Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Add whole numbers up to 6 digits.
• Subtract whole numbers up to 6 digits.
• Multiply a 3-digit number by a 2-digit number.
• Divide a 4-digit number by a 1-digit number.
• Solve word problems using these operations.

Lesson summary

This week, we will continue our exploration of whole numbers and operations, focusing on addition, subtraction, multiplication, and division. A strong understanding of these operations is essential for everyday life in South Africa. Whether you're calculating the change you receive at a spaza shop, sharing sweets with your friends, budgeting your pocket money, or figuring out how many bricks are needed to build a small wall, these skills are vital. We will build upon what you learned in Grade 4, tackling larger numbers and more complex problems.

Lesson notes

Addition: Addition is the process of combining two or more numbers to find their total. We use the "+" symbol to represent addition. In Grade 5, we work with larger numbers, so the column method becomes crucial.

Column Method: Align the numbers vertically according to their place value (ones, tens, hundreds, thousands, ten-thousands, hundred-thousands). Start adding from the ones column, and if the sum is 10 or more, carry over the tens digit to the next column.

Example 1: Adding the population of two small towns. Town A has 23,456 residents and Town B has 15,879 residents. What is the total population of both towns? ``` 23456 + 15879 39335 ``` Explanation: 6 + 9 =

1

5. Write down 5 and carry-over 1 to the tens column. 1 (carried-over) + 5 + 7 =

1

3. Write down 3 and carry-over 1 to the hundreds column. 1 (carried-over) + 4 + 8 =

1

3. Write down 3 and carry-over 1 to the thousands column. 1 (carried-over) + 3 + 5 =

9. Write down 9. 2 + 1 =

3. Write down

3. Therefore, the total population is 39,335 residents.

Subtraction: Subtraction is the process of finding the difference between two numbers. We use the "-" symbol to represent subtraction. Borrowing (or regrouping) is often necessary when subtracting larger numbers.

Column Method with Borrowing: Similar to addition, align numbers according to place value. If a digit in the top number is smaller than the corresponding digit in the bottom number, borrow from the digit to its left. Remember that when you borrow 1 from a column, it adds 10 to the next column to the right.

Example 2: Calculating the profit for selling vetkoek. A street vendor made R15,250 in sales and spent R8,785 on ingredients. How much profit did they make? ``` 15250 08785 06465 ``` Explanation: 0 - 5: We need to borrow. Borrow 1 from the 5 (tens column), making it 4, and adding 10 to the ones column, making it 10. 10 - 5 = 5. 4 - 8: We need to borrow. Borrow 1 from the 2 (hundreds column), making it 1, and adding 10 to the tens column, making it 14. 14 - 8 = 6. 1 - 7: We need to borrow. Borrow 1 from the 5 (thousands column), making it 4, and adding 10 to the hundreds column, making it 11. 11 - 7 = 4. 4 - 8: We need to borrow. Borrow 1 from the 1 (ten-thousands column), making it 0, and adding 10 to the thousands column, making it 14. 14 - 8 = 6. 0 - 0 =

0. Therefore, the profit is R6,

4

6

5. Multiplication: Multiplication is repeated addition. We use the "×" symbol to represent multiplication.

Expanded Notation Method: Break down the numbers into their expanded form (e.g., 23 = 20 + 3) and then multiply each part. This helps to understand the place value.

Standard Algorithm: The traditional method of multiplication, which involves multiplying each digit of one number by each digit of the other number and then adding the results.

Example 3: Calculating the total number of loaves of bread produced per week. A bakery produces 345 loaves of bread per day. How many loaves are produced in 14 days?

Using the standard algorithm: ``` 345 x 14 1380 (345 x 4) +3450 (345 x 10) 4830 ``` Explanation: Multiply 345 by 4: 4 x 5 = 20 (write down 0, carry-over 2). 4 x 4 = 16 + 2 (carried-over) = 18 (write down 8, carry-over 1). 4 x 3 = 12 + 1 (carried-over) =

1

3. Write down

1

3. So, 345 x 4 =

1

3

8

0. Multiply 345 by 10: This is the same as 345 with a 0 added at the end:

3

4

5

0. Add the two results: 1380 + 3450 =

4

8

3

0. Therefore, the bakery produces 4,830 loaves of bread in 14 days.

Division: Division is the process of splitting a number into equal groups. We use the "÷" symbol to represent division.

Long Division: A method used to divide large numbers. It involves breaking down the division problem into smaller, more manageable steps.

Example 4: Sharing apples equally. 1,253 apples need to be shared equally among 5 schools. How many apples will each school get, and how many will be left over? ``` 250 R 3 5 | 1253 -10 ---- 25 -25 ---- 03 -0 ---- 03 ``` Explanation: How many times does 5 go into 1? It doesn't, so we look at

1

2. How many times does 5 go into 12? 2 times (2 x 5 = 10). Write 2 above the 2 in 1253 and subtract 10 from 12, leaving

2. Bring down the next digit (5) to make

2

5. How many times does 5 go into 25? 5 times (5 x 5 = 25). Write 5 above the 5 in 1253 and subtract 25 from 25, leaving

0. Bring down the next digit (3) to make

3. How many times does 5 go into 3? 0 times (0 x 5 = 0). Write 0 above the 3 in 1253 and subtract 0 from 3, leaving

3. The number left over (3) is the remainder.

Therefore, each school will get 250 apples, and there will be 3 apples left over. Guided Practice (With Solutions)

Question 1: A farmer harvested 45,678 oranges on Monday and 32,987 oranges on Tuesday. How many oranges did the farmer harvest in total?

Solution: ``` 45678 + 32987 78665 ``` The farmer harvested a total of 78,665 oranges. We used addition with carrying over to solve this problem.

Question 2: A school has 1,542 learners. If 675 learners are girls, how many are boys?