Lesson Notes By Weeks and Term v5 - Grade 10
Interpreting and communicating answers and calculations – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Interpreting and communicating answers and calculations – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 10
Term: 1st Term
Week: 1
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Mathematical Literacy is not just about numbers; it's about making sense of the world around you using numbers and data. This week, we're focusing on something incredibly important: interpreting and communicating answers and calculations. It’s not enough to just get the right answer; you need to understand what that answer means in the real world and be able to explain it clearly to others.
Think about it: you might calculate the cost of a taxi fare, but can you explain to a friend why it costs that much based on distance and time? Or maybe you figure out how much paint you need for your room, but can you explain the result to the hardware store employee to ensure you buy the right amount?
2.1 Interpretation in Context: The most important thing is to understand what your calculations mean in the real world. Let's say you calculate that you need 2.5 liters of paint to paint a wall. What does that 2.5 actually mean? It means you need enough paint to cover the wall, and you'll need to buy at least 3 litres, as paint usually isn't sold in half litre quantities.
Example 1: Scenario: You're planning a party and need to buy cool drinks. Each cool drink costs R7.50, and you have R
1
5
0. You calculate 150 / 7.50 =
2
0. Interpretation: The number 20 represents the maximum number of cool drinks you can buy with R
1
5
0. Communication: "I can buy a maximum of 20 cool drinks with my R150 budget." Example 2: Scenario: You calculate the Body Mass Index (BMI) of a friend and get
2
8. Interpretation: This number doesn't mean much on its own. You need to compare it to a BMI chart. A BMI of 28 usually falls into the "Overweight" category.
Communication: "Your BMI is 28, which according to BMI charts, means you are classified as overweight." 2.2 Units and Rounding: Always include the correct units in your answer. Units are essential for clarity and avoiding mistakes. If you're calculating distance, is it meters (m), kilometers (km), or miles? If you're calculating time, is it seconds, minutes, or hours? Also, rounding must be appropriate to the context.
Example 3: Scenario: You calculate the length of fencing needed for a garden and get 15.784 meters.
Rounding and Interpretation: You likely need to buy fencing in whole meters. Rounding to the nearest meter makes sense, giving you 16 meters.
Communication: "I need approximately 16 meters of fencing for my garden." Example 4: Scenario: You calculate the amount of medicine a patient needs and get 2.375 ml.
Rounding and Interpretation: In this case, precision is critical. You would not round to 2 ml or 3 ml. Depending on the available syringes, you might need to round to 2.38 ml. Consult with a healthcare professional.
Communication: "The patient requires 2.375 ml of medicine, to be administered with a high degree of precision." 2.3 Mathematical Vocabulary: Using the correct mathematical terms makes your explanations clear and professional. Be sure to use words like "percentage," "ratio," "proportion," "estimate," "increase," "decrease," "profit," "loss," etc., correctly.
Example 5: Scenario: A store is having a 20% off sale. A shirt originally costs R
1
2
0. Calculation: 20% of R120 is (20/100) 120 = R
2
4. The discounted price is R120 - R24 = R
9
6. Communication: "The shirt is on sale for 20% off, which is a discount of R
2
4. The new price of the shirt is R96." 2.4 Reasonableness of Answers: Always ask yourself if your answer makes sense. This is a crucial skill in Mathematical Literacy. Develop a sense of what's reasonable based on the context of the problem.
Example 6: Scenario: You calculate the cost of petrol for a trip and get an answer of R10,
0
0
0. Reasonableness: This is highly unlikely for most trips within South Africa. You would need to re-check your calculations for errors (did you use the correct petrol price? Did you calculate the distance correctly?). 2.5 Step-by-Step Calculations: Clear and logical step-by-step calculations are crucial for communicating your thought process. Label each step and explain what you're doing. This allows others to follow your reasoning and identify any potential errors.
Example 7: Scenario: Calculating the total cost of groceries: Bread: R15.50 Milk: R18.00 Eggs: R35.00 Apples: R22.50 Step 1: List the individual prices: Bread = R15.50 Milk = R18.00 Eggs = R35.00 Apples = R22.50 Step 2: Add the prices together: Total Cost = R15.50 + R18.00 + R35.00 + R22.50 = R91.00 Step 3: State the Final Answer: The total cost of the groceries is R91.00 Guided Practice (With Solutions)
Question 1: You are planning a braai for 15 people. You estimate that each person will eat 200g of meat. Meat costs R80 per kilogram. Calculate the total cost of the meat.
Solution: Step 1: Calculate the total amount of meat needed (in grams): 15 people 200g/person = 3000g Step 2: Convert grams to kilograms: 3000g / 1000g/kg = 3kg Step 3: Calculate the total cost: 3kg R80/kg = R240 Communication: "I need to buy 3 kilograms of meat for the braai. This will cost a total of R240." Question 2: You are saving up to buy a new phone that costs R
4
5
0
0. You earn R50 per hour working part-time. How many hours do you need to work to save enough money? If you can only work 10 hours per week, how many weeks will it take? Round up to the nearest week.
Solution: Step 1: Calculate the total hours needed: R4500 / R50/hour = 90 hours Step 2: Calculate the number of weeks: 90 hours / 10 hours/week = 9 weeks Communication: "I need to work a total of 90 hours to save enough money for the phone. If I work 10 hours per week, it will take me 9 weeks." Question 3: A shop is offering a 15% discount on all shoes. A pair of shoes you want costs R
6
5
0. What is the discounted price?