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Mathematical Literacy
Level 2
National Certificate Vocational
1Future Managers Mathematical Literacy 2
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What we will be covering
• Numbers
• Finance
• Space, Shape and Orientation
• Communicating information with numbers, graphs and tables
• Patterns and Relationships
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Numbers
• Getting help from your calculator
• Use numbers to solve problems
• Calculations to solve problems
• Measurement tools and techniques to solve problems
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Finance
• Income, expenses and financial planning
• Read financial information and make decisions
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Space, Shape and Orientation
• Spaces, shapes and time
• Calculations to solve space and shape problems
• Maps, Grids and Routes
• Diagrams and Instructions
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Communicating information with numbers, graphs and
tables• Use numbers to get answers
• Collect information to answer questions
• Present information
• Analyse and interpret information
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Patterns and relationships
• Patterns for different relationships
• Using information to solve problems
• Translate between different representations of relationships
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Numbers
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Getting help from your calculator
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Numbers• Getting help from your calculator
• Use numbers to solve problems
• Count, order and estimate
• Calculations to solve problems
• Measurement tools and techniques to solve problems
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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)
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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
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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.
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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
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Memory Keys
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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
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Constant Functions
• You can use your calculator to perform constant functions by pressing the equals key
• Try the following:
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Numbers
• Getting help from your calculator
• Use numbers to solve problems
• Count, order and estimate
• Calculations to solve problems
• Measurement tools and techniques to solve problems
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Use Numbers to Solve Problems
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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
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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 2
Mathematical Literacy pg 9
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The Decimal System
Mathematical Literacy 2
821657.324
Mathematical Literacy pg 9
800 000 + 20 000 + 1000 + 600 + 50 + 7 + 0.3 + 0.02 + 0.004
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Moving the Decimal Place
Mathematical Literacy 2
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
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Positive and Negative Numbers
Mathematical Literacy 2
-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
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Uses of Negative Numbers• Debt
• Temperature
• Moving backwards
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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
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Fractions and Percentages
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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
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Expressing Fractions
Mathematical Literacy 2
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:
Mathematical Literacy 2
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Converting Decimals to Common Fractions
Mathematical Literacy 2
Mathematical Literacy pg 17
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%
Mathematical Literacy 2
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
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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
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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
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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
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Comparing Fractions and Percentages
Mathematical Literacy 2
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
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Numbers
• Getting help from your calculator
• Use numbers to solve problems
• Count, order and estimate
• Calculations to solve problems
• Measurement tools and techniques to solve problems
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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
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Adding and subtracting large numbers
• To add a large number:
538
+642
1180
To subtract a large number:
841
-768
73
Mathematical Literacy 2
4
37
Carry 1 over
“Borrow” 10 from the column to the left
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MultiplyTo multiply 32 x 54
Mathematical Literacy 2
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
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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
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Add and Multiply
• When combining addition, multiplication, division and subtraction, the order of the calculation is important.
• The correct order is known as BODMAS
Mathematical Literacy 2
Mathematical Literacy pg 31
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BODMAS
• Brackets
• Of
• Division
• Multiplication
• Addition
• Subtraction
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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 =
Mathematical Literacy 2
44
44140
60
156
2612
2
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Ratios and Proportions
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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
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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
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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
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Measurement Tools and Techniques to Solve Problems
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Numbers• Getting help from your calculator
• Use numbers to solve problems
• Count, order and estimate
• Calculations to solve problems
• Measurement tools and techniques to solve problems
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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
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Units of Measurement• Distance:
– millimetre (mm)– centimetre (cm)– metre (m)– kilometre (km)
• Temperature:– Celsius (°C)
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Units of Measurement
• Volume– millilitre (ml)– litre (l)– kilolitre (kl)
• Time– Seconds (s)– Minutes (min)– Hours (h)
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Units of Measurement
• Mass– milligram (mg)– Gram (g)– kilogram (kg)– ton (t)
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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
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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
Mathematical Literacy 2 62Future Managers
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Measuring Instruments• Length / Distance
– Tape Measure
– Ruler
– Odometer
– GPS
• Weight– Scale
• Volume– Pump
– Container
– Syringe
• Temperature– Thermometer