Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Perform calculations with whole numbers, decimals, fractions, and percentages.
• Apply the correct order of operations (BODMAS).
• Estimate answers to check if they are reasonable.
• Solve real-world problems like budgeting and discounts.
• Use a calculator effectively and accurately.

Lesson summary

This week, we delve into the crucial skills of working with numbers and calculations. Mathematical Literacy isn't just about numbers in a textbook; it's about understanding the world around us. From managing your pocket money to understanding electricity bills, from calculating discounts at the supermarket to interpreting statistics in news reports, numbers are everywhere. Being comfortable and confident with numbers empowers you to make informed decisions and navigate everyday life effectively in South Africa. Understanding numbers and calculations helps you participate more fully in the economy and advocate for yourself and your community.

Lesson notes

2.1 The Four Basic Operations Addition (+): Combining two or more quantities.

Example: If you earn R250 from a part-time job and R100 from helping your neighbour, your total earnings are R250 + R100 = R

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0. Subtraction (-): Finding the difference between two quantities.

Example: If you have R150 and spend R75 on airtime, you have R150 - R75 = R75 left. Multiplication (× or ): Repeated addition.

Example: If you work 5 hours at a rate of R40 per hour, your earnings are 5 × R40 = R

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0. Division (÷ or /): Sharing a quantity equally into groups.

Example: If a loaf of bread costs R18 and you want to buy as many as possible with R100, you can buy R100 ÷ R18 = 5.55... Since you can't buy part of a loaf, you can buy 5 loaves. 2.2 Working with Decimals, Fractions, and Percentages Decimals: Numbers with a decimal point, representing parts of a whole. Understanding place value is crucial (tenths, hundredths, thousandths, etc.).

Example: R25.50 is read as twenty-five Rand and fifty cents.

Fractions: Representing parts of a whole, expressed as a numerator (top number) over a denominator (bottom number).

Example: 1/2 represents one out of two equal parts.

Percentages: Representing parts of a whole as a fraction of

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0. The symbol "%" means "out of one hundred."

Example: 25% is the same as 25/100 or 0.

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5. To find a percentage of a number, convert the percentage to a decimal and multiply.

Example: To find 15% of R500, calculate 0.15 × R500 = R75. 2.3 Order of Operations (BODMAS/PEMDAS) To ensure consistent results, we follow a specific order when performing calculations with multiple operations: Brackets / Parentheses Orders / Exponents Division and Multiplication (from left to right) Addition and Subtraction (from left to right)

Example: 5 + 3 × 2 - (10 ÷ 2) = 5 + 3 × 2 - 5 = 5 + 6 - 5 = 11 - 5 = 6 2.4 Estimation Estimation is approximating a calculation to get a rough answer. This is a valuable skill for checking the reasonableness of calculator results and making quick decisions. Round numbers to the nearest ten, hundred, or thousand to simplify the calculation.

Example: Estimate the total cost of items priced at R98, R52, and R

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7. Rounding to the nearest ten, we get R100 + R50 + R150 = R

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0. The actual cost is R297, so our estimate is close. 2.5 Calculator Usage Calculators are useful tools, but it's crucial to understand how to use them correctly. Enter numbers and operations carefully. Pay attention to the order of operations. Use brackets where necessary to group operations. Interpret the results in the context of the problem. A calculator might give you 3.666666667, but in a real-world scenario like buying loaves of bread, you can only buy 3 whole loaves. 2.6 Worked Examples Example 1: Sarah earns R65 per hour at a local shop. She works 20 hours a week. What is her gross weekly income?

Solution: Gross weekly income = R65/hour × 20 hours = R1300 Example 2: A pair of jeans costs R

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0. There is a 20% discount. What is the discounted price?

Solution: Discount amount = 20% of R350 = 0.20 × R350 = R

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0. Discounted price = R350 - R70 = R280 Example 3: A taxi charges a fixed rate of R15 plus R8 per kilometre. If you travel 12km, what is the total cost?

Solution: Cost per kilometre = R8 × 12 km = R

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6. Total cost = R15 + R96 = R111 Example 4: You want to buy a cellphone that costs R

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0. You have saved R

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0. How much more money do you need to save?

Solution: Amount still needed = R2500 - R800 = R1700 Example 5: A spaza shop buys a case of cool drinks for R

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0. There are 24 cool drinks in a case. They sell each cool drink for R

8. What is the profit on each cool drink and the total profit for the case?

Solution: Cost per cool drink = R120 / 24 = R

5. Profit per cool drink = R8 - R5 = R

3. Total profit = R3/cool drink * 24 cool drinks = R72 Guided Practice (With Solutions)

Question 1: A packet of biscuits costs R15.

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0. How much will 3 packets cost?

Solution: Cost of 3 packets = R15.50 × 3 = R46.50

Commentary: This question requires simple multiplication of a decimal number.

Question 2: You have R200 and want to buy airtime for R55, a cool drink for R12, and a snack for R

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8. How much money will you have left?

Solution: Total spent = R55 + R12 + R28 = R95 Money left = R200 - R95 = R105

Commentary: This problem combines addition and subtraction. Remember to add up the expenses first, then subtract from the total amount.

Question 3: Calculate: 25 + (15 - 5) × 2 Solution: Following BODMAS: Brackets: (15 - 5) = 10 Multiplication: 10 × 2 = 20 Addition: 25 + 20 = 45

Commentary: This emphasizes the correct order of operations.

Question 4: A store offers a 15% discount on a shirt that originally costs R

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0. What is the sale price?

Solution: Discount amount = 15/100 R220 = 0.15 R220 = R33 Sale price = R220 - R33 = R187

Commentary: This combines percentage calculations with subtraction.

Question 5: Estimate the answer to 198 x

5. Solution: Round 198 to 200 200 x 5 = 1000

Commentary: Using rounding makes estimation easier.