Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Multiply multi-digit whole numbers.
• Divide multi-digit whole numbers using long division.
• Solve real-world word problems.
• Estimate answers to check your work.
• Apply the order of operations (BODMAS).

Lesson summary

This week, we're continuing our exploration of whole numbers and operations. Understanding whole numbers and how to add, subtract, multiply, and divide them is absolutely crucial in our daily lives in South Africa. Whether you're helping your family budget for groceries, calculating distances when travelling, or sharing sweets with your friends, you're using these skills! This week, we will focus primarily on multiplication and division of whole numbers, building upon our knowledge of addition and subtraction from last week. We’ll also look at problem-solving using all four operations.

Lesson notes

Multiplication of Whole Numbers Multiplication is a quick way of adding the same number multiple times. For example, 3 x 4 means adding 3 four times (3 + 3 + 3 + 3 = 12).

We will explore two key methods: column multiplication and expanded notation. a) Column Multiplication (Standard Algorithm) This is a structured way to multiply numbers, especially larger ones.

Example 1: 23 x 14 Write the numbers one above the other, aligning the units digits. ``` 23 x 14 ---- ``` Multiply the top number (23) by the units digit of the bottom number (4). 4 x 3 =

1

2. Write down the 2, carry-over the 1. 4 x 2 =

8. Add the carry-over 1 to get

9. Write down 9. ``` 23 x 14 ---- 92 ``` Multiply the top number (23) by the tens digit of the bottom number (1). Remember that this '1' represents 10, so we are multiplying by

1

0. Therefore, we put a '0' as a placeholder in the units column of the next row. 1 x 3 =

3. Write down 3 in the tens column. 1 x 2 =

2. Write down 2 in the hundreds column. ``` 23 x 14 ---- 92 230 ---- ``` Add the two rows together. ``` 23 x 14 ---- 92 230 ---- 322 ``` Therefore, 23 x 14 = 322 Example 2: 135 x 25 Set up the problem: ``` 135 x 25 ---- ``` Multiply 135 by 5: 5 x 5 =

2

5. Write down 5, carry-over 2. 5 x 3 =

1

5. Add the carry-over 2: 15 + 2 =

1

7. Write down 7, carry-over 1. 5 x 1 =

5. Add the carry-over 1: 5 + 1 =

6. Write down 6. ``` 135 x 25 ---- 675 ``` Multiply 135 by 20 (remember the '0' placeholder): ``` 135 x 25 ---- 675 2700 ---- ``` Add the results: ``` 135 x 25 ---- 675 2700 ---- 3375 ``` Therefore, 135 x 25 = 3375 b) Expanded Notation This method breaks down the numbers into their place values and then multiplies.

Example: 23 x 14 Expand the numbers: 23 = 20 + 3 14 = 10 + 4 Multiply each part of the first number by each part of the second number: 20 x 10 = 200 20 x 4 = 80 3 x 10 = 30 3 x 4 = 12 Add all the results together: 200 + 80 + 30 + 12 = 322 Therefore, 23 x 14 = 322 Division of Whole Numbers Division is the process of splitting a number into equal groups. We'll focus on long division. Long Division

Example: 144 ÷ 6 Write the problem in the long division format: ``` ______ 6 / 144 ``` How many times does 6 go into 1 (the first digit of 144)? It doesn't. How many times does 6 go into 14 (the first two digits of 144)? It goes in 2 times (2 x 6 = 12). Write the 2 above the 4 in 144. ``` 2____ 6 / 144 ``` Subtract 12 from 14: 14 - 12 =

2. Write the 2 below the 12. ``` 2____ 6 / 144 -12 ---- 2 ``` Bring down the next digit (4) from 144 next to the 2. ``` 2____ 6 / 144 -12 ---- 24 ``` How many times does 6 go into 24? It goes in 4 times (4 x 6 = 24). Write the 4 above the last 4 in 144. ``` 24 6 / 144 -12 ---- 24 ``` Subtract 24 from 24: 24-24 = 0. ``` 24 6 / 144 -12 ---- 24 -24 ---- 0 ``` Therefore, 144 ÷ 6 = 24 Example with Remainder: 79 ÷ 5 Set up: ``` ____ 5 / 79 ``` 5 goes into 7 once (1 x 5 = 5). Write 1 above the 7. ``` 1___ 5 / 79 ``` Subtract: 7 - 5 = 2. ``` 1___ 5 / 79 -5 --- 2 ``` Bring down the 9: ``` 1___ 5 / 79 -5 --- 29 ``` 5 goes into 29 five times (5 x 5 = 25). Write 5 above the 9. ``` 15 5 / 79 -5 --- 29 ``` Subtract: 29 - 25 = 4. ``` 15 5 / 79 -5 --- 29 -25 --- 4 ``` Since there are no more digits to bring down, the 4 is the remainder.

Therefore, 79 ÷ 5 = 15 remainder 4 (or 15 R 4). Estimating Answers Estimating helps us check if our answers are reasonable. We round the numbers to the nearest ten or hundred before calculating.

Example: Estimate 28 x 11 Round 28 to

3

0. Round 11 to 10. 30 x 10 =

3

0

0. So, the answer should be around 300. (The actual answer is 308, so our estimate is close!).

Example: Estimate 153 ÷ 5 Round 153 to 150 150 ÷ 5 =

3

0. So the answer should be around 30. (The actual answer is 30 remainder 3, so our estimate is close!). Order of Operations (BODMAS/PEMDAS) When a problem involves multiple operations, we follow the order of operations: Brackets / Parentheses Orders / Exponents Division and Multiplication (from left to right) Addition and Subtraction (from left to right)

Example: 2 + 3 x 4 Multiply first: 3 x 4 = 12 Add: 2 + 12 = 14 Therefore, 2 + 3 x 4 = 14

Example: (10 - 4) ÷ 2 Brackets first: 10 - 4 = 6 Divide: 6 ÷ 2 = 3 Therefore, (10 - 4) ÷ 2 = 3 Guided Practice (With Solutions)

Question 1: A farmer has 35 rows of mielies (corn). Each row has 18 mielies plants. How many mielies plants are there in total?

Solution: We need to find the total number of plants, which means we need to multiply the number of rows by the number of plants in each row. 35 x 18 = ? Let's use column multiplication. ``` 35 x 18 280 (35 x 8) 350 (35 x 10 - remember the 0 placeholder) 630 ``` Therefore, there are 630 mielies plants in total.

Question 2: A baker makes 252 koeksisters. He wants to pack them into boxes, with each box holding 6 koeksisters. How many boxes does he need?

Solution: We need to divide the total number of koeksisters by the number of koeksisters per box to find out how many boxes are needed. 252 ÷ 6 = ? Let's use long division.