NCV 2 Mathematical Literacy Hands-On Training Module 1

Mathematical Literacy

Level 2

National Certificate Vocational

1Future Managers Mathematical Literacy 2

What we will be covering

• Numbers

• Finance

• Space, Shape and Orientation

• Communicating information with numbers, graphs and tables

• Patterns and Relationships

Mathematical Literacy 2 2Future Managers

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

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Getting help from your calculator


Numbers• Getting help from your calculator


• Count, order and estimate




Keys on the Calculator

• The Ten Numbers

• Four Function Keys

• The Clear Keys (These keys can vary greatly from calculator to

calculator)

• The Memory Keys (depending on your calculator)


Doing calculations

• To work out a calculation you press the keys as follows: . Your calculator will display the answer

• For multiplication and division, you do the same: (Try this now)

• To add a series of numbers: • And to multiply a series of numbers


Correcting Mistakes

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

Mathematical Literacy 2

Text book page 3

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How the Keys Work

• Generally speaking, C and CA clear all entries into the calculator

• CE clears the last entry only 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.

- or


Memory Keys


Memory Keys

adds the result of the calculation to memory 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:


Numbers







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

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The Decimal System


821657.324


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

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Moving the Decimal Place


821657324

• It moves to the left when we divide by 10

•It moves to the right when we multiply by 10

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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


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

• Anything with a negative sign is less than zero

• Anything without a sign or with a positive sign is greater than zero

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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


Common Fractions: ½

Decimals: 0.5

Percentage: 50%

Ratio 1:2

Numerator

Denominator

Terminator

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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:


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Converting Decimals to Common Fractions



1000

• 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

• On the top line of the fraction, write the digits after the decimal point

0.625=

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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

Answer: =44.44%


420

945

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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:

Therefore your discount is R180 and the amount you pay is R600 – 180 = R420


ComparisonsQuestion: 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

50% 50%

25% 25% 25% 25%

10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

1 / 20

5%

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Calculations to solve problems


Numbers







Outcomes

• At the end of this outcome, you will be able to:– 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

+642

1180

To subtract a large number:

841

-768

73


4

37

Carry 1 over

“Borrow” 10 from the column to the left

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MultiplyTo multiply 32 x 54


32x54

1. Line up the 32 and the 54 as follows:

1282. Now multiply 32 by the four

1604. Multiple 32 by 5 17285. Add the two totals together

3. Put down a zero 0

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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



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BODMAS

• Brackets

• Of

• Division

• Multiplication

• Addition

• Subtraction


Examples• 32 + 3 x 4 =• 32 + (3x4) =• (32 + 3) x 4 = • 7 + 5 x 10 + 3 =• (7 + 5) x (10 + 3) =• 6 + 10% of 200 =• 3 + 4 – 5 + 10 = • 4 x 3 6 =


44

44140

60

156

2612

2

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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 x to y can be expressed as x:y or x / (x + 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 x per 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• Getting help from your calculator






Outcomes• At the end of this outcome, you will be able to:

– 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)


Units of Measurement

• Volume– millilitre (ml)– litre (l)– kilolitre (kl)

• Time– Seconds (s)– Minutes (min)– Hours (h)


Units of Measurement

• 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

– Tape Measure

– Ruler

– Odometer

– GPS

• Weight– Scale

• Volume– Pump

– Container

– Syringe

• Temperature– Thermometer

NCV 2 Mathematical Literacy Hands-On Training Module 1

Education

numbers future managers

mathematical literacy

calculator use numbers

negative numbers

series of numbers

calculator ce

graphs andtables use

use positive