Lesson Notes By Weeks and Term v3 - Primary 4
Division
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Division
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Subject: General Mathematics
Class: Primary 4
Term: 3rd Term
Week: 5
Theme: Basic Operations
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Watch on YouTubeSee Facebook postDivide two or three digit numbers by:.numbers up to 9 with or with out remainder.multiples of 10 up to 50 Solve quantitative aptitude problems in volving division.
Basic Operations Write '16' below the '16'. ``` 12__ 8 | 96 8 --- 16 16 ``` Subtract: 16 - 16 =
0. Write '0' below the '16'. ``` 12__ 8 | 96 8 --- 16 16 --- 0 ``` The remainder is
0. So, 96 ÷ 8 =
1
2. Each basket will have 12 oranges.
Worked Example 2: Dividing a 3-digit number by a 1-digit number (with remainder)
Problem: A baker made 457 loaves of bread. He wants to supply them equally to 6 shops. How many loaves will each shop receive, and how many will be left over? (457 ÷ 6)
Solution:
1. Set up: ``` ____ 6 | 457 ```
2. Divide the first digit of the dividend (4) by the divisor (6): 6 cannot go into
4. So, consider the first two digits (45).
3. Divide 45 by 6: How many 6s are in 45? Seven (7), because 6 × 7 = 42. (6 × 8 = 48, which is too big). Write '7' above the '5' in the quotient. ``` _7__ 6 | 457 ```
4. Multiply the quotient digit (7) by the divisor (6): 7 × 6 =
4
2. Write '42' below the '45'. ``` _7__ 6 | 457 42 ```
5. Subtract 42 from 45: 45 - 42 =
3. Write '3' below the '42'. ``` _7__ 6 | 457 42 --- 3 ```
6. Bring down the next digit of the dividend (7) beside the remainder (3): This forms the new number '37'. ``` _7__ 6 | 457 42 --- 37 ```
7. Repeat the process: Divide: How many 6s are in 37? Six (6), because 6 × 6 = 36. (6 × 7 = 42, too big). Write '6' next to the '7' in the quotient. ``` _76_ 6 | 457 42 --- 37 ``` Multiply: 6 × 6 =
3
6. Write '36' below the '37'. ``` _76_ 6 | 457 42 --- 37 36 ``` Subtract: 37 - 36 =
1. Write '1' below the '36'. ``` _76_ 6 | 457 42 --- 37 36 --- 1 ``` The remainder is
1. So, 457 ÷ 6 = 76 remainder
1. Each shop will receive 76 loaves, and 1 loaf will be left over. B. Dividing Two or Three-Digit Numbers by Multiples of 10 up to 50 This type of division can often be simplified by understanding place value and the effect of zeros. Divisors like 10, 20, 30, 40,
5
0. Worked Example 3: Dividing a 2-digit number by a multiple of 10 Problem: Mama Nkechi has 80 yam seedlings. She wants to plant them in rows, with 20 seedlings in each row. How many rows will she have? (80 ÷ 20)
Solution (Method 1: Cancelling Zeros): Both 80 and 20 end in zero. Cancel one zero from each. The problem becomes 8 ÷ 2. 8 ÷ 2 =
4. So, 80 ÷ 20 =
4. Mama Nkechi will have 4 rows.
Solution (Method 2: Long Division - for understanding):
1. Set up: ``` ____ 20 | 80 ```
2. Divide 80 by 20: How many 20s are in 80?
Count in 20s: 20, 40, 60,
8
0. That's 4 times. Write '4' above the '0' in the quotient. ``` _4__ 20 | 80 ```
3. Multiply 4 by 20: 4 × 20 =
8
0. Write '80' below the '80'. ``` _4__ 20 | 80 80 ```
4. Subtract 80 from 80: 80 - 80 = 0. ``` _4__ 20 | 80 80 --- 0 ``` Result: 80 ÷ 20 =
4. Worked Example 4: Dividing a 3-digit number by a multiple of 10 Problem: A community group collected 350 plastic bottles for recycling. They can pack 50 bottles into one sack. How many sacks do they need? (350 ÷ 50)
Solution (Method 1: Cancelling Zeros): Both 350 and 50 end in zero. Cancel one zero from each. The problem becomes 35 ÷ 5. 35 ÷ 5 =
7. So, 350 ÷ 50 =
7. They _4__ 20 | 80 80 --- 0 ``` Result: 80 ÷ 20 =
4. Worked Example 4: Dividing a 3-digit number by a multiple of 10 Problem: A community group collected 350 plastic bottles for recycling. They can pack 50 bottles into one sack. How many sacks do they need? (350 ÷ 50)
Solution (Method 1: Cancelling Zeros): Both 350 and 50 end in zero. Cancel one zero from each. The problem becomes 35 ÷ 5. 35 ÷ 5 =
7. So, 350 ÷ 50 =
7. They need 7 sacks.
Solution (Method 2: Long Division - for understanding):
1. Set up: ``` ____ 50 | 350 ```
2. Divide 350 by 50: How many 50s are in 350? Think of 35 divided by 5, which is
7. Write '7' above the '0' in the quotient. ``` _7__ 50 | 350 ```
3. Multiply 7 by 50: 7 × 50 =
3
5
0. Write '350' below the '350'. ``` _7__ 50 | 350 350 ```
4. Subtract 350 from 350: 350 - 350 = 0. ``` _7__ 50 | 350 350 --- 0 ``` Result: 350 ÷ 50 =
7. C. Solving Quantitative Aptitude Problems involving Division These are word problems that require students to read carefully, identify the relevant numbers, and determine that division is the operation needed to solve the problem. Keywords like "share equally," "distribute," "how many in each group," "how many groups" often indicate division.
Worked Example 5: Quantitative Aptitude Problem: A tailor has 184 meters of fabric. If she uses 4 meters of fabric to sew one uniform for a school child, how many uniforms can she sew?
Solution:
1. Identify the total quantity: 184 meters (dividend).
2. Identify the quantity per item/group: 4 meters (divisor).
3. Determine the operation: To find out how many uniforms can be sewn from the total fabric, division is required.
4. Perform the division (184 ÷ 4): ``` _46_ 4 | 184 16 (4 x 4 = 16) --- 24 24 (6 x 4 = 24) --- 0 ``` The tailor can sew 46 uniforms.
3. Teaching and Learning Activities Phase 1: Introduction and Review (10 minutes)
Teacher Activity: Begin by reviewing the concept of division as "sharing equally" or "grouping". Ask students for simple division facts (e.g., "If I have 12 pencils and want to share them among 3 students, how many will each get?").
Introduce the terms: dividend, divisor, quotient, remainder using simple examples.
Student Activity: Students actively participate in answering simple division questions, recalling multiplication facts, and identifying the components of a division problem.
Phase 2: Division by Single-Digit Numbers (20 minutes)
Teacher Activity:
1. Model division of a 2-digit number by a 1-digit number using concrete manipulatives (e.g., bottle caps, seeds, small stones). For example, take 48 seeds and demonstrate sharing them equally into 4 groups, showing the concept of dividing tens first, then units.
2. Introduce the long division algorithm for 2-digit numbers by 1-digit numbers, explicitly linking it to the manipulative demonstration. Use an example like 75 ÷ 5.
3. Model division of a 3-digit number by a 1-digit number with and without remainder using the long division method.
Emphasize place value and the steps: Divide, Multiply, Subtract, Bring Down. Use Example 2 (457 ÷ 6) on the board, explaining each step carefully.
Student Activity:
1. Students observe the teacher's demonstration with manipulatives and then mimic the process with their own materials (if available) or by drawing.
2. Students follow along as the teacher works through long division examples on the board, copying steps into their notebooks.
3. Students attempt simple 2-digit by 1-digit and 3-digit by 1-digit division problems individually or in pairs, guided by the teacher.
Phase 3: Division by Multiples of 10 (up to 50) (15 minutes) * Teacher Activity:
1. Explain division by 10, 20, 30, 40,
5
0. Start with a clear example like 120 ÷ 10, showing how cancelling a zero from both the dividend and divisor simplifies the problem (12 ÷ 1 = 12).
2. Extend this concept to other multiples of
1
0. Model examples like Division Term: 3rd Term Week: 7 ---
1. Overview and Learning Objectives This topic introduces students to the concept of division beyond basic facts, focusing on dividing larger numbers efficiently. Division is a fundamental arithmetic operation essential for sharing, grouping, and solving various real-life problems. In the Nigerian context, understanding division is crucial for everyday activities such as sharing resources (e.g., food items, money) among family members or community groups, calculating costs per item in markets, or distributing goods. Upon completion of this lesson, students will be able to: Divide two or three-digit numbers by single-digit numbers (up to 9), accurately determining the quotient and any remainder. Divide two or three-digit numbers by multiples of 10 (up to 50), understanding how to handle zeros and find exact or approximate quotients. Solve practical word problems that require the application of division skills, connecting mathematical concepts to daily Nigerian experiences. These objectives are directly applicable to situations like sharing bags of rice among several families in a community, calculating how many bottles of palm oil can be bought with a certain amount of money, or determining how many market stalls can be served by a hawker with a specific number of goods.
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 division is called the quotient. If a number cannot be divided equally, the leftover amount is called the remainder.
Dividend: The total quantity to be divided.
Divisor: The number by which the dividend is divided (the number of groups or the size of each group).
Quotient: The result of the division (the number in each group or the number of groups).
Remainder: The amount left over after dividing as evenly as possible. The remainder must always be less than the divisor.
Method: Long Division Long division is a systematic method for dividing larger numbers, especially when mental calculation is difficult.
It involves a series of steps: Divide, Multiply, Subtract, Bring Down. A. Dividing Two or Three-Digit Numbers by Numbers up to 9 (with or without remainder) This involves applying the long division method. Students should have a firm grasp of multiplication facts up to 9 x
9. Worked Example 1: Dividing a 2-digit number by a 1-digit number (no remainder)
Problem: A farmer harvested 96 oranges. He wants to pack them equally into 8 baskets. How many oranges will be in each basket? (96 ÷ 8)
Solution:
1. Set up: ``` ____ 8 | 96 ```
2. Divide the first digit of the dividend (9) by the divisor (8): How many 8s are in 9? One (1). Write '1' above the '9' in the quotient. ``` 1___ 8 | 96 ```
3. Multiply the quotient digit (1) by the divisor (8): 1 × 8 =
8. Write '8' below the '9'. ``` 1___ 8 | 96 8 ```
4. Subtract 8 from 9: 9 - 8 =
1. Write '1' below the '8'. ``` 1___ 8 | 96 8 --- 1 ```
5. Bring down the next digit of the dividend (6) beside the remainder (1): This forms the new number '16'. ``` 1___ 8 | 96 8 --- 16 ```
6. Repeat the process (Divide, Multiply, Subtract, Bring Down): Divide: How many 8s are in 16? Two (2). Write '2' next to the '1' in the quotient. ``` 12__ 8 | 96 8 --- 16 ``` Multiply: 2 × 8 =
1
6. Write '16' below the '16'. ``` 12__ 8 | 96 8 --- 16 16 ``` Subtract: 16 - 16 =
0. Write '0' below the '16'. ``` 12__ 8 | 96 8 --- 16 16 --- 0 ``` The remainder is
0. So, 96 ÷ 8 =
1
2. Each basket will have 12 oranges.
Worked Example 2: Dividing a 3-digit number by a 1-digit number (with remainder)
Problem: A baker made 457 loaves of bread. He wants to supply them equally to 6 shops. How many loaves will each shop