Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Apply various mathematical skills to solve complex, multi-step problems.
• Interpret and analyze data from tables, graphs, and maps.
• Develop and use financial documents like budgets and payslips.
• Use measurement and scale to solve problems with maps and plans.
• Critically evaluate the validity of data and information.

Lesson summary

This week focuses on integrated exam preparation, utilizing mixed real-life tasks relevant to the South African context. Mathematical Literacy is not just about calculations; it’s about applying mathematical reasoning to everyday situations, understanding data, and making informed decisions. This preparation aims to equip you with the skills necessary to confidently tackle any mathematical literacy question in your final exams. From budgeting your future salary to understanding the impact of interest rates on loans, the skills we develop this week are vital for navigating the complexities of modern life in South Africa.

Lesson notes

This week's focus necessitates revisiting and integrating several key Mathematical Literacy concepts.

These include: Percentages: Understanding percentage increase, decrease, discounts, and commissions is crucial. Remember, "percent" means "out of one hundred." We use percentages extensively in financial calculations, such as calculating VAT or interest.

Ratio and Proportion: Ratios compare two quantities, while proportions state that two ratios are equal. We use them in scaling recipes, maps, and even understanding voting outcomes.

Financial Mathematics: Includes simple and compound interest, loan repayments, budgets, income statements, and tax calculations. Understanding these concepts is vital for managing your personal finances and understanding the South African economy.

Measurement: Covers length, area, volume, mass, time, and temperature. Knowing how to convert between units is essential. Maps, Plans, and Models: Understanding scale and direction is crucial for interpreting maps and plans. Detailed Explanations with

Examples: Percentages: Example 1: VAT Calculation: A pair of shoes costs R450 (excluding VAT). Calculate the price including VAT at 15%.

Solution: VAT amount = 15/100 R450 = R67.50 Price including VAT = R450 + R67.50 = R517.50 Example 2: Discount: A store offers a 20% discount on a TV priced at R

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0. What is the sale price?

Solution: Discount amount = 20/100 R6000 = R1200 Sale price = R6000 - R1200 = R4800 Ratio and Proportion: Example 1: Map Scale: A map has a scale of 1:50,

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0. This means 1 cm on the map represents 50,000 cm (or 500 meters or 0.5 km) in reality. If two towns are 5 cm apart on the map, what is the actual distance between them?

Solution: Actual distance = 5 cm 50,000 = 250,000 cm = 2500 meters = 2.5 km Example 2: Recipe Scaling: A recipe for 4 people requires 200g of flour. You want to make the recipe for 6 people. How much flour do you need?

Solution:* The ratio of people is 4:6, which simplifies to 2:

3. Amount of flour needed = (3/2) 200g = 300g Financial Mathematics: Example 1: Simple Interest: You invest R2000 at a simple interest rate of 8% per annum for 3 years. How much interest will you earn?

Solution: Simple Interest = Principal Rate Time = R2000 8/100 * 3 = R480 Example 2: Compound Interest: You invest R5000 at a compound interest rate of 10% per annum for 2 years, compounded annually. What is the total amount after 2 years?

Solution: Year 1: Interest earned = R5000 10/100 = R

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0. Total amount = R5000 + R500 = R5500 Year 2: Interest earned = R5500 10/100 = R

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0. Total amount = R5500 + R550 = R6050 Example 3: Loan Repayments: You take out a loan of R10,000 at an interest rate of 12% per annum, to be repaid over 5 years. Calculate the monthly repayment using an online loan calculator or financial formulas (note: the full formula for loan repayment is complex and usually provided in exams, so understanding how to use a provided formula is key). The focus is on understanding the impact of interest rates and loan terms.

Measurement: Example 1: Area Calculation: A rectangular room is 5 meters long and 4 meters wide. What is the area of the room?

Solution: Area = Length Width = 5 m * 4 m = 20 square meters Example 2: Volume Calculation: A rectangular tank is 2 meters long, 1 meter wide, and 1.5 meters high. What is the volume of the tank in liters? (Remember 1 cubic meter = 1000 liters)

Solution: Volume = Length Width Height = 2 m 1 m * 1.5 m = 3 cubic meters Volume in liters = 3 cubic meters 1000 liters/cubic meter = 3000 liters Maps, Plans, and Models: Example 1: Using a Scale to find distance: A map has a scale of 1:

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

Solution: 8cm 250000 = 2000000 cm 2000000cm = 20000m = 20km.

Therefore, the cities are 20km apart.

Example 2: Finding area using a scale: You have a plan with a scale of 1:

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0. A rectangular garden on the plan measures 10cm by 5cm. What is the actual area of the garden in square meters?

Solution: Actual Length = 10cm 50 = 500cm = 5m Actual Width = 5cm 50 = 250cm = 2.5m Actual Area = 5m 2.5m = 12.5 square meters Guided Practice (With Solutions)

Question 1: A cellphone is advertised for R3500 including VAT at 15%. What was the original price of the cellphone before VAT was added?

Solution: Let the original price be 'x'. Then, x + 15% of x = R

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0. This means 1.15x = R

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0. Therefore, x = R3500 / 1.15 = R3043.48 (rounded to two decimal places).

Commentary: This problem involves working backward from a price that includes VAT to find the original price. It requires understanding the relationship between the original price and the price including VA

T. Question 2: A farmer has a rectangular field that measures 120 meters in length and 80 meters in width. He wants to fence the field. Fencing costs R45 per meter. What will be the total cost of fencing the field?

Solution: Perimeter of the field = 2 (length + width) = 2 (120 m + 80 m) = 2 * 200 m = 400 m.