Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Interpret answers in a real-world context.
• Communicate mathematical findings clearly.
• Draw conclusions and make decisions from results.
• Identify potential errors or limitations in calculations.

Lesson summary

In Mathematical Literacy, performing calculations is only half the battle. The other crucial part is interpreting what your calculations mean and then communicating that meaning clearly and accurately to others. This week, we focus specifically on refining your ability to draw conclusions from numerical results and express them in a way that is easily understood by someone who might not be familiar with the calculations themselves. This is an essential skill for navigating everyday life in South Africa, from understanding your payslip to making informed financial decisions or interpreting statistics in news reports.

Lesson notes

a) Interpreting Numerical Answers in Context The core idea here is that a number by itself is meaningless. It's only when we understand what that number represents that it becomes useful. For example, the number "5000" could mean anything. But if we know it represents "the monthly rental cost of a house in Soweto," it suddenly has real-world significance. When interpreting answers, consider these questions: What does the number represent? Identify the units and the quantity being measured. (e.g., Rand, kilograms, hours, percentage) What is the context? What situation or problem does the calculation relate to? Is the answer reasonable? Does the result make sense in the given context? If the calculation involved calculating the distance between Johannesburg and Cape Town and you got an answer of 5km, you know something is wrong! What are the implications? What does this answer tell us about the situation? What decisions or actions might we take based on this information?

Example 1: A tuck shop owner buys a box of 24 Simba chips for R

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0. She sells each packet for R

4. Calculation: Profit per packet = Selling price - Cost price. Cost price per packet = R60 / 24 = R2.

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0. Profit per packet = R4 - R2.50 = R1.50 Interpretation: The tuck shop owner makes a profit of R1.50 for every packet of Simba chips she sells. This means that for every 24 packets sold (one box), she makes a profit of R1.50 * 24 = R36. b) Communicating Mathematical Findings Clearly Communication involves expressing your interpretation in a way that is easy for others to understand.

This includes: Using clear and concise language: Avoid jargon and technical terms unless you are sure your audience understands them.

Using correct units: Always include the appropriate units (e.g., Rand, kg, hours, %).

Providing context: Briefly explain the problem and the calculations you performed.

Structuring your explanation logically: Start with the problem, describe the calculations, and then state your conclusions.

Using visual aids: Tables, charts, and graphs can help to illustrate your findings.

Example 2: Scenario: Calculating the average cost of transport for a student.

Data: A student spends R15 per day on taxi fare to school. There are 20 school days in a month.

Calculation: Total monthly transport cost = R15/day * 20 days = R300 Communication: "The student's monthly transport cost is R

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0. This was calculated by multiplying the daily taxi fare of R15 by the number of school days in a month, which is 20." c) Drawing Logical Conclusions and Making Informed Decisions Interpreting results allows us to draw conclusions and make informed decisions. This involves analyzing the results in light of the context and considering any limitations.

Example 3: Scenario: Comparing two mobile data plans.

Plan A: R100 for 5GB of data.

Plan B: R150 for 10GB of data.

Calculations: Cost per GB for Plan A: R100 / 5GB = R20/GB Cost per GB for Plan B: R150 / 10GB = R15/GB Conclusion: Plan B is more cost-effective (R15/GB) than Plan A (R20/GB).

Informed Decision: If the student anticipates needing more than 5GB of data, Plan B is the better option because it offers a lower cost per GB.

However, if they only need a small amount of data, Plan A might be sufficient and cheaper overall. d) Identifying Errors and Limitations Calculations are only as good as the data they are based on. It’s crucial to acknowledge potential errors or limitations in the data or the calculation process itself. For example, rounding errors can accumulate and affect the final result. Assumptions made in the calculation can also impact the validity of the interpretation.

Example 4: Scenario: Estimating the water consumption of a household.

Calculation: Assuming each person uses 100 liters of water per day, a household of 4 people would use 4 * 100 = 400 liters per day.

Limitation: This calculation assumes that everyone uses the same amount of water, which may not be true. Some people might use more or less water than others. The calculation doesn't account for water used for gardening or other purposes. It's an estimate, not an exact measure. A higher water bill than expected might be explained by water leaks or unusually high usage. Guided Practice (With Solutions)

Question 1: A hawker buys a crate of tomatoes for R

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0. There are 60 tomatoes in the crate. He estimates that 10% of the tomatoes will be rotten and unsellable. He wants to sell the remaining tomatoes for R3 each. Calculate his expected profit.

Solution: Number of rotten tomatoes: 10% of 60 = (10/100) * 60 = 6 tomatoes.

Number of sellable tomatoes: 60 - 6 = 54 tomatoes.

Total revenue from selling tomatoes: 54 tomatoes * R3/tomato = R

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2. Profit: R162 - R120 = R

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2. Interpretation: The hawker's expected profit from selling the tomatoes is R

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2. Question 2: A cell phone company offers a contract for R299 per month. This includes 2GB of data and 100 minutes of call time. If you exceed the data limit, you will be charged R50 per GB.