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MATHEMATICAL LITERACY STUDY GUIDE Grade 12
A member of the FUTURELEARN group
Mathematical Literacy Study guide
1812-E-MAL-SG01
Í2,È-E-MAL-SG01NÎ
Grade 12
CAPS aligned
E Brönn A Kies
Study Guide G12 ~ Mathematical Literacy
CONTENTS Lesson elements ................................................................................................................ 5 Preface ................................................................................................................................ 6 Assessment requirements ................................................................................................ 6 The assessment programme ............................................................................................ 7 Year planning ..................................................................................................................... 7 UNIT 1: REVIEW OF BASIC SKILLS ................................................................................. 9 Part 1: Rounding ..................................................................................................... 9 Activity 1 ......................................................................................................... 9 Part 2: Rounding to the nearest 10, 100, 1 000..................................................... 10 Activity 2 ....................................................................................................... 10 Part 3: Scientific notation ...................................................................................... 11 Activity 3 ....................................................................................................... 11 Part 4: Percentages .............................................................................................. 12 Activity 4 ....................................................................................................... 15 Part 5: Ratios ........................................................................................................ 16 Activity 5 ....................................................................................................... 17 Part 6: Rates ......................................................................................................... 18 Activity 6 ....................................................................................................... 18 Part 7: Proportions ................................................................................................ 19 Activity 7 ....................................................................................................... 20 UNIT 2: MEASUREMENT ................................................................................................. 21 Lesson 1: Revision – Measurement ...................................................................... 21 Activity 8 ....................................................................................................... 21 Lesson 2: Time...................................................................................................... 22 Activity 9a ..................................................................................................... 22 Activity 9b ..................................................................................................... 24 Lesson 3: Temperature ......................................................................................... 24 Activity 10 ..................................................................................................... 24 Lesson 4: Travel and timetables ........................................................................... 25 Activity 11a ................................................................................................... 26 Activity 11b ................................................................................................... 27 Lesson 5: Tide timetables ..................................................................................... 28 Activity 12 ..................................................................................................... 29
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Study Guide G12 ~ Mathematical Literacy
UNIT 3: FINANCE ............................................................................................................. 30 Revision activity ............................................................................................ 31 Lesson 6: Break-even analysis ............................................................................. 35 Activity 13 ..................................................................................................... 38 Lesson 7: The budget and revenue and expenditure of the government .............. 39 Activity 14a ................................................................................................... 40 Activity 14b ................................................................................................... 40 Activity 15 ..................................................................................................... 43 Lesson 8: Running a business .............................................................................. 44 Activity 16 ..................................................................................................... 45 Activity 17 ..................................................................................................... 46 Activity 18 ..................................................................................................... 47 Activity 19 ..................................................................................................... 48 Activity 20 ..................................................................................................... 48 UNIT 4: DATA HANDLING ............................................................................................... 49 Lesson 9: Interpreting statistics ............................................................................. 49 Activity 21 ..................................................................................................... 51 Activity 22 ..................................................................................................... 52 Activity 23 ..................................................................................................... 53 Activity 24 ..................................................................................................... 60 Activity 25 ..................................................................................................... 60 Lesson 10: Summarise data with quartiles and percentiles .................................. 71 Activity 26 ..................................................................................................... 78 UNIT 5: MORE FINANCES ............................................................................................... 83 Lesson 11: Hire purchase ..................................................................................... 83 Activity 27 ..................................................................................................... 83 Activity 28 ..................................................................................................... 85 Lesson 12: Interest................................................................................................ 85 Activity 29 ..................................................................................................... 89 Lesson 13: Loans .................................................................................................. 89 Activity 30 ..................................................................................................... 92 Activity 31 ..................................................................................................... 93 Lesson 14: Annuities and investments .................................................................. 95 Activity 32 ..................................................................................................... 98 Lesson 15: Inflation ............................................................................................... 98 Activity 33 ................................................................................................... 100 UNIT 6: MAPWORK ........................................................................................................ 102 Revision activity .......................................................................................... 103 Lesson 16: Travel costs ...................................................................................... 108 Activity 34 ................................................................................................... 111 Activity 35 ................................................................................................... 112
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Study Guide G12 ~ Mathematical Literacy
Lesson 17: Compass directions .......................................................................... 113 Lesson 18: Longitudes and latitudes ................................................................... 114 Activity 36 ................................................................................................... 118 Activity 37 ................................................................................................... 119 Activity 38 ................................................................................................... 120 Lesson 19: Scales ............................................................................................... 120 Activity 39 ................................................................................................... 121 UNIT 7: MEASUREMENT – PERIMETER, AREA, VOLUME ......................................... 125 Lesson 20: Calculating the perimeter .................................................................. 127 Activity 40 ................................................................................................... 129 Lesson 21: Calculate area .................................................................................. 131 Activity 41 ................................................................................................... 132 Lesson 22: Calculate volume .............................................................................. 133 Activity 42 ................................................................................................... 138 Activity 43 ................................................................................................... 141 Lesson 23: Body mass index .............................................................................. 144 Activity 44 ................................................................................................... 146 Lesson 24: Medicine dosages ............................................................................. 146 Activity 45 ................................................................................................... 148 Activity 46 ................................................................................................... 148 UNIT 8: FINANCES – TAX, EXCHANGE RATES .......................................................... 149 Lesson 25: Unemployment Insurance Fund (UIF)............................................... 149 Activity 47 ................................................................................................... 149 Lesson 26: Income Tax ....................................................................................... 150 Activity 48 ................................................................................................... 153 Activity 49 ................................................................................................... 155 Lesson 27: Calculate the net salary .................................................................... 156 Activity 50 ................................................................................................... 157 Lesson 28: Exchange rates ................................................................................. 159 Activity 51 ................................................................................................... 160 Activity 52 ................................................................................................... 161 UNIT 9: MAPS AND PLANS ........................................................................................... 162 Lesson 29: Floor plans ........................................................................................ 166 Activity 53 ................................................................................................... 167 Activity 54 ................................................................................................... 168 Lesson 30: Profile maps ...................................................................................... 169 Lesson 31: Elevations ......................................................................................... 169 Activity 55 ................................................................................................... 171 Lesson 32: Models and instructions .................................................................... 172 Activity 56 ................................................................................................... 172
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Study Guide G12 ~ Mathematical Literacy
UNIT 10: PROBABILITY ................................................................................................. 174 Lesson 33: Probability ......................................................................................... 174 Activity 57 ................................................................................................... 177 Activity 58 ................................................................................................... 179 Lesson 34: Probability to win the Lotto................................................................ 181 Lesson 35: Prediction.......................................................................................... 183 Activity 59 ................................................................................................... 185 Lesson 36: Expression of probability in the media .............................................. 186 BIBLIOGRAPHY ............................................................................................................. 189
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Study Guide G12 ~ Mathematical Literacy
LESSON ELEMENTS LEARNING AIMS What candidates should know at the end of the lesson. Taken from CAPS.
IMPORTANT TERMINOLOGY New terminology to extend understanding of the subject as part of the lesson.
DEFINE Definitions of concepts to help candidates understand the content.
IMPORTANT A summary or explanation of key concepts explained in the lesson.
TIPS Information in addition to the content to guide candidates through the learning process.
FOR THE CURIOUS Encouragement for candidates to do in-depth research about the content on his/her own.
ACTIVITY Formative assessment to test candidates’ progress and knowledge of the lesson completed.
EXERCISE Formative assessment to test candidates’ progress and knowledge of the unit completed.
CORE CONTENT Reinforcement of core of content; in-depth explanation of a specific section of the lesson.
STUDY/REVISION Demarcation or summary of work to be revised in preparation for tests and examinations.
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Study Guide G12 ~ Mathematical Literacy
Preface Recommended book Any additional book can be used in conjunction with this study guide. It is always a good idea to refer to other textbooks, in addition to the study guide, to gain a broader perspective on the subject. • The Answer Series 3 in 1 Mathematical Literacy • Mathematical Literacy for the Classroom
Assessment requirements In this facilitator’s guide, you will note that there are constant references to TL1, TL2, TL3 and TL4. This is the thinking level that is required to answer the specific question that is being asked. The thinking levels represent the following skills: Thinking level 1: Knowing Thinking level 2: Applying routine procedures in familiar contexts Thinking level 3: Applying multi-step procedures in a variety of contexts Thinking level 4: Reasoning and reflecting When tasks, investigations and especially tests and examinations are set, the guidelines below are used to allocate a number of marks to a specific thinking level. Distribution of marks according to the thinking levels: Percentage of marks allocated
Thinking levels Thinking level 1: Knowing
30% (±5%)
Thinking level 2: Applying routine procedures in familiar contexts
30% (±5%)
Thinking level 3: Applying multi-step procedures in a variety of contexts
20% (±5%)
Thinking level 4: Reasoning and reflecting
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20% (±5%)
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Study Guide G12 ~ Mathematical Literacy
The assessment programme Refer to my.Impaq for assessment tasks, examinations and the assessment plan.
Year planning 1 2 3 4 5 6
UNIT
7 8 9 10
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THEME REVIEW OF BASIC SKILLS MEASUREMENT FINANCE DATA HANDLING MORE FINANCES MAPWORK MEASUREMENT (PERIMETER, AREA, VOLUME) FINANCES – TAX & EXCHANGE RATES MAPS AND PLANS PROBABILITY REVISION
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TERM 1: JANUARY – MARCH
TERM 2: APRIL – JUNE
TERM 3: JULY – AUGUST SEPTEMBER: PRELIMINARY EXAMINATION NOVEMBER: FINAL EXAMINATION
Study Guide G12 ~ Mathematical Literacy
Suggested time to spend on each unit: Term 1
2
3
Unit 1 2 3 4 5 6 7 8 9 10
Theme Review of basic skills Measurement Finance Data handling More finances Mapwork Measurement (perimeter, area, volume) Finances – tax and exchange rates Maps and plans Probability
Number of weeks Own time/worked in 1 3 5 2 1 4 1 3 2
The time allocation per topic is only a guideline and can be adapted to the pace of candidates. It is nevertheless important to know that the lessons in question have to be completed before tests or examinations can be written.
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Study Guide G12 ~ Mathematical Literacy
Unit
1
UNIT 1: REVIEW OF BASIC SKILLS Learning objectives After completing this unit, you should be able to do the following: • Apply basic mathematical skills. • Understand rounding, scientific notation, percentages, ratio, proportion and complete calculations.
Part 1: Rounding EXAMPLES Round the following numbers to the number of decimal places indicated in brackets: 1.1
3,14823 (2 decimal places) Answer: ≈ 3,15
Note: Look at the third decimal. A number less than 4 makes no difference to the second decimal. If the third decimal is 5 and higher, the second decimal should be rounded up to the next number. 1.2
1.3
23,89432 (3 decimal places) Answer: ≈ 23,894 215,899 (2 decimal places) Answer: ≈ 215,90 Activity 1
Round the following numbers to TWO decimal places: 1. 2,3568 2. 0,356789 3. 1,9999 4. 13,4386 5. 234,8765
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Study Guide G12 ~ Mathematical Literacy
Unit
Part 2: Rounding to the nearest 10, 100, 1 000 EXAMPLES 2.1
2.2
2.3
Round the following numbers to the nearest 10: 2.1.1 65 ≈ 70 2.1.2 16 ≈ 20 2.1.3 173 ≈ 170 2.1.4 589 ≈ 590
Round the following numbers to the nearest 100: 2.2.1 65 ≈ 100 2.2.2 1 082 ≈ 1 100
Round the following numbers to the nearest 1 000: 2.3.1 5 999 ≈ 1 000 2.3.2 4 956 ≈ 5 000 Activity 2
Round the following numbers to the nearest 10, 100 of 1 000: 1. 2. 3. 4. 5.
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58 (nearest 10) 345 (nearest 100) 1 367 (nearest 1 000) 1 356 (nearest 10, 100 and 1 000, respectively) 2 835 (nearest 10, 100 and 1 000, respectively)
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Study Guide G12 ~ Mathematical Literacy
Unit
Part 3: Scientific notation Important One million: 1 000 000 (6 zeroes) One billion: 1 000 000 000 (9 zeroes) One trillion: 1 000 000 000 000 (12 zeroes) Scientific notation is used for very large or very small numbers. It is written differently to make it easier to read. EXAMPLES •
Convert 0,0043 to scientific notation.
•
Convert 81 500 to scientific notation.
• • • •
14 000 000 → can be written as 1,4 x 107 582 000 000 000 → can be written as 5,82 x 1011 0,0000018 → can be written as 1,8 x 10–6 0,00000000005 → can be written as 5,0 x 10–11 Activity 3
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Write the following numbers in scientific notation: 1.1. 4 800 000 1.2. 2 500 1.3. 0,00000012 1.4. 0,00023
2.
Write the following as an ordinary number: 2.1. 3,4 x 105 2.2. 6,28 x 109 2.3. 2,3 x 10–6 2.4. 4,5 x 10–9
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Study Guide G12 ~ Mathematical Literacy
Unit
1
Part 4: Percentages Percentages are expressed as a common fraction or as a decimal number, e.g. 25% = 4.1
25
100
= 0,25
Calculation of percentage
EXAMPLES 4.1.1 Calculate 15% of R1 200. Note: remember the word “of” means multiplication. 15
100
× R1 200 = R180,00
Sequence on calculator: 15 ÷ 100 x 1 200 = 26
4.1.2 Janet gets 40 for a Mathematical Literacy test. What is her percentage for the test? 26 × 100 = 65% 40
Sequence on calculator: 26 ÷ 40 x 100 = 4.2
Determining new values for given percentages
EXAMPLES 4.2.1
A packet of chips costs R3,20 without VAT (value-added tax). How much will you pay if VAT is added? (VAT is 15%) 15
100
× R3,20 = R0,48
or
R3,20 + R0,48 = R3,68 You will pay R3,68.
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R3,20 × 115% = R3,68
Study Guide G12 ~ Mathematical Literacy
4.2.2
Unit
1
A vendor increases his prices by 6%. If the original price is R21,99, what will the price be after the increase? 6
100
or
× R21,99 = R1,32
R21,99 × 106% = R23,31
R1,32 + R21,99 = R23,31
The new price will be R23,31.
4.2.3
A shop has a sale with 25% off all jeans. What will you pay for a pair of jeans if the original price was R395,00? 25
100
or
× R395 = R98,75
100 – 25 = 75% 75% x R395 = R296,25
R395 − R98,75 = R296,25
The pair of jeans will now cost R296,25.
4.2.4
The petrol price decreases with 4,5%. How much will we pay now if we previously paid R12,30 per litre? 4,5
100
or
× R12,30 = R0,5535
100 – 4,5 = 95,5%
R12,30 – R0,5535 = R11,75
95,5% x R12,30 = R11,75
We will now pay R11,75. 4.3
Determining the original value when a percentage is given Important Remember that the original value must be determined – the previous amount, before it was increased or decreased. 4.3.1
A slab of chocolate costs R15,10, VAT included. VAT is 15%. What is the price of the chocolate without VAT? P: price without VAT P x 115% = R15,10
P=
15,10
115%
[115% = 100% + 15%]
or
R15,10 ÷ 1,15
P = R13,13 The original price was R13,13.
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Study Guide G12 ~ Mathematical Literacy
4.3.2
Unit
1
A butcher increases his meat prices by 6%. Boerewors now costs R25,75/kg. What was the original price before the increase? P: original price P x 106% = R25,75 P = 25,75 ÷ 106% = R24,29 The original price was R24,29.
4.3.3
A shoe shop has a sale at 25% discount. If the selling price of a pair of sneakers is now R348,25, what was the original price before the discount? P: original price (100% – 25% = 75%) P x 75% = R348,25 P = R348,25 ÷ 75% = R464,33 The original price of the sneakers was R464,33.
4.4
Percentage increase and percentage reduction The following formula is useful to calculate the increase and decrease in percentages. current value − previous value
4.4.1
previous value
× 100
In 2014, a school had 1 252 learners and by 2015, there were 1 385 learners in the school. By which percentage did the enrolment increase? current value − previous value previous value
1 385−1 252 1 252
= 10,62%
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(Do not enter %)
× 100
14
× 100