Mathematical Literacy
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Mathematical Literacy
Study guide
Grade 12
CAPS aligned
E Brönn A Kies
2212-E-MAL-SG01
Lesson elements
LEARNING AIMS
What candidates should know at the end of the lesson. Taken from CAPS.
IMPORTANT TERMINOLOGY
New terminology to extend understanding of the subject as part of the lesson.
Sample
IMPORTANT
A summary or explanation of key concepts explained in the lesson.
ACTIVITY
Formative assessment to test candidates’ progress and knowledge of the lesson completed.
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 12 Mathematical Literacy 3 in 1
• Mathematical Literacy for the Classroom Grade 12 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
The assessment programme
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.
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 3,14823 (2 decimal places)
Answer: ≈ 3,15
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 4 changed to a 5.
1.2 23,89432 (3 decimal places)
Answer: ≈ 23,894
1.3 215,899 (2 decimal places)
Answer: ≈ 215,90
Activity 1
Round the numbers to TWO decimal places:
1. 2,3568
2. 0,356789
3. 1,9999
4. 13,4386
5. 234,8765
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 65 ≈ 70
2.1.2 16 ≈ 20 2.1.3 173 ≈ 170 2.1.4 589 ≈ 590
2.2 Round the numbers to the nearest 100:
2.2.1 65 ≈ 100
2.2.2 1 082 ≈ 1 100
2.3
Round the numbers to the nearest 1 000:
2.3.1 5 999 ≈ 6 000
2.3.2 4 956 ≈ 5 000
Activity 2
Round the numbers to the nearest 10, 100 or 1 000:
1. 58 (nearest 10)
2. 345 (nearest 100)
3. 1 367 (nearest 1 000)
4. 1 356 (nearest 10, 100 and 1 000)
5. 2 835 (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)
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).
SampleFor 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
14 000 000 1,4 × 107
582 000 000 000 5,82 × 1011
0,000 001 8 1,8 × 10-6
0,000 000 000 05 5,0 × 10-11
Scientific notation
506 791,14 5,0679114 × 105
Activity 3
0, 0 0 4 3 = 4,3 × 10-3 Sample
1. Write the numbers in scientific notation:
1.1 4 800 000
1.2 2 500
1.3 0,00000012
1.4 0,00023
2. Write the following as an ordinary number: 2.1 3,4 × 105
2.2 6,28 × 109
2.3 2,3 × 10-6
2.4 4,5 × 10-9 8 1 5 0 0 = 8,15 × 104
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. 25% = 25 100 OR = 0,25
4.1 Calculation of percentage
To calculate a percentage of an amount, write the per cent as a fraction and multiply by the amount.
cent
× amount
EXAMPLES
4.1.1 Calculate 15% of R1 200
Note: The word ‘of’ means multiplication.
× R1 200 = R180,00
Sequence on calculator: (15 ÷ 100) × 1 200 =
4.1.2 Louisa gets 26 40 in a Mathematical Literacy test What is her percentage for the test?
× 100 = 65%
Sequence on calculator: 26 ÷ 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 pack of AA batteries costs R39,80 without VAT
How much will you pay after VAT is added?
(In South Africa, the VAT rate is currently 15%)
15
100 × R39,80 = R5,97 OR R39,80 × 115% = R45,77
R39,80 + R5,97 = R45,77
You will pay R45,77 after VAT is added.
4.2.2 A shop owner increases his prices by 6%.
If the original price of a product is R21,99, what will the price be after the increase?
6
100 × R21,99 = R1,32 OR R21,99 × 106% = R23,31
R1,32 + R21,99 = R23,31
The new price is R23,31.
4.2.3 A clothing shop has a sale with 25% off all jeans
What will you pay for a pair of jeans that was originally priced at R395,00?
25
100 × R395,00 = R98,75 OR 100% – 25% = 75%
Sample
R395,00 – R98,75 = R296,25 75% × R395,00 = R296,25
You will now pay R296,25 for the pair of jeans.
4.2.4 The petrol price decreases with 4,5%
How much will motorists now pay for a litre of petrol if the price was R12,30/ℓ?
4,5
100 × R12,30 = R0,5535 OR 100% – 4,5% = 95,5%
R12,30 – R0,5535 = R11,75 95,5% × R12,30 = R11,75
Motorists will now pay R11,75/ℓ.
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 A chocolate bar costs R15,10, VAT included. VAT is 15%. What was the price of the chocolate bar before VAT was added?
P: price without VAT
P × 115% = R15,10 (115% = 100% + 15%)
P = 15,10 115% OR R15,10 ÷ 1,15
P = R13,13
The original price of the chocolate bar was R13,13.
4.3.2 A butcher increases his prices by 6%, which means that boerewors now costs R250,75/kg. What was the original price before the increase?
P: original price
P × 106% = R250,75
P = 250,75 ÷ 106% = R236,56
The original price of the boerewors was R236,56
Sample
4.3.3 A shoe shop has a sale with all items at 25% discount If the selling price of a pair of shoes is now R348,25, what was the original price before the discount?
P: original price (100% – 25% = 75%)
P × 75% = R348,25
P = R348,25 ÷ 75% = R464,33
The original price of the shoes was R464,33.
4.4 Percentage increase and decrease
We can use the following formula to determine percentage increase or decrease:
Percentage increase/decrease = current value previous value previous value × 100
EXAMPLES
4.4.1 In 2020, a school had 1 252 learners and in 2021, there were 1 385 learners. By what percentage has the enrolment increased?
Percentage
4.4.2 In 2019, a factory produced 625 faulty items and in 2020, only 506. By what percentage did the faulty items decrease?
Percentage decrease =
The negative value indicates a decrease. In this example, the percentage of faulty items decreased by 19,04%.
Activity 4
1. Calculate:
1.1 35% of R1 500
1.2 33⅓% of R4 500
2. Fatima gets 46 75 in a Geography test. What is her percentage? Round your answer to the nearest percentage.
3. A shop assistant forgot to add VAT when she calculated the price of several items.
The following items must be recalculated:
• Chocolate bars at R6,25
• Sweets at R3,45
• Chips at R4,20
• Soft drink cans at R5,85
Calculate the correct new price of each item. VAT is 15%.
4. Nico buys a second-hand motorcycle at R25 000, 15% VAT included. What would the motorcycle have cost before VAT was added?
5. The petrol price decreases with 1,3% and motorists now pay R12,34/ℓ How much did motorists pay for a litre of petrol before the decrease?
6. A handbag that previously cost R235,00 now costs R135,00. Calculate the percentage discount to the nearest whole number.
7. What percentage is 36 minutes of an hour?
Sample8. After an inflation increase of 6,5%, a bag of groceries now costs R456,00. What was the cost of the same bag of groceries before the increase?
9. A company has 312 employees, of which 176 are female. What percentage of the employees are male? Round your answer to the nearest whole number.
10. Millicent earns R15 457,00 per month. She previously earned R14 450. The average salary increase at her company was 5%. Show by calculation that Millicent’s new salary is in line with the company average.
• 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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