7449 lg pp 240806 - agriseta · 2006-09-21 · so 1: critically analyse the use of mathematical...

LLeeaarrnneerr GGuuiiddee PPrriimmaarryy AAggrriiccuullttuurree

TThhee uussee ooff MMaatthheemmaattiiccss iinn SSoocciiaall,,PPoolliittiiccaall aanndd EEccoonnoommiicc

RReellaattiioonnss

My name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Company: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commodity: . . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . .

NQF Level: 1 US No: 7449

The availability of this product is due to the financial support of the National Department of Agriculture and the AgriSETA. Terms and conditions apply.

Critically analyse how mathematics is used in social, political and economic relations

Primary Agriculture NQF Level 1 Unit Standard No: 7449 22

Version: 01 Version Date: July 2006

BBeeffoorree wwee ssttaarrtt…… Dear Learner - This Learner Guide contains all the information to acquire all the knowledge and skills leading to the unit standard:

Title: Critically analyse how mathematics is used in social, political and economic relations

US No: 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 Mark

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

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.

EEnnjjooyy tthhiiss lleeaarrnniinngg eexxppeerriieennccee!!

Are you enrolled in a: Y N

Learnership?

Skills Program?

Short Course?

Please mark the learning program you are enrolled in:

Your facilitator should explain the above concepts to you.




HHooww ttoo uussee tthhiiss gguuiiddee …… 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.

MMyy NNootteess …… 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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WWhhaatt aarree wwee ggooiinngg ttoo lleeaarrnn?? 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




WWhhaatt wwiillll II bbee aabbllee ttoo ddoo?? 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.

LLeeaarrnniinngg AAssssuummeedd ttoo bbee iinn PPllaaccee 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.

LLeeaarrnniinngg OOuuttccoommeess 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.




AAnn IInnttrroodduuccttiioonn IIss mmaatthh iimmppoorrttaanntt??

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:

AAttttiittuuddeess aanndd mmiissccoonncceeppttiioonnss

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…




TTiicckk ooffff ttrruuee oorr ffaallssee::

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!

WWhheenn ddooeess tthhee mmoosstt ppoowweerrffuull lleeaarrnniinngg uussuuaallllyy ooccccuurr??

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!




SSeessssiioonn

11

MMaatthheemmaattiiccaall llaanngguuaaggee aanndd rreellaattiioonnsshhiippss iinn tthhee wwoorrkkppllaaccee

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.

11..11 HHooww mmaatthheemmaattiiccss iiss uusseedd iinn tthhee wwoorrkkppllaaccee??

Please complete Activity 1 in your learner workbook

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




11..22 SSaallaarriieess aanndd wwaaggeess 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.

SSaallaarriieess

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

WWaaggeess

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.




Wage = Fixed hourly rate x 7 days x 9 hours R 630 = R 10 x 7 x 9

GGrroossss PPaayy

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)

DDeedduuccttiioonnss

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




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.

NNeett PPaayy

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

EEmmppllooyyeerr’’ss CCoonnttrriibbuuttiioonnss

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).




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.

11..33 SSaallaarryy iinnccrreeaasseess

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





MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11..44 PPrroodduuccttiivviittyy rraattiiooss 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?


MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




11..55 MMaatthheemmaattiiccaall rreellaattiioonnsshhiippss aanndd llaanngguuaaggee tthhaatt rreepprreesseenntt aa ppaarrttiiccuullaarr ppeerrssppeeccttiivvee 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!

11..66 DDiiffffeerreenntt ffoorrmmss ooff ccoommppaarriissoonnss

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.




11..77 DDiiffffeerreenncceess

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.


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.

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .

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11..88 VVeerrssuuss

Versus: Means "against" or "opposed to".


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

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .

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11..99 MMaanniippuullaattiioonn ooff ggrraapphhss tthhrroouugghh cchhooiiccee ooff ggrraapphh,, ssccaallee ooff aaxxeess aanndd nnaattuurree ooff aaxxeess

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:

PPiiee cchhaarrttss

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 pertonBlock 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.




LLiinnee ggrraapphhss

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:

10121416182022242628

Monday

Tuesd

ay

Wednes

day

Thursd

ayFrid

ay

Series1

Let’s discover why the change looks so different…




11..1100 UUssee ooff ddiiffffeerreenntt aavveerraaggeess:: mmeeaann,, mmeeddiiaann,, mmooddee

WWhhaatt iiss aann aavveerraaggee??

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.




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).

HHooww ddoo yyoouu ccaallccuullaattee tthhee mmeeaann??

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:


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.




WWhhaatt aabboouutt rreeaall lliiffee aavveerraaggeess??

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!)

DDeecciimmaall aannsswweerrss ((iimmppoossssiibbllee aannsswweerrss))

The mean value is sometimes an 'impossible' number.


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




DDiissttoorrtteedd aavveerraaggeess

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.




RRaannggee

Range is the difference between the highest and lowest values in a set of data.


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.




TThhee mmeeddiiaann

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.




TThhee mmooddee

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.

MMeeaann,, mmeeddiiaann aanndd mmooddee ttooggeetthheerr

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.




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!


MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




Concept I understand

this concept 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

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SSeessssiioonn 22

MMaatthheemmaattiiccaall llaanngguuaaggee aanndd rreellaattiioonnsshhiippss iinn tthhee eeccoonnoommyy

After completing this session, you should be able to: SO 2: Critically analyse the use of mathematical language and relationships in the economy.


Defining mathematical language and relationships in the economy.

• Budgeting.

• Mortgage.

• Fuel prices.

• Inflation.

• Exchange rates.

• Interest rates.

• Service charges.

• Pensions.

• Value of the rand.




Let’s define and understand each of the terms and concepts above

Term Definition Example

Budgeting Budget generally refers to a list of all planned

expenses

We budget to spend our weekly wage of R600 as follows: R 120 for food + R 50 for water and electricity + 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.

Mortgage

A loan to purchase a home, where the

property is used to guarantee repayment of

the loan

We take a mortgage of R 180 000.00 + interest of 10% over a 20 year period to buy a house. 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.




Term Definition Example

Service charges

The price that we pay for a public service.

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.

Pensions

The amount of the old age grant changes every year. In 2005 it is R780 per month.

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

Inflation

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.

Value of the rand

The value of the rand influences the quantity of goods South Africa can export and import.

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.

Exchange rates.

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.





MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



like to ask

• The ways in which mathematics is used is described.


• The impact of economic changes on the individual is described.

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SSeessssiioonn 33 MMaatthheemmaattiiccss iinn ssoocciiaall

rreellaattiioonnss

After completing this session, you should be able to: SO 3: Critically analyse the use of mathematics in social relations.


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.

33..11 WWaayyss iinn wwhhiicchh mmaatthheemmaattiiccss ccaann bbee uusseedd aass aa ffiilltteerr ffoorr ssoocciiaall ddiiffffeerreennttiiaattiioonn

Statistics: Interpreting and constructing graphs, mean, median and mode, frequency distribution, and histograms.

SSoocciiaall ddiiffffeerreennttiiaattiioonn

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.




SSttaattiissttiiccaall iinnffoorrmmaattiioonn ooff aallll oouurr ssoocciiaall rreessoouurrcceess aanndd mmaarrkkeettss

A few statistics about our country:

Population:

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.)

Age structure:

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:

2.2 children born/woman (2006 est.)




HIV/AIDS - adult prevalence rate:

21.5% (2003 est.)

HIV/AIDS - people living

with HIV/AIDS: 5.3 million (2003 est.)

HIV/AIDS - deaths:

370,000 (2003 est.)

Ethnic groups: 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.)

33..22 HHiissttoorriiccaall aanndd ppoossssiibbllee ffuuttuurree ccoonntteexxttss AAppaarrtthheeiidd ppoolliicciieess

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.

33..33 EEmmppllooyymmeenntt eeqquuiittyy 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.




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.

FFuullll ppootteennttiiaall "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."

BBrrooaadd--bbaasseedd ggrroowwtthh

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.




"Discrimination is at its most severe when race coincides with gender and/or disability."

HHooww ttoo aacchhiieevvee BBllaacckk EEccoonnoommiicc EEmmppoowweerrmmeenntt ((BBEEEE))

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 state-owned 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.




33..44 TThhee uussee ooff mmaatthheemmaattiiccss iinn tthhee mmeeddiiaa 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 ever-increasing 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.


MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



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.

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .




SSeessssiioonn 44

MMaatthheemmaattiiccaall llaanngguuaaggee aanndd rreellaattiioonnsshhiippss iinn ppoolliittiiccaall rreellaattiioonnss

After completing this session, you should be able to: SO 4: Critically analyse use of mathematics & mathematical language & relationships in political relations.


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.




44..11 HHooww mmaatthheemmaattiiccss iiss uusseedd iinn –– IInnccoommee ddiissttrriibbuuttiioonn

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."

LLaanngguuaaggee ppllaayyss aann iimmppoorrttaanntt rroollee iinn hhooww wwee uunnddeerrssttaanndd mmaatthheemmaattiiccss hheerree::

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.

44..22 HHooww mmaatthheemmaattiiccss iiss uusseedd iinn -- CCeennssuuss

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).


MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .






like to ask

• The ways in which mathematics is used is described.


• The impact of the use of mathematics in these contexts on individuals and social groups is described.

BBiibblliiooggrraapphhyy BBooookkss::

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)

WWoorrlldd WWiiddee WWeebb::

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




TTeerrmmss && CCoonnddiittiioonnss 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.

AAcckknnoowwlleeddggeemmeennttss PPrroojjeecctt MMaannaaggeemmeenntt::

M H Chalken Consulting

IMPETUS Consulting and Skills Development

DDeevveellooppeerr:: Cabeton Consulting

AAuutthheennttiiccaattoorrss::

Rural Integrated Engineering

TTeecchhnniiccaall EEddiittiinngg::

Mr R H Meinhardt

OOBBEE FFoorrmmaattttiinngg::

Ms P Prinsloo

DDeessiiggnn::

Didacsa Design SA (Pty) Ltd

LLaayyoouutt::

Ms P van Dalen

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:


SAQA US ID UNIT STANDARD TITLE

7449 Critically analyse how mathematics is used in social, political and economic relations

SGB NAME NSB REGISTERING PROVIDER

SGB Math. Literacy Mathematics and Math Sciences

NSB 10-Physical, Mathematical, Computer and Life Sciences

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 2006-12-03 SAQA 1351/03

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.


2. 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.

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


1. The ways in which mathematics is used is described.


%, graphs, differences, ratio and proportion.




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.


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


1. Ways in which mathematics can be used as a filter for social differentiation are described.


Social differentiation includes examples such as entrance qualifications; number of women doing mathematics.


2. The significance attached to number by different societies is described.


Spiritual; superstitious; aesthetic; political.


3. The use of mathematics in the media is described.


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


1. The ways in which mathematics is used is described.


Percentage, graphs, differences, ratio and proportion.




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.


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.

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