Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Multiply multi-digit numbers using the column method.
• Divide multi-digit numbers using long division.
• Solve word problems involving multiplication and division.
• Estimate answers to check if they are reasonable.
• Understand the link between multiplication and division.

Lesson summary

This week, we delve deeper into whole numbers and operations, focusing on multiplication and division of larger numbers. These skills are crucial for everyday activities, from budgeting your pocket money at the tuck shop to calculating how much food is needed for a family gathering. Understanding these concepts provides a strong foundation for more advanced mathematical concepts in later grades. Imagine a farmer calculating how many rows of maize to plant or a shopkeeper determining the cost of several items; both rely on multiplication and division. Mastering these operations helps us solve practical problems efficiently and accurately.

Lesson notes

Multiplication: Multiplication is a shortcut for repeated addition. For example, 5 x 3 means adding 5 to itself 3 times (5 + 5 + 5 = 15). When multiplying larger numbers, the column method helps keep track of place value.

Column Method: This involves aligning numbers vertically according to their place value (ones, tens, hundreds, etc.). We multiply each digit of the bottom number by each digit of the top number, starting from the ones place. We then add the results, taking into account the place value.

Example 1: 123 x 21 Write the numbers vertically, one above the other, aligning the ones place: ``` 123 x 21 ------ ``` Multiply 123 by the ones digit of 21 (which is 1): ``` 123 x 21 ------ 123 (1 x 123) ``` Multiply 123 by the tens digit of 21 (which is 2). Remember that this 2 represents 20, so we add a '0' in the ones place of the next line. ``` 123 x 21 ------ 123 2460 (20 x 123) ------ ``` Add the two results together: ``` 123 x 21 ------ 123 2460 ------ 2583 ``` Therefore, 123 x 21 = 2583 Example 2: Imagine a school in Soweto needs to buy 35 soccer balls at R85 each. How much will they spend?

Write the problem: 85 x 35 Use the column method: ``` 85 x 35 ----- 425 (5 x 85) 2550 (30 x 85) ----- 2975 ``` The school will spend R2975 on soccer balls.

Division: Division is the process of splitting a number into equal groups. The number being divided is called the dividend, the number we are dividing by is the divisor, and the answer is the quotient. Sometimes, there is a remainder which is the amount left over after dividing as evenly as possible.

Long Division: This method helps us divide larger numbers.

Example 1: 462 ÷ 11 Write the problem in long division format: ``` ____ 11 | 462 ``` How many times does 11 go into 4? It doesn't. How many times does 11 go into 46? It goes 4 times (4 x 11 = 44). Write the 4 above the 6 in 462. ``` 4___ 11 | 462 ``` Multiply 11 by 4 and write the result (44) under 46. ``` 4___ 11 | 462 44 ``` Subtract 44 from 46, which gives 2. ``` 4___ 11 | 462 44 -- 2 ``` Bring down the next digit (2) from 462 next to the

2. Now we have 22. ``` 4___ 11 | 462 44 -- 22 ``` How many times does 11 go into 22? It goes 2 times (2 x 11 = 22). Write the 2 above the 2 in 462. ``` 42 11 | 462 44 -- 22 ``` Multiply 11 by 2 and write the result (22) under 22. ``` 42 11 | 462 44 -- 22 22 ``` Subtract 22 from 22, which gives 0. ``` 42 11 | 462 44 -- 22 22 -- 0 ``` Therefore, 462 ÷ 11 = 42 Example 2: A farmer has 345 apples and wants to divide them equally among his 15 workers. How many apples will each worker get?

Write the problem: 345 ÷ 15 Use long division: ``` 23 15 | 345 30 -- 45 45 -- 0 ``` Each worker will get 23 apples.

Inverse Operations: Multiplication and division are inverse operations, meaning they "undo" each other. For example, if 5 x 4 = 20, then 20 ÷ 4 =

5. Understanding this relationship can help you check your answers.

Estimation: Estimating helps us to check if our answers are reasonable. We can round numbers to the nearest ten or hundred before multiplying or dividing.

Example: To estimate 21 x 38, round 21 to 20 and 38 to

4

0. Then 20 x 40 =

8

0

0. So, the answer to 21 x 38 should be around

8

0

0. The actual answer is 798, so our answer is reasonable. Guided Practice (With Solutions)

Question 1: Multiply 64 x 23 using the column method.

Solution: ``` 64 x 23 ---- 192 (3 x 64) 1280 (20 x 64) ---- 1472 ``` Therefore, 64 x 23 =

1

4

7

2. We multiplied each digit of 23 by 64, remembering the place value for the '2' (which is 20).

Question 2: Divide 575 ÷ 25 using long division.

Solution: ``` 23 25 | 575 50 -- 75 75 -- 0 ``` Therefore, 575 ÷ 25 =

2

3. We determined how many times 25 goes into 57, subtracted, brought down the 5, and then determined how many times 25 goes into

7

5. Question 3: A shop sells sweets for R12 each. If someone buys 15 sweets, how much will they pay?

Solution: This is a multiplication problem: R12 x 15 ``` 12 x 15 ---- 60 (5 x 12) 120 (10 x 12) ---- 180 ``` They will pay R

1

8

0. Question 4: 432 learners need to be transported to a sports event. If each bus can carry 36 learners, how many buses are needed?

Solution: This is a division problem: 432 ÷ 36 ``` 12 36 | 432 36 -- 72 72 -- 0 ``` 12 buses are needed. Independent Practice (Questions Only) Multiply 78 x

4

5. Divide 624 ÷

1

3. A farmer harvests 288 oranges and wants to pack them into boxes of 24 each. How many boxes will he need? A school wants to buy 17 new desks at R255 each. How much will they spend in total? If 35 learners each donate R15 to a charity, how much money is raised in total? Divide 975 by

2

5. What is 144 multiplied by 16? Sarah has 528 beads. She wants to make 22 necklaces. How many beads can she use for each necklace if she uses the same number of beads for each? A tuck shop buys sweets in bulk. They buy 32 packets of sweets with 48 sweets in each packet. How many sweets do they have in total? A stadium has 2385 seats divided into 15 sections. How many seats are in each section?