Lesson Notes By Weeks and Term v5 - Grade 12
Integrated exam preparation using mixed real-life tasks – Week 8 focus
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Integrated exam preparation using mixed real-life tasks – Week 8 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 12
Term: Term 4
Week: 8
Theme: General lesson support
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This week's focus is on integrated exam preparation using mixed real-life tasks. This is crucial because the Mathematical Literacy exam, and Mathematical Literacy in general, assesses your ability to apply mathematical concepts to everyday situations. Success in the exam requires more than just knowing formulas; it demands the ability to critically analyse problems, extract relevant information, and use appropriate mathematical tools to find solutions that make sense in a South African context. This week serves as a vital opportunity to consolidate your understanding and refine your problem-solving skills across a range of practical scenarios.
This week, we'll integrate various Mathematical Literacy topics to simulate real-world problems.
Here are the key concepts we'll be using: Budgeting: A budget is a plan for managing income and expenses. It involves identifying sources of income, categorizing expenses (fixed, variable, discretionary), and tracking spending. Effective budgeting involves setting financial goals and making informed decisions about how to allocate resources. In South Africa, budgeting is particularly important due to factors like income inequality and the high cost of living. Consider the impact of inflation and interest rates on your budget.
Example: A household in Soweto has a monthly income of R12,
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0. Their fixed expenses (rent, transport, school fees) amount to R7,
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0. Variable expenses (food, electricity, water) average R3,
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0. They want to save R500 per month. Calculate their discretionary spending allowance.
Solution: Total expenses (excluding savings) = R7,000 + R3,000 = R10,
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0. Available income after fixed and variable expenses = R12,000 - R10,000 = R2,
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0. Discretionary spending allowance = R2,000 - R500 (savings) = R1,
5
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0. This amount can be used for entertainment, clothing, or other non-essential items.
Data Handling: Data is everywhere. Understanding how to interpret data presented in tables, graphs (bar graphs, pie charts, line graphs), and charts is crucial. Pay attention to labels, scales, and units. Calculate averages (mean, median, mode), range, and percentages. Relate data to real-world contexts.
Example: A table shows the unemployment rates in South Africa for the past 5 years. Interpret the trend and discuss possible contributing factors.
Solution: Analyse the data to identify if the unemployment rate is increasing, decreasing, or fluctuating. Discuss potential reasons for the observed trend, such as economic growth, government policies, or global events. Consider the impact of unemployment on communities.
Financial Calculations: This includes calculating simple and compound interest, VAT, discounts, markups, and exchange rates. Understand the difference between nominal and effective interest rates. Be able to compare different financial products (loans, investments).
Example: A store in Durban offers a 15% discount on a TV that originally costs R5,
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0. Calculate the discount amount and the final price. Also, calculate the VAT (15%) on the final price.
Solution: Discount amount = 15/100 R5,000 = R
7
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0. Price after discount = R5,000 - R750 = R4,
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0. VAT amount = 15/100 R4,250 = R637.
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0. Final price including VAT = R4,250 + R637.50 = R4,887.
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0. Measurement: Converting units (e.g., meters to centimeters, kilograms to grams, liters to milliliters), calculating area, volume, and perimeter are essential. Understanding scale drawings is also important.
Example: A recipe calls for 250ml of milk. You only have a measuring cup that measures in liters. How many liters of milk do you need?
Solution: 1 liter = 1000 ml.
Therefore, 250 ml = 250/1000 = 0.25 liters.
Probability: Probability is the chance of an event occurring. It is expressed as a fraction, decimal, or percentage. Understand the difference between independent and dependent events.
Example: What is the probability of rolling a 6 on a standard six-sided die?
Solution: There is one favorable outcome (rolling a 6) and six possible outcomes (1, 2, 3, 4, 5, 6).
Therefore, the probability is 1/
6. Maps, Plans and other Representations of the Physical World: Interpret scale, calculate actual distances from map measurements, understand directions and bearings.
Example: A map has a scale of 1:50,
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0. Two towns are 5cm apart on the map. What is the actual distance between the towns in kilometers?
Solution: 1 cm on the map represents 50,000 cm in reality.
Therefore, 5 cm represents 5 * 50,000 = 250,000 cm.
Convert cm to km: 250,000 cm = 2500 m = 2.5 km. The actual distance between the towns is 2.5 km. Guided Practice (With Solutions)
Question 1: Thando earns R8,000 per month after deductions.
Her monthly expenses are: Rent R2,500, Transport R800, Groceries R2,000, Electricity R500, Cellphone R
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0. She wants to save 10% of her income. How much money does she have left for entertainment and other expenses?
Solution: Calculate total expenses: R2,500 + R800 + R2,000 + R500 + R300 = R6,100 Calculate desired savings: 10% of R8,000 = 0.10 * R8,000 = R800 Calculate total expenses including savings: R6,100 + R800 = R6,900 Calculate money left for entertainment and other expenses: R8,000 - R6,900 = R1,100
Commentary: This question integrates budgeting and percentage calculations. It reinforces the importance of tracking expenses and setting savings goals.
Question 2: A graph shows the number of reported crimes in Gauteng over the last 10 years. In 2013, there were 450,000 reported crimes. In 2023, there were 380,000 reported crimes. Calculate the percentage decrease in reported crimes from 2013 to 2023.