Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Analyze complex, real-life scenarios.
• Apply skills in Finance, Measurement, Data, and Maps.
• Communicate solutions clearly and effectively.
• Critically evaluate the reasonableness of solutions.
• Practice time management for exam conditions.

Lesson summary

This week, we kick off our intensive exam preparation for Mathematical Literacy. We'll be focusing on tackling mixed, real-life tasks – the kind you'll definitely encounter in your final exam and, more importantly, in your daily life after school. Mathematical Literacy isn't just about numbers; it's about understanding the world around you and making informed decisions as a South African citizen. This means being able to budget your money, understand your electricity bill, interpret news reports about unemployment, and much more. We will be analyzing complex scenarios requiring the integration of various mathematical literacy skills.

Lesson notes

This section will focus on reinforcing key concepts commonly tested in integrated tasks.

We will revisit: Finance: Budgeting, income and expenses, taxation (including PAYE, UIF), simple and compound interest, banking (account fees, interest rates), loans (hire purchase), insurance (premiums, claims), exchange rates.

Measurement: Units of measurement (metric and imperial), conversions, perimeter, area, volume, scale drawings and maps, time zones.

Data Handling: Collecting, organizing, and representing data (tables, graphs, charts), interpreting data (mean, median, mode, range, percentiles), probability.

Probability: Basic probability calculations, understanding probability in real-life events.

Maps and Plans: Working with scale, interpreting symbols and keys, calculating distances. Detailed Explanations and

Examples: Finance - Compound Interest: Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. This means that you earn interest on your interest.

The formula for compound interest is: A = P (1 + r/n)^(nt)

Where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = the annual interest rate (as a decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for Example (South African Context): Sipho invests R5000 in a fixed deposit account that pays 8% interest per annum, compounded quarterly. How much will he have in the account after 5 years?

Solution: P = R5000 r = 8% = 0.08 n = 4 (compounded quarterly) t = 5 years A = 5000 (1 + 0.08/4)^(4*5) A = 5000 (1 + 0.02)^20 A = 5000 (1.02)^20 A = 5000 * 1.485947 A = R7429.74 Therefore, Sipho will have approximately R7429.74 in his account after 5 years.

Measurement - Scale and Maps: Scale is the ratio of a distance on a map or drawing to the corresponding actual distance on the ground. It's crucial for calculating real-world distances from maps.

Example (South African Context): A map of Gauteng has a scale of 1:250,

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0. Two towns are 8 cm apart on the map. What is the actual distance between the towns in kilometers?

Solution: Scale: 1 cm on map = 250,000 cm in reality Distance on map: 8 cm Actual distance: 8 cm * 250,000 = 2,000,000 cm Convert to kilometers: 2,000,000 cm / 100 cm/m = 20,000 m 20,000 m / 1000 m/km = 20 km The actual distance between the two towns is 20 km.

Data Handling - Interpreting Graphs: Understanding how to read and interpret graphs is important for making informed decisions. This includes understanding the axes, the scale, and any trends shown in the graph.

Example (South African Context): Consider a bar graph showing the average monthly rainfall in Cape Town. The graph shows that June has the highest average rainfall at 100mm. You need to interpret this information in the context of planning a school trip. You understand that if you travel to Cape Town in June, it is very likely to rain.

Probability - Basic Probability: Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and

1. Example (South African Context): In a lottery draw with numbers 1-49, what is the probability of choosing the correct 6 numbers? This involves calculating combinations, which is a common question type. Guided Practice (With Solutions)

Question 1: Thando earns a gross monthly salary of R12,

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0. Her deductions include PAYE (R2,500), UIF (1%), and a medical aid contribution of R

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0. Calculate Thando's net salary.

Solution: Calculate UIF: R12,000 * 0.01 = R120 Calculate Total Deductions: R2,500 + R120 + R800 = R3,420 Calculate Net Salary: R12,000 - R3,420 = R8,580 Thando's net salary is R8,

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0. Question 2: A rectangular garden is 8 meters long and 5 meters wide. Calculate the perimeter and area of the garden. If fencing costs R55 per meter, what will it cost to fence the entire garden?

Solution: Perimeter: 2(length + width) = 2(8m + 5m) = 2(13m) = 26 m Area: length width = 8m 5m = 40 m² Fencing Cost: 26 m * R55/m = R1430 The perimeter is 26 meters, the area is 40 square meters, and the cost to fence the garden is R

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0. Question 3: A survey was conducted amongst 200 Grade 12 learners to find out their favourite subjects.

The results were: Maths (80), English (60), Science (40), Other (20). Represent this data as a pie chart and determine the percentage of learners who prefer Maths.

Solution: Calculate percentages: Maths: (80/200) 100% = 40% English: (60/200) 100% = 30% Science: (40/200) 100% = 20% Other: (20/200) 100% = 10% Draw the Pie Chart: Represent each subject as a slice of the pie, proportional to its percentage. (Omitted here as Markdown cannot render charts directly). 40% of the learners prefer Maths. Independent Practice (Questions Only) A fridge is priced at R8,000 cash or on hire purchase with a 15% deposit and 24 monthly installments of R380.