Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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.

Performance objectives

• Solve multi-step word problems with all four operations.
• Apply commutative and associative properties.
• Follow the order of operations (BODMAS).
• Use estimation to check if answers are reasonable.
• Develop problem-solving strategies for real-world scenarios.

Lesson summary

This week, we will delve deeper into whole numbers and the four basic operations: addition, subtraction, multiplication, and division. Understanding these operations is crucial not just for mathematics class, but also for everyday life in South Africa. From calculating the cost of groceries at the spaza shop to managing your pocket money and understanding how much data you have left on your phone, these skills are essential. We'll also look at problem solving strategies using these operations.

Lesson notes

2.1 Review of Basic Operations: Let's recap the four basic operations. Addition (+): Combining two or more numbers to find their total or sum.

Subtraction (-): Finding the difference between two numbers. Multiplication (× or ): Repeated addition of the same number. Division (÷ or /): Splitting a number into equal groups or parts. 2.2 Order of Operations (BODMAS/PEMDAS): When a problem involves more than one operation, we need to follow a specific order: Brackets (or Parentheses) Orders (or Exponents) Division and Multiplication (from left to right) Addition and Subtraction (from left to right)

Remember: BODMAS helps us to solve equations and expressions correctly, ensuring we all get the same answer!

Example 1 (BODMAS): Calculate: 2 + (3 × 4) - 6 ÷ 2 Brackets: 3 × 4 = 12 Division: 6 ÷ 2 = 3 The problem becomes: 2 + 12 - 3 Addition: 2 + 12 = 14 Subtraction: 14 - 3 = 11 Therefore, 2 + (3 × 4) - 6 ÷ 2 = 11 2.3 Properties of Addition and Multiplication: Commutative Property: The order in which you add or multiply numbers doesn't change the answer.

Addition: a + b = b + a (e.g., 5 + 3 = 3 + 5)

Multiplication: a × b = b × a (e.g., 2 × 7 = 7 × 2)

Associative Property: The way you group numbers when adding or multiplying doesn't change the answer.

Addition: (a + b) + c = a + (b + c) (e.g., (2 + 3) + 4 = 2 + (3 + 4))

Multiplication: (a × b) × c = a × (b × c) (e.g., (2 × 3) × 4 = 2 × (3 × 4)) These properties are useful for simplifying calculations and checking answers. Example 2 (Commutative and Associative Properties): Calculate: 17 + 23 + 7 Using the commutative property: We can rearrange the numbers to make the addition easier. 17 + 7 + 23 Using the associative property: We can group the numbers. (17 + 7) + 23 = 24 + 23 = 47 2.4 Problem Solving with Remainders: In division, the remainder is the amount left over when one number cannot be divided exactly by another.

Example 3 (Remainders): A farmer has 25 apples and wants to pack them into boxes that hold 4 apples each. How many boxes can he fill completely, and how many apples will be left over?

Divide 25 by 4: 25 ÷ 4 = 6 with a remainder of

1. The farmer can fill 6 boxes completely. There will be 1 apple left over. The remainder is 1 in this case. Understanding the remainder is crucial. In some problems, we ignore it; in others, we round up to the next whole number. In this case, the context clearly says the farmer packs apples into boxes so leftover apples can't be packed into an incomplete box. 2.5 Multi-Step Word Problems These problems require us to use more than one operation to find the solution. We need to read carefully, identify the key information, and decide which operations to use and in what order.

Example 4 (Multi-Step): A group of 3 friends collected 245 recyclable cans on Monday. On Tuesday, they collected 180 cans. They want to divide the cans equally among themselves. How many cans will each friend receive?

Find the total number of cans: 245 + 180 = 425 cans Divide the total cans by the number of friends: 425 ÷ 3 = 141 with a remainder of 2 Each friend will receive 141 cans, and there will be 2 cans remaining. 2.6 Estimation Estimation is an important skill. It helps us to quickly approximate the answer and check if our calculated answer is reasonable.

Example 5 (Estimation): Estimate the answer to 489 +

7

1

2. Round each number to the nearest hundred: 489 ≈ 500 and 712 ≈ 700 Estimated answer: 500 + 700 = 1200 This estimated answer is close to the actual answer, indicating that our calculation is likely correct. Guided Practice (With Solutions)

Question 1: Calculate: 15 + (20 ÷ 4) × 3 - 8 Solution: Brackets: 20 ÷ 4 = 5 Multiplication: 5 × 3 = 15 The problem becomes: 15 + 15 - 8 Addition: 15 + 15 = 30 Subtraction: 30 - 8 = 22 Therefore, the answer is

2

2. Question 2: A school buys 12 boxes of crayons. Each box contains 24 crayons. If they distribute the crayons equally among 8 classrooms, how many crayons will each classroom receive?

Solution: Find the total number of crayons: 12 × 24 = 288 crayons Divide the total crayons by the number of classrooms: 288 ÷ 8 = 36 crayons Therefore, each classroom will receive 36 crayons.

Question 3: Nomusa has 150 beads. She uses 25 beads to make a bracelet and 32 beads to make a necklace. How many beads does she have left?

Solution: Find the total number of beads used: 25 + 32 = 57 beads Subtract the beads used from the total beads: 150 - 57 = 93 beads Therefore, Nomusa has 93 beads left.

Question 4: Estimate the answer to 23 x

7

8. Then calculate the exact answer.

Solution: Estimation: Round each number to the nearest ten: 23 ≈ 20 and 78 ≈ 80 Estimated answer: 20 x 80 = 1600 Exact answer: 23 x 78 = 1794 Independent Practice (Questions Only)

Calculate: 36 ÷ (9 - 3) + 4 × 2 A shop sells sweets for R5 each. If Thando buys 7 sweets and pays with a R50 note, how much change will he receive? Sipho has 250ml of juice. He drinks 85ml of it. How much juice is left? A bakery makes 144 cupcakes.