Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Apply unit conversions to household budgeting (water, electricity).
• Interpret statistical data from tables and graphs.
• Use maps and scale drawings for distance problems.
• Apply financial math concepts (interest, loans).
• Calculate mean, median, mode, and range from data sets.

Lesson summary

This week is dedicated to intensive exam preparation using mixed, real-life tasks, focusing on integrating concepts learned throughout the year. Mathematical Literacy aims to equip you with the skills to understand and critically engage with quantitative information encountered daily. It's not just about calculations; it's about applying mathematics to solve problems in personal finance, health, civics, and more. This exam preparation week emphasizes the ability to identify relevant information, select appropriate mathematical tools, perform accurate calculations, interpret results in context, and communicate findings effectively.

Lesson notes

This section provides a review of key concepts needed to successfully tackle mixed real-life tasks. 2.1 Unit Conversions & Proportional Reasoning: Unit Conversions: Converting between different units of measurement is fundamental. Be comfortable converting between meters, centimeters, kilometers, liters, milliliters, kilograms, grams, hours, minutes, etc. Understand common South African specific units, like the size of a building plot in square meters.

Example: If electricity costs R2.50 per kilowatt-hour (kWh), and you used 2500 Wh, how much did it cost? First, convert Wh to kWh: 2500 Wh / 1000 = 2.5 kWh.

Cost: 2.5 kWh R2.50/kWh = R6.

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5. Proportional Reasoning: Solving problems where two quantities are related proportionally (directly or inversely).

Direct Proportion: As one quantity increases, the other increases at the same rate (e.g., the more you work, the more you earn).

Inverse Proportion: As one quantity increases, the other decreases (e.g., the more workers on a job, the less time it takes).

Example: If 3 painters can paint a house in 5 days, how long will it take 5 painters, assuming they work at the same rate? This is an inverse proportion. Let 'x' be the number of days. 3 painters 5 days = 5 painters * x days. 15 = 5x. x = 3 days. 2.2 Interpreting Data (Tables, Graphs, Charts): Understanding the axes and labels of graphs and charts. Calculating percentages and percentage changes. Identifying trends and patterns in data. Drawing conclusions and making inferences based on the data.

Example: A bar graph shows the number of learners who passed Maths Literacy in the last five years. Analyze the graph to determine if performance is improving, declining, or remaining stable. Calculate the percentage change between the first and last year. Determine the modal year for pass rates.

South African context: Analyzing crime statistics, unemployment rates, or COVID-19 infection rates are common applications. 2.3 Maps, Scale Drawings & Navigation: Understanding map scales (e.g., 1:50,000 means 1 cm on the map represents 50,000 cm, or 500 meters, in reality). Calculating real-world distances using map scales. Using compass directions and bearings. Reading and interpreting road maps and GPS coordinates.

Example: A map has a scale of 1:25,

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0. Two towns are 8 cm apart on the map. What is the actual distance between the towns in kilometers? Actual distance = 8 cm 25,000 = 200,000 cm = 2,000 meters = 2 km. 2.4 Financial Mathematics: Simple Interest: Interest calculated only on the principal amount.

Formula: I = PRT (Interest = Principal Rate * Time).

Example: You invest R5,000 at a simple interest rate of 8% per year for 3 years. I = 5000 0.08 * 3 = R1,

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0. Total amount after 3 years = R5,000 + R1,200 = R6,

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0. Compound Interest: Interest calculated on the principal amount and accumulated interest.

Formula: A = P(1 + r/n)^(nt) (A = Amount, P = Principal, r = interest rate, n = number of times interest is compounded per year, t = time in years).

Example: You invest R5,000 at a compound interest rate of 8% per year, compounded annually, for 3 years. A = 5000(1 + 0.08/1)^(13) = R6,298.

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6. Loan Repayments: Understanding factors affecting loan repayments (interest rate, loan term, principal amount).

Inflation: The rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. 2.5 Measures of Central Tendency and Dispersion: Mean: The average of a set of numbers (sum of numbers divided by the number of numbers).

Median: The middle value in a sorted set of numbers.

Mode: The value that appears most frequently in a set of numbers.

Range: The difference between the highest and lowest values in a set of numbers.

Example: The following are the salaries of 7 employees in a small business: R8,000, R9,000, R9,000, R10,000, R11,000, R12,000, R30,

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0. Mean: (8000 + 9000 + 9000 + 10000 + 11000 + 12000 + 30000) / 7 = R12,714.29 Median: R10,000 (The middle value when sorted)

Mode: R9,000 (Appears twice)

Range: R30,000 - R8,000 = R22,000 2.6 Optimization Problems: Identifying constraints (limitations or restrictions). Formulating a mathematical model to represent the problem. Finding the optimal solution (e.g., minimizing cost, maximizing profit).

Example: You need to buy at least 5 liters of juice for a party. Orange juice costs R25 per liter, and apple juice costs R20 per liter. You have a budget of R

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0. What combination of orange and apple juice should you buy to minimize cost while meeting the minimum quantity requirement? This requires a trial-and-error approach, checking combinations that meet the budget and quantity constraints. Guided Practice (With Solutions)

Question 1: A family in Durban uses 15,000 liters of water in a month. The water company charges R15.00 per kiloliter (1000 liters) for the first 6 kiloliters, R20.00 per kiloliter for the next 4 kiloliters, and R30.00 per kiloliter for any amount over 10 kiloliters. Calculate the family's total water bill.