Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Use BODMAS to solve problems
• Solve multi-step word problems
• Estimate and check your answers
• Use the distributive property
• Understand multiples and factors

Lesson summary

This week, we will delve deeper into whole numbers and operations. Building on what we've learned in previous weeks, we will focus on solving problems involving multiple operations (addition, subtraction, multiplication, and division) and understanding the importance of the order of operations. In South Africa, understanding these concepts is crucial for everyday tasks like budgeting household expenses, calculating change when buying groceries at the spaza shop, or understanding how cell phone data bundles are calculated. This week provides the groundwork for more complex mathematical concepts you'll encounter later on. This week we will also look at word problems and breaking those down.

Lesson notes

2.1 Order of Operations (BODMAS/PEMDAS) When solving mathematical expressions with multiple operations, we need to follow a specific order to get the correct answer. This order is often remembered using the acronyms BODMAS or PEMDAS: BODMAS: Brackets Orders (powers, square roots, etc.) - We won't cover this in Grade 5, but it's good to be aware of it.* Division Multiplication Addition Subtraction PEMDAS: Parentheses Exponents (powers, square roots, etc.) - We won't cover this in Grade 5, but it's good to be aware of it.* Multiplication Division Addition Subtraction Important: Division and Multiplication have the same priority, so you perform them from left to right. Addition and Subtraction also have the same priority and are performed from left to right.

Example 1: Solve: 12 + 8 ÷ 2 - 3 x 2 Division: 8 ÷ 2 = 4 Multiplication: 3 x 2 = 6 Addition: 12 + 4 = 16 Subtraction: 16 - 6 = 10 Therefore, 12 + 8 ÷ 2 - 3 x 2 = 10 Example 2: Solve: (5 + 3) x 4 - 15 ÷ 3 Brackets: 5 + 3 = 8 Multiplication: 8 x 4 = 32 Division: 15 ÷ 3 = 5 Subtraction: 32 - 5 = 27 Therefore, (5 + 3) x 4 - 15 ÷ 3 = 27 2.2 Multi-Step Word Problems Solving word problems requires careful reading and understanding of what the problem is asking.

Here's a strategy: Read the problem carefully: Understand what the question is asking.

Identify the key information: What numbers are given? What operations are needed?

Plan your solution: Break the problem into smaller steps.

Solve the problem: Perform the necessary calculations, following the order of operations.

Check your answer: Does your answer make sense in the context of the problem? Is it reasonable?

Example 3: A tuck shop sells sweets for R2 each and chips for R5 each. Sarah buys 3 sweets and 2 packets of chips. How much does she spend in total?

Cost of sweets: 3 sweets x R2/sweet = R6 Cost of chips: 2 packets x R5/packet = R10 Total cost: R6 + R10 = R16 Therefore, Sarah spends R16 in total. 2.3 Estimation and Reasonableness Before solving a problem, it's a good idea to estimate the answer. This helps you check if your final answer is reasonable.

Example 4: Estimate the answer to 27 x

1

2. Round 27 to 30 and 12 to

1

0. Then, 30 x 10 =

3

0

0. So, the answer should be around

3

0

0. Now, calculate the exact answer: 27 x 12 =

3

2

4. This is close to our estimate, so it's likely correct. 2.4 Distributive Property The distributive property of multiplication over addition states that: a x (b + c) = (a x b) + (a x c) This can be useful for simplifying calculations.

Example 5: Calculate 7 x 13 using the distributive property. We can write 13 as (10 + 3). Then, 7 x 13 = 7 x (10 + 3) = (7 x 10) + (7 x 3) = 70 + 21 = 91. 2.5 Multiples and Factors Multiples: A multiple of a number is the result of multiplying that number by a whole number. For example, the multiples of 3 are 3, 6, 9, 12, and so on.

Factors: A factor of a number is a whole number that divides exactly into that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and

1

2. Example 6: What are the first five multiples of 6? 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 The first five multiples of 6 are 6, 12, 18, 24, and

3

0. Example 7: What are all the factors of 20? The numbers that divide exactly into 20 are 1, 2, 4, 5, 10, and

2

0. These are all the factors of

2

0. Guided Practice (With Solutions)

Question 1: Solve: 25 - 5 x 2 + 10 ÷ 5 Solution: Multiplication: 5 x 2 = 10 Division: 10 ÷ 5 = 2 Subtraction: 25 - 10 = 15 Addition: 15 + 2 = 17 Therefore, 25 - 5 x 2 + 10 ÷ 5 = 17 Question 2: Solve: (18 ÷ 3) + 4 x (7 - 2)

Solution: Brackets (first set): 18 ÷ 3 = 6 Brackets (second set): 7 - 2 = 5 Multiplication: 4 x 5 = 20 Addition: 6 + 20 = 26 Therefore, (18 ÷ 3) + 4 x (7 - 2) = 26 Question 3: Thando earns R50 per day working at a car wash. He works for 4 days and spends R80 on groceries. How much money does he have left?

Solution: Total earnings: R50/day x 4 days = R200 Money left: R200 - R80 = R120 Therefore, Thando has R120 left.

Question 4: Use the distributive property to calculate 6 x

1

5. Solution: We can write 15 as (10 + 5). Then, 6 x 15 = 6 x (10 + 5) = (6 x 10) + (6 x 5) = 60 + 30 =

9

0. Question 5: List all the factors of

1

8. Solution: The numbers that divide evenly into 18 are 1, 2, 3, 6, 9, and

1

8. Independent Practice (Questions Only)

Solve: 36 ÷ 4 + 7 x 3 - 9 Solve: 100 - (25 + 15) ÷ 8 x 2 Solve: 15 + 5 x 6 ÷ 3 - 20 A bakery sells muffins for R8 each. A school buys 25 muffins. They pay with R

2

5

0. How much change do they receive? Sipho has 4 boxes of crayons. Each box contains 12 crayons. He gives 15 crayons to his friend. How many crayons does Sipho have left? Use the distributive property to calculate 8 x

1

4. What are the first five multiples of 7? What are all the factors of 24? Nomusa buys 5 apples at R4 each and 3 bananas at R2 each. What is the total cost?

Solve: (5 x 4) + (12 / 2) - (3 x 1)