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MATHEMATICAL LITERACY STUDY GUIDE
Grade 10
A member of the FUTURELEARN group
Mathematical Literacy Study guide
CAPS aligned
A Kies
2010-E-MAL-SG01
Í4*È-E-MAL-SG01LÎ
Grade 10
Study Guide G10 ~ Mathematical Literacy
CONTENTS LESSON ELEMENTS ....................................................................................................... 4 PREFACE ......................................................................................................................... 5 ASSESSMENT REQUIREMENTS .................................................................................... 5 THE ASSESSMENT PROGRAMME ................................................................................. 6 YEAR PLAN ...................................................................................................................... 6 SUGGESTED TIME TO SPEND ON EACH UNIT............................................................. 7 UNIT 1: NUMBERS AND CALCULATIONS ..................................................................... 9 Lesson 1: Number formats and conventions ............................................................... 9 Activity 1.............................................................................................................. 11 Lesson 2: Numbers used in different contexts........................................................... 11 Activity 2.............................................................................................................. 13 Lesson 3: Operations using numbers and calculator skills ........................................ 14 Activity 3.............................................................................................................. 15 Lesson 4: BODMAS rule (order of operations) .......................................................... 15 Activity 4.............................................................................................................. 16 Lesson 5: Multiplication and division by 10, 100 and 1 000 ....................................... 16 Activity 5.............................................................................................................. 17 Lesson 6: Fractions ................................................................................................... 18 Activity 6.............................................................................................................. 20 Lesson 7: Estimation of anticipated solutions to calculations .................................... 21 Activity 7.............................................................................................................. 21 Activity 8.............................................................................................................. 23 Lesson 8: Rounding .................................................................................................. 23 Activity 9.............................................................................................................. 26 Lesson 9: Percentages .............................................................................................. 26 Activity 10............................................................................................................ 29 Lesson 10: Ratios...................................................................................................... 30 Activity 11............................................................................................................ 32 Lesson 11: Rate ........................................................................................................ 33 Activity 12............................................................................................................ 34 Lesson 12: Proportion ............................................................................................... 35 Activity 13............................................................................................................ 37 UNIT 2: PATTERNS, RELATIONSHIPS AND REPRESENTATIONS ............................ 38 Lesson 13: Graphs .................................................................................................... 38 Activity 14............................................................................................................ 42 Lesson 14: Linear relationships ................................................................................. 43 Activity 15............................................................................................................ 46 Lesson 15: Indirect/inverse proportion ...................................................................... 46 Activity 16............................................................................................................ 47 Lesson 16: Graphs with constant relationships ......................................................... 48 Activity 17............................................................................................................ 48 © Impaq
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Study Guide G10 ~ Mathematical Literacy
UNIT 3: MEASUREMENT – CONVERSIONS AND TIME .............................................. 49 Lesson 17: Conversions ............................................................................................ 49 Activity 18............................................................................................................ 52 Lesson 18: Telling time and calculations involving time ............................................ 53 Activity 19............................................................................................................ 56 Lesson 19: Calendars and timetables ....................................................................... 57 Activity 20............................................................................................................ 60 UNIT 4: FINANCIAL DOCUMENTS AND TARIFF SYSTEMS ....................................... 61 Lesson 20: Financial documents ............................................................................... 61 Activity 21............................................................................................................ 69 Lesson 21: Accounts ................................................................................................. 70 Activity 22............................................................................................................ 73 Lesson 22: Tariff systems.......................................................................................... 74 Activity 23............................................................................................................ 79 UNIT 5: MEASURING LENGTH, MASS, VOLUME AND TEMPERATURE ................... 80 Lesson 23: Measurement .......................................................................................... 80 Activity 24............................................................................................................ 86 UNIT 6: MAPWORK ........................................................................................................ 89 Lesson 24: Layout plans ........................................................................................... 92 Activity 25............................................................................................................ 96 Lesson 25: Floor plans .............................................................................................. 98 Activity 26.......................................................................................................... 101 Lesson 26: Scales ................................................................................................... 102 Activity 27.......................................................................................................... 108 UNIT 7: PROBABILITY ................................................................................................. 110 Lesson 27: Expression of probability ....................................................................... 110 Activity 28.......................................................................................................... 114 Lesson 28: Prediction of probability......................................................................... 115 Activity 29.......................................................................................................... 116 Lesson 29: Methods of finding possible outcomes .................................................. 117 Activity 30.......................................................................................................... 119 Lesson 30: Two-way tables ..................................................................................... 119 Activity 31.......................................................................................................... 120 UNIT 8: FINANCE – INCOME, EXPENDITURE, PROFIT/LOSS, INCOME-ANDEXPENDITURE STATEMENTS AND BUDGETS ........................................... 121 Lesson 31: Personal income and expenditure......................................................... 122 Activity 32.......................................................................................................... 124 Lesson 32: Budgets ................................................................................................. 125 Activity 33.......................................................................................................... 126 Lesson 33: Income-and-expenditure statements..................................................... 126 Activity 34.......................................................................................................... 127 © Impaq
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Study Guide G10 ~ Mathematical Literacy
UNIT 9: MEASUREMENT – PERIMETER/CIRCUMFERENCE AND AREA ................ 128 Lesson 34: Perimeter/circumference ....................................................................... 128 Activity 35.......................................................................................................... 135 Lesson 35: Area ...................................................................................................... 136 Activity 36.......................................................................................................... 143 UNIT 10: INSTRUCTIONS, ASSEMBLY DIAGRAMS AND PACKAGING .................. 145 Lesson 36: Instructions and assembly diagrams ..................................................... 145 Activity 37.......................................................................................................... 149 Lesson 37: Packaging ............................................................................................. 150 Activity 38.......................................................................................................... 154 UNIT 11: VAT, BANKING, INTEREST AND BANK CHARGES ................................... 155 Lesson 38: Value-added tax (VAT) ......................................................................... 156 Activity 39.......................................................................................................... 157 Lesson 39: Interest and interest rate ....................................................................... 158 Activity 40.......................................................................................................... 159 Lesson 40: Simple interest ...................................................................................... 159 Activity 41.......................................................................................................... 160 Lesson 41: Banking ................................................................................................. 160 Activity 42.......................................................................................................... 163 UNIT 12: DATA HANDLING AND STATISTICS ........................................................... 164 Lesson 42: Step 3: Sorting data .............................................................................. 165 Activity 43.......................................................................................................... 167 Lesson 43: Step 4: Representing data graphically .................................................. 167 Activity 44.......................................................................................................... 173 Lesson 44: Summary and analysis of data by calculating measures of central tendency ............................................................................................... 176 Activity 45.......................................................................................................... 179 BIBLIOGRAPHY ............................................................................................................. 181 ADDENDUM A: TERMINOLOGY.................................................................................... 184 ADDENDUM B: FORMULAE .......................................................................................... 189 ADDENDUM C: COLOUR PAGES ................................................................................. 195
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Study Guide G10 ~ Mathematical Literacy
Lesson elements LEARNING OBJECTIVES What you should know at the end of the lesson. Taken from CAPS.
IMPORTANT TERMINOLOGY New terminology to improve understanding of the subject as part of the lesson.
IMPORTANT A summary or explanation of the main concepts of a lesson.
ACTIVITY Formative assessment to test your progress and knowledge at the end of each lesson.
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Study Guide G10 ~ Mathematical Literacy
Preface Recommended books Any additional book may be used with this study guide. It is always a good idea to refer to other textbooks to develop a broader perspective on the subject. • •
The Answer Series: Grade 10 Mathematical Literacy 3 in 1 Mathematical Literacy for the Classroom Grade 10 Learner’s Book
Assessment requirements Note that there are constant references to TL1, TL2, TL3 and TL4 throughout this facilitator guide. These are the thinking levels required to answer the specific question 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. Mark distribution 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 Thinking level 3: Applying multi-step procedures in a variety of contexts Thinking level 4: Reasoning and reflecting
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30% (±5%) 20% (±5%) 20% (±5%)
Study Guide G10 ~ Mathematical Literacy
The assessment programme Refer to Impaq’s online platform for assessment tasks, examinations and the assessment plan.
Year plan Unit
Topic
1
Numbers and calculations
2
Patterns, relationships and representations
3
Measurement: Conversions and time
4
Finance: Financial documents and tariff systems
5
Measurement: Distance/length, weight (mass), volume and temperature
6
Mapwork
7
Probability
8
Finance: Income, expenditure, profit/loss, incomeand-expenditure statements, and budgets
9
Measurement: Perimeter and area
10
Instructions, assembly diagrams and packaging
11
Finance: VAT, banking, interest and bank charges
12
Data handling
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Term
Term 1 January – March
Term 2 April – June
Term 3 July – September
Term 4 October – November
Study Guide G10 ~ Mathematical Literacy
Suggested time to spend on each unit (according to CAPS) Week
Term 1
1
2
3
4
5
6
7
8
9
Contexts focusing on Numbers and calculations Topics
Contexts focusing on Patterns, relationships and representations Contexts focusing on Measurement (conversions and time)
Assessment
Assignment/investigation Control test (covering Numbers and calculations, Patterns, relationships and representations, and Measurement) Week
Term 2
1
2
3
4
5
6
7
8
9
8
9
8
9
Contexts focusing on Finance (financial documents and tariff systems)
Topics
Contexts focusing on Measurement (distance/length, weight (mass), volume and temperature) Contexts focusing on Maps, plans and other representations of the physical world (scale and mapwork) Contexts focusing on Probability Revision
Assessment
Assignment/investigation June examination (2 papers, 1 hour each, 50 marks each; covering Finance, Measurement, Mapwork and Probability, integrated with Numbers and Patterns) Week
Term 3
1
2
3
4
5
6
7
Contexts focusing on Finance (income, expenditure, profit/loss, incomeand-expenditure statements, and budgets) Topics
Assessment
Contexts focusing on Measurement (perimeter, area and volume) Contexts focusing on Maps, plans and other representations of the physical world (models and plans) Assignment/investigation Control test (covering Finance, Measurement and Models and plans, integrated with Numbers and Patterns) Week
Term 4
1
2
3
4
5
6
Contexts focusing on Finance (interest, banking and taxation) Topics
Contexts focusing on Data handling Revision
Assessment
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Assignment/investigation November examination (2 papers, 1½ hours each, 75 marks each; covering all topics in the curriculum)
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Study Guide G10 ~ Mathematical Literacy
Time allocation per topic serves as a guideline only and it can be adjusted to your own pace. Bear in mind that you must first complete the relevant Lessons before you will be allowed to take a test or the relevant examination. You need to spend 4,5 hours per week on Mathematical Literacy. Take note that this time allocation per week excludes all activities, assessments and examinations; it gives an indication only of the time that must be spent on theoretical aspects. If you tend to work more slowly, the necessary adjustments must be made to ensure that you still master all the work in time. Proposed instructional time per week: Subject
Time allocation per week (hour)
Home Language
4,5
First Additional Language
4,5
Mathematical Literacy
4,5
Life Orientation
2
Three optional subjects: Optional subject 1 Optional subject 2 Optional subject 3
4 4 4
Total
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Study Guide G10 ~ Mathematical Literacy
Unit
1
UNIT 1: NUMBERS AND CALCULATIONS Learning objectives At the end of the unit, you must be able to: • write numbers in different formats • write numbers in words • write words in numbers • describe numbers used in different contexts • do calculations using a calculator • apply the BODMAS rule • multiply and divide by 10, 100 and 1 000 • convert common fractions and decimal fractions • do calculations (addition, subtraction, multiplication and division) with fractions • round off within context • round off to the nearest 10, 100 and 1 000 • work with percentages • calculate the initial price of items • do calculations with rate and proportion • discuss the difference between direct and indirect proportion, and do calculations
Lesson 1: Number formats and conventions CONVENTION A fixed way of doing something. FORMAT A fixed form in which something is written down or expressed. Number formats and conventions refer to the different ways in which we can write and use numbers. In South Africa, it is a legal requirement to use a decimal comma in all numbers. A decimal fraction is therefore separated by a decimal comma from the rest of the number (integer). This legislation also applies to monetary amounts because cents can be written as a decimal fraction of a rand. NEVER use a decimal point, as that is NOT the convention. © Impaq
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Study Guide G10 ~ Mathematical Literacy
Unit
1
In large numbers consisting of three or more digits, spaces are used to divide the digits into groups of three for the sake of legibility. In numbers with decimal fractions, the digits on either side of the decimal sign are also divides into groups by using spaces. In some countries, a comma is used to divide digits into groups of three, but in South Africa we use spaces. This spacing, indicating the separation of numbers, is called thousands separators. EXAMPLES One million eighty-three thousand five hundred and five: 1 083 505 Two million one hundred and five thousand forty-eight: 2 105 048 Three thousand four hundred fifty-six comma nine two seven: 3 456,927 This convention facilitates the reading of numbers. Compare 400000 with 400 000. Write the number in words:
1 426 078,389 H
MILLIONS T U 1
THOUSANDS H T U 4 2 6
Thousands separator
HUNDREDS H T U 0 7 8
Thousands separator
THOUSANDTHS H T U 3 8 9
Decimal separator
One million four hundred twenty-six thousand seventy-eight comma three eight nine Value of each digit: 1: one million 4: four hundred thousands 0: zero hundreds 7: seventy 3: three tenths 8: eight hundredths
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2: twenty thousands 8: eight 9: nine thousandths
6: six thousands
Study Guide G10 ~ Mathematical Literacy
Unit
1
Activity 1 Study the number in the table. MILLIONS H T U 2 1. 2. 3.
THOUSANDS H T U 3 1 4
HUNDREDS H T U 4 5 6
THOUSANDTHS H T U 7 8
Write the number in words. Write the number in the correct format. Show the thousands separators and the decimal separator.
Lesson 2: Numbers used in different contexts Numbers are primarily used for counting or measuring. The types of numbers we use, however, depend on the specific contexts in which they occur. Sometimes we use whole number (integers) to indicate quantities or dimensions and at other times, we use ordinal numbers to indicate sequence. We also use numbers in the form of codes to identify someone/something, e.g., an ID number.
EXAMPLES OF NUMBERS USED IN DIFFERENT CONTEXTS • • • • •
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Dimensions, for example, length and mass Street numbers as used in a home address Integers, for example, the number of passengers on a plane Ordinal numbers, for example, Teboho winning the first prize and Sipho winning the second prize Numbers indicating monetary amounts
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Study Guide G10 ~ Mathematical Literacy
• •
Unit
1
Unemployment rate, matric pass rate, interest rate, etc., expressed as a percentage Numbers representing a code and having no value, for example, phone numbers, car registration numbers, and personal identification numbers (PINs)
Numbers can be represented or used in various ways. • Natural numbers (integers): a person has 10 fingers • Ordinal numbers: 1st place, 2nd place, 3rd place • Indication of location: flat on floor 3, number 11 311 or street number 701 in Park Street 701 Park Street • Whole numbers: 17 years; 1994; 33 000; 1 524 796 • Decimals: 15,3; 10,3; 0,24 • Percentages: 99%; 25%; 10,75% 1
1
7
•
Fractions:
•
Ratios: 1 : 4; 2 : 3
3
;4;8
Different number conventions are used in different contexts. •
Consider the flat number 811. The number 8 refers to the floor. The number 11 refers to the position of the flat. It means that flat 11 is located on the eighth floor.
•
The number on your movie ticket indicates the seat number where you must sit, e.g., B12 means that you must sit in row B, seat number 12.
•
On a cricket scoreboard, a number such as 14.4 means that 14 overs and 4 balls have already been bowled. Similarly, 128/6 does not mean 128 divided by 6 but rather that a team has scored 128 runs for the loss of 6 wickets. Runs Wickets Overs
128 6 14.4
Take note: A full stop is used in this case as it is the worldwide convention in cricket. •
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Positive and negative numbers: o Temperature: -4 °C means 4 °C below freezing point (0 °C) 0 °C means at freezing point 4 °C means 4 °C above freezing point 12
Study Guide G10 ~ Mathematical Literacy
Unit
1
o
Bank statements:
A balance of -R329 means that your account is overdrawn and that you owe the bank money, whereas a balance of R329 means that the bank owes you money.
o
Percentage:
Increases and decreases in share prices, commodities and currencies are expressed in percentage, e.g., +5,4% (increase) or -2,3% (decrease). Increase (green) Decrease (red)
See colour version in addendum C.
Activity 2
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First write the numbers using the correct thousands separators and then write them in words. 1.1 71507 1.2 780027 1.3 62,952 1.4 53448921
2.
Write the numbers. 2.1 Twenty-two thousand nine hundred 2.2 Eight million six hundred and thirty thousand 2.3 Two billion thirty-four million and ten 2.4 15175 million 2.5 3,2 billion
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Study Guide G10 ~ Mathematical Literacy
Unit
3.
In a radio advertisement, it is stated that the balloon payment on a car is ‘six seven four five seven’ rand. 3.1 Is this a large amount? Motivate your answer. 3.2 Why do you think this number is read out in digits instead of being read correctly?
4.
In each case, show which one of the two numbers is the greater. 4.1 12 or -12 4.2 -7 °C or -14 °C 4.3 R2 000 or -R5 000 4.4 -800 or -794
5.
The number of a flat is 1206. Discuss the possible location of the flat.
Lesson 3: Operations using numbers and calculator skills THE BASIC CALCULATOR
See colour version in addendum C.
A basic calculator can be used to do simple calculations quickly. © Impaq
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