Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate accurately and show your work.
• Explain what your answers mean in a real-world context.
• Use correct units and rounding.
• Identify assumptions made in calculations.
• Judge if an answer is reasonable.

Lesson summary

This week, we're diving into the crucial skill of interpreting and communicating answers and calculations in Mathematical Literacy. This isn't just about crunching numbers; it's about understanding what those numbers mean and how to effectively share that understanding with others. In everyday life, you'll use this to manage your personal finances, understand news reports, make informed purchasing decisions, and even advocate for changes in your community. Imagine needing to explain to your family why a new electricity tariff increase will impact your household budget or presenting a business plan to a potential investor. Clear communication of numerical information is essential.

Lesson notes

2.1 Accuracy and Precision: It's vital to understand the difference between accuracy and precision. Accuracy refers to how close a calculated or measured value is to the true or accepted value. Precision refers to how consistent and repeatable a measurement or calculation is. For example, if you repeatedly weigh an object and consistently get 5.2 kg, even though the actual weight is 5.5 kg, your measurements are precise (repeatable) but not accurate. 2.2 Units of Measurement: Always include appropriate units when presenting your answers. For example, if calculating area, the unit should be square meters (m²), square centimeters (cm²), etc. Failing to include units renders the answer meaningless. Be mindful of unit conversions. For example, if a recipe calls for 250g of flour, but you only have pounds, you'll need to convert between grams and pounds (1 pound ≈ 454g). 2.3 Rounding: Rounding is often necessary to simplify answers and present them in a more understandable way.

However, it's crucial to round appropriately.

Common rounding rules include: Rounding to the nearest whole number. Rounding to a specific number of decimal places (e.g., two decimal places for monetary values). Rounding to a specific number of significant figures (used in science and engineering).

Example: Suppose a calculation yields an answer of 12.

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8. Rounded to the nearest whole number: 13 Rounded to two decimal places: 12.57 Rounded to three significant figures: 12.6 The context of the problem determines the appropriate rounding level. For example, if you are calculating the number of people needed for a task, you need to round up to the nearest whole number, even if the decimal is less than 0.5 (you can't have a fraction of a person). 2.4 Interpreting Answers in Context: The most important part of Mathematical Literacy is understanding what your calculations mean. Don't just write down a number; explain it in words. For example, if you calculate the cost of borrowing money, don't just say "R5000"; say "The total interest paid on the loan will be R5000." Example 1: A local spaza shop buys a crate of 24 cool drinks for R

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6. They sell each cool drink for R6. a) Calculate the profit made on one cool drink. b) Calculate the total profit made on the crate of cool drinks. c) Express the profit as a percentage of the cost price.

Solution: a)

Cost per cool drink: R96 / 24 = R4 Profit per cool drink: R6 - R4 = R2 Interpretation: The spaza shop makes a profit of R2 on each cool drink sold. b)

Total profit: R2 x 24 = R48 Interpretation: The spaza shop makes a total profit of R48 on the entire crate of cool drinks. c)

Percentage profit: (Profit / Cost) x 100 = (R48 / R96) x 100 = 50% Interpretation: The spaza shop makes a profit of 50% on the cost price of the crate of cool drinks. This is a good profit margin.

Example 2: You want to buy a cellphone that costs R

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0. You have two options: Option 1: Pay cash.

Option 2: Pay R300 per month for 12 months. a) Calculate the total cost of the cellphone if you choose Option 2. b) Calculate how much more expensive Option 2 is compared to Option

1. Solution: a)

Total cost of Option 2: R300 x 12 = R3600 Interpretation: Paying in monthly installments will cost you a total of R3600. b)

Difference in cost: R3600 - R2500 = R1100 Interpretation: Paying in monthly installments will cost you R1100 more than paying cash. This is the cost of borrowing money (interest). 2.5 Identifying Limitations and Making Assumptions: Real-world problems often involve simplifying assumptions. It's important to recognize these assumptions and understand their potential impact on the accuracy of your results. For instance, when calculating travel time, you might assume a constant speed, which may not be realistic due to traffic or road conditions. Always state your assumptions clearly and consider how they might affect your conclusions.

Example: You're planning a taxi trip from Johannesburg to Pretoria, a distance of 60 km. The taxi company charges R8.50 per kilometer. a) Estimate the total cost of the trip. b) What assumptions did you make in your calculation? c) How could your estimate be inaccurate?

Solution: a)

Estimated cost: 60 km x R8.50/km = R510 Interpretation: The estimated cost of the taxi trip is R510. b)

Assumptions: The taxi will travel directly from Johannesburg to Pretoria. The rate of R8.50 per kilometer is constant for the entire journey. There are no extra charges (e.g., toll fees). c)

Inaccuracies: The taxi may take a longer route due to traffic or road closures, increasing the distance and the cost. The taxi company may charge additional fees, such as a call-out fee or toll fees, which would increase the cost. Traffic congestion might increase the time, and the meter might run according to both time and distance traveled. Guided Practice (With Solutions)

Question 1: A dress is on sale for 20% off. The original price of the dress is R450. a) Calculate the discount amount.