Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve multi-step financial problems in South African scenarios.
• Interpret and analyze data from tables and graphs.
• Apply measurement concepts like area and volume to practical situations.
• Use maps and scale diagrams to solve spatial problems.
• Demonstrate effective problem-solving strategies.

Lesson summary

Mathematical Literacy is about applying mathematical skills to real-life situations. As Grade 12 learners, you’re preparing for your final exams, and this week focuses on integrating all the topics you've covered throughout the year through realistic, mixed-task problems. This is crucial because the final exam assesses your ability to apply mathematical concepts, not just regurgitate formulas. Mastering this skill will equip you to make informed decisions in your future lives, whether it's managing personal finances, understanding loan agreements, interpreting data in the news, or contributing to informed community discussions.

Lesson notes

This week’s focus is on integrating all topics you have learnt throughout the year. This means the questions you will encounter may require you to use skills from different learning areas. Areas, Perimeter and Volume: It is vital to remember the formulae for different shapes as well as how to apply it to composite shapes. Area of a rectangle = Length x Breadth Area of a Triangle = ½ x base x perpendicular height Area of a circle = π x r² (where r is the radius) Circumference of a circle = 2 x π x r Volume of a rectangular prism = Length x Breadth x Height Example 1: Fencing a Yard (Area & Perimeter) Sipho wants to fence his rectangular yard in Soweto to keep his chickens safe. The yard measures 15 meters long and 10 meters wide. Fencing costs R45 per meter.

Perimeter: 2 (Length + Breadth) = 2 (15m + 10m) = 2 25m = 50m Cost: 50m R45/m = R2250 Now, suppose Sipho also wants to plant grass in his yard.

Area: Length Breadth = 15m * 10m = 150 m² Why: This example combines perimeter (fencing) and area (grass). It's relevant because many South Africans own property and need to manage costs associated with maintenance and improvements.

Budgets and Financial Documents: Understanding payslips, bank statements, and budgets is crucial.

Example 2: Calculating Net Salary Thandi earns a gross monthly salary of R12,

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0. Her deductions are: PAYE (tax): R2,500 UIF (Unemployment Insurance Fund): R120 Medical Aid: R800 Pension Fund: 7.5% of gross salary What is Thandi's net salary?

Calculate Pension Fund: 7.5/100 * R12,000 = R900 Total Deductions: R2,500 + R120 + R800 + R900 = R4,320 Net Salary: R12,000 - R4,320 = R7,680 Why: This directly relates to managing personal finances and understanding income tax, UIF, and other common deductions in South Africa.

Data Handling and Probability: Interpreting data in tables, charts, and graphs is essential for informed decision-making.

Example 3: Analyzing Unemployment Data The following table shows unemployment rates in South Africa for different age groups: | Age Group | Unemployment Rate (%) | |---|---| | 15-24 | 55.2 | | 25-34 | 36.8 | | 35-44 | 22.5 | | 45-54 | 14.3 | | 55-64 | 8.1 | What conclusions can you draw from this data? Unemployment is highest among younger people (15-24 age group). Unemployment decreases with age. Targeted interventions are needed to address youth unemployment.

Why: Understanding unemployment statistics is crucial for understanding social and economic challenges in South Africa.

Maps and Scale: Using maps to calculate distances and interpret information is an important skill.

Example 4: Calculating Distance on a Map On a map with a scale of 1:50,000, the distance between Johannesburg and Pretoria measures 10cm. What is the actual distance in kilometers?

Actual Distance in cm: 10cm * 50,000 = 500,000 cm Convert to meters: 500,000 cm / 100 = 5,000 m Convert to kilometers: 5,000 m / 1000 = 5 km Why: This relates to planning trips, understanding distances, and using maps or online navigation tools. Rate, Ratio and Proportion: These three concepts are very important when dealing with real-life tasks. Speed = Distance/Time Density = Mass/Volume Example 5: Calculating Best Buy Shop A sells a 2.5kg bag of maize meal for R35, while Shop B sells a 5kg bag for R

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5. Which is the better buy?

Solution: Shop A: R35 / 2.5kg = R14/kg Shop B: R65 / 5kg = R13/kg Shop B is the better buy because it is cheaper per kg.

Why: This relates to budgeting and ensuring money is spent wisely. Guided Practice (With Solutions)

Question 1: A tuck shop owner buys a box of 24 chocolate bars for R

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0. He wants to sell each chocolate bar for a profit of 40%. What should be the selling price of each chocolate bar?

Solution: Cost per chocolate bar: R180 / 24 = R7.50 Profit per chocolate bar: 40/100 * R7.50 = R3.00 Selling price per chocolate bar: R7.50 + R3.00 = R10.50

Commentary: This combines cost price, profit percentage, and selling price calculations – a common business scenario.

Question 2: A water tank is cylindrical with a radius of 1.5 meters and a height of 2 meters. Calculate the volume of water the tank can hold in liters. (Use π = 3.14)

Solution: Volume of cylinder: π r² h = 3.14 (1.5m)² 2m = 3.14 2.25m² 2m = 14.13 m³ Convert to liters: 1 m³ = 1000 liters, so 14.13 m³ = 14.13 * 1000 liters = 14130 liters

Commentary: This tests knowledge of volume calculations and unit conversions, applicable to water management and conservation.

Question 3: According to the graph below, what were the total sales for quarter 3 and 4 in thousands if quarter 3 had sales of R500 000 and Quarter 4 has sales of R750 000. (Assume a simple bar graph is presented).

Solution: Quarter 3 sales in thousands: 500 000/1000 = 500 Quarter 4 sales in thousands: 750 000/1000 = 750 Total sales: 500 + 750 = R1250 (Thousands)

Commentary:This is a common skill and requires you to interprete information given on a graph. Independent Practice (Questions Only) A baker needs to bake 150 cupcakes for a school function.