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MATHEMATICAL LITERACY FACILITATOR’S GUIDE
Grade 10
A member of the FUTURELEARN group
Mathematical Literacy Facilitator’s guide
CAPS aligned
A Kies
2010-E-MAL-FG01
Í4*È-E-MAL-FG01$Î
Grade 10
Facilitator’s 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 .................................................................................................................. 9 Lesson 2: Numbers used in different contexts............................................................. 9 Activity 2 .................................................................................................................. 9 Lesson 3: Operations using numbers and calculator skills ........................................ 10 Activity 3 ................................................................................................................ 10 Lesson 4: BODMAS rule (order of operations) .......................................................... 10 Activity 4 ................................................................................................................ 10 Lesson 5: Multiplication and division by 10, 100 and 1 000 ....................................... 11 Activity 5 ................................................................................................................ 11 Lesson 6: Fractions ................................................................................................... 11 Activity 6 ................................................................................................................ 11 Lesson 7: Estimation of anticipated solutions to calculations .................................... 12 Activity 7 ................................................................................................................ 12 Activity 8 ................................................................................................................ 12 Lesson 8: Rounding .................................................................................................. 13 Activity 9 ................................................................................................................ 13 Lesson 9: Percentages .............................................................................................. 14 Activity 10 .............................................................................................................. 14 Lesson 10: Ratios...................................................................................................... 15 Activity 11 .............................................................................................................. 15 Lesson 11: Rate ........................................................................................................ 16 Activity 12 .............................................................................................................. 16 Lesson 12: Proportion ............................................................................................... 17 Activity 13 .............................................................................................................. 17 UNIT 2: PATTERNS, RELATIONSHIPS AND REPRESENTATIONS .............................. 18 Lesson 13: Graphs .................................................................................................... 18 Activity 14 .............................................................................................................. 18 Lesson 14: Linear relationships ................................................................................. 18 Activity 15 .............................................................................................................. 18 Lesson 15: Indirect/inverse proportion ...................................................................... 19 Activity 16 .............................................................................................................. 19 Lesson 16: Graphs with constant relationships ......................................................... 20 Activity 17 .............................................................................................................. 20 © Impaq
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Facilitator’s Guide G10 ~ Mathematical Literacy
UNIT 3: MEASUREMENT – CONVERSIONS AND TIME................................................. 21 Lesson 17: Conversions ............................................................................................ 21 Activity 18 .............................................................................................................. 21 Lesson 18: Telling time and calculations involving time ............................................ 22 Activity 19 .............................................................................................................. 22 Lesson 19: Calendars and timetables ....................................................................... 23 Activity 20 .............................................................................................................. 23 UNIT 4: FINANCIAL DOCUMENTS AND TARIFF SYSTEMS ......................................... 24 Lesson 20: Financial documents ............................................................................... 24 Activity 21 .............................................................................................................. 24 Lesson 21: Accounts ................................................................................................. 25 Activity 22 .............................................................................................................. 25 Lesson 22: Tariff systems.......................................................................................... 25 Activity 23 .............................................................................................................. 25 UNIT 5: MEASURING LENGTH, MASS, VOLUME AND TEMPERATURE ..................... 27 Lesson 23: Measurement .......................................................................................... 27 Activity 24 .............................................................................................................. 27 UNIT 6: MAPWORK .......................................................................................................... 29 Lesson 24: Layout plans ........................................................................................... 29 Activity 25 .............................................................................................................. 29 Lesson 25: Floor plans .............................................................................................. 30 Activity 26 .............................................................................................................. 30 Lesson 26: Scale ....................................................................................................... 31 Activity 27 .............................................................................................................. 31 UNIT 7: PROBABILITY ..................................................................................................... 32 Lesson 27: Expression of probability ......................................................................... 32 Activity 28 .............................................................................................................. 32 Lesson 28: Prediction of probability........................................................................... 33 Activity 29 .............................................................................................................. 33 Lesson 29: Methods of finding possible outcomes .................................................... 33 Activity 30 .............................................................................................................. 33 Lesson 30: Two-way tables ....................................................................................... 35 Activity 31 .............................................................................................................. 35 UNIT 8: FINANCE – INCOME, EXPENDITURE, PROFIT/LOSS, INCOME-ANDEXPENDITURE STATEMENTS AND BUDGETS ............................................... 36 Lesson 31: Personal income and expenditure........................................................... 36 Activity 32 .............................................................................................................. 36 Lesson 32: Budgets ................................................................................................... 37 Activity 33 .............................................................................................................. 37
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Facilitator’s Guide G10 ~ Mathematical Literacy
Lesson 33: Income-and-expenditure statements....................................................... 37 Activity 34 .............................................................................................................. 37 UNIT 9: MEASUREMENT – PERIMETER/CIRCUMFERENCE AND AREA .................... 39 Lesson 34: Perimeter/circumference ......................................................................... 39 Activity 35 .............................................................................................................. 39 Lesson 35: Area ........................................................................................................ 39 Activity 36 .............................................................................................................. 39 UNIT 10: INSTRUCTIONS, ASSEMBLY DIAGRAMS AND PACKAGING....................... 41 Lesson 36: Instructions and assembly diagrams ....................................................... 41 Activity 37 .............................................................................................................. 41 Lesson 37: Packaging ............................................................................................... 42 Activity 38 .............................................................................................................. 42 UNIT 11: VAT, BANKING, INTEREST AND BANK CHARGES ....................................... 43 Lesson 38: Value-added tax (VAT) ........................................................................... 43 Activity 39 .............................................................................................................. 43 Lesson 39: Interest and interest rate ......................................................................... 43 Activity 40 .............................................................................................................. 43 Lesson 40: Simple interest ........................................................................................ 44 Activity 41 .............................................................................................................. 44 Lesson 41: Banking ................................................................................................... 44 Activity 42 .............................................................................................................. 44 UNIT 12: DATA HANDLING AND STATISTICS ............................................................... 45 Lesson 42: Step 3: Sorting data ................................................................................ 45 Activity 43 .............................................................................................................. 45 Lesson 43: Step 4: Representing data graphically .................................................... 46 Activity 44 .............................................................................................................. 46 Lesson 44: Summary and analysis of data by calculating measures of central tendency ................................................................................................. 48 Activity 45 .............................................................................................................. 48
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Facilitator’s Guide G10 ~ Mathematical Literacy
Lesson elements ACTIVITY Formative assessment to test learners’ progress and knowledge at the end of each lesson.
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Facilitator’s 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%)
Facilitator’s 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
Facilitator’s 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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Facilitator’s Guide G10 ~ Mathematical Literacy
Time allocation per topic serves as a guideline only and it can be adjusted to learners’ own pace. Bear in mind that learners must first complete the relevant lessons before being allowed to take a test or the relevant examination. Learners 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 learners tend to work more slowly, the necessary adjustments must be made to ensure that they 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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Facilitator’s Guide G10 ~ Mathematical Literacy
Unit
1
UNIT 1: NUMBERS AND CALCULATIONS Lesson 1: Number formats and conventions Activity 1 1.
Two million three hundred and fourteen thousand four hundred fifty-six comma seven eight TL 1
2.
2 314 456,78
TL 1
3.
2 314 456,78 Decimal separator Thousands separator Thousands separator
TL1
Lesson 2: Numbers used in different contexts Activity 2
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1.1
71 507 Seventy-one thousand five hundred and seven
TL 1
1.2
780 027 Seven hundred and eighty thousand twenty-seven
TL 1
1.3
62,952 Sixty-two comma nine five two
TL 1
1.4
53 448 921 Fifty-three million four hundred forty-eight thousand nine hundred twenty-one
TL 1
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Facilitator’s Guide G10 ~ Mathematical Literacy
Unit
1
2.1 2.2 2.3 2.4 2.5
22 900 8 630 000 2 034 000 010 15 175 000 000 3 200 000 000
TL 1 TL 1 TL 1 TL 1 TL 1
3.1 3.2
R67 457,00 is a large amount, as it is in the tens of thousands. To make it sound cheaper.
TL 4 TL 4
4.1 4.2 4.3 4.4
12 -7 °C R2 000 -794
TL 1
5.
Floor 12, flat 6
TL 2
Lesson 3: Operations using numbers and calculator skills Activity 3 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
6 221 58 180 3 900 4 222,4004 ≈ 4 222,40 36 3 22 -79,67325... ≈ -79,67
TL 1 TL 1 TL 1 TL 1 TL 1 TL 1 TL 1 TL 1 TL 1 TL 1
Lesson 4: BODMAS rule (order of operations) Activity 4 1.
2.
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16 – 8 × 3 = 16 – (8 × 3) = 16 – 24 = -8
TL 2
6 + 43 = 6 + 64 = 70
TL 2
10
Facilitator’s Guide G10 ~ Mathematical Literacy
3.
Unit
(3 × 6) + 5 × 7 – 10 = 18 + 35 – 10 = 43
1
TL 2
Lesson 5: Multiplication and division by 10, 100 and 1 000 Activity 5 1. 2. 3. 4. 5. 6. 7. 8.
Sum 19,57 × 10 125,345 × 100 1 475 × 1 000 0,468 × 100 1 234 ÷ 10 125,12 ÷ 100 12 544 ÷ 1 000 96 ÷ 100
Solution 195,7 12 534,5 1 475 000 46,8 123,4 1,251 2 12,544 0,96 TL 2
Lesson 6: Fractions Activity 6 1.
1
2.
3
3. 4.1
4
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1
= 0,75 = 75%
36
100 1 3
=
4.2
2
= 8 = 16 (any fraction that can be simplified to 4) 4
2 9
−
= 3
9
25
−
3
4 12 4−9+3 12
5
=
1
−2 12
÷ �3 × 3� =
1
9
TL 1 TL 1
= −6
2
TL 1
9
× �5� =
TL 3 2 5
11
TL 3
Facilitator’s Guide G10 ~ Mathematical Literacy
Unit
1
Lesson 7: Estimation of anticipated solutions to calculations Activity 7 1.
38 + 16 + 59 ≈ 40 + 20 + 60 ≈ 120 Real solution: 113
2.
978 + 2 382 ≈ 980 + 2 380 ≈ 3 360 Real solution: 3 360
3.
234 – 156 ≈ 230 – 160 ≈ 70 Real solution: 78
4.
32 + 18 + 43 – 23 ≈ 30 + 20 + 40 – 20 ≈ 70 Real solution: 70
5.
2,09 + 4,32 + 6,62 ≈3+4+7 ≈ 14,0 Real solution: 13,03
TL 2
Activity 8
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1.
16 × 17 = 17 × (10 + 6) = (17 × 10) + (17 × 6) = 170 + 102 = 272
2.
40 × 42 = 40 × (40 + 2) = (40 × 40) + (40 × 2) = 1 600 + 80 = 1 680
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Facilitator’s Guide G10 ~ Mathematical Literacy
Unit
3.
32 × 84 = 32 × (80 + 4) = (32 × 80) + (32 × 4) = 2 560 + 128 = 2 688
4.
15 × 28 = 15 × (20 + 8) = (15 × 20) + (15 × 8) = 300 + 120 = 420
5.
125 × 13 × 8 = (125 × 8) × 13 = 1 000 × 13 = 13 000
TL 2
Lesson 8: Rounding Activity 9 1.
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a)
4 569
10: 100: 1 000:
4 570 4 600 5 000
b)
12 075
10: 100: 1 000:
12 080 12 100 12 000
c)
1 895
10: 100: 1 000:
1 900 1 900 2 000
d)
7 892
10: 100: 1 000:
7 890 7 900 8 000
e)
678
10: 100: 1 000:
680 700 1 000
f)
2 157
10: 100: 1 000
2 160 2 200 2 000
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