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# NCV 2 Mathematical Literacy Hands-On Training Module 1

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### NCV 2 Mathematical Literacy Hands-On Training Module 1

1. 1. Mathematical Literacy Level 2 National Certificate Vocational Future Managers Mathematical Literacy 2 1
2. 2. What we will be covering • Numbers • Finance • Space, Shape and Orientation • Communicating information with numbers, graphs and tables • Patterns and Relationships Future Managers Mathematical Literacy 2 2
3. 3. Numbers • Getting help from your calculator • Use numbers to solve problems • Calculations to solve problems • Measurement tools and techniques to solve problems Future Managers Mathematical Literacy 2 3
4. 4. Finance • Income, expenses and financial planning • Read financial information and make decisions Future Managers Mathematical Literacy 2 4
5. 5. Space, Shape and Orientation • Spaces, shapes and time • Calculations to solve space and shape problems • Maps, Grids and Routes • Diagrams and Instructions Future Managers Mathematical Literacy 2 5
6. 6. Communicating information with numbers, graphs and tables • Use numbers to get answers • Collect information to answer questions • Present information • Analyse and interpret information Future Managers Mathematical Literacy 2 6
7. 7. Patterns and relationships • Patterns for different relationships • Using information to solve problems • Translate between different representations of relationships Future Managers Mathematical Literacy 2 7
8. 8. Numbers Future Managers 8
9. 9. Getting help from your calculator Future Managers Mathematical Literacy 2 9
10. 10. 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 Future Managers Mathematical Literacy 2 10
11. 11. 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) Future Managers Mathematical Literacy 2 11
12. 12. 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 Future Managers Mathematical Literacy 2 12
13. 13. Correcting Mistakes • A calculator may have any combination of the following keys: C, CE, CL, DEL, AC and or a Text book page 3 Future Managers Mathematical Literacy 2 13
14. 14. 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. Future Managers Mathematical Literacy 2 14
15. 15. 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 Future Managers Mathematical Literacy 2 15
16. 16. Memory Keys Future Managers Mathematical Literacy 2 16
17. 17. 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 Future Managers Mathematical Literacy 2 17
18. 18. Constant Functions • You can use your calculator to perform constant functions by pressing the equals key • Try the following: Tr y Tr y Future Managers Mathematical Literacy 2 18
19. 19. 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 Future Managers Mathematical Literacy 2 19
20. 20. Use Numbers to Solve Problems Future Managers Mathematical Literacy 2 20
21. 21. 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 Future Managers Mathematical Literacy 2 21
22. 22. 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 Future Managers Mathematical Literacy 2 22
23. 23. The Decimal System 821657.324 800 000 + 20 000 + 1000 + 600 + 50 + 7 + 0.3 + 0.02 + 0.004 Mathematical Literacy pg 9 Future Managers Mathematical Literacy 2 23
24. 24. 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 Future Managers Mathematical Literacy 2 24
25. 25. 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 Future Managers Mathematical Literacy 2 25
26. 26. 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 Future Managers Mathematical Literacy 2 26
27. 27. 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 Future Managers Mathematical Literacy 2 27
28. 28. Uses of Negative Numbers • Debt • Temperature • Moving backwards Future Managers Mathematical Literacy 2 28
29. 29. 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 Future Managers Mathematical Literacy 2 29
30. 30. Fractions and Percentages Future Managers Mathematical Literacy 2 30
31. 31. 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 Future Managers Mathematical Literacy 2 31
32. 32. Expressing Fractions Numerator Common Fractions: ½ Denominator Decimals: 0.5 Percentage: 50% Ratio 1:2 Terminator Future Managers Mathematical Literacy 2 32
33. 33. 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  Future Managers Mathematical Literacy 2 33
34. 34. 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 Mathematical Literacy pg 17 Future Managers Mathematical Literacy 2 34
35. 35. 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% Future Managers Mathematical Literacy 2 35
36. 36. 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 Future Managers Mathematical Literacy 2 36
37. 37. 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 Future Managers Mathematical Literacy 2 37
38. 38. 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 Future Managers Mathematical Literacy 2 38
39. 39. 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 Future Managers Mathematical Literacy 2 39
40. 40. 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% Future Managers Mathematical Literacy 2 40
41. 41. Calculations to solve problems Future Managers Mathematical Literacy 2 41
42. 42. 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 Future Managers Mathematical Literacy 2 42
43. 43. 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 Future Managers Mathematical Literacy 2 43
44. 44. 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
45. 45. 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 Future Managers Mathematical Literacy 2 45
46. 46. 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 Future Managers Mathematical Literacy 2 46
47. 47. 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 Future Managers Mathematical Literacy 2 47
48. 48. 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 pg 31 Future Managers Mathematical Literacy 2 48
49. 49. BODMAS • Brackets • Of • Division • Multiplication • Addition • Subtraction Future Managers Mathematical Literacy 2 49
50. 50. 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 Future Managers Mathematical Literacy 2 50
51. 51. Ratios and Proportions Future Managers Mathematical Literacy 2 51
52. 52. 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 Future Managers Mathematical Literacy 2 52
53. 53. 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 Future Managers Mathematical Literacy 2 53
54. 54. 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 Future Managers Mathematical Literacy 2 54
55. 55. Measurement Tools and Techniques to Solve Problems Future Managers Mathematical Literacy 2 55
56. 56. 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 Future Managers Mathematical Literacy 2 56
57. 57. 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 Future Managers Mathematical Literacy 2 57
58. 58. Units of Measurement • Distance: – millimetre (mm) – centimetre (cm) – metre (m) – kilometre (km) • Temperature: – Celsius (°C) Future Managers Mathematical Literacy 2 58
59. 59. Units of Measurement • Volume – millilitre (ml) – litre (l) – kilolitre (kl) • Time – Seconds (s) – Minutes (min) – Hours (h) Future Managers Mathematical Literacy 2 59
60. 60. Units of Measurement • Mass – milligram (mg) – Gram (g) – kilogram (kg) – ton (t) Future Managers Mathematical Literacy 2 60
61. 61. 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 Future Managers Mathematical Literacy 2 61
62. 62. 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 Future Managers Mathematical Literacy 2 62
63. 63. Measuring Instruments • Length / Distance • Volume – Tape Measure – Pump – Ruler – Container – Odometer – Syringe – GPS • Temperature • Weight – Thermometer – Scale