NCV 2 Mathematical Literacy Hands-On Training Module 1

Mathematical Literacy

Level 2

National Certificate Vocational

Future Managers Mathematical Literacy 2 1

What we will be covering
• Numbers
• Finance
• Space, Shape and Orientation
• Communicating information with numbers,
graphs and tables
• Patterns and Relationships


Numbers

• Getting help from your calculator
• Use numbers to solve problems
• Calculations to solve problems
• Measurement tools and techniques to solve
problems


Finance
• Income, expenses and financial planning
• Read financial information and make decisions


Space, Shape and Orientation
• Spaces, shapes and time
• Calculations to solve space and shape problems
• Maps, Grids and Routes
• Diagrams and Instructions


Communicating information
with numbers, graphs and
tables
• Use numbers to get answers
• Collect information to answer questions
• Present information
• Analyse and interpret information


Patterns and relationships
• Patterns for different relationships
• Using information to solve problems
• Translate between different representations of
relationships


Numbers

Future Managers 8

Getting help from your
calculator


Numbers
• Count, order and estimate
problems


Keys on the Calculator
• The Ten Numbers
T 1e
• Four Function Keys
Four
• The Clear Keys
È (These keys can vary greatly from calculator to
calculator)
• The Memory Keys
The (depending on your calculator)


Doing calculations
• To work out a calculation you press the keys as follows:
TT o. Your calculator will display the answer 
• For multiplication and division, you do the same: For
(Try this now)
• To add a series of numbers: TTo TTTo
• And to multiply a series of numbers
A A nd t
AA


Correcting Mistakes
• A calculator may have any combination of the
following keys: C, CE, CL, DEL, AC and or a

Text book page 3

How the Keys Work
• Generally speaking, C and CA clear all entries
into the calculator
• CE clears the last entry only
C and del, clear one number only
• Spend five minutes with your calculator now,
finding out how your calculator works.


How to correct mistakes
• If you press the wrong number, you can use your
calculator’s CE key (or backspace or del if your
calculator has these keys)
• If you have made a mistake and entered it into
your calculator, you may need to correct the
mistake with the opposite calculation procedure.
m s -- i or o
i


Memory Keys


Memory Keys
Madds the result of the calculation to memory
a subtracts the result of the calculation from
memory
• RCL or MRC or MR recalls the contents of the
memory


Constant Functions
• You can use your calculator to perform constant
functions by pressing the equals key
• Try the following:
Tr y
Tr y


Numbers
problems


Use Numbers to Solve
Problems


Outcomes
• At the end of this outcome, you will be able to:
– Use numbers to count, order and estimate
– Use positive and negative numbers as directional
indicators
– Use fractions, decimal and percentages as parts of a
whole


Count, order and estimate
• The number system that we use is the decimal
system, consisting of the numbers 0-9
• There are many other number systems, for
example binary consisting of just 0 and 1 which
is used by computers

Mathematical Literacy pg 9

The Decimal System

821657.324

800 000 + 20 000 + 1000 + 600 + 50 + 7 + 0.3 + 0.02 + 0.004


Moving the Decimal Place

•It moves to the right when we multiply by
10
• It moves to the left when we divide by 10

821657324

Estimation
• An estimate is just an informed guess
• We use estimation when it would be difficult to
do a full calculation, and we don’t need to be
accurate


Positive and Negative
Numbers
• Anything with a negative sign is less than
zero
• Anything without a sign or with a
positive sign is greater than zero

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8


Positive and Negative
Numbers
• The further to the left on the negative side, the larger the
digits, but the smaller the value of the digits
• The arrows on the line represent negative numbers
continuing on to the left, and positive numbers
continuing on to the right
• The numbers on the number line are all integers or
whole numbers
• Between the whole numbers, lie various fractions


Uses of Negative Numbers
• Debt
• Temperature
• Moving backwards


Symbols in Maths
• = Is the same as
∀ ≠ Is not the same as
∀ < Is greater than
∀ > Is less than
∀ ≥ Is greater than or equal to
∀ ≤ Is less than or equal to
∀ + Add
∀ − Subtract
∀ ÷ Divide
∀ × Multiply

Fractions and Percentages


Fractions and Percentages
• A fraction means “less than one of”
• With the pizza on the previous page, each piece
of the pizza was one eighth of the total
• Add together all 8 pieces and you have eight
eighths or a whole pizza
• 1½ means one pizza plus a half of a pizza
• This is the same as 3/2 meaning 3 halves of a
pizza


Expressing Fractions

Numerator
Common Fractions: ½
Denominator
Decimals: 0.5
Percentage: 50%
Ratio 1:2

Terminator


Converting Fractions to
Decimals

• To change a fraction to a decimal, divide
the top number by the bottom number
• What is 1/8 as a decimal?
• Using your calculator:
M h
at M M M M



Converting Decimals to
Common Fractions
• On the top line of the fraction, write the
digits after the decimal point
• On the bottom line of the fraction, write
the number 1 followed by the same number
of zero’s as digits after the comma

625
0.625=
1000


Converting Fractions to
Percentages
1. Divide the numerator by the denominator to get the
fraction in decimal format
2. Multiply the answer by 100 to get a percentage
3. Add a % sign to your answer
420
945
Answer: A w : s i gn t o your
ns er
=44.44%


Percentages

• A percentage is a fraction out of 100
• 10% therefore means 10 out of 100
• A percentage can also be written as a ratio
10:100


Calculating a % of a whole
• We use this when we want to say “some percent of”
Example: A clothing store is offering a 30% on all clothes.
You buy R600 worth of clothes, how much discount do
you receive?
Answer: A w : i ve
ns er
AA

Therefore your discount is R180 and the amount you pay
is R600 – 180 = R420


Comparisons
Question: Which shop gives the bigger discount:
Shop A discounting R10 from R30 or shop B
discounting R13 from R38?
Answer:
Shop A: 10 ÷ 30 x 100 = 33.3%
Shop B: 13 ÷ 38 x 100 = 34.21%
Therefore Shop B gives a bigger discount


Comparisons
• R200 is divided between Nomsa, Shehaan and
James in the ratio 4:2:2. How much does each
person get?
Answer: There are eight equal parts (4 +2 +2)
Nomsa gets 4 eights = 4 ÷ 8 x 200 = R100
Shehaan and James each get 2 eighths = 2 ÷ 8 x
100 = R50


Comparing Fractions and
Percentages
½ ½
¼ ¼ ¼ ¼
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
1 / 20

50% 50%
25% 25% 25% 25%
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
5%


Calculations to solve
problems


Numbers
problems


Outcomes
– Perform calculations using a pen and paper out of your head
– Add and subtract to simplify calculations where possible and/
or useful
– Use ratios and proportions to solve problems
– Use estimation to anticipate and evaluate the result of a
calculation and/or measurement
– Estimate an “unknown” to solve a problem


Adding and subtracting large
numbers
• To add a large number:
538
4
Carry 1 over
+642
1180
To subtract a large number:
841
7 3

-768 “Borrow” 10 from the
column to the left
73

Mathematical Literacy 2
Future Managers 44

Multiply
To multiply 32 x 54
1. Line up the 32 and the 54 as follows: 32
2. Now multiply 32 by the four
x54
3. Put down a zero
128
1600
4. Multiple 32 by 5
1728
5. Add the two totals together


Rounding Off
• Often, when we have long and complicated numbers, we
round them off to simplify them.
• We do this, when we don’t need a high degree of accuracy
Examples:
• Newlands rugby stadium has a capacity of 50 000 people
(50900)
• You can’t buy 2½ packets of boerewors for a party, you
will round it up to 3
• If you have 3.25 litres of water, you can only fill 3 one
litre water bottles, so you will round down


How to Round Off
• Look at the number and find the digit that you want to
round off to.
• Find the decimal to the immediate right of it. If it is
from 0-4 then the digit you are rounding to stays the
same. If it is 5-9 then it increases by one.
• Eg. 763243 to the nearest hundred is: 743200
• E.g.. 823790 to the nearest hundred is 823800


Add and Multiply
• When combining addition, multiplication,
division and subtraction, the order of the
calculation is important.
• The correct order is known as BODMAS


BODMAS
• Brackets
• Of
• Division
• Multiplication
• Addition
• Subtraction


Examples
• 32 + 3 x 4 = 44
• 32 + (3x4) = 44
• (32 + 3) x 4 = 140
• 7 + 5 x 10 + 3 = 60
• (7 + 5) x (10 + 3) = 156
• 6 + 10% of 200 =
26
• 3 + 4 – 5 + 10 =
12
• 4x3÷6=
2


Ratios and Proportions


Ratios
• A ratio is used to calculate the relative sizes or
quantities of two things
• Example: The ratio of Energade concentrate to
water to make Energade
• The ratio of xto y can be expressed as x or x/ (x
:y
+ y)
• A ratio doesn’t have units


Proportion
• Direct Proportion – If one quantity rises, the
other quantity rises with it
• E.g. Distance covered vs. time
• Indirect proportions – If one quantity rises, the
other quantity falls
• E.g. Price of Petrol vs. number of litres that you
can buy for a certain amount


Rates
• Rates are expressed as xper y
• Rates are used to compare different kinds of
quantities
• Most often rates will be expressed in terms of
time


Measurement Tools and
Techniques to Solve Problems


Numbers
problems


Outcomes
– Select measuring instruments to measure length, weight,
volume, temperature and time intervals
– Select and use formulae to calculate measurements and solve
problems
– Perform conversions between units as needed
– Explain the degree of accuracy and / or precision when
measurements and / or related calculations are needed
– Use and apply rates to solve contextual problems


Units of Measurement
• Distance:
– millimetre (mm)
– centimetre (cm)
– metre (m)
– kilometre (km)
• Temperature:
– Celsius (°C)


• Volume
– millilitre (ml)
– litre (l)
– kilolitre (kl)
• Time
– Seconds (s)
– Minutes (min)
– Hours (h)


• Mass
– milligram (mg)
– Gram (g)
– kilogram (kg)
– ton (t)


kilo, centi, milli,
• kilo means thousands e.g. one kilometre equals
one thousand metres
• centi means hundredths e.g. one centimetre
equals 1 /100 of a metre
• milli means thousandths e.g. one millimetre
equals 1/1000 of a metre


Convert
• If converting from a large unit to a small then
you need to multiply e.g. to get from litres to
millilitres you multiply by 1000
• If converting from a small unit to a large unit,
you need to divide e.g. 10mm = 1cm


Measuring Instruments
• Length / Distance • Volume
– Tape Measure – Pump
– Ruler – Container
– Odometer – Syringe
– GPS
• Temperature
• Weight – Thermometer
– Scale

NCV 2 Mathematical Literacy Hands-On Training Module 1

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