Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate and interpret rates like speed, fuel consumption, and exchange rates.
• Solve problems using ratio and proportion.
• Calculate amounts with and without VAT.
• Convert between different units of measurement.
• Apply rounding rules correctly.

Lesson summary

This week, we're building upon your existing knowledge of numbers and calculations. Mathematical Literacy isn't just about doing sums; it's about understanding how numbers influence our everyday decisions and empower us to make informed choices, particularly in the South African context. Whether it's managing personal finances, understanding news articles filled with statistics, or participating in community projects, a solid grasp of numerical concepts is essential. We will be focusing on rates, ratio and proportion, and the impact of VAT. This is particularly important for understanding budgeting, comparing prices, and understanding the impact of government policies on personal finances.

Lesson notes

a)

Rates: A rate is a comparison of two quantities with different units. Common examples include speed (km/h), fuel consumption (litres/100km), wage rates (Rands/hour), and exchange rates (Rands/Dollar). It's crucial to pay attention to the units involved.

Formula: Rate = Quantity 1 / Quantity 2 Example 1: A taxi travels 150 km in 2 hours. Calculate the average speed. Speed = Distance / Time Speed = 150 km / 2 hours Speed = 75 km/h Example 2: Petrol costs R22.50 per litre. How much will 45 litres cost? Cost = Rate x Quantity Cost = R22.50/litre x 45 litres Cost = R1012.50 Exchange Rates: Exchange rates fluctuate constantly. Understanding them is vital for international trade and travel. If the exchange rate is R19.50 per US Dollar, it means you need R19.50 to buy one US Dollar. To convert Rands to Dollars, you divide by the exchange rate. To convert Dollars to Rands, you multiply.

Example 3: A pair of jeans costs $30 in the USA. How much will it cost in Rands if the exchange rate is R19.50/Dollar? Cost in Rands = $30 x R19.50/Dollar Cost in Rands = R585 b)

Ratio and Proportion: Ratio: A ratio compares two or more quantities of the same unit.

It can be written as a:b, a/b, or "a to b". Ratios should be simplified to their lowest terms.

Example 1: In a class of 30 learners, 18 are girls and 12 are boys. What is the ratio of girls to boys? Ratio of girls to boys = 18:12 Simplifying by dividing both sides by 6, we get 3:2 Proportion: A proportion states that two ratios are equal.

Direct Proportion: As one quantity increases, the other increases proportionally.

Example 2: A worker earns R150 for every hour worked. How much will they earn if they work 8 hours? This is direct proportion because as the number of hours increases, the earnings increase. Earnings = R150/hour 8 hours = R1200 Inverse Proportion: As one quantity increases, the other decreases proportionally.

Example 3: It takes 4 workers 6 hours to complete a task. How long will it take 8 workers to complete the same task, assuming they all work at the same rate? This is inverse proportion because as the number of workers increases, the time to complete the task decreases. Total work = 4 workers 6 hours = 24 worker-hours Time for 8 workers = 24 worker-hours / 8 workers = 3 hours c)

Value Added Tax (VAT): VAT is a consumption tax levied on most goods and services in South Africa. The current VAT rate is 15%. It's added to the price of most items you buy.

Calculating VAT: VAT amount = Price VAT rate Price including VAT: Price (inclusive of VAT) = Price (exclusive of VAT) + VAT amount Price (inclusive of VAT) = Price (exclusive of VAT) * (1 + VAT rate) Price excluding VAT (given the inclusive price): Price (exclusive of VAT) = Price (inclusive of VAT) / (1 + VAT rate)

Example 1: A loaf of bread costs R12 (excluding VAT). What is the price including VAT? VAT amount = R12 0.15 = R1.80 Price including VAT = R12 + R1.80 = R13.80 Alternatively: Price including VAT = R12 (1 + 0.15) = R12 * 1.15 = R13.80 Example 2: A shirt costs R230 (including VAT). What was the price before VAT was added? Price excluding VAT = R230 / 1.15 = R200 d)

Units of Measurement: Being able to convert between units of measurement is crucial. You need to understand both the metric (SI) system (meters, kilograms, litres) and sometimes the imperial system (feet, pounds, gallons), especially when dealing with products imported from other countries.

Common Conversions: 1 metre = 100 centimetres 1 kilometre = 1000 metres 1 kilogram = 1000 grams 1 litre = 1000 millilitres e)

Rounding: Rounding is crucial for estimation and presenting numbers in a meaningful way. Be mindful of the context when rounding. For example, you can't round the number of people to a decimal. Common rules include rounding to the nearest whole number, nearest ten, nearest hundred, or to a specific number of decimal places. Guided Practice (With Solutions)

Question 1: A car travels 360 km on 30 litres of petrol. Calculate the fuel consumption in litres per 100 km.

Solution: Fuel consumption = (Litres used / Distance travelled) 100 Fuel consumption = (30 litres / 360 km) 100 Fuel consumption = 0.0833 litres/km 100 Fuel consumption = 8.33 litres/100 km

Commentary: This problem involves calculating a rate (fuel consumption). We set up the ratio of litres to kilometers and then scaled it to find the litres used per 100 km, as is the standard measure.

Question 2: A recipe requires flour and sugar in the ratio 5:

2. If you want to make a larger batch using 750g of flour, how much sugar do you need?

Solution: Let the amount of sugar be 'x' grams.

We have the proportion: 5/2 = 750/x Cross-multiply: 5x = 2 750 5x = 1500 x = 1500 / 5 x = 300 g

Commentary: This is a direct proportion problem. We set up a proportion with the known ratio and the given amount of flour, then solved for the unknown amount of sugar.

Question 3: A store is selling a TV for R4600 inclusive of VAT. What is the price of the TV excluding VAT?