Measure, estimate and calculate - Home Page- AgriSeta Estimate and Calculate Physical quantities,...

LLeeaarrnneerr GGuuiiddee PPrriimmaarryy AAggrriiccuullttuurree

MMeeaassuurree,, eessttiimmaattee aanndd ccaallccuullaattee

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

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

NQF Level: 2 US No: 12444

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

Measure, Estimate and Calculate Physical quantities, and Explore, Describe and Represent geometrical relationships in 2-dimensions, in different life or workplace contexts

Primary Agriculture NQF Level 2 Unit Standard No: 12444 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: Measure, Estimate and Calculate Physical quantities, and Explore, Describe and Represent geometrical relationships in 2-dimensions, in different life or workplace contexts.

US No: 12444 NQF Level: 2 Credits: 3

The full unit standard will be handed to you by your facilitator. 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 48976 2 120

National Certificate in Mixed Farming Systems 48977 2 120

National Certificate in Plant Production 48975 2 120

This Learner Guide contains all the information, and more, as well as the activities that you will be expected to do during the course of your study. Please keep the activities that you have completed and include it in your Portfolio of Evidence. Your PoE will be required during your final assessment.

This Learner Guide contains all the information, and more, as well as the activities that you will be expected to do during the course of your study. Please keep the activities that you have completed and include it in your Portfolio of Evidence. Your PoE will be required during your final assessment.

WWhhaatt iiss aasssseessssmmeenntt aallll aabboouutt?? 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.

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.




Assessment takes place at different intervals of the learning process and includes various activities. Some activities will be done before the commencement of the program whilst others will be done during programme delivery and other after completion of the program.

The assessment experience should be user friendly, transparent and fair. Should you feel that you have been treated unfairly, you have the right to appeal. Please ask your facilitator about the appeals process and make your own notes.

HHooww ttoo uussee tthhee aaccttiivviittyy sshheeeettss…… Your activities must be handed in from time to time on request of the facilitator for the following purposes:

The activities that follow are designed to help you gain the skills, knowledge and attitudes that you need in order to become competent in this learning module.

It is important that you complete all the activities and worksheets, as directed in the learner guide and at the time indicated by the facilitator.

It is important that you ask questions and participate as much as possible in order to play an active roll in reaching competence.

When you have completed all the activities and worksheets, hand this workbook in to the assessor who will mark it and guide you in areas where additional learning might be required.

You should not move on to the next step in the assessment process until this step is completed, marked and you have received feedback from the assessor.

Sources of information to complete these activities should be identified by your facilitator.

Please note that all completed activities, tasks and other items on which you were assessed must be kept in good order as it becomes part of your Portfolio of Evidence for final assessment.

EEnnjjooyy tthhiiss lleeaarrnniinngg eexxppeerriieennccee!!




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:

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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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 shownin 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.




WWhhaatt aarree wwee ggooiinngg ttoo lleeaarrnn??

What will I be able to do? ........................................……...........……………………… 6

Learning outcomes…………………………………………..…………………………………… 6

Introduction ………………………………….…………………………………………………… 6

Learner Tips………………………………………………………………………………………… 7

Session 1 Measurement............................................……………………………….. 8

Session 2 Geometrical Shapes..................................………………………………. 29

Session 3 Estimate, Measure and Calculate.............……………………………….. 54

Session 4 Transformations of 2D Geometric figures……………………………….. 76

Am I ready for my test? .....................................……….................... 91

Checklist for Practical assessment ............................………............. 96

Paperwork to be done ........................................................……….... 97

Bibliography ............................................................………………….. 98

Terms & Conditions ...........................................................………….. 98

Acknowledgements ............................................................……….... 98

SAQA Unit Standard




WWhhaatt wwiillll II bbee aabbllee ttoo ddoo?? In this Learning Guide, you will cover the content and skills you need to master the following learning outcomes:

Estimate a measurement Use common measuring instruments Understand and simplify SI Units Convert between SI and Imperial Units Identify properties of geometric shapes Understand the Pythagorean Theorem Estimate, measure and calculate length, breadth, perimeter, area, mass,

temperature and time with correct measuring instruments Understand scales in drawings Understand the differences and similarities between two-and three-dimensional

figures Understand what causes a figure to be symmetrical Understand what perspective is and how it impacts on the visual experience

LLeeaarrnniinngg OOuuttccoommeess At the end of this learning module, you must is able to demonstrate a basic knowledge and understanding of:

Properties of geometric shapes. Length, area, mass, temperature, time. Scale drawing.

IInnttrroodduuccttiioonn During a learning program, you will sometimes be instructed to find additional information on a topic and to use the information you found to show that you understand the topic as part of completing a learning task or assignment. In this guide we will help you to deal with daily mathematical problems, which requires sound knowledge of the mathematical principles. Although we never consider our mathematical skills as part of our daily activities, we actually deal with these concepts all day, every day by being o time for work, producing a certain amount of work, working with our money, making a sandwich and so on.

This learning guide supports the mathematics that you encounter every day and although the knowledge is confined to the learning guide, the application of these mathematical skills is limitless in daily life and work. All you need to add is to look around in your work, home and social life and you will begin to see how good you really are at doing mathematics for life.

Wishing you happy learning!!!




LLeeaarrnneerr TTiippss There are many activities for this Module. Get organized before you begin, by making sure you have a folder to organize your completed written work into a Portfolio of Evidence.

As you read through the module, make your own notes. Keep all your notes in a file. They will be useful in later modules and for your assessment activities.

Keep a simple journal about what you are learning. Each week, write comments about the course, about what you are learning and whether or not you are finding it useful.

Talk to your facilitator about any difficulties you are having with information or ideas. Your facilitator is a learning resource for you.

Throughout this course think about your own experiences as much as possible. Try to relate what you are learning to your own real life experiences. This will make the course more meaningful for you.

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

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SSeessssiioonn 11

MMeeaassuurreemmeenntt

After completing this session, you should be able to: SO 1: Estimate, measure and calculate physical quantities to solve problems in practical situations.

When you have finished working through this session, you should be able to:

estimate a measurement use common measuring instruments understand and simplify SI Units convert between SI and Imperial Units

In this session we explore the following concepts:

We will look at the complete view related to measurement and explore their application, convert larger and smaller measurement and compare metric with

imperial measurement

11..11 MMeeaassuurreemmeennttss Measurement is how we determine the exact capacity of something that is in solid, liquid or gas form.

EEssttiimmaattiioonn

Long ago when people were building pyramids, they required a lot of measuring skills. It is interesting to look at how people developed a system of measures. They started by comparing two quantities, which led to phrases such as ‘taller than’, ‘longer than’, ‘heavier than’, ‘holds more than’, etc. People still do this by themselves when they are working on the land.




For example, we may measure various lengths by counting our stride or by using a piece of cane. We choose our unit measure from what is readily available around us, and this is what men did when they started to measure. They used what are called natural units. For longer distances, units such as a ‘stone-throw’, a ‘day’s journey’ were used. In the same way, for measuring capacity (how much a container can hold) natural units such as a ‘handful’, a ‘Bowl’ was used.

For measuring time, natural happenings were used, such as the ‘seasons (wet and dry)’, ‘day and night’, ‘the waxing and waning of the moon’, ‘at cockcrow’. These natural units (how many more can you think of?) were, of course, not very accurate. For example, a ‘hand-span’ depends upon the size of the person's hand and a ‘bowl- full’ depends upon the size of the bowl. This variation caused much argument and disagreement amongst traders. When comparing more than two quantities, however, they found it necessary to introduce a standard and simple system. So, as trading and commerce developed, it became more and more essential to have units that were the same. Sets of Standard Units had to be devised and introduced.

WWhhyy ddoo wwee mmeeaassuurree??

We measure to find out something about an object.

A carpenter needs to know the length of a piece of wood. It has to be right size.

A baker needs to know how much flour he/she is b buying. If he/she is baking a lot, he /she needs a g greater quantity.

If a person works in the city, he needs to know how long the train journey is. He doesn’t want be late for work!




In the past, each culture used their own system of measuring things. You might have come across some of them, and you may be using some even today.

Stride Foot

Eventually, people decided that there must be an international measurement system where all ranges can be measured according to an agreed standard.

11..22 MMeeaassuurriinngg IInnssttrruummeennttss For each type of measurement, there is a particular measuring instrument

which is most suitable to do the job. It will be impossible to list all the possible

measuring instruments, thus we will look at the most common instruments and welcome your knowledge and experience to enhance understanding of this section.

When using any measuring instruments, ensure that measurement is:

accurate precise viewed squarely off the scale of the measuring instrument

RRuulleerr

A ruler that is in good condition is a practical instrument for measuring shorter, straight lines (linear lines). We can measure millimetres and centimetres with a ruler. (A ruler is not suitable to measure long lengths and round shapes.)

If you need to measure using a ruler, you will place the 0cm measurement at the start of the line and read the measurement at the end of the line on the comparative point on the ruler.




Length of line = 13cm or 130mm

In engineering, we use millimetres as the common measurement. Centimetres are mo re often used for domestic purposes.

Take care when reading measurements:

ensure that you have placed the 0mm exactly on the pre-determined point ensure that you have a square view of the measurement

VVeerrnniieerr CCaalliippeerr

The vernier caliper is used to make semi- accurate measurements for inside, outside and depth dimensions.

Standard vernier calipers are available in sizes 150mm to 250mm. Custom- made vernier calipers can be made to specifications if required. Graduations,

(that determine the accuracy of the instrument) are usually 0,02mm or

0,05mm on the vernier scale.




MMeeaassuurriinngg TTaappeess

A measuring tape is used when a ruler is

too short to measure the distance or length. We

use the measuring tape to measure

short distances in metres.

Measuring tapes are usually gradated in millimetres, centimetres and meters.

MMeeaassuurriinngg CCyylliinnddeerrss oorr JJuuggss

When we need to measure the capacity of a container to determine how many millilitres or litres are in the container, we use measuring cylinders or jugs. These cylinders or jugs have markings that show the measurement. You will notice that when you want to take a measurement of liquid, the level of the liquid does not form a straight line, but a line that is curved at the edges. You need to:

stand level with the line ignore the curved edges squarely look at the level take the measurement where the straight line forms




TThheerrmmoommeetteerrss

Temperature is measured using a thermometer. A thermometer is often filled with mercury and the higher the temperature rises, the more the mercury expands and shows the temperature reading.

In many workplaces, temperature gauges are used to replace thermometers, but essentially they do the same job.

The point, at which the coloored liquid or mercury ends, is where the measurement is taken.

SSccaalleess

Spring or Kitchen Scales

When we need to find the mass of an item, then we use a spring scale (as per the example on the left) or a kitchen scale.

We measure in grams or kilograms how heavy something.

WWaattcchheess aanndd CClloocckkss

We can measure time on either an analogue or digital clock.

An analogue clock is marked in 12 hour intervals and the clock hands need to pass the 12 for the second time to indicate a 24 hour period.




To indicate the period between 12 o’clock midnightand12 o’clock midday, we use the a.m. abbreviation i.e.5:00 a.m. To indicate the period between 12 o’clock noon and 12 o’ clock midnight, we use the p.m. abbreviation i.e. 5:00 p.m.

A digital clock works on a 24 hour basis. We do not use a.m or p.m to indicate the Time of day, because 5:00 a.m is 05h00 And 5:00 p.m is 17h00

17:00

EElleeccttrriicc MMeetteerrss

Electric meters are instruments used to measure electrical values. The two most common meters are the ammeter (which measures ampere) and the voltmeter (which measures volts).

The ammeter and voltmeter are variations of the galvanometer. Inside a galvanometer is a small magnet that sets up a magnetic field. This magnetic field generates a force that we can measure when current flows through a coil.

Below, the meter mechanisms are shown schematically.

The ammeter diverts electricity through a coil via a shunt (illustrated beneath the device), measuring the amount of current flowing through the circuit in amperes. It is connected in series, or directly in the line of the circuit. The voltmeter is connected in parallel, so that the light bulb falls between its two connections into the circuit. It is designed to measure potential differences. To ensure that it removes a minimum of current from the circuit, the voltmeter’s resistance (shown by the jagged black line beneath the device) must be very high. 1




11..33 SSII aanndd IImmppeerriiaall MMeeaassuurreemmeennttss SSII UUnniittss

The System International (S.I) has common units to measure quantities that make communicating measurement between countries easy. The most important measurement concepts are discussed further.

In 1960, the 11th General Conference on Weights and Measures was held in Paris, France. The International System of Units was established here and is commonly referred to as the SI units (Système International d’Unitès).

The SI unit system is based on the metric system, which means that we use 10 (and its subsequent multiples) as the base number to increment various measures.

1 meter = 10 decimeters = 100 centimeters = 1000 millimeters

In the metric system, we use the as described in the headings that follow.

(Please note, short definitions, and in some cases illustrations, have been added to improve your understanding of the terminology. Where applicable, further explanations will be presented in later modules.)

a) Length

Name of Base SI Unit Symbol Value in terms of

other SI units

Length Meter m

Length is the distance between two points i.e.

A B

We often estimate length by giving large steps that are approximately 1 meter in length.




b) Mass


other SI units

Mass Kilogram kg

Mass is the measurement for the quantity of substance

present in a body.

Mass is different from weight. Weight is a measure of the attraction of

the earth for a given mass and is measured in Newton.

The common measuring instruments for mass are scales. Scales can take many forms and the more an item weighs, the larger the scale.

The simplest and oldest weighing mechanism is the equal-arm balance. It has an equal-arm balance which is a bar with two pans hanging from each end and a support at the center of the bar. The bar balances on this center support.

To use an equal-arm balance, an object of unknown weight is placed in one of the pans, and objects of known weight are added to the other pan until the bar holding the pans is balanced; then the weight of the unknown load is the same as the known weight in the other pan.

A spring scale has a platform that is linked to a spring. The spring either extends or squeezes together to balance the load on the platform. A needle indicates the weight of the load. Many bathroom scales are spring scales.

In your job, you will come across electronic scales. They are modern versions of scales and are much faster and more accurate than the mechanical scales. Electronic scales can also be linked to computer systems.

c) Time


other SI units

Time Seconds S

Time is what we use to measure the period that an action or event takes to occur.

During the day, time can be estimated by using the sun and its position as a guide.




We measure time in hours, minutes and seconds. When you are watching athletics, you will see that the top athletes like Marion Brown win the second comer with hundreds or thousands of a second. We usually use a timer, a watch or a clock to measure duration.

d) Capacity


other SI units

Capacity Liter l

Capacity refers to the amount of substance (usually a liquid) that is contained in a specific space.

When we buy a 2- liter coca-cola, we expect it to contain 2 liters of coca-cola.

e) Temperature


other SI units

Temperature Degree Celsius °C

Temperature is the condition or degree of warmness or cold ness of a body.

The weather report shows us the maximum and minimum temperature of the next 24 hour period. We usually use a thermometer to measure temperature. In South Africa, we use degrees Celsius and in some other countries Fahrenheit is the standard measure for temperature. If you need to convert from Celsius to Fahrenheit, then we use the following formula:

F = C x 9/5 + 32




We must convert 30° Celsius to Fahrenheit: F = C x 9/5 + 32 = 30 x 9/5 + = 54 + 32 = 86°F

And if we need to convert 60 Fahrenheit to ° Celsius, then we use the following formula:

C = (5[F – 32]) ° 9 = (5[60 – 32]) ° 9 = (5[28]) ° 9 = 140 ° 9 = 15,5°C

f) Area


other SI units

Area Square Metre m²

Area is the size that a plane surface or two-dimensional shape takes up between its boundary lines (length and breadth). Area is calculated by multiplying the length with the breadth.

The blocks in the figure below shows how much space this figure takes up and this is called the area of the figure. The answer will always be followed by the measure (i.e. meter) squared e.g. m2.

g) Volume


other SI units

Volume is the amount of solid mass that a solid three-dimensional figure occupies (length, breadth and height or depth). Volume is calculated by multiplying length by breadth by height (or depth).




Time = Distance SpeedDistance = Speed(Velocity) x Time

h) Velocity


other SI units

Velocity Metre per second m/s

Velocity is the rate of motion or speed that something travels at in a particular direction.

When calculating velocity, we divide the distance travelled by time it took to travel the distance.

D

Speed(Velocity) = Distance Time S T

i) Acceleration


other SI units

Acceleration Metre per second squared m/s²

Acceleration is the rate at which velocity of an object is increased per unit of time.

j) Density


other SI units

Density Kilogram over cubic metre Kg/m³

Density is the relation between mass and bulk and refers to the solidness of matter. It is the ratio between mass and volume.




k) Frequency


other SI units

Frequency Hertz Hz 1/s

Frequency is the rate at which something occurs in one second. It is expressed in hertz (Hz). A frequency of 1 Hz means that there is 1 cycle or oscillation per second.

l) Force


other SI units

Force Newton N Kg m/s²

Force is the influence that is used so that change or movement takes place. Force can make things move, bring something to rest or make objects change direction.

m) Pressure


other SI units

Pressure / Stress Pascal Pa N/m²

Pressure is the force that is applied by a liquid or gas on a body or surface between bodies.

n) Energy


other SI units Energy / Work / Quantity of

Heat Joule J Nm

Energy is the ability of matter to do work as the result of its motion or its position in relation to forces acting on it

(o) Power

Name of Base SI Unit Symbol

Value in terms of other SI

units

Power Watt W J/s

Power is the rate at which work is performed or energy transferred.




(p) Electric Potential


other SI units

Electric Potential Volt V W/A

Electric potential is the pressure that causes electrons to flow in an electric current.

(q) Electric Resistance


other SI units

Electric Resistance Ohm Ω V/A

Electric resistance is the opposition a device or material offers to the flow of an electrical current.

(r) Electric Current


other SI units

Electric Current Ampere A

The electrical current is the flow of electricity in a circuit.

(s) Thermodynamic Temperature


other SI units

Thermodynamic Temperature Kelvin K

Thermodynamic temperature is the relationship between thermal energy (heat) and matter. Thermodynamics is central to the automotive industry. The automobile engine can be more efficient if the thermodynamics are improved i.e. increase the heat burning the fuel, decrease the exhaust gas temperature.

Zero Kelvin is equal to -273,16°C.




SSiimmpplliiffyyiinngg UUnniittss ooff MMeeaassuurreemmeenntt

The multiplication factor and prefix of metric units of measurement is the same throughout.

Multiplication Factor Scientific Notation Prefix Symbol

1 000 000 000 000 000 000 1018 Exa E 1 000 000 000 000 000 1015 Peta P

1 000 000 000 000 1012 Tera T 1 000 000 000 109 Giga G

1 000 000 106 Mega M 1 000 103 Kilo k 100 102 Hecto H 10 101 Deka da 0,1 10-1 Deci d 0,01 10-2 Centi c 0,001 10-3 Milli m

0,000 001 10-6 Micro µ 0,000 000 001 10-9 Nano n

0,000 000 000 001 10-12 Pico p 0,000 000 000 000 001 10-15 Femto f

0,000 000 000 000 000 001 10-18 Atto a a) Imperial Units

The Imperial system of measurement is still used in countries such as the United Kingdom. It is a more complicated system than the metric system. It was used quite widely in the English colonies and thus gained popularity. However, most Western countries have converted to the metric system.

1 mile = 5 280 feet = 63 360 inches




(b) Conversions between SI and Imperial System

To Convert From Multiply by To Convert From Multiply by

Inches to centimeters 2,540 Centimetres to inches 0,3937

Pounds to kilograms 0,4536 Kilograms to pounds 2,205

Pounds to grams 453,6 Grams to pounds 0,002205

Ounces to grams 28,35 Grams to ounces 15,43

Yards to metres 0,9144 Metres to yards 1,094

Feet to metres 0,3048 Metres to feet 3,281

Miles to kilometers 1,609 Kilometres to miles 0,6214

Tons to kilograms 1016 Kilograms to tons 0,0009842

Gallons to litres 4,456 Litres to gallons 0,22

Acres to hectares 0,4047 Hectares to acres 2,471 Square inches to square centimeters 6,452 Square centimeters to

square inches 0,1550

Square feet to square metres 0,0929 Square metres to

square feet 10,76

Square yards to square metres 0,8361 Square metres to

square yards 1,196

Square miles to square kilometers 2,590 Square kilometers to

square miles 0,3861

Cubic inches to cubic centimeters 16,39 Cubic centimeters to

cubic inches 0,06102

Cubic feet to cubic metres 0,02832 Cubic metres to cubic

feet 35,31

Cubic yards to cubic metres 0,7646 Cubic metres to cubic

yards 1,308

We have to convert 12 cubic yards to cubic metres: 12 x 0,7646 = 9,1752 m3




Please complete Activity 1 at the end of this session.

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

Concept (SO 1) I understand this concept

Questions that I still would like to ask

Scales on the measuring instruments are read correctly.

Quantities are estimated to a tolerance acceptable in the context of the estimation.

The appropriate instrument is chosen to measure a particular quantity.

Calculations are carried out correctly.

Appropriate units are used in measurement and calculation.

Rough sketches are interpreted or used correctly to represent and describe situations.

Scales are used correctly in interpreting and describing situations through scale diagrams.




1. Write down the measurement in millimetres, centimetres and metres of the following lines:

a)

b) c)

d)

e)

Exercise 01: Complete the following task. 11

SSOO 11 AACC 11 My Name:

. . . . . . . . . . . . . . . . . . My Workplace: . . . . . . . . . . . . . . . . . . My ID Number:

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




2. Draw straight lines in your workbook that are of the following lengths:

a) 150mm b) 0,025m c) 8,75cm d) 0,00019km e) 4mm

a) b) c) d) e)

3. Convert the following units from SI to Imperial:

a) 34cm to inches b) 22 litres to gallons c) 70 kilometres to miles d) 78 kilograms to pounds e) 144 square metres to square yards f) 56 metres to feet and yards

a)

b)

c)

d)

e)

f)




4. Convert the following units from Imperial to SI:

a) 16 ounces to grams b) 34 yards to meters c) 6,5 gallons to liters d) 487 feet to meters e) 19 acres to hectares f) 56 tons to kilograms g) 45 inches to centimeters h) 321 cubic inches to cubic meters i) 1092 miles to kilometers j) 12 pounds to kilograms

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

5. Estimate the length, breadth and height of the classroom.




6. Convert the following:

a) Convert 600C to Fahrenheit b) Convert 1000F to degrees Celsius c) Calculate the area of a field of 50m length and 15m breadth. d) A tractor drives 48 km in 2 hours. What is its velocity? e) A train travels at 120km/hr for 3 hours. How far did it travel?

a)

b)

c)

d)

e)

7. Convert the following:

a) 10g to kg b) 5cm to m c) 6km to m d) 10km to m e) 2l to ml f) 150ml to l g) 455kg to g

a)

b)

c)

d)

e)

f)

g)

Facilitator comments: Assessment:




SSeessssiioonn 22

GGeeoommeettrriiccaall SShhaappeess

After completing this session, you should be able to: SO 2: Explore transformations of two-dimensional geometric figures.

When you have finished working through this session, you should be able to:

Identify properties of geometric shapes. Understand the Pythagorean Theorem. In this session we will deal with the key characteristics of geometric shapes

and learn how to use the Pythagorean Theorem to solve problems.

22..11 PPrrooppeerrttiieess ooff GGeeoommeettrriicc SShhaappeess Each geometric shape has its own characteristics by which you can identify and recognize

Geometry is the study of how lines interact with each other to form angles and shapes. It is necessary to appreciate the logical reasoning that goes with understanding the concepts of geometry so that its principles may be applied in various situations.

We start with definitions and axioms (fundamental principles) as our foundation, and build up to the more complex theorems step-by-step.

TTrriiaanngglleess

When lines meet each other they create shapes. A shape made by three lines is called a triangle. Tri means three; therefore triangle means that there are three angles. Triangles always have three interior angles. Triangles have different characteristics by which we can identify the different triangles. Angles of a triangle always add up to 1800.




Scalene Triangle

A scalene triangle is a triangle of which each of the three sides is of different lengths. In other words AB ≠ BC ≠ AC

A

B C

Isosceles Triangle

Any triangle of which two sides are equal in length and two interior angles are of equal size is called an isosceles triangle.

A

B C In ∆ ABC:

AB = AC and ∠B = ∠C

N.B. ∆ is a symbol for showing a triangle




Equilateral Triangle

An equilateral triangle is a triangle of which all three sides are of equal length and all three angles are of equal size.

P

Q R

In ∆PQR PQ = QR = PR

Therefore: All three interior angles are equal

∠P = ∠Q = ∠R = 600

Right-angled Triangle

In a right-angled triangle, one of the angles is 90°.

In ∆PQR: ∠PQR = 90° i.e. it is a right angle. The longest side in any right-angled triangle is called a hypotenuse ∴ PR = Hypotenuse.

Remember that the angles of a triangle add up to 1800


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




QQuuaaddrriillaatteerraallss

Any shape that is formed when four lines meet at different points is called a quadrilateral. The points at which the lines meet are called vertices. We call it a quad for short. (‘Quad’ means four.)

A quad will always have four interior angles because there will be four corners i.e. vertices to create four angles. The four angles always add up to 3600.

rectangle

trapezium

trapezoid

rhombus

parallelogram




Rectangles

A quad with two pairs of opposite sides equal in length and also

parallel to each other. All angles are 90.

AB = DC And AD = BC Opposite sides are equal AB // DC And AD // BC Opposite sides are parallel AC = DB Diagonals are equal in length AE = EC And DE = EB Diagonals cut each other in half ∠A = ∠B = ∠C = ∠D = 90° All interior angles are 900

A rectangle with four sides equal in length and with all interior angles as right angles is called a square.

AB = DC And AD = BC Opposite sides are equal AB // DC And AD // BC Opposite sides are parallel AC = DB Diagonals are equal in length AE = EC And DE = EB Diagonals cut each other in half ∠AEB = 900 Diagonals cut each other at 900 ∠A = ∠B = ∠C = ∠D = 90° All interior angles are 900 ∠ΒΑΕ = 450 Diagonals cut the interior angles in half




Parallelograms

A parallelogram is a quad with two pairs of opposite sides equal in length and parallel to each other but no interior angle is a right angle.

A B

C D AB = DC And AD = BC Opposite sides are equal AB // DC And AD // BC Opposite sides are parallel AE = EC And DE = EB Diagonals cut each other in half ∠A = ∠D and ∠C = ∠B Opposite angles are equal

Rhombus

A rhombus is a quad of which all four sides are equal in length but none of the interior angles are equal to a right angle.

AB = DC And AD = BC Opposite sides are equal AB // DC And AD // BC Opposite sides are parallel AE = EC And DE = EB Diagonals cut each other in half ∠A = ∠B And ∠C = ∠D Opposite angles are equal ∠AEB = 900 Diagonals cut each other at 900




Trapeziums

Trapeziums (a quad with one pair of opposite sides parallel to each other but not necessarily equal in length)

A B

C D AB // DC

P Q

S R PQ // SR

Kite

A quad that has two pairs of adjacent sides equal in length and opposite sides not equal in length.

A

B D

C AB = AD and BC = CD





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

CCiirrcclleess

A circle is formed when a continuous line (circumference) starts at 0 and ends at 360. The centre of a circle is that point which is the equal distance of any lines from the circumference of the circle. The radius of a circle is the line which starts at the centre of the circle and intersects with the circumference of the circle. The diameter of a circle is the line that joins two ends of the circumference and cuts through the centre of the circle.

circumference

diameter (d)

centre radius (r)

AAnngglleess

Right Angles

A right angle is an angle that is formed when 2 lines intersect at 90°.




∠PQR = Right angle.

We always indicate a right angle with the symbol indicated below.

And you write it as: ⊥PQR

The Acute Angle

An acute angle is any angle smaller than 90° i.e. smaller than a right angle.

The right angle is shown by the dotted line to help you understand it easier. The arrow indicates which angle we are dealing with.

A

C

B

A A

C B B

C ∠ABC = Acute angle.




The Straight Angle

The straight angle is an angle that equals 180. Any straight line is 180 and is therefore a straight angle.

P Q R

P

R

Q Q

P

R

∠PQR = 180°

The Obtuse Angle

Obtuse angles are any angles greater than 90° but smaller than 180° i.e. it is a rotation between a right angle and a straight angle.

R

P Q

∠PQR = Obtuse angle




The Revolution

A revolution is any angle that is 360°. (I.e. 2 straight angles or 4 right angles)

The Reflex Angle

A reflex angle is any angle greater than 180° but less than 360° i.e. it is an angle between a straight angle and a revolution.

P Q

R ∠PQR = Reflex angle.




Supplementary Angles

The sum of all the angles that lay along a straight line, will add up to 180°.

S

P Q R

PQR is a line and ∠PQS + ∠SQR = 180°

Any group of angles, which add up to 180,° are supplementary i.e.

∠PQS and ∠SQR are supplementary or ∠PQS is a supplement of ∠SQR.

Opposite Angles

When two lines intersect each other, vertically opposite angles are equal:

A

D

E C

B

Line AB intersect/meet line CD at E.

∠AED is vertically opposite to ∠BEC

∠AED = ∠BEC ∠AEC = ∠DEB




PPaarraalllleell AAnndd TTrraannssvveerrssaall LLiinneess

Parallel lines create many angles when a line intersects them. PQ//RS line PQ is parallel to RS (// means parallel to) and CD intersects lines PQ and RS. CD is called a transversal CD cuts PQ at A and RS at B to create many angles. Remember previous theorems:

• ∠1 = ∠3 and ∠2 = ∠4 (pairs of opposite angles on vertex A)

• ∠5 = ∠7 and ∠6 = ∠8 (pairs of opposite angles on vertex B)

• ∠1 + ∠2 = 180°; ∠3 + ∠4 = 180°; ∠1 + ∠4 = 180°;

and ∠2 + ∠3 = 180° (angles along a line on line PQ at vertex A) • ∠5 + ∠6 =180°; ∠7 + ∠8 = 180°; ∠5 + ∠8 = 180°

and ∠6 + ∠7 = 180°(angles along a line on line RS at vertex B)

The pairs of angles created by the transversal on the parallel lines can be named as follows:

a. Corresponding Angles

• ∠1 and ∠5; ∠2 and ∠6; ∠3 and ∠7; ∠4 and ∠8; are called corresponding angles.

• The corresponding angles are equal to each other in pair’s i.e.

∠1 = ∠5; ∠2 = ∠6; ∠3 = ∠7 and ∠4 = ∠8.

b. Alternate Angles

• 4 and 6; 3 and 5; are called Alternate angles.

• The alternate angles are equal to each other in pairs, i.e. 3 = 5 and 4 = 6.

• Alternate angles are always inside parallel lines.

In conclusion basic geometry involves many terms which needs to be known in definition and also in application:




c. Complementary Angles

• any group of angles which add up to 90°.

d. Perpendicular Angles

C • When two lines meet each other at 90° then they

are perpendicular to each other.

AB meets CD at 90° A B

D ∴ AB⊥ CD at B since ∠ABC = 90° and ∠ABD = 90°

( ⊥ means perpendicular to)


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

22..22 PPyytthhaaggoorreeaann TThheeoorreemm TThhee PPyytthhaaggoorreeaann TThheeoorreemm

In any right-angled triangle, the square of the hypotenuse (the longest side, i.e. the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is called the Pythagorean Theorem.

P R Q In ∆PQR: PR = Hypotenuse ∴ PR X PR = (PQ X PQ) + (QR X QR) ∴ PR2 = PQ2 + QR2




In ∆PQR, line PQ is 3cm and line QR is 2cm

PR2 = PQ2 + QR2

PR2 = 32 + 22 PR2 = 9 + 4 PR2 = 13 PR = √13 = 3.6055512

AAppppllyyiinngg tthhee PPyytthhaaggoorreeaann TThheeoorreemm

The Pythagorean theorem can be used to solve problems where right angled triangles are involved. In your daily surroundings, you will find many applications for the Pythagorean theorem such as roof trusses, stairs etc. The following example will assist you in solving Pythagorean problems:

A

Hypotenuse

θ

C Adjacent Side B

Measure the following sides of the triangle with a ruler:

• BC • AC

Measure the angles with a protractor:

• ∠ABC • ∠BAC • ∠ACB

Calculate the hypotenuse using the formula:

• AB2 = AC2 + BC2 Hypotenuse = Opposite2 + Adjacent2




Sides Angles

Adjacent 8cm (BC)

Opposite 4cm

(AC) Hypotenuse AB2 = 82 + 42

(AB) = 64 + 16 = 80

AB = √80 = 8.9442719

≈ 8,9cm

∠ABC 27°

∠BAC 63° ∠ACB 90°


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

Concept (SO 2) I understand this concept

Questions that I still would like to ask

Properties of symmetrical shapes are recognised and described.

The concept of lines of symmetry in 2-dimensional figures is explored using paper folding and reflections in the lines of symmetry.

The concept of transformation in terms of reflections, translations and rotations is identified and explained using concrete materials.

The descriptions are based on correct application of transformations and other geometrical properties.

Designs, based on transformations and other geometrical properties are innovative, and correct geometrically.




1. Identify the following triangles:

a)

b)

c)

d)

Exercise 02: Complete the following tasks: 22

SSOO 22 My Name:


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




2. Calculate the sizes of the angles marked a-h

a)

b)

c)

d)

e)

f)





1. Identify each of the following quadrilaterals

a)

b)

c)

d)

e)

f)

g)

h)


SSOO 22 My Name:


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




2. Determine the sizes of the sides and angles labeled of a-k

a)

b)

c)

d)





1. Draw the following figures with the correct tools.

a) rectangle with measurements 40mm x 50mm b) square with one side 35mm c) triangle with sides 25mm x 35mm x 50mm d) circle with a radius of 5mm

Describe the above figures characteristics:

a)

b)

c)

d)


SSOO 22 My Name:


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




2. Calculate the unknown angles in each case.

1.

2.

3.

4.

5.

6.

7.




Calculations

1)

2)

3)

4)

5)

6)

7)





1. Calculate the value of the unknown side in each of the following right-angled triangles, by using the Theorem of Pythagoras. (A calculator may be used)

a) P

? 30 cm

Q 40cm R

b) D

120 cm 150 cm

E F ?


SSOO 22 My Name:


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




2. A farmer has a field of 70x110m. Work out the length of the diagonal of the field.

3. A farmer needs to secure a pole of 6m with a rope. The rope needs to be tied to the top of the pole and to a hook 3m from the base of the pole. How long must the rope be? Draw a diagram to help you.





SSeessssiioonn 33 EEssttiimmaattee,, MMeeaassuurree aanndd

CCaallccuullaattee When you have finished working through this session, you should be able to:

Estimate, measure and calculate length, breadth, perimeter, area mass, temperature and time with correct measuring instruments.

Understand scales in drawings. In this session we will deal with the key aspects of estimation and calculation

of measurement of different shapes and learn how to use scales.

33..11 EEssttiimmaattiinngg,, MMeeaassuurriinngg aanndd CCaallccuullaattiinngg Estimation allows us to arrive at a ‘nearly correct’ answer that is close enough for all practical purposes. Estimation is used when an exact answer is not yet required.

• When we want to estimate the size of a room, we will not necessarily measure it with a measuring tape, but give large steps that are roughly equal to a metre. In this case we are ‘estimating’ the size of the room.

• However, when we need to work out the exact answer, then we will measure the exact space with a suitable measuring instrument. This way we can establish an exact answer.

• We want to lay a carpet in a specific room. We will use a measuring tape to get the exact measurement. Otherwise, the carpet may be too small for the room or even too big.

• No matter whether you have estimated or measured, if you want to work out, for instance, the size of a room, you will need to calculate to arrive at a suitable answer.

LLeennggtthh aanndd bbrreeaaddtthh

Length is always the longer side(s) of a shape, while breadth is the shorter sides of a shape. In the example below, length is indicated by the double line while breadth is indicated by the single line. Length and breadth is measured in meters. Any shape that has length and breadth is a two dimensional shape.

You can estimate the length and breadth with your fingers. The length of one side is about six fingers long (i.e. one finger may be 2cm wide, so we can estimate that the length of this is 6 x 2 = 12cm) and the breadth is about 2 fingers long i.e. 2 x 2 = 4cm. Eventually you will be able to estimate the lengths by merely measuring it with your eye.




PPeerriimmeetteerr aanndd CCiirrccuummffeerreennccee

Perimeter Perimeter Perimeter is the distances from one point on the

outside border of a shape, all the way around, back to the same point again. Perimeter and circumference is measured in metres.

Point A

To calculate the perimeter of a rectangle, square, parallelogram:

P = 2 lengt hs + 2 breadths

and the answer is in mm, cm, m or km

To calculate the perimeter of the figure below: 10cm

2cm

P

=

2l + 2b

= 2(10) + 2(2) = 20 + 4 = 24 cm

To calculate the perimeter of any straight lined shape with more than four angles:

P = total sum of the length of all straight sides.




Circumference

Circumference is similar to perimeter, but circumference is the word we use to describe the ‘perimeter’ of a circular shape.

Point A

To calculate the circumference of a circle:

C = 2π r

(where π is 22/7 or 3,14)

To calculate the circumference of the circle below, where π = 3,14:

Diameter 5cm

AArreeaa

Area is the amount of space a shape takes up in two dimensions i.e. length and breadth. The example below shows how a shape with a length of 5cm and a breath of 4cm, takes up a 20cm space. Area is measured in square metres.

5cm

C = 2πr = 2(3,14)(5÷2) = 2(3,14)(2,5) = 15,7 cm




If you measure a space such as a room, then you will estimate the length and breadth by using a stride. A stride is a very large step and is the distance between the heel of the back foot and the toe of the front foot.

Stride

Rectangle To calculate the area of any rectangular shape we use the formula: A = lb (length x breadth) and the answer is in mm2 or cm 2 or m2 or km2

To calculate the area of the shape above: A = lb

= 5 x 4

= 20cm2

Circle To calculate the area of a circle: A = π r2

To calculate the area of the following circle:

5cm A = π r2

= 3,14(52) = 3,14 x 25 = 78,5cm2

Triangle To calculate the area of a triangle:

A = 1/2base x height

A = 1/2 (4) x 3 3cm

= 2 x 3 = 6 cm2 4cm




Trapezium

There are two methods to determine the area of a trapezium. One method is by formula and the second method is by breaking the shape into rectangles and triangles.

Method 1:

A= ½ sum of // sides x perpendicular height = ½((24 + 8) x 5 = 80m2

Method 2:

A = Area 1 + area 2 + area 3 = ½ x 4 x 5 + 8x5 + ½ x 12x5 =10 + 40 + 30m2 =80m2

Parallelogram A = base x height = 15mx8m = 120m2

AARREEAA PPRROOBBLLEEMM SSOOLLVVIINNGG

Sometimes the area that we have to calculate has an irregular shape. It seems impossible to then calculate the area, but a little clever thinking will help you to identify regular shapes within the irregular shape and you can then apply the regular formula.




G

Calculate the area of the shape below: A B

10cm

C G

D

F E 8cm

The whole shape (without the holes) looks like a rectangle. We work out the length and the breadth of the rectangle i.e. Area = l x b

= 10cm x (3 + 3)cm = 10cm x 6cm = 60cm2

F E

Then calculate the area of the missing triangle in the bottom left corner and subtract it from the total area.

The height of the triangle is 3cm. The base of the triangle is the difference between the length of side AB and side EF.

Base of Triangle = Side AB - Side EF = 10cm - 8cm = 2cm

Therefore: Area of Triangle = 1/2 base x height = 1/2 x 3 x 2 = 3cm2

Total Area of Rectangle - Missing Corner

= 60cm2 - 3cm2

= 57cm3




Finally, we calculate the area of the half circle (or semi-circle) in the middle right hand side and then subtract it from the total area that we had left over in b).

We can work out the diameter and radius of the half-circle by subtracting the two equal sides (BC and DE) from the total breadth of 6cm (3cm + 3cm).

Total Area of the Semi-Circle

=

1/2(π r2)

= 1/2 (3,14[3+3-2+2]2

= 1/2 (3,14[6-4]2 = 1/2 (3,14[2]2 = 1/2 (3,14 x 4) = 1/2 x 12.56

= 6,28 cm2

Volume

Volume is the space that a container can take on the inside. In order to determine the volume of a container, we need to add another dimension to the shape i.e. the height or depth.

Up to now, we have calculated the area of a shape, working with the length and the breadth. The length is one dimension, the breadth is the second dimension. If we now add height or depth to a shape, we add a third dimension and we can see how much go into it. The dotted lines in the figure below show how we have added the third dimension i.e. depth.

Ar

ea of the Shape

Length ⊥ breadth ⊥ height




All three sides meet at a 90° angle and the sides are perpendicular to each other. To calculate the volume, we multiply the length by the breadth by the height. The unit of measurement is also multiplied and we end up with cubic metres i.e. m3.

∴ Volume = length x breadth x height.

The box below is 3cm x 3cm x 3cm. We fill the box with 1cm x 1cm x 1cm cubes. This illustrates the volume of 1cm3 cubes that can fit into the box i.e. 27 square boxes or 27 cm3.

Example 1:

3cm 5cm Volume = area x height Or depth

= (l x b) x h 4cm = (5cm x 4cm) x 3cm = 20cm2 x 3cm = 60cm3

5cm




Example 2:

3cm

Volume = area x height or depth = (1/2b x h) x d = (1/2 x 5 x 4) x 3 = 10cm2 x 3cm = 30cm3

4cm 5cm

Example 3: Volume = area x height or depth

= (π r2) x h = (22/7 x 52) x 4 = (22/7 x 25) x 4 = 78,57 x 4 = 314,28cm3

4cm 5cm


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




Angles

Where two lines, that are not parallel, intersect, and angle is formed. We measure angles in degrees (°) and we use a protractor to measure angles. All angles on the lines intersecting below are indicated by a

We use a protractor as follows:

Place the 0° line of the protractor on top of the base line of the angle (in this case ABD).

Make sure the centre point of the protractor lies directly on top of where the two lines meet (point B).

Start from the 0° point and move clockwise to where the secondary line cuts through the point on the protractor (in this case 70°).

If you want to measure angle CBD, your baseline would now be BC and you would place the 0° line of the protractor on top of BC, making sure the central point of the protractor is on top of point B and you will take the measurement (∠CBD will be 110° in this case).

C

A B D

There are a number of common angles that we need to familiarise ourselves with. For information on these angles go back to section 1.4.




DDrraawwiinngg SSccaalleess

Drawing scales are used to reduce the size of a large article so that it can be represented on a piece of paper. Maps normally use scale to indicate to which extent a piece of land has been reduced.

The same principle is used in engineering drawings to illustrate the size of a component or engineering object.

A scale is the ratio of

the distance between two points on a map vs. the actual distance between two points on a surface

Scales can be represented in one of three ways:

as a ratio 1:1 500 000 as a fraction 1/1 500 000

as a graphic scale

Which means that for each 1 unit of measurement on the map, the distance is 1 500 000 of the same units of measurement on the real surface.

A scale drawing is a drawing where the accurate dimensions of an object or figure or area are reduced or enlarged. The scale drawing is the exact duplication of the original figure, shape or object, but it is smaller. An area is shown on a map as the drawing below. The scale on the map is 1:1 500 000. We measure the length and breadth of this drawing, which is 10cm x 5cm. We can then calculate the actual size of the area land, represented on the map.

1 : 1 500 000 1 x 5 : 1 500 000 x 5 5 : 7 500 000

So for every 5cm we measure on the drawing, the real measurement on land is 7 500 000cm (or 7,5 km).

1 : 1 500 000 1 x 10 : 1 500 000 x 10 10 : 15 000 000

The length in this case will be 15km on land.




Scales are very convenient in representing large areas on small scale so that an overall picture can be seen.

The triangle below shows how scale minimizes and maximizes the size of the triangle.


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

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1. A field is 30m long and 15 m wide. Calculate

a) the perimeter

b) the area of the field.

2. A circular irrigator has a diameter of 50m. Calculate

1. the perimeter/circumference of the irrigated area

2. the surface area of the irrigated part of the field.


My Name:


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




3. A sheep dipping tank on a farm has the following dimensions: length = 5m, breadth=2m and depth = 1,2m. Calculate the volume of water that this tank can hold.

4. A farmer wants to fence off a piece of land as a paddock for his horses. There are, however, certain problems. One side of the land is cut off due to overhead power lines. On another side there is a very dangerous hole. See the diagram below to visualize the land. The shaded area represents the paddock that he can create.




Calculate:

a. the length of wire he will need for the perimeter

b. the surface area of the paddock.

5. Below is a diagram of a shed. The roof of the shed needs to be waterproofed with a certain type of paint called KeepDri.




a) calculate the surface area of the roof (remember that there are two halves to the roof!)

b) If 5l of KeepDri paint coats 15m2 of roof, how many 5l tins of paint must he buy?

c) If one 5l tin of KeepDri paint costs R150, how much will it cost him to paint the roof?





1. In the diagram below two scales are shown, Scale A and Scale B, both scales recording kilograms:

80 70 10

60 20

50 30 40

Scale A Scale B

a) What mass is indicated on Scale A?

b) Scale B must be calibrated to record a mass of 120 kg and must have 10 kg intervals. Redraw the diagram above and indicate with an arrow a mass of 100 kg.

Exercise 07:Complete the following tasks: 77

My Name:


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




2. The diagram below represents a feeding trough with dimensions as shown.

b

h y

x

a) Determine a formula for the volume (V) of the trough in terms of x, b, y and h.

b) A formula for the surface area (A) of the trough in terms of x, b, y and h.

c) Calculate the surface area if h = 30mm ; b = 40mm and x = 80mm




3. In the diagram below calculate the length of BC and hence the area of the quadrilateral ABCD.

D

60mm

A E 80mm

44mm 44mm

B C




4. Match the scale drawing that will best suit the reproduction of the object:

Scale Object a) 1:10 South Africa b) 1:2 Ant c) 1cm:1m House d) 1:10 000 Pen e) 10:1 Your place of work f) 1000:1 Telephone g) 100 000:1 h) 1cm:200km

5. In the diagram above AB // CF and AE and BD are straight lines. Calculate, giving reasons,

(a)

(b)

(c)




6. Look at the three angles drawn below:

P

A

Q R B C D

a) Estimate the size of each angle.

∠PQR

∠ACB

∠ACD

b) Measure each angle with a protractor.

∠PQR

∠ACB

∠ACD




c) Say whether each angle is acute, obtuse, right, straight or reflex angle.

∠PQR

∠ACB

∠ACD





SSeessssiioonn 44

TTrraannssffoorrmmaattiioonnss ooff 22DD GGeeoommeettrriicc ffiigguurreess

In this session we explore the following concepts:

Transformations of Two-dimensional (2D) Geometric Figures. Parallel and Transversal Lines. Symmetry. Perspective.

A two-dimensional figure is a figure that has only two dimensions i.e. length and breadth.

Length Breath

A three-dimensional figure is a figure that has three dimensions i.e. length, breadth and height or depth.

Length Depth Breath

We can change a two-dimensional figure, by adding to it height or depth.




The figure below shows how we added depth by drawing parallel lines (indicated by the ----- lines).

For Example

Length Breath

44..11 SSyymmmmeettrryy When a shape is symmetrical, it means that if we cut through the centre of the shape, both sides of the shape will be exactly the same size and shape. If we were to draw this triangle on a piece of paper and fold the paper in half, then the shape will be identical on both sides of the folding line.

Please note that should the line of symmetry be changed in the shape above, the shape will no longer be symmetrical.




The following examples show their symmetry:

44..22 PPeerrssppeeccttiivvee Perspective is the point from where you are viewing an item.




If you stand directly above a can of condensed milk, then you will see this figure: But if you are looking at the same can of condens ed milk at another angle, you may see it as follows:

We have to draw the layout of our lounge using a top view perspective. It may look like this:


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




1. Draw the following two-dimensional shapes and transform them to three- dimensional shapes by adding a height or depth of 3cm.

a) Square with dimensions 250mm

b) Rectangle with dimensions 300mm by 200mm

c) Right-angled triangle with an adjacent side of 3cm and an opposite side of 2cm

d) Circle with a diameter of 400mm

e) Semi-circle with a radius of 1cm.

Exercise 08:Complete the following tasks: 88

My Name:


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




2. Redraw these objects as if you are looking from the top:

a) b)

c) d)




3. Find at least 3 objects (not discussed in this learning guide) that are symmetrical. Redraw them in your workbook and indicate the lines of symmetry.





1. Peter has a piece of land. He has put a fence around it so that his sheep can stay inside. The land is 300m x 800m. How large is the area that his sheep can use?

2. Thandi lives in a rondawel. She wants to paint the walls of the rondawel. The man at the paint shop told her that she would use about 5l of paint per ten square meters. She wants to work out how many litres of paint she needs to buy. The diameter of the rondawel is 5m. The walls are 2 meters high.

3. Martin wants to lay a carpet in his lounge, dining room and passage. His wife Martha writes down the measurements.

Lounge 3m x 4,5m

Dining Room 3,5m x 3m

Passage 1,5m x 4m

Self-Check No 1: Complete the following tasks: SSeellff

CChheecckk

My Name:


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




a. How much carpeting will Martin have to buy to cover all three areas?

b. If the carpet he buys costs R39,93 per square meter, how much will it cost him to carpet out the whole area?

4. Sheila brews beer. She has a tank in which she keeps the beer. The tank is 3 metres high and has a diameter of 2m. How much beer can she hold in such a tank?

5. Thabo wants to build a rectangular container for water. This is for his cattle to drink water from. He wants the container to measure 2m x 0,75m x 1m. How much water will this container hold?




6. The dimensions of a carton box are 56cm x 340mm x 0,75m. How many small boxes that are 10cm3 can you fit into the big box?

7. Kevin works on the production line of a factory that produces steel drums. The drums he makes have a radius of 50cm and a height of 1m. What is the volume of such a drum?




8. The floorplan of a factory is shown in the diagram below. The grey area is thestand on which the factory stands.

a. Calculate the entire area of the factory, without the parking and loading bays.




b) The stand is twice as long as it is wide. Calculate the area of the stand.

9. In the figure below, line PR is extended at both ends. Calculate the size of each of the angles of ∆PQR, giving reasons for your calculations:

155° P

Q 80° R




10. Jabu has to do deliveries at all the points marked on the map below. The scale is 1cm:1km. He has to work out the shortest distance so that he can do all the deliveries. He needs to start and end at point A.




11. Calculate the value of each of the unknown angle in each of the following:

a) B

x 60°

A D C ADC is a straight line

b)

∠AXY = 50°

AB//CD//EF








AAmm II rreeaaddyy ffoorr mmyy tteesstt?? Check your plan carefully to make sure that you prepare in good time. You have to be found competent by a qualified assessor to be declared

competent. Inform the assessor if you have any special needs or requirements before

the agreed date for the test to be completed. You might, for example, require an interpreter to translate the questions to your mother tongue, or you might need to take this test orally.

Use this worksheet to help you prepare for the test. These are examples of possible questions that might appear in the test. All the information you need was taught in the classroom and can be found in the learner guide that you received.

1. I am sure of this and understand it well 2. I am unsure of this and need to ask the Facilitator or Assessor to explain what it means

Questions 1. I am sure

2. I am unsure

1. Identify the types of angles and triangles shown in the diagrams below: a)

b)

c)

d)




e)

f)

(6)

2. Calculate the sizes of the angles indicated by the letters a – o. You must give reasons.

a)

b)

c) d)

e)

(15)




3. Identify the following shape and measure the sides and angles indicated by letters a – c

(4)

4. Use the table below to convert the following units:

To Convert From Multiply by To Convert From Multiply by

Inches to centimeters 2,540 Centimetres to inches 0,3937

Pounds to kilograms 0,4536 Kilograms to pounds 2,205

Pounds to grams 453,6 Grams to pounds 0,002205

Ounces to grams 28,35 Grams to ounces 15,43

Yards to metres 0,9144 Metres to yards 1,094

Feet to metres 0,3048 Metres to feet 3,281

Miles to kilometers 1,609 Kilometres to miles 0,6214

Tons to kilograms 1016 Kilograms to tons 0,0009842

Gallons to litres 4,456 Litres to gallons 0,22

a. 24cm to inches b. 100 kilometres to mile c. 15 yards to meters d. 78 kilograms to

pounds e. 120 pounds to kilograms f. 150g to kg g. 1,5l to ml

(7)




5. For each of the following diagrams calculate the shaded area. a)

b)

(8) (8)

6. A farmhouse has a tank for the collection of rain water. The tank measures 5m in diameter and is 5 m high. Calculate the volume of the tank.

(4)




7. A farmer has a tap in one corner of his shed. The tap needs to be moved to the opposite corner as shown on the diagram.

a) Calculate how much piping the farmer must order to complete the job.

b) If the piping costs R54.50 per meter, calculate how much the pipes will cost.

(6)

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

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CChheecckklliisstt ffoorr pprraaccttiiccaall aasssseessssmmeenntt …… Use the checklist below to help you prepare for the part of the practical assessment when you are observed on the attitudes and attributes that you need to have to be found competent for this learning module.

Observations Answer Yes or No

Motivate your Answer (Give examples, reasons, etc.)

Can you identify problems and deficiencies correctly?

Are you able to work well in a team?

Do you work in an organised and systematic way while performing all tasks and tests?

Are you able to collect the correct and appropriate information and / or samples as per the instructions and procedures that you were taught?

Are you able to communicate your knowledge orally and in writing, in such a way that you show what knowledge you have gained?

Can you base your tasks and answers on scientific knowledge that you have learnt?

Are you able to show and perform the tasks required correctly?

Are you able to link the knowledge, skills and attitudes that you have learnt in this module of learning to specific duties in your job or in the community where you live?

The assessor will complete a checklist that gives details of the points that are checked and assessed by the assessor.

The assessor will write commentary and feedback on that checklist. They will discuss all commentary and feedback with you.

You will be asked to give your own feedback and to sign this document. It will be placed together with this completed guide in a file as part of

you portfolio of evidence.




The assessor will give you feedback on the test and guide you if there are areas in which you still need further development.




PPaappeerrwwoorrkk ttoo bbee ddoonnee …… Please assist the assessor by filling in this form and then sign as instructed.

Learner Information Form

Unit Standard 12444

Program Date(s)

Assessment Date(s)

Surname

First Name

Learner ID / SETA Registration Number

Job / Role Title

Home Language

Gender: Male: Female:

Race: African: Coloured: Indian/Asian: White:

Employment: Permanent: Non-permanent:

Disabled Yes: No:

Date of Birth

ID Number

Contact Telephone Numbers

Email Address

Postal Address

Signature:




BBiibblliiooggrraapphhyy Gray, D.E, 2004. Doing research in the real world. Sage . London.

‘Life skills’ by Edna Rooth

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

DDoonnoorrss::

South Cape College

AAuutthheennttiiccaattoorr::

Ms C Almeida

TTeecchhnniiccaall EEddiittiinngg::

Ms C Almeida

OOBBEE FFoorrmmaattttiinngg::

Ms P Prinsloo

DDeessiiggnn::

Didacsa Design SA (Pty) Ltd

LLaayyoouutt::

Ms A. du Plessis




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:

Implement soil fertility and plant nutrition practices

SAQA US ID UNIT STANDARD TITLE

116311 Implement soil fertility and plant nutrition practices

SGB NAME REGISTERING PROVIDER

SGB Primary Agriculture

FIELD SUBFIELD

Field 01 - Agriculture and Nature Conservation Primary Agriculture

ABET BAND UNIT STANDARD TYPE NQF LEVEL CREDITS

Undefined Regular Level 4 3

REGISTRATION STATUS

REGISTRATION START DATE

REGISTRATION END DATE

SAQA DECISION NUMBER

Registered 2004-10-13 2007-10-13 SAQA 0156/04

PURPOSE OF THE UNIT STANDARD

A learner achieving this unit standard will be able to set up and supervise the implementation of soil preparation and maintain and conserve soil in a safe, effective and responsible manner with consideration to the environment. Learners will gain specific knowledge and skills in soil and plant nutrition and will be able to operate in a plant production environment implementing sustainable and economically viable production principles. They will be capacitated to gain access to the mainstream agricultural sector, in plant production, impacting directly on the sustainability of the sub-sector. The improvement in production technology will also have a direct impact on the improvement of agricultural productivity of the sector.

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING

It is assumed that a learner attempting this unit standard will demonstrate competence against unit standard • NQF 3: Manage Soil Fertility and Plant Nutrition. • NQF 4: Implement a data collection plan. • NQF 4: Execute sustainable resource use and quality control. • NQF 4: Plan and maintain environmentally sound agricultural processes.

UNIT STANDARD RANGE

Whilst range statements have been defined generically to include as wide a set of alternatives as possible, all range statements should be interpreted within the specific context of application.

Range statements are neither comprehensive nor necessarily appropriate to all contexts. Alternatives must however be comparable in scope and complexity. These are only as a general guide to scope and complexity of what is required.

UNIT STANDARD OUTCOME HEADER

N/A

Specific Outcomes and Assessment Criteria:

SPECIFIC OUTCOME 1

Interpret recommendations and set up a nutritional programme based on recommendations.

OUTCOME RANGE

Recommendations may be from an analytical laboratory, and nutritional programmes may include application of agrochemicals, organic material, lime, etc.

ASSESSMENT CRITERIA

ASSESSMENT CRITERION 1

A soil nutrition programme is developed based on a recommendation.


Stock levels are maintained and orders are placed timeously.

SPECIFIC OUTCOME 2

Implement soil utilization plan for specified crops.

OUTCOME RANGE

Soil depth, drainage, infiltration rate, pH, water holding capacity, field capacity, soil horizons, soil aeration, erosion risks, organic content, texture, clay content, structure, biological content, compaction.

ASSESSMENT CRITERIA


The ability to select the appropriate soil for various crops is demonstrated.


The influence of soil characteristics or crop growth is explained.

SPECIFIC OUTCOME 3

Identify and interpret symptoms of nutritional deficiencies, and make full recommendations.

OUTCOME RANGE

Macronutrients may include (among others) Nitrogen, Phosphorous, Potassium, Calcium, Magnesium and Sulphur. Micronutrients may include (among others) Boron, Zinc, Iron, Molybdenum and Manganese.

ASSESSMENT CRITERIA


Colour changes on plants are interpreted and related to specific nutrient deficiencies.


Full recommendations for both macro- and micronutrients are proposed and presented.


Soil and leaf samples for are taken for laboratory analysis.

SPECIFIC OUTCOME 4

Manage soil improvement according to soil properties.

OUTCOME RANGE

Soil improvement methods may include tillage operations (mechanical, non mechanical, organic, minimum and zero tillage.

ASSESSMENT CRITERIA


The appropriate soil preparation method is selected.


Records are maintained over time and changes in soil properties are analysed and used in management programmes

UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS

The assessment of qualifying learners against this standard should meet the requirements of established assessment principles. It will be necessary to develop assessment activities and tools, which are appropriate to the contexts in which the qualifying learners are working. These activities and tools may include an appropriate combination of self-assessment and peer assessment, formative and summative assessment, portfolios and observations etc. The assessment should ensure that all the specific outcomes; critical cross-field outcomes and essential embedded knowledge are assessed. The specific outcomes must be assessed through observation of performance. Supporting evidence should be used to prove competence of specific outcomes only when they are not clearly seen in the actual performance. Essential embedded knowledge must be assessed in its own right, through oral or written evidence and cannot be assessed only by being observed. The specific outcomes and essential embedded knowledge must be assessed in relation to each other. If a qualifying learner is able to explain the essential embedded knowledge but is unable to perform the specific outcomes, they should not be assessed as competent. Similarly, if a qualifying learner is able to perform the specific outcomes but is unable to explain or justify their performance in terms of the essential embedded knowledge, then they should not be assessed as competent. Evidence of the specified critical cross-field outcomes should be found both in performance and in the essential embedded knowledge. Performance of specific outcomes must actively affirm target groups of qualifying learners not, unfairly discriminate against them. Qualifying learners should be able to justify their performance in terms of these values. • Anyone assessing a learner against this unit standard must be registered as an assessor with the relevant ETQA.

• Any institution offering learning that will enable achievement of this unit standard or assessing this unit standard must be accredited as a provider with the relevant ETQA. • Moderation of assessment will be overseen by the relevant ETQA according to the moderation guidelines in the relevant qualification and the agreed ETQA procedures.

UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE

The person is able to demonstrate a basic knowledge of: • Sampling procedures. • Chemical, properties of soil - pH, nutrient status and degradation. • Physical properties of soil - Texture, structure, soil profiles, crust formation, erosion types, compaction, and degradation. • Biological properties of soil and processes. • Soil ecology e.g. soil organisms, food webs, role of water and oxygen in soil. • Soil health and conservation. • Role of living organisms. • Conservation practices - Runoff control, contours. • Tillage operations - mechanical, non mechanical, organic, minimum and zero Tillage and application of nutrients (liquid and solid) Primary and secondary soil preparation methods. • Soil preparation and fertiliser/ compost application equipment. • Nutrients - mixtures, limes, calcite and dolomite lime, single nutritients and compost, liquids, etc. • Calibration of equipment. • Chemical, physical and biological properties, degradation and rehabilitation. • Characteristics of the nutrients. • Role of nutrients in the plant. • Rules and regulations for storage and handling of agro-chemicals transport. • Crop requirements. • Soil water relationships. • Mulching and ploughing in of mulch layer. • Pollution prevention. • Biological processes. • Mineral cycles e.g. Nitrogen.

UNIT STANDARD DEVELOPMENTAL OUTCOME

N/A

UNIT STANDARD LINKAGES

N/A

Critical Cross-field Outcomes (CCFO):

UNIT STANDARD CCFO IDENTIFYING

Problem Solving: Relates to all specific outcomes.

UNIT STANDARD CCFO WORKING

Teamwork: Relates to all specific outcomes.

UNIT STANDARD CCFO ORGANIZING

Self-management: Relates to all specific outcomes.

UNIT STANDARD CCFO COLLECTING

Interpreting Information: Relates to all specific outcomes.

UNIT STANDARD CCFO COMMUNICATING

Communication: Relates to all specific outcomes.

UNIT STANDARD CCFO SCIENCE

Use Science and Technology: Relates to all specific outcomes.

UNIT STANDARD CCFO DEMONSTRATING

The world as a set of related systems: Relates to all specific outcomes.

UNIT STANDARD CCFO CONTRIBUTING

Self-development: Relates to all specific outcomes.

UNIT STANDARD ASSESSOR CRITERIA

N/A

UNIT STANDARD NOTES

N/A

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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