Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Interpret answers in a real-world context with correct units.
• Apply appropriate rounding rules based on the situation.
• Communicate findings clearly using explanations, tables, or graphs.
• Calculate and interpret percentages for discounts, VAT, and increases.
• Identify potential sources of error in calculations.

Lesson summary

This week, we delve deeper into the crucial skill of interpreting and communicating answers and calculations within the context of Mathematical Literacy. It's not enough to just get the "right" answer; you must also understand what that answer means in the real world and be able to clearly explain it to others. This is especially important in South Africa, where you will encounter calculations related to budgeting, housing, employment, and civic participation. Incorrect interpretation can lead to poor financial decisions, misunderstandings, and even exploitation.

Therefore, developing this skill empowers you to be an informed and active citizen.

Lesson notes

Understanding Units: Every number has a unit attached to it, telling us what we are counting or measuring. Ignoring units can lead to significant errors.

Examples of units include: Rands (R), kilograms (kg), meters (m), hours (h), litres (L), etc.

Example 1: You calculate that it will take 3.5 to drive from Johannesburg to Durban. 3.5 what? Is it 3.5 seconds, 3.5 hours, 3.5 days? Obviously, it's 3.5 hours. Communicating "3.5" without specifying "hours" is incomplete and misleading. The correct answer is 3.5 hours.

Rounding: Rounding simplifies numbers but can also introduce inaccuracies. The level of accuracy needed depends on the context. Rounding should make sense in the real world.

Rounding Rules: Generally, round up if the digit to the right of the rounding place is 5 or greater; round down if it's less than

5. Context is Key: If you're calculating the number of bricks needed for a wall, you can't buy a fraction of a brick. Round up to ensure you have enough. If you're calculating the cost of petrol, you might round to the nearest cent (two decimal places).

Example 2: Suppose you calculate the number of people who can fit into a taxi as 15.

7. Can you have 0.7 of a person? No. You must round down to 15, as the taxi can only safely and legally carry a whole number of passengers. Rounding up to 16 would be unsafe and incorrect in this context.

Interpreting Results in Context: Calculations are meaningless without understanding their relevance to the situation.

This involves: Understanding what the numbers represent. Connecting the calculated value to the original problem. Drawing conclusions based on the result.

Example 3: You calculate that your monthly electricity bill will be R

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5

0. Does this fit within your budget? Can you afford this amount, or do you need to cut back on electricity usage? The calculation is just the first step; interpreting it in terms of your financial situation is crucial.

Clear Communication: Presenting your findings clearly is essential.

This involves: Using correct terminology. Explaining your reasoning. Using appropriate formats (e.g., tables, graphs, written explanations). Specifying the units.

Example 4: Instead of just writing "The answer is 5," write "The answer is 5 litres, which is the amount of water needed to fill the bucket." Percentages: Percentages are a fundamental part of everyday life. Understanding percentage increase, decrease, discounts, markups, VAT, and inflation is critical.

Percentage Increase/Decrease: `[(New Value - Original Value) / Original Value] 100%` Discounts: `Original Price (Discount Percentage / 100)` VAT (Value Added Tax): VAT in South Africa is currently 15%.

To calculate the price including VAT: `Price before VAT 1.15` Example 5: A loaf of bread costs R14.

0

0. Next month it costs R15.

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0. What is the percentage increase? `[(15.50 - 14.00) / 14.00] 100% = (1.50/14.00) 100% = 10.71%` Therefore, the price of bread increased by 10.71%.

Sources of Error: Recognizing where errors might occur and their potential impact is important for critical thinking.

Errors can arise from: Incorrect data: Using wrong figures in your calculations.

Calculation mistakes: Making arithmetic errors.

Rounding errors: Rounding too early or inappropriately.

Assumptions: Making unrealistic or inaccurate assumptions.

Example 6: When calculating the cost of transport, you might assume a constant petrol price.

However, petrol prices fluctuate. This assumption introduces a potential error in your calculation. Recognizing this allows you to refine your estimate by considering a range of possible petrol prices. Guided Practice (With Solutions)

Question 1: You want to buy a new cellphone that costs R

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0. You have saved R

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8

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0. What percentage of the phone's price have you saved?

Solution: Identify what you need to calculate: The percentage of the phone's price that is covered by your savings.

Formula: `(Amount Saved / Total Price) 100%` Calculation: `(R1800 / R2500) 100% = 0.72 * 100% = 72%` Answer: You have saved 72% of the phone's price.

Commentary: The unit is a percentage. We've shown that you have covered the majority of the cost, but you still need to save another 28%.

Question 2: A shirt is on sale for 20% off. The original price was R

1

5

0. What is the sale price?

Solution: Calculate the discount amount: `R150 (20/100) = R150 * 0.20 = R30` Subtract the discount from the original price: `R150 - R30 = R120` Answer: The sale price is R

1

2

0. Commentary: The unit is Rands (R). This problem demonstrates how to calculate a discount and the importance of understanding percentages in retail situations.

Question 3: You are baking cookies. The recipe calls for 1.75 cups of flour. You only have a measuring cup that measures in quarter cups (0.25 cups). How many quarter cups of flour do you need to add?

Solution: Divide the total amount of flour by the size of each measuring cup: `1.75 cups / 0.25 cups/cup = 7` Answer: You need to add 7 quarter cups of flour.