Lesson Notes By Weeks and Term v5 - Grade 5
Whole numbers and operations (Grade 5) – Week 5 focus
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Whole numbers and operations (Grade 5) – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 5
Term: 1st Term
Week: 5
Theme: General lesson support
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This week, we're diving deeper into whole numbers and how we operate with them. We’ll be focusing on multiplication and division, specifically how to multiply and divide larger numbers effectively. This isn't just about memorizing rules; it's about understanding how these operations work and applying them to solve problems we encounter every day. For example, imagine you are helping your family plan a braai for Heritage Day. You need to calculate how much meat to buy based on how many people are coming and how much each person will eat. Or maybe you're sharing sweets equally among your friends. Understanding multiplication and division makes these tasks much easier!
Multiplication: Multiplying 3-digit numbers by 2-digit numbers We've already learned how to multiply smaller numbers. Now, we'll extend this knowledge to larger numbers using the column method. The column method helps us to break down the multiplication into smaller, manageable steps. How does it work?
Write the numbers vertically: Place the 3-digit number on top and the 2-digit number below, aligning the units, tens, and hundreds columns.
Multiply by the units digit: Multiply the units digit of the 2-digit number by each digit of the 3-digit number, starting from the right (units column). Remember to carry over if the result is 10 or more.
Multiply by the tens digit: Multiply the tens digit of the 2-digit number by each digit of the 3-digit number, starting from the right.
Important: Because you are multiplying by the TENS digit, you need to write a '0' in the units column of this line before you start multiplying! This is because multiplying by, for example, 20, is the same as multiplying by 2 and then by
1
0. Putting the 0 there is the multiplying by 10 part.
Add the results: Add the two rows of numbers you've calculated to get the final answer.
Example 1: Multiply 234 by 15. ``` 234 x 15 1170 (5 x 234) + 2340 (10 x 234) 3510 ``` Explanation: First, we multiplied 234 by 5, which gave us
1
1
7
0. Next, we multiplied 234 by 10 (remember the zero!), which gave us
2
3
4
0. Finally, we added 1170 and 2340 to get the answer:
3
5
1
0. Example 2: A farmer plants 12 rows of mielies, with 145 mielies in each row. How many mielies are planted in total? ``` 145 x 12 290 (2 x 145) + 1450 (10 x 145) 1740 ``` Explanation: We need to multiply 145 by
1
2. Following the column method, we find that the farmer planted 1740 mielies in total.
Division: Dividing 3-digit numbers by 1-digit numbers with remainders Dividing a 3-digit number by a 1-digit number involves figuring out how many times the smaller number fits completely into the larger number. Sometimes, the division is not exact, and we have a remainder. How does it work? We can use long division or repeated subtraction. Here, we will use long division. Write the numbers in the long division format: The 3-digit number (dividend) goes inside the "house," and the 1-digit number (divisor) goes outside.
Divide the first digit: See how many times the divisor goes into the first digit of the dividend. Write the quotient (the result of the division) above the first digit.
Multiply and subtract: Multiply the quotient by the divisor and write the result below the first digit of the dividend. Subtract.
Bring down the next digit: Bring down the next digit of the dividend next to the result of the subtraction.
Repeat: Repeat steps 2-4 until you have divided all the digits of the dividend.
Remainder: If there is a number left after the last subtraction, that is the remainder.
Example 1: Divide 375 by 4. ``` 93 R 3 ------ 4 | 375 -36 ------ 15 -12 ------ 3 ``` Explanation: 4 goes into 37 nine times (9 x 4 = 36). We write '9' above the '7'. Subtract 36 from 37, leaving
1. Bring down the 5 to make 15. 4 goes into 15 three times (3 x 4 = 12). We write '3' above the '5'. Subtract 12 from 15, leaving
3. The remainder is
3. Therefore, 375 divided by 4 is 93 with a remainder of 3. (93 R 3)
Example 2: A group of 256 learners needs to be divided into 8 equal teams for a sports day. How many learners will be in each team, and will there be any learners left over? ``` 32 ------ 8 | 256 -24 ------ 16 -16 ------ 0 ``` Explanation: 8 goes into 25 three times (3 x 8 = 24). We write '3' above the '5'. Subtract 24 from 25, leaving
1. Bring down the 6 to make 16. 8 goes into 16 two times (2 x 8 = 16). We write '2' above the '6'. Subtract 16 from 16, leaving
0. The remainder is
0. Therefore, 256 divided by 8 is
3
2. Each team will have 32 learners, and there will be no learners left over. Relationship between Multiplication and Division Multiplication and division are inverse operations. This means that one operation "undoes" the other. If you multiply a number by another number, you can then divide the result by the second number to get back the original number.
Example: 3 x 4 = 12 12 ÷ 4 = 3 This relationship is very useful for checking your answers in division. If you divide a number and get a quotient and a remainder, you can multiply the quotient by the divisor and add the remainder to check if you get back the original dividend.
Checking division calculations: Dividend = (Quotient x Divisor) + Remainder
Example: We divided 375 by 4 and got 93 R
3. Let's check if our answer is correct. (93 x 4) + 3 = 372 + 3 = 375 Since we get back the original dividend (375), our division is correct! Guided Practice (With Solutions)
Question 1: Multiply 312 by
2
3. Solution: ``` 312 x 23 936 (3 x 312) + 6240 (20 x 312) 7176 ``` Therefore, 312 x 23 =
7
1
7
6. Explanation: We applied the column method systematically, multiplying by the units digit (3) and then the tens digit (20) before adding the results.