%, Anglican 3.8%,
other Christian 36%, Islam 1.5%, other 2.3%, unspecified 1.4%,
none 15.1% (2001 census)
Languages:
IsiZulu 23.8%, IsiXhosa 17.6%, Afrikaans 13.3%, Sepedi 9.4%,
English 8.2%, Setswana 8.2%, Sesotho 7.9%, Xitsonga 4.4%,
other 7.2% (2001 census)
Literacy:
Definition: age 15 and over can read and write
Total population: 86.4%
Male: 87%
Female: 85.7% (2003 est.)
3.2 Historical and possible future contexts
Apartheid policies
Under past political regimes like Apartheid, there was political discrimination
against specific racial and gender groups who were classed according to their
statistical status and effectively excluded from living in specific areas, owning
property and certain levels of education.
3.3 Employment equity
South Africa's policy on black economic empowerment (BEE) is not simply a moral
initiative to redress the wrongs of the past. It is a pragmatic growth strategy that
aims to realise the country's full economic potential.
In the decades before South Africa achieved democracy in 1994, the apartheid
government systematically excluded African, Indian and coloured people collectively known as "black people" - from meaningful participation in the country's
economy.
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Critically analyse how mathematics is used in social, political and economic relations
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NQF Level 1
Unit Standard No: 7449
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This inevitably caused much poverty and suffering - and a profoundly sick economy.
The distortions in the economy eventually led to a crisis, started in the 1970s, when
gross domestic product growth fell to zero, and then hovered at about 3.4% in the
1980s. At a time when other developing economies with similar resources were
growing, South Africa was stagnating.
Full potential
"Our country requires an economy that can meet the needs of all our economic
citizens - our people and their enterprises - in a sustainable manner," the
Department of Trade and Industry (DTI) says in its BEE strategy document.
"This will only be possible if our economy builds on the full potential of all
persons and communities across the length and breadth of this country."
Despite the many economic gains made in the country's 12 years of democracy growth hit 5.1% in 2005 - the racial divide between rich and poor remains. The
DTI points out that such inequality can have a profound effect on political
stability:
"Societies characterised by entrenched gender inequality or racially or ethnically
defined wealth disparities are not likely to be socially and politically stable,
particularly as economic growth can easily exacerbate these inequalities."
Broad-based growth
Black economic empowerment is not affirmative action, although employment
equity forms part of it. Nor does it aim to merely take wealth from white people
and give it to blacks. It is simply a growth strategy, targeting the South African
economy's weakest point: inequality.
"No economy can grow by excluding any part of its people, and an economy that
is not growing cannot integrate all of its citizens in a meaningful way," the DTI
says.
"As such, this strategy stresses a BEE process that is associated with growth,
development and enterprise development, and not merely the redistribution of
existing wealth."
There is a danger, recognised by the government, that BEE will simply replace
the old elite with a new black one, leaving fundamental inequalities intact. For
this reason the strategy is broad-based, as shown in the name of the legislation
enacted in 2004: the Broad Based Black Economic Empowerment Act.
"Government’s approach [is] to situate black economic empowerment within the
context of a broader national empowerment strategy … focused on historically
disadvantaged people, and particularly black people, women, youth, the
disabled, and rural communities," the DTI says.
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Critically analyse how mathematics is used in social, political and economic relations
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Unit Standard No: 7449
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"Discrimination is at its most severe when race coincides with gender and/or
disability."
How to achieve Black Economic Empowerment (BEE)
Black economic empowerment is driven by legislation and regulation. An integral
part of the BEE Act of 2004 is the balanced scorecard, which measures
companies' empowerment progress in four areas:
Direct empowerment through ownership and control of enterprises and
assets.
Management at senior level.
Human resource development and employment equity.
Indirect empowerment through:
•
Preferential procurement,
•
Enterprise development, and
•
Corporate social investment - a residual and open-ended category.
This scorecard is defined and elaborated in the recently released BEE codes of
good practice, which will soon be passed into law.
The codes will be binding on all state bodies and public companies, and the
government will be required to apply them when making economic decisions on:
Procurement,
Licensing and concessions,
Public-private partnerships, and
The sale of state-owned assets or businesses.
Private companies must apply the codes if they want to do business with any
government enterprise or organ of state - that is, to tender for business, apply
for licences and concessions, enter into public-private partnerships, or buy stateowned assets.
Companies are also encouraged to apply the codes in their interactions with one
another, since preferential procurement will affect most private companies
throughout the supply chain.
Different industries have also been encouraged to draw up their own charters on
BEE, so that all sectors can adopt a uniform approach to empowerment and how
it is measured.
The DTI has all the relevant documents and information on black economic
empowerment (in English) available on request.
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NQF Level 1
Unit Standard No: 7449
37
3.4 The use of mathematics in the media
In this age of rapid information expansion and technology, the ability to manage
data and information is an indispensable skill for every citizen. There is an everincreasing need to understand how information is processed and translated into
useable knowledge. Learners should acquire these skills for critical encounter with
information and to make informed decisions.
Mathematics is a language that uses notations, symbols, terminology, conventions,
models and expressions to process and communicate information.
Everyday, we are bombarded by numbers. The source of information using numbers
is frequently on the news. Daily newspapers, magazines, TV and radio news, report
stories which include numbers. Often, these numbers go by so fast, we don't have
time to stop and process them.
Please complete
Activity 6 in your
learner workbook
My Notes …
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.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concept
I understand
this concept
Questions that I still would
like to ask
• Ways in which mathematics can be
used as a filter for social
differentiation are described.
• The significance attached to number
by different societies is described.
• The use of mathematics in the media
is described.
My Notes …
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Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Session
4
NQF Level 1
Unit Standard No: 7449
38
Ma t h e ma t i c a l l a n gu a ge a n d
r e l a t i on s h i p s i n p ol i t i c a l
r e l a t i on s
After completing this session, you should be able to:
SO 4: Critically analyse use of mathematics & mathematical
language & relationships in political relations.
In this session we explore the following concepts:
The use of mathematics and mathematical language and relationships in
political relations.
•
Income distribution.
•
Elections.
•
Opinion polls.
•
Census.
•
Voting.
We define statistics as the study of a large population on the basis of a small
data sample. We make inferences about the population based on the sample
data. What is data? We are mainly interested in numerical data. For us, data
are numbers that describe a numerical characteristic of a certain number of
members of the population. We may talk about data on height, weight,
number of typos, and so on. In this course we talk about data in the context
of statistics.
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
39
4.1 How mathematics is used in – Income
distribution
Income Distribution:
A description of the fractions of a population that are at various levels of
income. The larger the differences in income, the "worse" the income
distribution is usually said to be, the smaller the "better."
Language plays an important role in how we
understand mathematics here:
The following are examples of a population:
If we are studying the income distribution of South Africans, then the population is the
whole South African population.
If we are studying the income distribution of the immigrant American population, then
the population is the whole immigrant American population.
4.2 How mathematics is used in - Census
Census:
A census is the process of obtaining information about every member of a
population (not necessarily a human population). It can be contrasted with
sampling in which information is only obtained from a subset of a
population. As such it is a method used for accumulating statistical data,
and it is also vital to democracy (voting).
Please complete
Activity 7 in your
learner workbook
My Notes …
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Version: 01
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Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
Concept
NQF Level 1
I understand
this concept
Unit Standard No: 7449
40
Questions that I still would
like to ask
• The ways in which mathematics is
used is described.
• Ways in which mathematical
relationships and language can be
used to represent particular
perspectives are described.
• The impact of the use of
mathematics in these contexts on
individuals and social groups is
described.
Bibliography
Books:
Encyclopaedia Brittanica – South African Version
Wikepedia – International Version
Project Literacy Maths Module 4 Volume 1 and 2
Chandler, D. G., & Brosnan, P. A. (1994). Mathematics textbook changes from
before to after 1989. Focus on Learning Problems in Mathematics, 16(4), 1-9
Fan, L., & Kaeley, G. S. (1998). Textbooks use and teaching strategies: An
empirical study. (ERIC Document Reproduction Service No. ED419790)
Lappan, G. (1999). Revitalizing and refocusing our efforts. Mathematics Teacher,
92(7), 648-53
Sosniak, L. A., & Perlman, C. L. (1990). Secondary education by the book. Journal
of Curriculum Studies, 22(5), 427-42
Sturino, G. (2002). Mathematics textbook use by secondary school teachers: A
case study. (Doctoral thesis, OISE/UT Library)
World Wide Web:
wordnet.princeton.edu/perl/webwn
http://en.wikipedia.org/wiki/Calculator#A_basic_calculator
www.en.wikipedia.org/wiki
http://www.mathwords.com/b.htm
enchantedlearning.com
www.bbcskillswise.co.uk
Version: 01
Version Date: July 2006
Critically analyse how mathematics is used in social, political and economic relations
Primary Agriculture
NQF Level 1
Unit Standard No: 7449
41
Terms & Conditions
This material was developed with public funding and for that reason this material
is available at no charge from the AgriSETA website (www.agriseta.co.za).
Users are free to produce and adapt this material to the
maximum benefit of the learner.
No user is allowed to sell this material whatsoever.
Acknowledgements
Project Management:
M H Chalken Consulting
IMPETUS Consulting and Skills Development
Developer:
Cabeton Consulting
Authenticators:
Rural Integrated Engineering
Technical Editing:
Mr R H Meinhardt
OBE Formatting:
Ms P Prinsloo
Design:
Didacsa Design SA (Pty) Ltd
Layout:
Ms P van Dalen
Version: 01
Version Date: July 2006
All qualifications and unit standards registered on the National Qualifications Framework are
public property. Thus the only payment that can be made for them is for service and
reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted,
the South African Qualifications Authority (SAQA) should be acknowledged as the source.
SOUTH AFRICAN QUALIFICATIONS AUTHORITY
REGISTERED UNIT STANDARD:
Critically analyse how mathematics is used in social, political and economic relations
SAQA US ID
UNIT STANDARD TITLE
7449
Critically analyse how mathematics is used in social, political and economic
relations
SGB NAME
NSB
SGB Math. Literacy
Mathematics and Math
Sciences
NSB 10-Physical, Mathematical,
Computer and Life Sciences
REGISTERING PROVIDER
FIELD
SUBFIELD
Physical, Mathematical, Computer and Life Sciences
Mathematical Sciences
ABET BAND
UNIT STANDARD TYPE
NQF LEVEL
CREDITS
ABET Level 4
Regular-Fundamental
Level 1
2
REGISTRATION STATUS
REGISTRATION START DATE REGISTRATION
END DATE
SAQA
DECISION
NUMBER
Reregistered
2003-12-03
SAQA 1351/03
2006-12-03
PURPOSE OF THE UNIT STANDARD
People credited with this unit standard are able to:
analyse critically the use of mathematical language and relationships in the work place and in the
economy;
analyse critically the use of mathematics in social relations;
analyse critically the use of mathematics and mathematical language and relationships in political
relations.
LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING
The following competencies at ABET Numeracy level 4 are assumed to be in place:
the ability to work with numbers in various contexts;
the ability to work with patterns in various contexts.
UNIT STANDARD OUTCOME HEADER
Critically analyse the use of mathematical language
Specific Outcomes and Assessment Criteria:
SPECIFIC OUTCOME 1
Critically analyse the use of mathematical language and relationships in the workplace.
OUTCOME RANGE
Wage negotiations, salary increases, and productivity as a ratio.
ASSESSMENT CRITERIA
ASSESSMENT CRITERION 1
1. The ways in which mathematics is used in the workplace are described.
ASSESSMENT CRITERION RANGE
Percentage, graphs, differences, ratio and proportion.
ASSESSMENT CRITERION 2
2. Ways in which mathematical relationships and language can be used to represent particular perspectives
are described.
ASSESSMENT CRITERION RANGE
Different forms of comparisons such as differences versus ratio.
Manipulation of graphs through choice of graph, scale of axes and nature of axes.
Use of different averages: mean, median, mode.
More than one perspective is to be described.
SPECIFIC OUTCOME 2
Critically analyse the use of mathematical language and relationships in the economy.
OUTCOME RANGE
Budgeting, banks: interest rates, mortgage, service charges; fuel prices; pensions; inflation; value of the
rand and exchange rates.
ASSESSMENT CRITERIA
ASSESSMENT CRITERION 1
1. The ways in which mathematics is used is described.
ASSESSMENT CRITERION RANGE
%, graphs, differences, ratio and proportion.
ASSESSMENT CRITERION 2
2. Ways in which mathematical relationships and language can be used to represent particular perspectives
are described.
ASSESSMENT CRITERION RANGE
Different forms of comparisons such as differences versus ratio.
Manipulation of graphs through choice of graph, scale of axes and nature of axes.
Use of different averages: mean, median, and mode.
More than one perspective to be described.
ASSESSMENT CRITERION 3
3. The impact of economic changes on the individual is described.
SPECIFIC OUTCOME 3
Critically analyse the use of mathematics in social relations.
OUTCOME RANGE
Social differentiation: gender, social mobility, race; historical and possible future contexts, e.g. employment
equity; apartheid policies.
ASSESSMENT CRITERIA
ASSESSMENT CRITERION 1
1. Ways in which mathematics can be used as a filter for social differentiation are described.
ASSESSMENT CRITERION RANGE
Social differentiation includes examples such as entrance qualifications; number of women doing
mathematics.
ASSESSMENT CRITERION 2
2. The significance attached to number by different societies is described.
ASSESSMENT CRITERION RANGE
Spiritual; superstitious; aesthetic; political.
ASSESSMENT CRITERION 3
3. The use of mathematics in the media is described.
ASSESSMENT CRITERION RANGE
Adverts, reports, sports.
SPECIFIC OUTCOME 4
Critically analyse use of mathematics & mathematical language & relationships in political relations
OUTCOME NOTES
Critically analyse the use of mathematics and mathematical language and relationships in political
relations.
OUTCOME RANGE
Income distribution; census; elections; voting; opinion polls.
ASSESSMENT CRITERIA
ASSESSMENT CRITERION 1
1. The ways in which mathematics is used is described.
ASSESSMENT CRITERION RANGE
Percentage, graphs, differences, ratio and proportion.
ASSESSMENT CRITERION 2
2. Ways in which mathematical relationships and language can be used to represent particular perspectives
are described.
ASSESSMENT CRITERION RANGE
Different forms of comparisons such as differences versus ratio.
Manipulation of graphs through choice of graph, scale of axes and nature of axes.
Use of different averages: mean, median, and mode.
More than one perspective to be described.
ASSESSMENT CRITERION 3
3. The impact of the use of mathematics in these contexts on individuals and social groups is described.
UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS
Critical Cross-field Outcomes (CCFO):
UNIT STANDARD CCFO IDENTIFYING
Identify and solve mathematical problems in which responses display that responsible decisions using
critical and creative thinking have been made.
UNIT STANDARD CCFO ORGANIZING
Organise and manage oneself and one`s activities responsibly and effectively.
UNIT STANDARD CCFO COLLECTING
Collect, analyse, organise and critically evaluate mathematical information and show how mathematics is
used in social, political and economic relations.
UNIT STANDARD CCFO COMMUNICATING
Communicate effectively using mathematical symbols.
UNIT STANDARD CCFO DEMONSTRATING
Understand the world as a set of related systems by recognising that problem-solving contexts do not exist
in isolation.
All qualifications and unit standards registered on the National Qualifications Framework are public property. Thus the only
payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is
reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.