Mathematical Literacy
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Reg. No.: 2011/011959/07
Mathematical Literacy
Study Guide
Grade 11
CAPS
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.
Sample
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.
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 11 Mathematical Literacy 3 in 1
• Mathematical Literacy for the Classroom Grade 11 Learner’s Book
Assessment requirements
Note that there are constant references to TL1, TL2, TL3 and TL4 throughout the 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 marks to a specific thinking level.
Mark distribution according to the thinking levels
Topics
Suggested time to spend on each unit (according to CAPS)
Contexts focusing on Patterns, relationships and representations
Contexts focusing on Measurement (conversions and time)
Contexts focusing on Finance (financial documents, tariff systems and break-even analysis)
Assessment Assignment/investigation
Control test (covering measurement and finance, integrated with numbers and patterns concepts) Term 2
Contexts focusing on Finance (interest, banking, inflation)
Contexts focusing on Measurement (length, mass, volume, temperature)
Topics
Contexts focusing on Maps, plans and other representations of the physical world (scale and mapwork)
Revision
Assessment Assignment/investigation
June examination (2 papers, 1½ hours each, 75 marks each; covering Finance, Measurement and Maps, integrated with Numbers and Patterns concepts)
Term 3
Contexts focusing on Measurement (perimeter, area and volume)
Contexts focusing on Maps, plans and other representations of the physical world (models and plans)
Topics
Contexts focusing on Finance (taxation)
Contexts focusing on Probability
Assessment Assignment/investigation
Control test (covering Measurement, Models and plans, Finance and Probability, integrated with Numbers and Patterns concepts)
Term 4
Contexts focusing on Finance (exchange rates)
Topics
Contexts focusing on Data handling
Revision
Assessment Assignment/investigation
November examination (2 papers, 2 hours each, 100 marks each; covering all topics in the curriculum)
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:
Learning objectives
At the end of the unit, you must be able to:
• apply basic mathematical skills
• understand rounding, scientific notation, percentages, ratios and proportion, and do calculations
Part 1: Rounding
When we use rounding, we need to be aware of the context of the problem. Context is the circumstances in which something occurs. This will determine whether we round up or round down as well as to how many decimal places we need to round up or down.
Important
When we round numbers, we cannot simply say the original number is equal to the rounded number For this reason, we don’t use the =, but the ≈
≈ means almost equal to OR more or less the same (rounded OR estimated)
EXAMPLES
Round the following numbers to the number of decimal places indicated in brackets:
1.1 8,25632 (2 decimal places)
Solution: ≈ 8,26
UNIT 1: REVIEW OF BASIC SKILLS Sample
Note: Look at the third decimal. A number less than 4 makes no difference to the second decimal. If the third decimal is 5 or higher, the second decimal should then be greater, therefore the 5 changed to a 6.
1.2 16,89432 (3 decimal places)
Solution: ≈ 16,894
1.3 428,899 (2 decimal places)
Solution: ≈ 428,90
Activity 1
Round the numbers to TWO decimal places:
1. 4,3568
2. 18,3578
3. 1,9999
4. 45,4386
5. 834,8765
6. 29,99124
7. 492,6324
8. 9,3334
9. 16,448
10. 74,97553
Part 2: Rounding to the nearest 10, 100 and 1 000
Use place values to help you when rounding numbers. For example, if you must round numbers to the nearest 10, you must look at the Units column.
Rounding to the nearest 10
Numbers smaller than 5 in the Units column are rounded to the previous ten. Numbers larger than 5 in the Units column are rounded to the next ten.
Rounding to the nearest 100
Numbers smaller than 5 in the Tens column are rounded to the previous 100. Numbers larger than 5 in the Tens column are rounded to the next 100.
Rounding to the nearest 1 000
Numbers smaller than 5 in the Hundreds column are rounded to the previous 1 000. Numbers larger than 5 in the Hundreds column are rounded to the next 1 000.
EXAMPLES
2.1 Round the numbers to the nearest 10:
2.1.1 75 ≈ 80
2.1.2 17 ≈ 20
2.1.3 163 ≈ 160
2.1.4 689 ≈ 690
2.1.5 3 ≈ 0
2.2
Round the numbers to the nearest 100:
2.2.1 75 ≈ 100
2.2.2 2 082 ≈ 2 100
2.2.3 43 ≈ 0
2.3 Round the numbers to the nearest 1 000:
2.3.1 899 ≈ 1 000
2.3.2 3 956 ≈ 4 000
2.3.3 282 ≈ 0
Activity 2
Round the numbers to the nearest 10, 100 or 1 000:
1. 48 (nearest 10)
2. 245 (nearest 100)
3. 2 367 (nearest 1 000)
4. 4 356 (nearest 10, 100 and 1 000)
5. 3 835 (nearest 10, 100 and 1 000)
Part 3: Scientific notation
Important
One million: 1 000 000 (6 zeros)
One billion: 1 000 000 000 (9 zeros)
One trillion: 1 000 000 000 000 (12 zeros)
Sample
We use scientific notation to write very large or very small numbers in a way that makes it easy to read. The number is written using a number between 1 and 10, which is then multiplied by a power of 10.
For large numbers, put a decimal comma after the first digit so the number is between 1 and 10. Count the number of places from the decimal comma to the end of the number – this will tell you what power of 10 to use. Remove any zeros and write the number multiplied by 10 to the power of ���� (���� being the number of places from the decimal comma to the end of the number).
For very small numbers, count the number of places from the decimal comma until you have a number between 1 and 10. Remove any zeros in front of the decimal comma and write the number multiplied by 10 to the power of negative ����
EXAMPLES
• Write 81 500 in scientific notation.
• Write 0,0043 in scientific notation.
Decimal notation Scientific notation
34 000 000 3,4 × 107
734 000 000 000 7,34 × 1011
0,000 001 4 1,4 × 10-6
0,000 000 000 03 3,0 × 10-11 674 965,38 6,7496538 × 105
Activity 3
1. Write the numbers in scientific notation:
1.1 2 700 000 1.2 4 500 1.3 0,000 000 56 1.4 0,000 18
2. Write the following as an ordinary number: 2.1 6,4 × 105 2.2 7,23 × 109 2.3 4,3 × 10-6 2.4 7,5 × 10-9 8 1 5 0 0 = 8,15 × 104 0, 0 0 4 3 = 4,3 × 10-3 Sample
Part 4: Percentages
A percentage is a way of expressing the parts of a whole (the numerator) as a value out of 100. It is always written with the % symbol directly after the number. A percentage can also be written as a fraction. The denominator will always be 100. The term ‘per cent’ derives from the Latin word per centum, which means ‘per hundred’ or ‘for every hundred’.
Percentages can be expressed as a common fraction or as a decimal number, e.g 83% = 83 100 OR = 0,83
4.1 Calculation of percentage
To calculate a percentage of an amount, write the per cent as a fraction and multiply by the amount. per cent 100 × amount
EXAMPLES
4.1.1 Calculate 25% of R5 000,00.
Note: The word ‘of’ means multiplication.
25 100 × R5 000 = R1 250,00
Sequence on calculator: (25 ÷ 100) × 5 000 =
4.1.2 Thandi gets 28 40 in a Mathematical Literacy test. What is her percentage for the test?
28 40 × 100 = 70%
Sequence on calculator: (28 ÷ 40) × 100 =
4.2 Determining new values for given percentages
Sometimes we need to calculate the new price of an item or product after it has been increased by a certain percentage, e.g. VAT (Value added tax) which is levied on the original price.
EXAMPLES
4.2.1 A packet of biscuits costs R15,30 without VAT. How much will you pay after VAT is added? (In South Africa, the VAT rate is currently 15%)
15
100 × R16,00 = R2,40 OR R16,00 × 115% = R18,40
R16,00 + R2,40 = R18,40
You will pay R18,40 after VAT is added.
4.2.2 A vendor increases his prices by 8%. If the original price is R45,99, what will the price be after the increase?
8
100 × R45,99 = R3,68 OR R45,99 × 108% = R49,67
R45,99 + R3,68 = R49,67
The new price is R49,67.
4.2.3 A shoe shop has a sale with 25% off all shoes. What will you pay for a pair of shoes that was originally priced at R645,00?
25
Sample100 × R645,00 = R163,50 OR 100% – 25% = 75%
R645,00 – R163,50 = R490,50 75% × R645,00 = R490,50
You will now pay R490,50 for the pair of shoes.
4.2.4 The petrol price decreases with 2,5%.
How much will motorists now pay for a litre of petrol if the price was R14,40/ℓ?
2,5
100 × R14,40 = R0,36 OR 100% – 2,5% = 97,5%
R14,40 – R0,36 = R14,04
Motorists will now pay R14,04/ℓ.
97,5% × R14,40 = R14,04
4.3 Determining the initial value when new values and percentages are given
Sometimes we need to calculate the original price of an item or product before it has been decreased by a certain percentage, e.g. discount on products during a sale.
Important
You must determine the original value – the previous value, before it was increased or decreased.
EXAMPLES
4.3.1 Dishwashing liquid costs R23,10, VAT included. VAT is 15%. What was the dishwashing liquid’s price before VAT was added?
P: price without VAT
P × 115% = R23,10 (115% = 100% + 15%)
P = 23,10 115% OR R23,10 ÷ 1,15
P = R20,09
The dishwashing liquid’s original price was R20,09.
4.3.2 A butchery increases their prices by 9%, which means that biltong now costs R195,10/kg. What was the original price before the increase?
Sample
P: original price
P × 109% = R195,10
P = 195,10 ÷ 109% = R178,99
The biltong’s original price was R178,99.
4.3.3 A computer shop has a sale with all items at 25% discount. If a printer’s selling price is currently at R1 538,40, what was the original price before the discount?
P: original price (100% – 25% = 75%)
P × 75% = R1 538,40
P = R1 538,40 ÷ 75% = R2 051,20
The printer’s original price was R2 051,20.
4.4 Percentage increase and decrease
We can use the following formula to determine percentage increase or decrease:
Percentage increase/decrease = current
EXAMPLES
× 100
4.4.1 In 2019, a school had 1 538 learners and in 2020, there were 1 645 learners. By what percentage has the enrolment increased?
Percentage
Sample
4.4.2 In 2018, a glass factory produced 796 faulty glasses and in 2019, only 675. By what percentage did the faulty glasses decrease? Percentage decrease
The negative value indicates a decrease. In this example, the percentage of faulty glasses decreased by 15,20%.
• Comprehensive explanations of mathematical concepts in plain language.
• Practical, everyday examples.
• Activities that test learners’ knowledge application and reasoning.
• The facilitator’s guide contains step-by-step calculations and answers.
• Includes a formula sheet and an alphabetical list of mathematical terms for easy reference.
• Use in school or at home.
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