Lesson Notes By Weeks and Term v3 - Primary 6
Division
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Division
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Subject: General Mathematics
Class: Primary 6
Term: 3rd Term
Week: 2
Theme: Basic Operations
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This topic focuses on extending students' understanding of division to include more complex scenarios involving 2-digit and 3-digit divisors for both whole numbers and decimals. Division is a fundamental arithmetic operation crucial for everyday problem-solving, such as fair sharing, budgeting, calculating averages, and distribution of resources. Mastery of this concept equips learners with essential quantitative skills applicable in various real-life situations within Nigerian communities, including market transactions, resource allocation, and simple financial planning.
Basic Operations A school received 12,380 exercise books to distribute equally among 145 classes. How many exercise books will each class receive? (Round to the nearest whole number if there's a remainder, or state remainder).
Solution: Divide 12,380 by 145. ``` 85 _______ 145 | 12380 -1160 (145 x 8 = 1160) ----- 780 (Bring down 0) -725 (145 x 5 = 725) ---- 55 ``` Step 1: Consider the first few digits of the dividend (1238). How many times does 145 go into 1238?
Estimate: 1200 / 140 is approximately 120/14 ≈
8. So, try 8. (145 × 8 = 1160). Write '8' above the '8' of
1
2
3
8. Step 2: Multiply 8 by 145: 8 × 145 =
1
1
6
0. Step 3: Subtract 1160 from 1238: 1238 - 1160 =
7
8. Step 4: Bring down the next digit (0), forming
7
8
0. Step 5: Repeat: How many times does 145 go into 780?
Estimate: 780 / 140 is approximately 78/14 ≈
5. So, try 5. (145 × 5 = 725). Write '5' next to '8' in the quotient.
Step 6: Multiply 5 by 145: 5 × 145 =
7
2
5. Step 7: Subtract 725 from 780: 780 - 725 =
5
5. The remainder is
5
5. Answer: Each class will receive 85 exercise books, with 55 books remaining. B. Division of Decimal Numbers by 2-digit and 3-digit Numbers When dividing a decimal by a whole number, the process is similar to dividing whole numbers. The crucial step is to place the decimal point in the quotient directly above the decimal point in the dividend.
Worked Example 3: Division of a Decimal by a 2-digit Number Problem: A tailor has 56.75 metres of fabric to make school uniforms. If each uniform requires 25 metres of fabric (this example is flawed, should be 2.5, or a smaller number for uniforms), let's rephrase: A tailor has 56.75 metres of fabric to make trousers. If each pair of trousers requires 2.5 metres of fabric (this is division by decimal, not whole number), let's rephrase again for the performance objective: A tailor has 56.75 metres of fabric. If she makes 25 identical dresses, how much fabric is used for each dress?
Solution: Divide 56.75 by 25. ``` 2.27 _______ 25 | 56.75 -50 (25 x 2 = 50) --- 67 (Bring down 7) -50 (25 x 2 = 50) --- 175 (Bring down 5) -175 (25 x 7 = 175) ---- 0 ``` Step 1: Divide 56 by
2
5. It goes 2 times. Write '2' above the '6'.
Step 2: Multiply 2 by 25 (50). Subtract from 56 (remainder 6).
Step 3: Bring down the next digit (7). Now we have
6
7. Place the decimal point in the quotient directly above the decimal point in the dividend.
Step 4: Divide 67 by
2
5. It goes 2 times. Write '2' after the decimal point in the quotient.
Step 5: Multiply 2 by 25 (50). Subtract from 67 (remainder 17).
Step 6: Bring down the next digit (5). Now we have
1
7
5. Step 7: Divide 175 by
2
5. It goes 7 times. Write '7' after '2' in the quotient.
Step 8: Multiply 7 by 25 (175). Subtract from 175 (remainder 0).
Answer: Each dress requires 2.27 metres of fabric.
Worked Example 4: Division of a Decimal by a 3-digit Number Problem: A total rainfall of 185.75 mm was recorded uniformly over 125 days during the rainy season. What was the average daily rainfall?
Solution: Divide 185.75 by 125. ``` 1.486 ________ 125 | 185.750 (Add a zero for further precision if needed) -125 (125 x 1 = 125) ---- 607 (Bring down 7, place decimal point) -500 (125 x 4 = 500) ---- 1075 -1000 (125 x 8 = 1000) ----- 750 -750 (125 x 6 = 750) ---- 0 ``` Step 1: Divide 185 by
1
2
5. It goes 1 time. Write '1' above the '5'.
Step 2: Multiply 1 by 125 (125). Subtract from 185 (remainder 60).
Step 3: Bring down the next digit (7). Place the decimal point in the quotient directly above the Division Term: 3rd Term Week: 11 ---
1. Overview and Learning Objectives This topic focuses on extending students' understanding of division to include more complex scenarios involving 2-digit and 3-digit divisors for both whole numbers and decimals. Division is a fundamental arithmetic operation crucial for everyday problem-solving, such as fair sharing, budgeting, calculating averages, and distribution of resources. Mastery of this concept equips learners with essential quantitative skills applicable in various real-life situations within Nigerian communities, including market transactions, resource allocation, and simple financial planning. Upon completion of this lesson, students will be able to: Accurately divide whole numbers by 2-digit and 3-digit numbers. Accurately divide decimal numbers by 2-digit and 3-digit numbers. Solve practical problems (quantitative aptitude) that require division by 2-digit and 3-digit numbers, applying their understanding to realistic scenarios.
2. Key Concepts and Explanations Division is the process of splitting a number (the dividend) into equal parts or groups, determined by another number (the divisor). The result of the division is called the quotient, and any amount left over is the remainder. A. Division of Whole Numbers by 2-digit and 3-digit Numbers The standard method for division is Long Division. The steps remain consistent regardless of the number of digits in the divisor, but require careful estimation and multiplication.
Steps for Long Division (DMSB Method):
1. Divide (D): Divide the first part of the dividend by the divisor.
2. Multiply (M): Multiply the quotient digit by the divisor.
3. Subtract (S): Subtract the product from the part of the dividend used.
4. Bring Down (B): Bring down the next digit from the dividend.
5. Repeat: Repeat the DMSB steps until all digits of the dividend have been used.
Worked Example 1: Division by a 2-digit Number (Whole Number)
Problem: A farmer harvested 4,375 yams and wants to pack them into sacks, with each sack containing 35 yams. How many sacks will be needed?
Solution: Divide 4,375 by 35. ``` 125 _______ 35 | 4375 -35 (35 x 1 = 35) --- 87 (Bring down 7) -70 (35 x 2 = 70) --- 175 (Bring down 5) -175 (35 x 5 = 175) ---- 0 ``` Step 1: Consider the first two digits of the dividend,
4
3. How many times does 35 go into 43? It goes 1 time. Write '1' above the '3' of
4
3. Step 2: Multiply the quotient digit (1) by the divisor (35): 1 × 35 =
3
5. Step 3: Subtract 35 from 43: 43 - 35 =
8. Step 4: Bring down the next digit from the dividend (7), forming
8
7. Step 5: Repeat: How many times does 35 go into 87? It goes 2 times (since 35 × 2 = 70, and 35 × 3 = 105, which is too large). Write '2' next to '1' in the quotient.
Step 6: Multiply the new quotient digit (2) by the divisor (35): 2 × 35 =
7
0. Step 7: Subtract 70 from 87: 87 - 70 =
1
7. Step 8: Bring down the next digit from the dividend (5), forming
1
7
5. Step 9: Repeat: How many times does 35 go into 175? It goes 5 times (since 35 × 5 = 175). Write '5' next to '2' in the quotient.
Step 10: Multiply the new quotient digit (5) by the divisor (35): 5 × 35 =
1
7
5. Step 11: Subtract 175 from 175: 175 - 175 =
0. The remainder is
0. Answer: 125 sacks will be needed.
Worked Example 2: Division by a 3-digit Number (Whole Number)
Problem: A school received 12,380 exercise books to distribute equally among 145 classes. How many exercise books will each class receive? (Round to the nearest whole number if there's a remainder, or state remainder).
Solution: Divide 12,380 by 145. ``` 85 _______ 145 | 12380 -1160 (145 x 8 = 1160) ----- 780 (Bring down 0) -725 (145 x 5 = 725) ---- 55 ``` * Step 1: Consider the first few digits of the dividend (1238). How many times does 145 go into 1238?
Estimate: 1200 / 140 is approximately 120/14 ≈ for further precision if needed) -125 (125 x 1 = 125) ---- 607 (Bring down 7, place decimal point) -500 (125 x 4 = 500) ---- 1075 -1000 (125 x 8 = 1000) ----- 750 -750 (125 x 6 = 750) ---- 0 ``` Step 1: Divide 185 by
1
2
5. It goes 1 time. Write '1' above the '5'.
Step 2: Multiply 1 by 125 (125). Subtract from 185 (remainder 60).
Step 3: Bring down the next digit (7). Place the decimal point in the quotient directly above the decimal point in the dividend. Now we have
6
0
7. Step 4: Divide 607 by
1
2
5. Estimate: 600/120 =
5. Try 4 (125 × 4 = 500). Write '4' after the decimal point in the quotient.
Step 5: Multiply 4 by 125 (500). Subtract from 607 (remainder 107).
Step 6: Bring down the next digit (5). Now we have
1
0
7
5. Step 7: Divide 1075 by
1
2
5. Estimate: 1000/125 =
8. Try 8 (125 × 8 = 1000). Write '8' after '4' in the quotient.
Step 8: Multiply 8 by 125 (1000). Subtract from 1075 (remainder 75).
Step 9: Add a zero to the dividend (185.750) and bring it down. Now we have
7
5
0. Step 10: Divide 750 by
1
2
5. It goes 6 times. Write '6' after '8' in the quotient.
Step 11: Multiply 6 by 125 (750). Subtract from 750 (remainder 0).
Answer: The average daily rainfall was 1.486 mm. C. Quantitative Aptitude Involving Division Quantitative aptitude problems often present real-world scenarios where students must identify the appropriate operation to solve the problem. For division, common scenarios include: Fair Sharing: Distributing items equally among a group.
Grouping: Determining how many groups of a certain size can be made from a total.
Finding Averages: Summing quantities and dividing by the count.
Rate Problems: Calculating unit rates (e.g., cost per item, speed).
Keywords/Phrases indicating division: "share equally," "distribute among," "how many per," "average," "split into groups," "per person/item/unit." Worked Example 5: Quantitative Aptitude (Word Problem)
Problem: A cooperative society in a rural Nigerian community saved ₦75,600 over a year. If they want to share this amount equally among their 105 members, how much will each member receive?
Solution: Divide ₦75,600 by 105. ``` 720 _______ 105 | 75600 -735 (105 x 7 = 735) ---- 210 (Bring down 0) -210 (105 x 2 = 210) ---- 00 (Bring down 0, 105 into 0 is 0) ``` Step 1: Consider
7
5
6. How many times does 105 go into 756?
Estimate: 700/100 =
7. Try 7. (105 × 7 = 735). Write '7' above '6'.
Step 2: Subtract 735 from 756, which gives
2
1. Step 3: Bring down the next digit (0) to make
2
1
0. Step 4: How many times does 105 go into 210? It goes 2 times. (105 × 2 = 210). Write '2' next to '7'.
Step 5: Subtract 210 from 210, which gives
0. Step 6: Bring down the last digit (0). How many times does 105 go into 0? 0 times. Write '0' next to '2'.
Answer: Each member will receive ₦720.
3. Teaching and Learning Activities
A. Introduction (5-10 minutes)
Teacher Activity: Begin by reviewing basic division concepts (e.g., 60 ÷ 5, 120 ÷ 10). Pose a simple real-life problem involving sharing, such as "If 48 oranges are shared equally among 6 children, how many does each get?" Student Activity: Students recall basic division facts and solve the simple introductory problem. Briefly discuss different ways they might solve it (e.g., repeated subtraction, multiplication facts).
B. Development (40-50 minutes) Teacher Activity 1 (Division of Whole Numbers by 2-digit Divisors): Present a problem requiring division by a 2-digit number (e.g., "Divide 567 by 21"). Model the long division process on the board, explaining each step (DMSB) clearly. Emphasize estimation techniques for finding quotient digits. Work through Example 1 (yams problem) from Key Concepts.
Student Activity 1: Students copy the example and follow along. Students attempt a similar problem individually or in pairs (e.g., "Divide