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
• Use the correct order of operations (BODMAS)
• Estimate answers to check your work
• Solve division problems with remainders

Lesson summary

This week, we will delve deeper into working with whole numbers and focus on applying the four basic operations (addition, subtraction, multiplication, and division) in more complex scenarios and problem-solving situations. Understanding whole numbers and operations is crucial for everyday life. From calculating the cost of groceries at a local spaza shop to figuring out how many school textbooks need to be distributed among learners, these skills are essential. Being able to manipulate numbers confidently builds a strong foundation for future mathematical concepts.

Lesson notes

Order of Operations (BODMAS/PEMDAS): When a mathematical expression has more than one operation, we need to follow a specific order to get the correct answer. This order is often remembered using the acronyms BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Division and Multiplication are done left to right. Addition and Subtraction are done left to right.

Brackets/Parentheses: Always solve the operations inside brackets or parentheses first.

Orders/Exponents: Then, evaluate any powers or exponents (we'll cover these in later grades but its important to note).

Division and Multiplication: Perform division and multiplication from left to right.

Addition and Subtraction: Finally, do addition and subtraction from left to right.

Multi-Step Word Problems: These problems require you to perform more than one operation to find the solution. It's important to read the problem carefully, identify the key information, and decide which operations to use in what order.

Estimation: Estimation involves finding an approximate answer to a problem. It helps us to check if our final answer is reasonable. We can round numbers to the nearest ten, hundred, or thousand to make the calculation easier. For example, 478 can be rounded to 500 for estimation purposes.

Division with Remainders: When dividing, sometimes the number doesn't divide evenly. The amount left over is called the remainder. For example, if we divide 23 by 5, we get 4 with a remainder of 3, because 5 x 4 = 20, and 23 - 20 =

3. The remainder must always be smaller than the divisor.

Worked example

Example 1: Order of Operations

Calculate: 15 + (6 x 2) - 8 ÷ 4

Solution:

Brackets first: 6 x 2 = 12

The expression becomes: 15 + 12 - 8 ÷ 4

Division next: 8 ÷ 4 = 2

The expression becomes: 15 + 12 - 2

Addition next: 15 + 12 = 27

Subtraction last: 27 - 2 = 25

Therefore, 15 + (6 x 2) - 8 ÷ 4 = 25

Why:* Following BODMAS/PEMDAS ensures everyone arrives at the same correct answer.

Example 2: Multi-Step Word Problem

A farmer harvests 350 mangoes. He sells 215 mangoes at the market. He then divides the remaining mangoes equally among 5 neighbours. How many mangoes does each neighbour receive?

Solution:

Find the number of mangoes remaining: 350 - 215 = 135 mangoes

Divide the remaining mangoes among the neighbours: 135 ÷ 5 = 27 mangoes

Therefore, each neighbour receives 27 mangoes.

Why:* This breaks down a real-world problem into simpler subtraction and division steps.

Example 3: Estimation

Estimate the answer to 523 +

2

8

9. Solution:

Round 523 to the nearest hundred: 500

Round 289 to the nearest hundred: 300

Add the rounded numbers: 500 + 300 = 800

Therefore, the estimated answer is 800. (The actual answer is 812, so the estimation is close.)

Why:* Estimation provides a quick way to verify if your detailed calculation is reasonable.

Example 4: Division with Remainder

Divide 754 by

1

2. Solution:

12 goes into 75 six times (12 x 6 = 72). Write 6 above the 5 in

7

5

4.

Subtract 72 from 75, leaving

3.

Bring down the 4 to make 34.

12 goes into 34 two times (12 x 2 = 24). Write 2 above the 4 in

7

5

4.

Subtract 24 from 34, leaving

1

0. Therefore, 754 ÷ 12 = 62 remainder

1

0. Why:* Demonstrates the long division process with a remainder, reinforcing the concept of not always dividing evenly.

Guided Practice (With Solutions)

Question 1: Evaluate: 20 - 3 x 4 + 6

Solution:

Multiplication first: 3 x 4 = 12

Expression becomes: 20 - 12 + 6

Subtraction next: 20 - 12 = 8

Addition last: 8 + 6 = 14

Answer: 14

Commentary:* This question emphasizes the correct application of BODMAS/PEMDA

S. Question 2: A tuck shop buys 15 boxes of sweets. Each box contains 24 sweets. They sell all the sweets for R2 each. How much money do they make?

Solution:

Find the total number of sweets: 15 x 24 = 360 sweets

Calculate the total money earned: 360 x R2 = R720

Answer: R720

Commentary:* This question requires two multiplication operations to solve a practical problem.

Question 3: Estimate: 987 ÷ 9

Solution:

Round 987 to the nearest hundred: 1000

Divide the rounded number by 9: 1000 ÷ 10 (Rounding 9 to 10 for easier estimation) = 100

Answer: Approximately 100

Commentary:* This highlights estimation skills and rounding to simplify calculations.

Question 4: Divide 435 by

1

5. Solution:

15 goes into 43 two times (15 x 2 = 30). Write 2 above the 3 in

4

3

5.

Subtract 30 from 43, leaving

1

3.

Bring down the 5 to make 135.

15 goes into 135 nine times (15 x 9 = 135). Write 9 above the 5 in

4

3

5.

Subtract 135 from 135, leaving

0. Answer: 29

Commentary: This question focuses on long division without a remainder.

Independent Practice (Questions Only)

Calculate: 36 ÷ 6 + 5 x 2 - 1

A bakery makes 250 loaves of bread each day. They sell each loaf for R

1

2. How much money do they make in a week?

Estimate the answer to 7654 -

2

3

4

5.

Divide 867 by

2

1.

A school has 456 learners. They want to divide the learners into 12 equal groups. How many learners will be in each group? Will there be any learners left over?

Sarah earns R55 per hour. She works for 8 hours a day for 5 days. How much money does she earn in total?

What is (25 + 15) ÷ 8 + 3 x 4 ?

A shopkeeper buys 144 apples. He throws away 12 rotten apples. He packs the remaining apples into bags of

6. How many bags does he need?

Estimate: 123 x 7

Divide 9876 by 32.