9010 Demonstrate an understanding of the use of different number bases and measurement units and an awareness of error in the context of relevant calculations

9010 Demonstrate an understanding of the use of different number bases and measurement units and an
awareness of error in the context of relevant calculations Learner Guide
1
LEARNING UNIT: 9010 Demonstrate an understanding of
the use of different number bases and
measurement units and an awareness
of error in the context of relevant
calculations
CREDITS: 02
NQF LEVEL: 03
LEARNER MANUAL
LEARNING PROGRAMME
DEVELOPED BY YELLOWMEDIA
PUBLISHERS

2
Welcome to the programme
Follow along in the guide as the training practitioner takes you through
the material. Make notes and sketches that will help you to
understand and remember what you have learnt.
Take notes and share information with your colleagues. Important and
relevant information and skills are transferred by sharing!
This learning programme is divided into sections. Each section is preceded by a
description of the required outcomes and assessment criteria as contained in the
curriculum. These descriptions will define what you have to know and be able to do in
order to be awarded the credits attached to this learning programme.
These credits are regarded as building blocks towards achieving the Qualification upon
successful assessment and can never be taken away from you!
Programme methodology
The programme methodology includes facilitator
presentations, readings, individual activities, group
discussions and skill application exercises.
Know what you want to get out of the programme from the
beginning and start applying your new skills immediately.
Participate as much as possible so that the learning will be
interactive and stimulating.
The following principles were applied in designing the course:
 Because the course is designed to maximise interactive learning, you are
encouraged and required to participate fully during the group exercises
 As a learner you will be presented with numerous problems and will be required to
fully apply your mind to finding solutions to problems before being presented with
the course presenter’s solutions to the problems
 Through participation and interaction the learners can learn as much from each
other as they do from the course presenter
 Although learners attending the course may have varied degrees of experience in
the subject matter, the course is designed to ensure that all delegates complete the
course with the same level of understanding
 Because reflection forms an important component of adult learning, some learning
resources will be followed by a self-assessment which is designed so that the
learner will reflect on the material just completed.

3
This approach to course construction will ensure that learners first apply their minds to
finding solutions to problems before the answers are provided, which will then maximise
the learning process which is further strengthened by reflecting on the material covered by
means of the self-assessments.
Different types of activities you can expect
To accommodate your learning preferences, a variety of different types of activities are
included in the formative and summative assessments.
They will assist you to achieve the outcomes (correct results) and should guide you
through the learning process, making learning a positive and pleasant experience.
The table below provides you with more information related to the types of activities.
Icons Type of assessment Description
Formative knowledge
assessment:
This comprises of questions
to assess your knowledge.
You must obtain at least 80%
in each assessment criterion.
Teamwork Self-Assessment
Form
After you completed this
course, you will be required
to assess your own
behaviour regarding team
work.
Work place experience After you completed this
to assess your own
behaviour regarding work
experience.
Project research After you completed this
to assess your own
behaviour regarding
research.

4
Learner Administration
Attendance Register
You are required to sign the Attendance Register every day you attend training sessions
facilitated by a facilitator.
Programme Evaluation Form
On completion you will be supplied with a “Learning programme Evaluation Form”. You are
required to evaluate your experience in attending the programme.
Please complete the form at the end of the programme, as this will assist us in improving
our service and programme material. Your assistance is highly appreciated.
Learner Support
The responsibility of learning rests with you, so be proactive and ask questions and seek
assistance and help from your facilitator, if required.
Please remember that this learning programme is based on outcomes based education
principles which implies the following:
 You are responsible for your own learning – make sure you manage your study,
research and workplace time effectively.
 Learning activities are learner driven – make sure you use the Learner Guide and
Formative Assessment Workbook in the manner intended, and are familiar with the
workplace requirements.
 The Facilitator is there to reasonably assist you during contact, practical and
workplace time for this programme – make sure that you have his/her contact
details.
 You are responsible for the safekeeping of your completed Formative Assessment
Workbook and Workplace Guide
 If you need assistance please contact your facilitator who will gladly assist you.
 If you have any special needs please inform the facilitator.

5
Learner Expectations
Please prepare the following information. You will then be asked to
introduce yourself to the instructor as well as your fellow learners
Your name
The organisation you represent
Your position in the organisation
What do you hope to achieve by attending this programme / what are your
expectations?

6
Information about this module
Overview
9010 Demonstrate an understanding of the use of different number bases and
measurement units and an awareness of error in the context of relevant calculations
.
Scope of the programme
The learning contained within this module will enable learners to:
 Convert numbers between the decimal number system and the binary number
system.
 Work with numbers in different ways to express size and magnitude.
 Demonstrate the effect of error in calculations.
Entry Level Requirements
The credit value is based on the assumption that people starting to learn towards
this unit standard are competent in Mathematical Literacy and Communications at
NQF level 2
Target group
Mode of delivery
This module will be delivered to you in a four day facilitated workshop. During these four
days you will be required to complete formative activities during class time as well as after
class in your own study time.
Unit standard alignment
Unit standard Number : 9010 Demonstrate an understanding of the use of different number
bases and measurement units and an awareness of error in the context of relevant calculations
NQF Level :03
Credits :02
Learning time
It will take the average learner approximately 02 learning hours to master the outcomes of
this programme.
Assessment
 Formative assessment will take place during the learning process in class through
means of exercises. You will be required to complete activities as part of a group in
class as well as individual activities. These formative activities will help prepare you
for your final assessment.
 Summative assessment will be conducted at the end of this learning process
through means of a Portfolio of Evidence.

7
In order to assess whether a learner can actually demonstrate the desired outcomes,
assessment criteria are included in the unit standard. Each outcome has its own set of
assessment criteria.
The assessment criteria describe the evidence that is needed that will show that the
learner has demonstrated the outcome correctly.
It is of utmost importance that the learner fully understands the assessment criteria as
listed in the unit standard, as it is the only way in which the learner will know what he will
be assessed against.
The final or summative assessment is the most important aspect of this training
program. It is during this process that the learner will be declared competent or not yet
competent.
Range statements
This unit standard covers:
Approximation in relation to the use of computing technologies, the distinction
between exact and approximate answers in a variety of problem settings. More
detailed range statements are provided for specific outcomes and assessment
criteria as needed.
Remember: Also included in the unit standard are the range
statements in support of the assessment criteria. The range
statements indicate detailed requirements of the assessment
criteria.
The learner guide
The learner guide is included in this material under various learning units. The
learner guide has been designed in such a manner that the learner is guided in a
logical way through the learning material and requirements of the unit standard.
RPL assessment
The assessment of RPL learners will be conducted in the same way as for those of new
learners. The assessment pack is exactly the same and will therefore be used for new
learners as well as RPL Learners. It must however be noted that learners who are
applying for RPL must provide proof of previous learning and subject related experience
prior to the assessment.
This proof or evidence can be in the format of certified copies (certificates) of previous
learning programs that have been attended.
All the evidence will be assessed and authenticated before a learner will be allowed to
enrol for an RPL program.

8
Contents
Welcome to the programme.................................................................................................2
Programme methodology.....................................................................................................2
Different types of activities you can expect..........................................................................3
Learner Administration.........................................................................................................4
Learner Support...................................................................................................................4
Learner Expectations...........................................................................................................5
Information about this module..............................................................................................6
Learning Unit 1: .................................................................................................................11
Computational Tools ...................................................................................................................12
Calculators....................................................................................................................................12
How to Use a Calculator.............................................................................................................16
Calculations ..................................................................................................................................19
Addition Algorithms .....................................................................................................................22
Subtraction Algorithms................................................................................................................24
Multiplication Algorithms.............................................................................................................26
Division Algorithms......................................................................................................................27
Formative assessment.......................................................................................................30
Role play...................................................................................................................................30
Activity: 01...............................................................................................................................30
Learning Unit 2: .................................................................................................................34
What are irrational numbers? ....................................................................................................35
Solutions Involving Irrational Numbers.....................................................................................36
The History of Measurement Instruments ...............................................................................37
Measurement Systems...............................................................................................................40
Measuring Instruments ...............................................................................................................44
Role play...................................................................................................................................52
Project.......................................................................................................................................53
Group Activity: 05..................................................................................................................53
Learning Unit 3: .................................................................................................................54
Strategies to Estimate the Length of Objects..........................................................................55
Approximations ............................................................................................................................56
Role play...................................................................................................................................59
Activity: 06...............................................................................................................................59

9
Project.......................................................................................................................................60
Annexure 1: Growth Action Plan.......................................................................................64
Annexure 2: Words that are new to me.............................................................................65
Annexure 3: Training Evaluation.......................................................................................66
Annexure 4: Evaluation of Facilitator ................................................................................67
2. Bibliography .............................................................................................................68
SECTION C: SELF REFLECTION..............................................................................69
Self-Assessment ..........................................................................................................71
Learner Evaluation Form...........................................................................................72

10
Learning path:
Convert numbers between the decimal number
system and the binary number system.
Work with numbers in different ways to express
size and magnitude.
Demonstrate the effect of error in calculations.

11
Learning Unit 1:
At the end of this module learners will be able to:
Introduction
1. Conversion between binary and decimal numbers is done correctly.
2. Basic addition and subtraction calculations in the binary number system
are done correctly.
3. Practical applications of the decimal and binary system are explained
correctly.
Conclusion
Convert numbers between the decimal
number system and the binary number
system

12
Computational Tools
Arithmetic computations are generally performed in one of three ways:
 Mentally
 With paper and pencil, or
 With a machine, e.g. calculator or abacus.
The method chosen depends on the purpose of the calculation. If we need rapid, precise
calculations, we would choose a machine. If we need a quick, ballpark estimate or if the numbers
are “easy,” we would do a mental computation.
Calculators
Computation can be defined as the act or process of computing;
calculation; reckoning.
A calculator (also known as a calculating machine) is a small
electronic or mechanical device that performs calculations,
requiring manual action for each individual operation.

13
A calculator performs arithmetic operations on numbers. The simplest calculators can do only
addition, subtraction, multiplication, and division.
A simple calculator
More sophisticated calculators can handle exponential operations, roots, logarithms, trigonometric
functions, and hyperbolic functions.
A sophisticated calculator

14
An exponent is a quantity representing the power to which some
other quantity is raised. (e.g. y2
)
A logarithm is an exponent used in mathematical calculations to
depict the perceived levels of variable quantities.
(Both of these concepts will be explained in more detail later)

15
Most calculators these days require electricity to operate. Portable, battery-powered calculators
are, however, still popular.
The Slide Rule
Before 1970, a more primitive form of calculator, the slide rule, was commonly used. It consisted of
a slate of wood, called the slide that could be moved in and out of a reinforced pair of slats. Both
the slide and the outer pair of slats had calibrated numerical scales. A movable, transparent sleeve
called the cursor was used to align numerals on the scales. The slide rule did not require any
source of power, but its precision was limited, and it was necessary to climb a learning curve to
become proficient with it.
A shop keeper’s abacus
One of the most primitive calculators, the abacus is still used in some regions of the Far East.

16
The abacus uses groups of beads to denote numbers. Like the slide rule, the abacus requires no
source of power. The beads are positioned in several parallel rows, and can be moved up and
down to denote arithmetic operations. It is said that a skilled abacus user can do some calculations
just as fast as a person equipped with a battery-powered calculator.
As calculators became more advanced during the 1970s, they became able to make computations
involving variables (unknowns). These were the first personal computers (PCs). Today's personal
computers can still perform such operations, and most are provided with a virtual calculator
program that actually looks, on screen, like a handheld calculator. The buttons are actuated by
pointing and clicking.
Calculator Icon on a PC
How to Use a Calculator
Using a calculator is an important skill. A few quick steps can help anyone use the device.
Step 1
Learn the symbols associated with math. Basic calculators are dominated by a few standard
symbols including a plus sign (+) for addition problems, a minus sign (-) for subtraction, a
multiplication symbol (x or *), a division sign (÷) and an equal sign (=).
Step 2
It is important to understand the processes that go along with the signs.

17
If you don't understand the process of division, it's useless to know the sign because you won't be
able to use it successfully. By first learning basic math principles, you can use a calculator to put
those processes to work.
Step 3
Get accustomed with the layout of a calculator. Most calculators have numbers in the middle,
starting with zero at the bottom of the layout and working upwards, in rows of three, to the number
nine. Basic math symbols are generally placed to the right of the numbers. The percentage button
(%) and square root button can be found with the math symbols.
Step 4
Use a graphing or scientific calculator when you learn more math processes. These calculators
perform more difficult mathematical processes and can handle longer strings of numbers. When
you learn various formulas and do longer problems, graphing and scientific calculators can do
much of the work for you. The layout of a scientific calculator is shown below.
On -
button
Number
buttons Basic Math
operations
buttons
Display
Percenta
ge button
Square
Root
button
Press for total
Decimal
button

18
Basic Calculator Operations
Most calculators today have the following operations, which you need to know how to use:
Operation English Equivalent
+ plus, or addition
- minus or subtraction, Note: there is DIFFERENT key to make a
positive number into a negative number, perhaps marked (-) or NEG
known as "negation"
* or X
times, or multiply by
/ over, divided by, division by
^ raised to the power
yx
y raised to the power x
Sqrt or square root
ex
"Exponentiate this," raise e to the power x
LN Natural Logarithm, take the log of

19
SIN Sine Function
SIN-1
Inverse Sine Function, arcsine, or "the angle whose sine is"
COS Cosine Function
COS-1
Inverse Cosine Function, arccosine, or "the angle whose cosine is"
TAN Tangent Function
TAN-1
Inverse Tangent Function, arctangent, or "the angle whose tangent
is"
( ) Parentheses, "Do this first"
Store (STO) Put a number in memory for later use
Recall Get the number from memory for immediate use
Calculations
The order of entry of the key strokes is important when doing calculations on a calculator. It might
be helpful to consult the operator's manual that came with your calculator if you have any specific
questions on how your calculator works.
The Order of Operations
When doing more than one operation we need follow a set of rules regarding which calculations to
do first.
For example, what is the "right" answer to?
Should we go "left to right" and just do the + first and get 30, or do we do the × first and get 15?
Well, in order to avoid confusion and get the correct answer, mathematicians decided long ago that
all calculations should be done in the same order. You may have learned the order of operations
as being: Please Excuse My Dear Aunt Sally! where the words stand for Parentheses,
Exponentiation, Multiplication or Division, Addition or Subtraction.
So what is the correct answer for our problem?
3 + 2 × 6 =

20
The order of operations would say that in the absence of parentheses, you would multiply 2×6 first,
then add 3, so the result should be
Rounding Numbers
Another issue to deal with when performing operations is how to state the answer. For example,
when a 20 centimeter wire is divided into 3 equal pieces, we would divide 20 by 3 to get the length
of each piece.
The 6 repeats forever. How is this number reported? It is rounded to some usually pre-determined
number of digits or decimal places. "Digits" means the total number of numbers both left and right
of the decimal point. "Decimal places" refers specifically to the number of numbers to the right of
the decimal point.
For comparison, let's try rounding this number to 2 decimal places -- two numbers to the right of
the point. To round, look at the digit after the one of interest -- in this case the third decimal place --
and use the rule:
If the digit is 0, 1, 2, 3 or 4 rounds down
if the digit is 5, 6, 7, 8 or 9 round up
15!
20/3 = 6.6666…

21
In the example 6.666666666666.....the next digit is 6 so we round up, giving 6.67 as the desired
answer. If instead the instruction was to round the number 20/3 to 2 digits the answer would have
been 6.7 (two digits, one of which is a "decimal place").
Sometimes rounding is the result of an approximation. If you had 101 or 98 meters of some wire, in
each case you would have "about 100 meters."
Each algorithm is a list of well-defined instructions for completing a task. Starting from an initial
state, the instructions describe a computation that proceeds through a well-defined series of
successive states, eventually terminating in a final ending state.
An algorithm is a precise rule (or set of rules) specifying how to
solve some problem
Below is an algorithm that tries to figure out why the lamp doesn't
turn on and tries to fix it using the steps.

22
Below are mathematical algorithms that you need to familiarize yourself with in order to apply them
in calculations.
Addition Algorithms
Left-to-Right Algorithm
A. Starting at the left, add column-by-column, and adjust the result.
B. Alternate procedure: For some students this process becomes so automatic that they
start at the left and write the answer column by column, adjusting as they go without
writing any in-between steps.
If asked to explain, they say something like this:
“Well, 200 plus 400 is 600, but (looking at the next column) I need to adjust that, so write 7. Then,
60 and 80 is 140, but that needs adjusting, so, write 5. Now, 8 and 3 is 11, no more to do, write 1.”
This technique easily develops from experiences with manipulatives, such as base-10 blocks and
money, and exchange or trading games, and is consistent with the left-to-right patterns learned for
reading and writing.
Partial Sums Algorithm
Add the numbers in each column. Then add the partial sums.
2 6 8
+4 8 3
1. Add 6 14 11
2. Adjust 10's and 100's 7 4 11
3. Adjust 1's and 10's 7 5 1
2 6 8
+4 8 3
61
41
1
7 5 1

23
268
+483
1. Add 100's 600
2. Add 10's 140
3. Add 1's +11
4. Add partial sums 751
Students who use this type of algorithm often show more awareness of place value than those who
learned the traditional method. This procedure works well for larger numbers too.
Rename-Addends Algorithm (Opposite Change)
If a number is added to one of the addends and the same number is subtracted from the other
addend, the result remains the same. The purpose is to rename the addends so that one of the
addends ends in zeros.
This strategy indicates a good number sense and some understanding of equivalent forms.
A. Rename the first addend, and then the second.
268 -> (+2) -> 270 -> (+30) -> 300
+483 -> (-2) -> +481 -> (-30) -> +451
Add 751
Explanation: Adjust by 2, and then by 30.
B. Rename the first addend, and then the second.
268 -> (-7) -> 261 -> (-10) -> 251
+483 -> (+7) -> +490 -> (+10) -> +500
Add 751

24
Counting-on Algorithm
A. Rename the first addend, and then the second.
268 + 483
Begin at 268 and count by 100’s, 4 times: 368, 468, 568, 668; then count by 10’s, 8
times: 678, 688, 698, 708, 718, 728, 738, 748; continue to count by l’s, 3 times: 749,
750, 751.
B. Counting-on algorithm alternate method.
With larger numbers children may use a combination of counting on and counting back.
Begin at 268 and count by 100’s, 5 times: 368, 468, 568, 668, 768; then count back by
10’s, twice: 758, 748; continue to count by 1’s, 3 times: 749, 750, 751.
Subtraction Algorithms
Add-Up Algorithm
Add up from the subtrahend (bottom
number) to the minuend (top number).
932
-356
Students may mentally keep track of the
numbers that are added or use paper to
record the addends on the side. Most of us
often use some form of this method when
making change.
Left-to-Right Algorithm
Starting at the left, subtract column by column.

25
932
-356
1. Subtract 100's 932
-300
2. Subtract 10's 632
-50
3. Subtract 1's 582
-6
576
Rename Subtrahend Algorithm (also called Same Change)
If the same number is added to or subtracted from the minuend (top number) and subtrahend
(bottom number), the result remains the same. The purpose is to rename both the minuend and
the subtrahend so that the subtrahend ends in zero.
This type of solution method shows a strong ability to hold and manipulate numbers mentally.
A. Add the same number
932 -> (+4) -> 936 -> (+44) -> 976
-356 -> (+4) -> -360 -> (+40) -> -400
Subtract 576
B. Add the same number
932 -> (-6) -> 930 -> (+54) -> 976
-356 -> (-6) -> -350 -> (+50) -> -400
Subtract 576

26
Two Unusual Algorithms
A. Subtract by adding column-by-column with adjustments. (Same problem as the previous
one.) Some students who use the add-up algorithm extend that to subtraction. They just write the
answer with no other remarks. Asked to explain, they say something like this:
“To get to 900 from 300, add 600; but the tens need help, so make it 5 [for 500]. To get to 130 from
50, add 80; but the ones need help, so write 7 [for 70]. To get to 12 from 6, add 6. No more to do.”
B. Write partial differences, negative if necessary, and adjust. A few students who love
negative numbers use some variation of the procedure shown here.
This method may be less common than some of the others. Yet, some students seem to have an
informal sense of working with negatives (deficits).
932
-356
1. Subtract 100's: 900-300 600
2. Subtract 10's: 30-50 -20
3. Subtract 1's: 2-4 -4
4. Add the partial differences 576
(600-20-4, done mentally)
Multiplication Algorithms
This algorithm is done from left to right, so that the largest partial product is calculated first. As with
left-to-right algorithms for addition, this encourages quick estimates of the magnitude of products
without necessarily finishing the procedure to find exact answers. To use this algorithm efficiently,
students need to be very good at multiplying multiples of 10, 100, and 1000. These skills also
serve very well in making ballpark estimates in problems that involve multiplication or division, and
introduces the * as a symbol of multiplication.
Partial-Product Algorithm
In the partial-product multiplication algorithm, each factor is thought of as a sum of ones, tens,
hundreds, and so on. For example, in 67 * 53, think of 67 as 60 + 7, and 53 as 50 + 3. Then each

27
part of one factor is multiplied by each part of the other factor, and all of the resulting partial
products are added together.
50 x 60
50 x 7
3 x 60
3 x 7
67
*53
3000
350
180
+21
3551
This method reinforces the understanding of place value and emphasizes the multiplication of the
largest product first.
Division Algorithms
The key question to be answered in many problems is, “How many of these are in that,” or “How
many n's are in m?” This can be expressed as division: “m divided by n,” or “m/n.”
One way to solve division problems is to use an algorithm that begins with a series of “at least/less
than” estimates of how many n’s are in m. You check each estimate. If you have not taken out
enough n’s from the m’s, take out some more; when you have taken out all there are, add the
interim estimates.
For example, 158/12 can be thought of as the question, “How many 12’s are in 158?” You might
begin with multiples of 10, because they are simple to work with. A quick mental calculation tells
you that there are at least ten 12’s in 158 (10 * 12 = 120), but less than twenty (since 20 * 12 =
240).
12)158
-120
38
-36
2
10
+3
13

28
You would record 10 as your first estimate and remove (subtract) ten 12’s from 158, leaving 38.
The next question is, “How many 12’s are in the remaining 38?” You might know the answer right
away (since three 12’s are 36), or you might sneak up on it: “More than 1, more than 2, a little more
than 3, but not as many as 4.” Taking out three 12’s leaves 2, which is less than 12, so you can
stop estimating.
To obtain the final result, you would add all of your estimates (10 + 3 = 13) and note what, if
anything is left over (2). There is a total of thirteen 12’s in 158; 2 are left over. The quotient is 13,
and the remainder is 2.
It is important to note that, in following this algorithm, students may not make the same series of
estimates. In the example, a student could have used 2 as a second estimate, taking out just two
12’s and leaving 14 still not accounted for—another 12, and a remainder of 2. The student would
reach the final answer in three steps rather than two. One way is not better than another.
12)158
-120
38
-24
14
-12
2
10
2
+1
13
The examples show one method of recording the steps in the algorithm.
One advantage of this algorithm is that students can use numbers that are easy for them to work
with. Students who are good estimators and confident of their extended multiplication facts will
need to make only a few estimates to arrive at a quotient, while others will be more
Comfortable taking smaller steps. More important than the course a student follows is that the
student understands how and why this algorithm works and can use it to get an accurate answer.
Another advantage of this algorithm is that it can be extended to decimals once students have a
pretty good sense of “How many n’s are in m?” Sometimes it may be desirable to express the
quotient as a decimal. Sometimes n may be larger than m (the divisor larger than the dividend), or
all the information is in decimal form. For the example 158 / 12, the estimates could be continued
by asking, “How many 12’s in the remainder 2?”

29
12)158.0
-120.0
38.0
-36.0
2.0
-1.2
.8
10.0
3.0
+0.1
13.1
A student with good number sense might answer, “At least one-tenth, since 0.1 * 12 is 1.2, but less
than two-tenths, since 0.2 * 2 = 2.4. The answer then could be l3.1 (12’s) in 158, and a little bit left
over.”
The question behind this algorithm, “How many of these are in that?” also serves well for estimates
where the information is given in “scientific notation” (see glossary). The uses of this algorithm with
problems that involve scientific notation or decimal information will be explored briefly in grades 5
and 6, mainly to build number sense and understanding of the meanings of division.

30
Formative assessment
Role play
Activity: 01
Instructions Conversion between binary and decimal numbers is done
correctly
Method Group Activity
Media Method Flipchart
Answers:
Critical Cross Field
Orgaisation
DEMONSTRATING
Marks 10

31
Project
Group Activity: 02
Instructions Basic addition and subtraction calculations in the binary
number system are done correctly
Answers:
Orgaisation
Communicating
Marks 05

32
Research PROJECT
Activity: 03
Instructions Explain Practical applications of the decimal and binary system
correctly
Method Individual Activity
Answers:
Orgaisation
COLLECTING
Marks 10

33
Essay –Reflexive
Take some time to reflect on what you have learnt in this module and assess your
knowledge against the following pointers. Write down your answers. Should you not be
able to complete each of these statements, go back to your notes and check on your
understanding? You can also discuss the answers with a colleague.
Convert numbers between the decimal number system and the binary number system

34
Learning Unit 2:
Introduction
1. The prefixes indicating magnitude in measurements are correctly related to the
decimal system.
2. Conversions between related units in different measurement systems are correctly
applied in real-life contexts.
Conclusion
Work with numbers in different ways to
express size and magnitude

35
What are irrational numbers?
An irrational number is any real number that is not rational. By real number we mean, loosely, a
number that we can conceive of in this world, one with no square roots of negative numbers (such
a number is called complex.)
Perhaps the best-known irrational numbers are π and √2.
π = 3.1415926535897932384626433832795 (and more...)
(People have calculated Pi to over one million decimal places and still there is no pattern.)
You cannot write down a simple fraction that equals Pi.
The popular approximation of 22
/7 = 3.1428571428571... Is close but not accurate.
Another clue is that the decimal goes on forever without repeating.
Square Root of 2
Let's look at the square root of 2 more closely.
Irrational numbers are numbers that can be written as decimals but not as
fractions.
If you draw a square (of size "1"), what is the distance across the
diagonal?

36
The answer is the square root of 2, which is 1.4142135623730950... (etc.)
Square Roots
Many square roots, cube roots, etc. are also irrational numbers. Examples:
√3 1.7320508075688772935274463415059 (etc.)
√99 9.9498743710661995473447982100121 (etc.)
But √4 = 2 (rational), and √9 = 3 (rational)...
... So not all roots are irrational.
Solutions Involving Irrational Numbers
It is impossible to record an irrational number as a complete decimal because the decimal
representation never ends or repeats. The current record for the decimal expansion of π, if
verified, stands at 5 trillion digits.
The earliest numerical approximation of π is almost certainly the value. In cases where little
precision is required, it may be an acceptable substitute.
For many purposes, 3.14 or 22/7 is close enough, although engineers often use 3.1416 (5
significant figures) or 3.14159 (6 significant figures) for more precision.
Practically, a physicist needs only 39 digits of π to make a circle the size of the observable
universe accurate to the size of a hydrogen atom.

37
The word measurement stems, via the Middle French term mesure, from Latin mēnsūra, and the
verb metiri.
The science of measurement is also called the field of metrology.
With the exception of a few seemingly fundamental constants, units of measurement are
essentially arbitrary; in other words, people make them up and then agree to use them. Nothing
dictates that an inch has to be a certain length, or that a mile is a better measure of distance than a
kilometre.
The History of Measurement Instruments
Weights and measures were among the earliest tools invented by man. Primitive societies needed
rudimentary measurement tools for many tasks: constructing dwellings of an appropriate size and
shape, fashioning clothing, or bartering food or raw materials.
Measurement is the process or the result of determining the magnitude of a
quantity, such as length or mass, relative to a unit of measurement, such as a
meter or a kilogram.

38
Length Measures
Among the earliest length measures was the foot, which varied from place to place For example,
three different Greek standards are known: the Doric foot, the Attic foot and the Samian foot. There
were two common sizes for a "foot" - the foot of 246 to 252 mm based on a man's bare foot - the
foot of 330 to 335 mm based on two hand measurements.
The first calibrated foot ruler, a measurement tool, was invented in 1675 by an unknown inventor.
Mass Measures
The early unit was a grain of wheat or barleycorn used to weigh the precious metals silver and
gold.
Larger units preserved in stone standards were developed that were used as both units of mass
and of monetary currency. The pound was derived from the mina used by ancient civilizations. A
smaller unit was the shekel, and a larger unit was the talent.
Calibrated means to be marked or divided into degrees

39

40
Measurement Systems
The Imperial System
Before SI units were widely adopted around the world, the British systems of English units and
later imperial units were used in Britain, the Commonwealth and the United States. The system
came to be known as U.S. customary units in the United States and is still in use there and in a few
Caribbean countries. These various systems of measurement have at times been called foot-
pound-second systems after the Imperial units for distance, weight and time.
Many Imperial units remain in use in Britain despite the fact that it has officially switched to the SI
system. Road signs are still in miles, yards, miles per hour, and so on, people tend to measure
their own height in feet and inches and milk is sold in pints, to give just a few examples.
The Metric System
The metric system is a decimal systems of measurement based on its units for length, the meter
and for mass, the kilogram. Metric units of mass, length, and electricity are widely used around the
world for both everyday and scientific purposes.
The metric system features a single base unit for many physical quantities. Other quantities are
derived from the standard SI units. Multiples and fractions of the units are expressed as powers of
ten of each unit.
The International System of Units (SI)
The International System of Units is the world's most widely used system of units, both in everyday
commerce and in science.
The SI was developed in 1960 from the meter-kilogram-second (MKS) system, rather than the
centimeter-gram-second (CGS) system, which, in turn, had many variants.
SI stands for the International System of Units which is the modern
form of the metric system.

41
At its development the SI also introduced several newly named units that were previously not a
part of the metric system. The SI units for the four basic physical quantities: length, time, mass,
and temperature are:
 meter (m) :SI unit of length
 second (s) :SI unit of time
 kilogram (kg) :SI unit of mass
 kelvin (K) :SI unit of temperature
To convert from meters to centimetres it is only necessary to multiply the number of meters by 100,
since there are 100 centimetres in a meter. Inversely, to switch from centimetres to meters one
multiplies the number of centimetres by 0.01 or divide centimetres by 100.
Length Measures
The imperial measures of length are:
Abbrev. Metric Table Information
Inch in or " 2.54 cm 12
inches
= 1 foot
The inch was originally the width of a thumb.
The name comes from uncia which is Latin for
'twelfth part' (see foot). An inch is considered to
be the width of a thumb (my thumb is 3/4 inch
wide).

42
Foot ft or ' 30.48 cm 12
inches
= 1 foot
3 feet =
1 yard
There was a Roman unit called a pes (plural
pedes) which means a foot, and was 29.59cm,
which is nearly the size of the modern foot. There
were twelve uncia to a pes as well. The foot has
been used in England for over a thousand years.
Yard Yd 91.44 cm 3 feet =
1 yard
1760
yards =
1 mile
A yard is a single stride. The word yard comes
from the Old English gyrd, meaning a rod or
measure. Henry I (1100-1135) decreed the lawful
yard to be the distance between the tip of his
nose and the end of his thumb. It was within a
tenth of an inch of the modern yard. A yard is
nearly a meter.
Mile mi or m 1.61 km 1760
yards =
1 mile
A mile is derived from mille, Latin for thousand,
since a Roman mile was mille passuum, a
thousand Roman paces or double strides, from
left foot to left foot. A passus was 5 pedes (see
foot), which would make 5000 feet to the mile.
The modern mile is 5280 feet or 1760 yards. In
the past every part of England had its own mile,
up to 2880 yards. In Ireland, the mile was 2240
yards well into the 20C. At school, we had to
learn that half a mile was 880 yards, and quarter
of a mile was 440 yards. People still say "about a
hundred yards" to mean a short walking
distance. Note that 'm' is the abbreviation for
both a mile and a meter!
Mass Measures

43
ounce oz 28.35 gm 16 oz =
1 lb
The abbreviation "oz" comes from 15th century
Italian, an abbreviation of "onza". "
pound Lb 453.59 gm 16 oz =
1 lb
14 lb =
1 stone
A pound is always written as "lb" to prevent
confusion with pound money "£". It is very old,
traced back to the Roman libra, which explains
its abbreviation.
stone st 6.35 kg 14 lb =
1 stone
The British weigh themselves in stone and the
Americans weigh themselves in pounds.
The stone was originally used for weighing agricultural commodities.
Cities in England would have official standard weights and measures. Merchants’ weights and
measures would be checked against this to make sure they weren't trying to cheat their customers.
Rough Conversion between Imperial and Metric
Britain is supposed to use metric measures. Volumes are not so much of a problem, as we buy
bottles or packs of this or that, and we have been allowed to keep our pints of beer! But we can
buy meat, and fruit and vegetables, by weight, and so we really ought to learn how to do this.
Formal conversions are too precise, so here is a rough-and-ready guide that you might be able to
keep in your head.
A bag of sugar weighs a kilo. This is slightly
heavier than the old days, when it weighed 2
lb.
If you're buying fruit and veg, then (roughly)
1 lb is half a kilo.
8 oz is between 200 grams and 250 grams.
A pack of butter is now 250 grams, but some
other goods choose 200 grams instead.
Here is a mnemonic: "Two and a quarter
pounds of jam weigh about a kilogram." (Or
of course anything else!)

44
Below are rough conversion charts. Work out what weight of meat or fruit or vegetables you
normally buy, and memorise the metric equivalent.
1 oz = 30 gm
2 oz = 60 gm
4 oz = 110 gm
8 oz = 230 gm
12 oz = 340 gm
1 lb = 450 gm
1 lb 4 oz = 570 gm
1 lb 8 oz = 680 gm
1 lb 12 oz = 800 gm
2 lb = 900 gm
Measuring Instruments
In the physical sciences, quality assurance, and engineering, measurement is the activity of
obtaining and comparing physical quantities of real-world objects and events. Established standard
objects and events are used as units, and the process of measurement gives a number relating the
item under study and the referenced unit of measurement. Measuring instruments, and formal
test methods which define the instrument's use, are the means by which these relations of
numbers are obtained. All measuring instruments are subject to varying degrees of instrument
error and measurement uncertainty.
100 gm = 3.5 oz
200 gm = 7 oz
300 gm = 10.5 oz
400 gm = 14 oz
500 gm = 1 lb 2 oz
600 gm = 1 lb 5 oz
700 gm = 1 lb 9 oz
800 gm = 1 lb 12 oz
900 gm = 2 lb
1 kilo = 2 lb 3 oz
A measurement is only as good as the instrument used.

45
Scientists, engineers and other humans use a vast range of instruments to perform their
measurements. These instruments may range from simple objects such as rulers and stopwatches
to electron microscopes and particle accelerators. Virtual instrumentation is widely used in the
development of modern measuring instruments.
The Rule
A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical
drawing, printing and engineering/building to measure distances and/or to rule straight lines.
Rulers have long been made of wood in a wide range of sizes. Plastics have been used since they
were invented; they can be molded with length markings instead of being scribed. Metal is used for
more durable rulers for use in the workshop; sometimes a metal edge is embedded into a wooden
desk ruler to preserve the edge when used for straight-line cutting. 12 inches or 30 cm in length is
useful for a ruler to be kept on a desk to help in drawing. Shorter rulers are convenient for keeping
in a pocket. Longer rulers, e.g., 18 inches (45 cm) are necessary in some cases. Rigid wooden or
plastic yardsticks, 1 yard long and meter sticks, 1 meter long, are also used.

46
Desk rulers are used for three main purposes: to measure, to aid in drawing straight lines and as a
straight guide for cutting and scoring with a blade. Practical rulers have distance markings along
their edges.
Retractable Tape Measure
Measuring instruments similar in function to rulers are made portable by folding (carpenter's folding
rule) or retracting into a coil (metal tape measure) when not in use. When extended for use they
are straight, like a ruler.
The steps in using a ruler are
Step Action
1 Measure with a ruler or tape measure. Find an object or distance between
two points you want to measure. This can be a length of wood, string, or
cloth, or a line on a sheet of paper
2 Place the Zero end of your rule at the end of your object, usually on the
left side. Make sure the end of the ruler is flush with your object, and use
your left hand to hold it in place.
3 Move to the opposite side of the object you are measuring, and read the
last number on your rule that is alongside the object. This will indicate the
"whole unit" length of the object, example: 8 inches (when measuring in
inches. Count the number of fraction marks (dashes) the object you are
measuring goes beyond the last whole number. If your ruler is marked in
1/8 inch increments, and you are 5 marks past the last whole unit number,
you will be 5/8 inches beyond the 8, and your length will be read "8 and
5/8 inches'. Simplify fractions if you can.

47
Step Action
4 Use a metric or decimal rule by reading the intermediate marks as tenths
of the unit the rule is marked in, or in case of a metric rule marked in
centimeters (cm), read the intermediate marks as millimeters (mm).
5 Use a tape measure (in this case, a retractable steel tape works best) to
measure between objects, for instance, walls. Slide the zero end of the
tape against one wall, or have a helper holds it, then pull out enough tape
to reach the opposite wall. Here, you should have two sizes of numbers,
the larger for feet (or meters), the smaller, for inches (or centimeters).
Read the feet (m) first, inches (cm), then fractions thereof. Example, a
distance may read "12 feet, 5 and 1/2 inches".
6 Use your 12 inch rule (or similar instrument, like a yardstick) to draw a
straight line. Lay it down on the surface you are drawing on, and lay your
pencil point along the edge of the rule, using it to guide you pencil as you
make your line.
Using a ruler to draw a straight line
Weighing scales
A weighing scale is a measuring instrument for determining the
weight or mass of an object.

48
People have needed to weigh objects, especially for trade, since the earliest known societies
Dozens of types of scales exist, but the simplest scale uses a beam and a pivot to balance the
weight of one known object with another.
A spring scale measures weight by the distance a spring deflects under its load.
Weighing scales are used in many industrial and commercial applications, and products from
feathers to loaded tractor-trailers are sold by weight.
Commercial Use

49
An exact scale is critical for restaurants and other food industries that must portion food for sale.
Meats, fruits and vegetables are usually sold by the pound; if you cannot correctly weigh an item
the price per pound could vary widely from the actual weight. Even at a profitable restaurant food
costs around one-third of the total sale price. Labor and food can total 50 to 75 percent of total
sales. Thus, even an error of only a few percentage points can have a large impact on a business's
profit.
Supermarket / Retail Scale
These scales are used in the bakery, delicatessen, seafood, meat, produce, and other perishable
departments. Supermarket scales can print labels and receipts (in bakery specially), marks
weight/count, unit price, total price and in some cases tare, a supermarket label prints weight/cunt,
unit price and total price.
Health

50
Specialised medical scales and bathroom scales are used to measure the body weight of human
beings. A weighing scale is an essential component to maintaining the health of your body and
measuring the progress of a growing child.
More modern weighing scales use digital calibration to give a more accurate and quicker reading.
Science
Chemists often deal with chemical equations that call for specific amounts of substances and
different concentrations of solutions.
If you wanted to make 1 gram of a 20 percent solution of sodium chloride (table salt), you would
need to measure out 0.2 grams of NaCl and 0.8 grams of water, otherwise you cannot get an exact
20 percent solution.
Sources of Error
Some of the sources of error in high-precision balances or scales are:
 Buoyancy, because the object being weighed displaces a certain amount of air, which must
be accounted for. Some high-precision balances may be operated in a vacuum.

51
 Error in mass of reference weight
 Air gusts, even small ones, which push the scale up or down
 Friction in the moving components that cause the scale to reach equilibrium at a different
configuration than a frictionless equilibrium should occur.
 Settling airborne dust contributing to the weight
 Mis-calibration over time, due to drift in the circuit's accuracy, or temperature change
 Mis-aligned mechanical components due to thermal expansion/contraction of components
 Magnetic fields acting on ferrous components
 Forces from electrostatic fields, for example, from feet shuffled on carpets on a dry day
 Chemical reactivity between air and the substance being weighed (or the balance itself, in
the form of corrosion)
 Condensation of atmospheric water on cold items
 Evaporation of water from wet items
 Convection of air from hot or cold items
 Gravitational anomalies for a scale, but not for a balance. I.e. using the scale near a
mountain; failing to level and recalibrate the scale after moving it from one geographical
location to another)
 Vibration and seismic disturbances; for example, the rumbling from a passing truck

52
Role play
Activity: 04
Instructions How are The prefixes indicating magnitude in measurements
are correctly related to the decimal system?
Answers:
Orgaisation
DEMONSTRATING
Marks 10

53
Project
Group Activity: 05
Instructions State how Conversions between related units in different
measurement systems are applied in real-life contexts
Answers:
Orgaisation
Communicating
Marks 05

54
Learning Unit 3:
Introduction
1. Symbols for irrational numbers such as 7c and 42 are left in formulae or steps to
calculations except where approximations are required.
2. Descriptions are provided of the effect of rounding prematurely in calculations.
3. The desired degree of accuracy is determined in relation to the practical context.
4. The final value of a calculation is expressed in terms of the required unit.
Conclusion
Demonstrate the effect of error in
calculations

55
Strategies to Estimate the Length of Objects
Thumb - from the knuckle to the tip is about an
inch (2.54 cm).
The distance between two knuckles on a person's
finger might be about an inch (2.54 cm).
A sheet of paper is almost a foot (30.48 cm) long.
A doorknob is about a yard (99.44 cm) from the
floor.

56
Strategies to Estimate the Mass of Objects
For small estimates, it is fairly easy to compare the mass of the unknown object to that of
something of a known mass.
If, for example, you pick up a rock, and it weighs about as much as a 2kg bag of ice, you can
estimate they weight of the rock to be about 2 kg.
If you can't pick up the rock, then it gets trickier. Either you just ballpark it (that boulder looks like it
weighs a quarter ton), or you do the more scientific way of doing things and know its approximate
density and guess it's volume and use that to determine its mass (density x volume=mass)
Approximations
An approximation (usually represented by the symbol ≈) is an inexact representation of something
that is still close enough to be useful.
Although approximation is most often applied to numbers, it is also frequently applied to such
things as mathematical functions, shapes, and physical laws.
Approximations may be used because incomplete information prevents use of exact
representations. Many problems in physics are either too complex to solve analytically, or
impossible to solve using the available analytical tools. Thus, even when the exact representation
is known, an approximation may yield a sufficiently accurate solution while reducing the complexity
of the problem significantly.

57
What is algebra?
Algebra is a branch of mathematics that uses mathematical statements to describe relationships
between things that vary over time. These variables include things like the relationship between
supply of an object and its price. When we use a mathematical statement to describe a
relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount.
These letters and symbols are referred to as variables.
The mathematical statements that describe relationships are expressed using algebraic terms,
expressions, or equations (mathematical statements containing letters or symbols to represent
numbers).
What is an algebraic expression?
The basic unit of an algebraic expression is a term. In general, a term is either a number or a
product of a number and one or more variables. Below is the term –3ax.
The numerical part of the term, or the number factor of the term, is what we refer to as the
numerical coefficient. This numerical coefficient will take on the sign of the operation in front of it.
The term above contains a numerical coefficient, which includes the arithmetic sign, and a variable
or variables. In this case the numerical coefficient is –3 and the variables in the term area and x.
Terms such as xz may not appear to have a numerical coefficient, but they do. The numerical
coefficient is 1, which is assumed.
Algebra is in a system for computation using letters or other
symbols to represent numbers, with rules for manipulating these
symbols

58
Algebraic Methods
Algebraic method refers to a method of solving an equation involving two or more variables where
one of the variables is expressed as a function of one of the other variables. There are typically two
algebraic methods used in solving these types of equations:
 the substitution method and the
 Elimination method.
One algebraic method is the substitution method. In this case, the value of one variable is
expressed in terms of another variable and then substituted in the equation. In the other algebraic
method – the elimination method – the equation is solved in terms of one unknown variable after
the other variable has been eliminated by adding or subtracting the equations. For example, to
solve:
8x + 6y = 16
-8x – 4y = -8
Using the elimination method, one would add the two equations as follows:
8x + 6y = 16
-8x – 4y = -8
2y = 8
Y= 4
The variable “x” has been eliminated.
Once the value for y is known, it is possible to solve for x by substituting the value for y in either
equation:
8x + 6y = 16
8x + 6(4) = 16
8x + 24 = 16
8x + 24 – 24 = 16 - 24
8x = -8
x= -1

59
Role play
Activity: 06
Instructions State why Symbols for irrational numbers such as 7c and 42
are left in formulae or steps to calculations except where
approximations are required
Answers:
Orgaisation
DEMONSTRATING
Marks 10

60
Project
Group Activity: 07
Instructions Provide Descriptions of the effect of rounding prematurely in
calculations
Answers:
Orgaisation
Communicating
Marks 05

61
Research PROJECT
Activity: 08
Instructions Determine The desired degree of accuracy in relation to the
practical context
Method Individual Activity
Answers:
Orgaisation
COLLECTING
Marks 10

62
Summative assessment
Simulation
ACTIVITY 01
Instructions How do you express The final value of in terms of the required
unit?
CCFO
ORGANISING
Mark 10
Answer:

63
Essay –Reflexive
Take some time to reflect on what you have learnt in this module and assess your
knowledge against the following pointers. Write down your answers. Should you not be
able to complete each of these statements, go back to your notes and check on your
understanding? You can also discuss the answers with a colleague.
Demonstrate the effect of error in calculations.

64
Annexure 1: Growth Action Plan
The personal development plan will enable you address any areas of weakness that you
identify during the course and stimulate your desire for personal growth.
Growth Action Plan
I have identified the following as areas in which I need to improve in order to
become competent. List in order of priority.
Actions to
be taken
Resources Completion date Evidence
Learner Name:
Learner Signature:
Facilitator Name:
Facilitator Signature:

65
Annexure 2: Words that are new to me
Compile a list of words that is new to you and discuss the meaning of the words with your
facilitator.
Term Description
e.g. characteristic
Trait, feature, quality, attribute, etc
Learner Name:
Learner Signature:

66
Facilitator Name:
Facilitator Signature:
Annexure 3: Training Evaluation
Training Program
Facilitator Name
Date
Ratings:
1 Poor
2 Areas for Improvement
3 Meet the standard requirements
4 Very Good
5 Excellent
Tick where appropriate:
Did the training relate to your job e.g. skills, knowledge? 1 2 3 4 5
Comments:
To what extent will your performance improve as a
result of attending this training
1 2 3 4 5
Comments:
To what extent would you recommend this course to others? 1 2 3 4 5
Comments:
Did this training meet your desired needs? 1 2 3 4 5
Comments:
Was the training material user friendly / easy to understand? 1 2 3 4 5

67
Annexure 4: Evaluation of Facilitator
Ratings:
1 Poor
2 Areas for Improvement
3 Meet the standard requirements
4 Very Good
5 Excellent
Tick where appropriate:
1 2 3 4 5
Preparation for the training
Knowledge of subject
Handling of questions
Interaction with participants
Voice clarity
Use of training aids (flip charts, handouts, etc)
Facilitator made training exciting
Recommendation of facilitator for future training
Other comments on Facilitator’s delivery of his training

68
2.Bibliography
Acknowledgements & Reference
The following web-sites have been used for research:
Learning unit Prescribed Learning Material /text
book
Supplier
Yellow Media Publishers
Senior learning material Developer:
Ms Duduzile Zwane
www.yellowmedia.co.za
dudu@yellowmedia.co.za

69
SECTION C: SELF REFLECTION
I enjoyed/did not enjoy this module because:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I enjoyed/did not enjoy this module because:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I found group work ___________________________________!!!
The most interesting thing I learnt was:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
I feel I have gained the necessary skills and knowledge to:
_____________________________________________________________

70
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
______________________________________________________________
______________________________________________________________
Please add the following to this module:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Some comments from my classmates about my participation in class:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
____________________________________________________________
_____________________________________________________________

71
Self-Assessment
Self-Assessment:
You have come to the end of this module – please take the time to
review what you have learnt to date, and conduct a self-assessment
against the learning outcomes of this module by following the
instructions below:
Rate your understanding of each of the outcomes listed below:
Keys:  - no understanding
 - Some idea
 - Completely comfortable
NO OUTCOME
SELF
RATING
  
1.
Convert numbers between the decimal number system and
the binary number system.
2.
Work with numbers in different ways to express size and
magnitude
3. Demonstrate the effect of error in calculations.

72
Learner Evaluation Form
Learning
Programme Name
Facilitator Name
Learner name
(Optional)
Dates of
Facilitation
Employer / Work
site
Date of
Evaluation
Learner Tip:
Please complete the Evaluation Form as thoroughly as you are able
to, in order for us to continuously improve our training quality!
The purpose of the Evaluation Form is to evaluate the following:
 logistics and support
 facilitation
 training material
 assessment
Your honest and detailed input is therefore of great value to us, and
we appreciate your assistance in completing this evaluation form!
A Logistics and Support Evaluation

73
No Criteria / Question
Poor
BelowStandard
Sufficient
AboveStandard
Excellent
1 Was communication regarding attendance of the
programme efficient and effective?
2 Was the Programme Coordinator helpful and efficient?
3 Was the training equipment and material used effective and
prepared?
4 Was the training venue conducive to learning (set-up for
convenience of learners, comfortable in terms of
temperature, etc.)?
Additional Comments on Logistics and Support
Poor
BelowStandard
Sufficient
AboveStandard
Excellent
B Facilitator Evaluation
1 The Facilitator was prepared and knowledgeable on the
subject of the programme
2 The Facilitator encouraged learner participation and input
3 The Facilitator made use of a variety of methods,
exercises, activities and discussions
4 The Facilitator used the material in a structured and
effective manner
5 The Facilitator was understandable, approachable and
respectful of the learners
6 The Facilitator was punctual and kept to the schedule
Additional Comments on Facilitation

74
Poor
Below
Standard
Sufficient
Above
Standard
Excellent
1 2 3 4 5
C Learning Programme Evaluation
1 The learning outcomes of the programme are
relevant and suitable.
2 The content of the programme was relevant
and suitable for the target group.
3 The length of the facilitation was suitable for
the programme.
4 The learning material assisted in learning new
knowledge and skills to apply in a practical
manner.
5 The Learning Material was free from spelling
and grammar errors
6 Handouts and Exercises are clear, concise
and relevant to the outcomes and content.
7 Learning material is generally of a high
standard, and user friendly
Additional Comments on Learning Programme
D Assessment Evaluation
Poor
Below
Standard
Sufficient
Above
Standard
Excellent
1 2 3 4 5
1 A clear overview provided of the assessment
requirements of the programme was provided
2 The assessment process and time lines were clearly
explained
3 All assessment activities and activities were discussed
Additional Comments on Assessment

75

9010 Demonstrate an understanding of the use of different number bases and measurement units and an awareness of error in the context of relevant calculations

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to 9010 Demonstrate an understanding of the use of different number bases and measurement units and an awareness of error in the context of relevant calculations

Similar to 9010 Demonstrate an understanding of the use of different number bases and measurement units and an awareness of error in the context of relevant calculations (20)

Recently uploaded

Recently uploaded (20)

9010 Demonstrate an understanding of the use of different number bases and measurement units and an awareness of error in the context of relevant calculations