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Mathematical Literacy Grade 12

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					Mathematical
  Literacy
 Grade 12
                             Table of Contents
                                                                           Page number
Module 1 Retirement and travel
Unit 1
Chapter 1   Personal and business finances (1)                                  4
Chapter 2   Personal and business finances (2)                                  7
Chapter 3   Must we carry on with the annuity?                                  9
Chapter 4   Personal finances at a glance                                      11
Chapter 5   My bank and I                                                      14

Unit 2
Chapter 1   Exchange rates                                                     16
Chapter 2   Finding places in Egypt                                            21
Chapter 3   Fluctuations in the currency                                       24
Chapter 4   My trip to a far country                                           27

Unit 3
Chapter 1   To buy or not to buy on credit                                     29
Chapter 2   What about importing it?                                           33
Chapter 3   What is the effect of taxes on me?                                 35
Chapter 4   To buy now or to wait                                              36

Module 2 Building a cottage
Unit 1
Chapter 1   The cottage                                                        39
Chapter 2   Surface area of polyhedra                                          42
Chapter 3   Volumes of polyhedra                                               51
Chapter 4   Trigonometric rations in right-angled triangles                    57
Chapter 5   Calculations on the roof of the cottage                            76
Chapter 6   The garden                                                         80
Chapter 7   Scale model of the house                                           83
Chapter 8   A visit to Kiev                                                    85

Module 3 Optimum wage of resources
Unit 1
Chapter 1   Who could earn four million rand the easiest?                      90
Chapter 2   Who must produce what?                                             94
Chapter 3   How to find the best price                                         102
Chapter 4   Does supply influence price?                                       106
Chapter 5   Does demand influence price?                                       111

Unit 2
Chapter 1   Does gender influence academic performance?                        115
Chapter 2   Which factors influence life expectancy?                           126
Chapter 3   Supplying the most needy schools with
                                                                               132
            resources


              Grade 12 Mathematical Literacy Learner’s Book Module 1 – 3
                                   Page 2 of 160
Unit 3
Chapter 1   What is the chance?                                            145
Chapter 2   How many learners are abusing substances?                      151
Chapter 3   The influence of the media on promoting
                                                                           153
            unprotected sex




              Grade 12 Mathematical Literacy Learner’s Book Module 1 – 3
                                   Page 3 of 160
 Unit 1
Activity 2
 Planning
Documents
                                                                                               SUBJECT FRAMEWORK: YEAR PLAN
School:                                                                                  Year:                                                                                     Term/Weeks:
                      Grade 10: Module 1                                                                          Grade 11: Module 1                                                                        Grade 12: Module 1
  Duration of                      Learning                                                Duration of         40            Learning                                               Duration of         40            Learning
                   40 hours
   module:                        outcomes:                                                 module:           hours         outcomes:                                                 module:          hours         outcomes:
     Learning                                                                                   Learning                                                                                Learning
                       Assessment standard                      Content                                            Assessment standard                       Content                                       Assessment standard                       Content
    Outcomes                                                                                   Outcomes                                                                                Outcomes
10.4: Data           10.4.1: Investigate           Interviews.                           11.1: Number and         11.1.1: In a variety of      Scientific calculator.              12.1: Number          12.1.1: Correctly apply        Appropriate statistical methods.
handling: The        situations in own life by:    Questionnaires.                       Operations in            contexts, find ways to                                           and Operations        problem-solving and            Sample population.
                                                                                                                                                    − b ± b 2 − 4ac
learner is able to   (a) Formulating questions     Use of data bases: tallies, tables,   Context: The             explore and analyse          x=                                  in Context: The       calculation skills to          Sources and samples.
collect,             on issues such as those       pie charts, histograms, single-bar,   learner is able to       situations that are                     2a                       learner is able to    situations and problems        Methods to summarise.
summarise,           related to:                   compound-bar graphs, line and         use knowledge of         numerically based by:        Digits.                             use knowledge of      dealt with.                    Statistical charts.
display and          (ii) People’s opinions.       broken-line graphs.                   numbers and their        (a) Estimating               Rounding.                           numbers and           12.1.2: Relate calculated      Scatter-plots.
analyse data and     (iii) Human rights and        Awareness of sources of error.        relationships to         efficiently.                 Positive exponents.                 their relationships   answers correctly and          Intuitively-placed lines.
to apply             inclusivity.                  Appropriate measures of central       investigate a range      (b) Wording with             Roots.                              to investigate a      appropriately to the           Variables (regression analyses not
knowledge of         (b) Collecting or finding     tendency: mean, median, mode,         of different contexts    complex formulae by          Ratio.                              range of different    problem situation by:          included).
statistics and       data by appropriate           range.                                which include            hand and with a              Proportion.                         contexts which        (a): Interpreting fractional   Positive linear association.
probability to       methods (e.g. interviews,     Formulate questions.                  financial aspects of     scientific calculator, for   Quantities.                         include financial     parts of answers in terms      Probability.
communicate,         questionnaires, the use of    Collect or find data.                 personal business        example:                     Value.                              aspects of            of the context.                Outcomes.
justify, predict     data bases) suited to the     Draw conclusions.                     and national issues.                                  Income.                             personal,             (b): Reworking a problem       Use and misuse of statistics in
and critically       purpose of drawing            Justify and use a variety of                                         − b ± b 2 − 4ac        Expenditure items.                  business and          if the first answer is not     society.
                                                                                                                   x=
interrogate          conclusions to the            methods.                                                                    2a              Optimal selling prices.             national issues.      sensible or if the initial     Measures of central tendency:
findings and draw    questions.                    Display data in statistical charts.                            (c) Showing awareness        Checking (profit margins).                                conditions change.             mean, median, mode, range.
conclusions.         10.4.2: Select, justify and   Critical interpretation.                                       of the significance of       Find ways to explore.                                     (c): Interpreting              Variance (interpretation only).
                     use a variety of methods      Conclusions.                                                   digits when rounding.        Analyse situations.                                       calculated answers             Standard deviation (interpretation
                     to summarise and display      Make predictions.                                              (d) Checking                 Estimating efficiency.                                    logically in relation to the   only)
                     data in statistical charts                                                                   statements and results       Working with complex formulae.                            problem and                    Quartiles.
                     and graphs inclusive of:                                                                     by doing relevant            Awareness of the significance.                            communicating                  Percentiles.
                     (a) Tallies.                                                                                 calculations.                Checking statements.                                      processes and results.         Investigate a problem.
                     (b)Tables.                                                                                   (e) Working with             Doing calculations.                                       12.1.3: Analyse and            Using appropriate statistical
                     (c) Pie charts.                                                                              positive exponents and       Relating calculated answers to                            critically interpret a wide    methods.
                     (d) Histogram (first                                                                         roots.                       problem situations.                                       variety of financial           Selecting a representative sample.
                     grouping the data).                                                                          (f) Involving ratio and      Interpreting fractional parts of                          (a): Personal and              Comparing data.
                     (e) Single-bar and                                                                           proportion in cases          answers in context.                                       business finances              Choose and interpret.
                     compound-bar graphs.                                                                         where more than two          Reworking a problem.                                      (b): The effects of            Describe trends.
                     (f) Line and broken-line                                                                     quantities are involved.     Interpreting calculated answers.                          taxation, inflation, and       Making predictions.
                     graphs.                                                                                      11.1.2: Relate               Investigate opportunities.                                changing interest rates on     Critically evaluate statistically-
                     10.4.3: Calculate and use                                                                    calculated answers           Determine profit.                                         personal credit,               based arguments.
                     appropriate measures of                                                                      correctly and                Analysing contributing variables.                         investment and growth          Make well-justified
                     central tendency and                                                                         appropriately to the         Estimating and checking (profit                           options.                       recommendations.
                     spread to make                                                                               problem situation by:        margins).                                                 (c): Financial and other       Represent and critically analyse.
                     comparisons and draw                                                                         (a) Interpreting                                                                       indicators.                    Draw conclusions.
                     conclusions, inclusive of                                                                    fractional parts of                                                                                                   Predict trends.
                     the:                                                                                         answers in terms of the                                                                                               Compare data by calculating.
                     (a) Mean                                                                                     context.
                     (b) Median
                     (c) Mode
                     (d) Range




                                                                                         Grade 12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                                                                                                        Page 122 of 154
     Learning                                                       Learning                                                       Learning
                      Assessment standard          Content                           Assessment standard            Content                          Assessment standard          Content
    Outcomes                                                       Outcomes                                                       Outcomes
10.4: Data           (d) Range                               11.1: Number and        (b) Reworking a                          12.1: Number          (d): The effects of
handling: The        10.4.4 Critically interpret             Operations in           problem if the first                     and Operations        currency fluctuations.
learner is able to   a single set of data and                Context: The            answer is not sensible                   in Context: The       (e): Critical engagement
collect,             representations thereof                 learner is able to      of if the initial conditions             learner is able to    with debates about
summarise,           (with awareness off                     use knowledge of        change.                                  use knowledge of      socially responsible trade.
display and          sources of error) in order              numbers and their       (c) Interpreting                         numbers and
analyse data and     to draw conclusions on                  relationships to        calculated answers                       their relationships
to apply             questions investigated                  investigate a range     logically in relation to                 to investigate a
knowledge of         and to make predictions.                of different contexts   the problem, and                         range of different
statistics and                                               which include           communicating                            contexts which
probability to                                               financial aspects of    processes and results.                   include financial
communicate,                                                 personal business       11.1.3: Investigate                      aspects of
justify, predict                                             and national issues.    opportunities for                        personal,
and critically                                                                       entrepreneurship and                     business and
interrogate                                                                          determine profit and                     national issues.
findings and draw                                                                    sustainability by
conclusions.                                                                         analysing contributing
                                                                                     variables, inclusive of:                 12.3: Space and       12.3.4: Use grids,
                                                                                     (a) Specifying and                       Measurement:          including the Cartesian
                                                                                     calculating the value of                 The learner is        plane and compass
                                                                                     income and expenditure                   able to measure       directions, in order to:
                                                                                     items.                                   using appropriate     (a): Determine locations.
                                                                                     (b) Determining optimal                  instruments, to       (b): Describe relative
                                                                                     selling prices.                          estimate and          positions.
                                                                                     (c) Estimating and                       calculate physical
                                                                                     checking profit margins.                 quantities, and to
                                                                                                                              interpret,
                                                                                                                              describe and
                                                                                                                              represent
                                                                                                                              properties of and
                                                                                                                              relationships
                                                                                                                              between 2-
                                                                                                                              dimensional
                                                                                                                              shapes and 3-
                                                                                                                              dimensional
                                                                                                                              objects in a
                                                                                                                              variety of
                                                                                                                              orientations and
                                                                                                                              positions.




                                                             Grade 12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                                                                           Page 123 of 154
Learning                                      Learning                                                       Learning
           Assessment standard   Content                   Assessment standard        Content                                 Assessment standard          Content
Outcomes                                      Outcomes                                                      Outcomes
                                                                                                        12.4: Data           12.4.1: Investigate a
                                                                                                        Handling: The        problem on issues such
                                                                                                        learner is able to   as those related to:
                                                                                                        collect,             (a): Social, environmental
                                                                                                        summarise,           and political factors.
                                                                                                        display and          (b): People’s opinions.
                                                                                                        analyse data and     (c): Human rights and
                                                                                                        to apply             inclusivity by:
                                                                                                        knowledge of         (i): Using appropriate
                                                                                                        statistics and       statistical methods.
                                                                                                        probability to       (ii): Selecting a
                                                                                                        communicate,         representative sample
                                                                                                        justify, predict     from a population with
                                                                                                        and critically       due sensitivity to issues
                                                                                                        interrogate          relating to bias.
                                                                                                        findings and draw    (iii): Comparing data from
                                                                                                        conclusions.         different sources and
                                                                                                                             samples.
                                                                                                                             12.4.2: Appropriately
                                                                                                                             choose and interpret the
                                                                                                                             use of methods to
                                                                                                                             summarise and display
                                                                                                                             data in statistical charts
                                                                                                                             and graphs including, the
                                                                                                                             use of scatter-plots and
                                                                                                                             intuitively-placed lines of
                                                                                                                             best fit to:
                                                                                                                             (a): Represent the
                                                                                                                             association between
                                                                                                                             variables (regression
                                                                                                                             analysis not included).
                                                                                                                             (b): Describe trends (e.g.
                                                                                                                             a positive linear
                                                                                                                             association).
                                                                                                                             12.4.4: Represent and
                                                                                                                             critically analyse data,
                                                                                                                             statistics and probability
                                                                                                                             values in order to draw
                                                                                                                             conclusions on problems
                                                                                                                             investigated and to
                                                                                                                             predict trends.




                                           Grade 12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                                               Page 124 of 154
                               WORK SCHEDULE


  Week:
            Module,                   Learning
   Date    unit and/or             Outcomes and                                       Assessment
started:                   Time                                 Content
            chapter                 Assessment                                          Tasks
   Date     numbers                  Standards
 ended:
                                                        Personal and business
                                        12.1.1
                                                            finance (1), (2)
                                        12.1.2
             Mod 1                                     Must we carry on with the
                                        12.1.3
             Unit 1       18 hrs                                annuity?                  n/a
                                        12.4.1
           Chapt.1 – 5                                  Personal finances at a
                                        12.4.2
                                                                 glance
                                        12.4.4
                                                            My bank and I
  Week:
            Module,                   Learning
   Date    unit and/or             Outcomes and                                       Assessment
started:                   Time                                 Content
            chapter                 Assessment                                          Tasks
   Date     numbers                  Standards
 ended:
                                        12.1.1              Exchange rates.
             Mod 1
                                        12.1.2          Finding places in Egypt.
             Unit 2       15 hrs                                                          n/a
                                        12.1.3        Fluctuations in the currency.
           Chapt.1 – 4
                                        12.3.4           My trip to a far country.
  Week:
            Module,                   Learning
   Date    unit and/or             Outcomes and                                       Assessment
started:                   Time                                 Content
            chapter                 Assessment                                          Tasks
   Date     numbers                  Standards
 ended:
             Mod 1                                     To buy or not to buy on
                                        12.1.2                                        Investigation
             Unit 3        7 hrs                               credit.
                                        12.1.3                                            Test
           Chapt.1 – 2                                 What about importing it?
  Week:
            Module,                   Learning
   Date    unit and/or             Outcomes and                                       Assessment
started:                   Time                                 Content
            chapter                 Assessment                                          Tasks
   Date     numbers                  Standards
 ended:
                                                             The cottage.
                                       12.1.1         Surface area of polyhedra.
                                    12.2.1(a), (b)      Volumes of polyhedra.          Chapter 6
                                    12.3.1(a)(i) –     Trigonometric rations in        Question 1
             Mod 2
                            40         (v), (b)         right-angled triangles.       and Question
             Unit 1
                           hours      12.3.3(a)       Calculations about the roof          2
           Chapt. 1 – 8
                                    12.3.4(a), (b)          of the cottage.            Chapter 7
                                       12.3.5                The garden.               Question 3
                                       12.3.6         Scale model of the cottage.
                                                            A visit to Kiev.




               Grade 12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                   Page 111 of 154
Unit number:      1
Chapter    2              Duration        3 hrs     Planned             Actual
number:                   of activity:    30 mins   date:               date:

Learning Outcomes and Assessment Standards:
12.1.1; 12.1.2; 12.1.3

Content:
Personal and business finances (2)

Activity:
Investment. Calculating interest.

Resources:
Calculator

Assessment
Tasks:
n/a

                               For assessment by the teacher:
Remedial:
Enrichment:
Reflection:
Homework:

Unit number:      1
Activity   3              Duration        3 hrs     Planned             Actual
number:                   of activity:    30 mins   date:               date:

Learning Outcomes and Assessment Standards:
12.1.2

Content:
Must we carry on with the annuity?

Activity:
Annuity funds. Calculating interest.

Resources:
Calculator

Assessment
Tasks:
n/a

                               For assessment by the teacher:
Remedial:
Enrichment:
Reflection:
Homework:




                  Grade12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                         Page 136 of 154
       P

  Learning and
Teaching Support
 Material (LTSM)
2.4      A loaf of bread costs R4. If inflation were to average 4,5% per annum, what
         will the cost of loaf of a bread be in 48 months?
2.5      A man needs to borrow R10 000 for 2 years. If the following terms are
         offered, find the amount he would have to pay back in each case and say
         which offer he should take:

2.5.1 2,25% per month compounded monthly.
2.5.2 23% per annum compounded half-yearly.
2.5.3 25% per annum compounded yearly.

3.       Discuss the following problem in your group:

         For their visit to Egypt Grandpa and Grandma will need about R30 000. They
         plan to invest R20 000 at 9% simple interest per year. Thabane reckons it will
         take about 5 years to have the amount in the account, but Grandpa thinks it
         will be at least 6 years. Who is more correct? Explain your reasoning.


Name:                                                      Grade:                   No.:       2–3

 CHECKLIST: TEACHER ASSESSMENT                                          1   2   3   4      5   6   7
         Correctly apply problem-solving and calculation skills to
12.1.1
         situations and problems dealt with.
         Analyse and critically interpret a wide variety of financial
12.1.3
         situations mathematically.




                                2


Personal and business finances (2)

1.       Read the following text:

                                                           TEXT


Will you be able to retire one day?

Yes. No matter what your income, regular saving and investing will allow you to
retire one day. This is also the way to become rich. Individuals may place their money
in savings accounts. Investing generally is seen as putting saved money into stocks,
mutual funds, commercial real estate, etc. Each of these investments carry more risk
than saving accounts.

Why shouldn’t you just keep your money in a savings account where it will be safe?
What if the annual interest rate is less than the rate of inflation? With inflation, your
money loses purchasing power. What if you save enough money for a mountain bike,
but when you take out the money you can only buy a tricycle? That’s why some
people put money in riskier, longer term investments that can provide a greater return.


                      Grade 12 Mathematical Literacy Learner’s Book Module 1 – 3
                                                   Page 7 of 160
Is there a secret to good investing? No, but a few basic rules help:
•       Live below your means.
•       Save early and often.
•       Take prudent risks to achieve higher returns. Remember that the stock market
        has beaten the returns on every other type of investment over the long run.


2.     Thabane visited a well-known bank to obtain information about savings. They
       provided him with the information in the following table. Use this table to
       answer the following questions.


                            NEDBANK LONDON INTEREST RATES
•      These rates are with effect from 07 August 2006. (All rates are subject to change)
•      NOTE – all rates are quoted as per annum rates.



                                    HIGH INTEREST CHEQUE ACCOUNT
CURRENCY                                    CAPITAL                                         INTEREST RATES
GBP                                         5 000 – 9 999                                   2,25%
                                            10 000 – 24 999                                 2,75%
                                            25 000 – Plus                                   3,25%
                                            TERM DEPOSIT ACCOUNT
                Minimum                                    Investment Terms
Currency
                Deposit                     1 Month 2 Months 3 Months 6 Months                           1 Year
GBP             5 000 Plus                  3,95%   4,01%      4,08%      4,21%                          4,40%
USD             7 500 Plus                  4,51%   4,57%      4,62%      4,71%                          4,74%
CHF             11 000 Plus                 0,47%   0,56%      0,65%      0,87%                          1,17%
EURO            10 000 Plus                 2,17%   2,23%      2,33%      2,53%                          2,75%
ZAR             35 000 Plus                 6,85%   7,05%      7,30%      7,65%                          8,20%



2.1   Is the amount deposited and the length of the investment in moths, directly or
      indirectly proportional? Explain your answer.
2.2   Grandpa wants to invest an amount of R40 000 for 6 months. What interest
      rate will he get on his investment?
2.3   What is the ratio between the interest rate on a 1 year investment of South
      African rand and the interest rate on an investment of Euros for the same
      period?
2.4   The interest rate on a cheque account balance of £5 000 (five thousand British
      pounds) is 2,25% and on a balance of £25 000 it is 3,25%.
2.4.1 Discuss in your group the reasons for this difference and calculate the
      difference in interest earned on a deposit of £5 000.
2.4.2 Calculate the interest earned on the same £5 000 if it is part of a £35 000
      deposit. Do you now understand why investors get richer all the time?




                     Grade 12 Mathematical Literacy Learner’s Book Module 1 – 3
                                                       Page 8 of 160
Name:                                                      Grade:                   No.:            2

 CHECKLIST: TEACHER ASSESSMENT                                        1   2    3        4   5   6       7
         Correctly applied problem-solving and calculation skills
12.1.1
         to situations and problems dealt with.
         Related calculated answers correctly and appropriately
12.1.2
         to the problem situation.
         Analysed and critically interpreted a wide variety of
12.1.3
         financial situations mathematically.




                               3


Must we carry on with the annuity?

1.       Thabane found the following very interesting information on an annuity fund.
         The amount invested per year was R2 000 and the interest rate was 8%. Look
         at the following and then help Thabane to come to a conclusion on his
         grandparents’ question about the annuity fund.

                                                             Retirement

                               600 000

                               500 000

                               400 000
                        Rand




                               300 000

                               200 000

                               100 000

                                        0
                                            0         10         20       30       40
                                                               Year
                                                S = Amount




                     Grade 12 Mathematical Literacy Learner’s Book Module 1 – 3
                                                   Page 9 of 160
3.     Reasoning: The learners do the calculations:

       Pit = 20 000 × 0,09 × 5
           = 9 000
       ∴ A = R 29 000

       Pit = 20 000 × 0,09 × 6
           = 10 800
       ∴ A = R 30 800

       Grandfather is correct. Discuss the answer.


                       2


ASSIGNMENT

Personal and business finances (2)
(12.1.1; 12.1.2; 12.1.3)

1.     Learners read the text.

2.     Learners study the table and answer the questions.
2.1    It is directly proportion because the higher the amount deposited, the higher
       the interest offered.

2.2    7,65%

2.3        ZAR : Euros
       = 6,20% : 2,75%
       = 2,25% : 1

2.4   The learners read the problem and answer the questions.
2.4.1 Learners discuss reasons: One possible answer is that banks want to draw big
      investors.

2.4.2 Difference:
      Pit = 5 000 × 0,0225 × 1
           = R112,50
       Pit = 5 000 × 0,0325 × 1
           = R162,50




                Grade 12 Mathematical Literacy Teacher’s Book Module 1 – 3
                                     Page 8 of 154

				
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