Lesson Notes By Weeks and Term v3 - Primary 3
Division
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Division
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Subject: General Mathematics
Class: Primary 3
Term: 1st Term
Week: 4
Theme: Basic Operations
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Watch on YouTubedivide whole numbers not exceeding 48 by 2, 3, 4, 5 and 6 with out remainder; express whole numbers not exceeding 48 as products of factors; find a missing factor in a given numbers; distinguish between factors and multiples; carry out correct division in everyday activities.
This section provides detailed explanations of the core concepts related to division, factors, and multiples, accompanied by Nigerian-contextualized examples. A. Division as Sharing and Grouping Division is the process of distributing a number of items into equal parts or groups. It answers the question "How many groups?" or "How many in each group?".
Sharing: This involves distributing a total quantity equally among a given number of people or containers. The result is the quantity each person or container receives.
Example: A farmer has 24 oranges and wants to share them equally among 4 children. How many oranges does each child get?
To solve: Distribute 24 oranges one by one to 4 children until all are given out.
Calculation: 24 ÷ 4 =
6. Each child gets 6 oranges.
Grouping: This involves taking a certain number of items at a time from a larger set to form groups. The result is the number of groups formed.
Example: A seamstress has 30 buttons. If she sews 5 buttons on each dress, how many dresses can she make?
To solve: Keep taking out groups of 5 from 30 until nothing is left.
Calculation: 30 ÷ 5 =
6. She can make 6 dresses. B. Division as Repeated Subtraction Division can also be understood as repeatedly subtracting the divisor from the dividend until the result is zero or less than the divisor. The number of times the subtraction occurs is the quotient.
Example: Divide 18 by 3 using repeated subtraction. 18 - 3 = 15 (1st subtraction) 15 - 3 = 12 (2nd subtraction) 12 - 3 = 9 (3rd subtraction) 9 - 3 = 6 (4th subtraction) 6 - 3 = 3 (5th subtraction) 3 - 3 = 0 (6th subtraction) Since 3 was subtracted 6 times, 18 ÷ 3 =
6. C. Factors of a Number Factors are whole numbers that divide another number exactly, without leaving a remainder. When two or more factors are multiplied together, they form a product.
How to find factors: Systematically test numbers starting from 1 up to the square root of the number (or simply up to the number itself for small numbers), checking for exact division.
Example 1: Find the factors of 12. 12 ÷ 1 = 12 (1 and 12 are factors) 12 ÷ 2 = 6 (2 and 6 are factors) 12 ÷ 3 = 4 (3 and 4 are factors) 12 ÷ 4 = 3 (already found) The factors of 12 are 1, 2, 3, 4, 6, and
1
2. Example 2: Express 20 as a product of factors. 20 = 1 x 20 20 = 2 x 10 20 = 4 x 5 The pairs (1,20), (2,10), (4,5) are factor pairs of
2
0. D. Multiples of a Number Multiples are the results of multiplying a number by other whole numbers (e.g., 1, 2, 3, 4...). They are essentially the numbers in the multiplication table of a given number.
How to find multiples: Multiply the given number by consecutive whole numbers.
Example: Find the first 5 multiples of 4. 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 The first 5 multiples of 4 are 4, 8, 12, 16,
2
0. E. Distinguishing Between Factors and Multiples Factors divide a number exactly. They are usually smaller than or equal to the number itself. (e.g., Factors of 10 are 1, 2, 5, 10). Multiples are products of a number. They are usually larger than or equal to the number itself. (e.g., Multiples of 10 are 10, 20, 30, 40...). F. Finding a Missing Factor If a product and one of its factors are known, division can be used to find the missing factor.
Concept: If `Factor 1 × Factor 2 = Product`, then `Product ÷ Factor 1 = Factor 2`. *Example 1: Find the missing factor in 5 x ? = number itself. (e.g., Factors of 10 are 1, 2, 5, 10). Multiples are products of a number. They are usually larger than or equal to the number itself. (e.g., Multiples of 10 are 10, 20, 30, 40...). F. Finding a Missing Factor If a product and one of its factors are known, division can be used to find the missing factor.
Concept: If `Factor 1 × Factor 2 = Product`, then `Product ÷ Factor 1 = Factor 2`.
Example 1: Find the missing factor in 5 x ? =
3
5. To find the missing factor, divide the product (35) by the known factor (5). 35 ÷ 5 =
7. So, the missing factor is 7. (5 x 7 = 35).
Example 2: A tailor uses 6 metres of fabric for each school uniform. If she used a total of 42 metres, how many uniforms did she make? (6 x ? = 42). 42 ÷ 6 = 7. * She made 7 uniforms. ? = 21 ? x 5 = 45 6 x ? = 42
F. Activity 5: Distinguishing Between Factors and Multiples (10 minutes)
Teacher Activity: Clearly defines and contrasts factors and multiples using simple language and examples already covered. "Remember, factors divide a number. Multiples are what you get when you multiply a number." Gives examples: "Is 4 a factor of 12 or a multiple of 12?" "Is 20 a factor of 5 or a multiple of 5?" Student Activity: Students respond to teacher's questions. Teacher writes two numbers (e.g., 6 and 18) and asks students to identify which is a factor/multiple of the other. Students categorize given numbers into "Factors of X" or "Multiples of Y".
G. Conclusion and Recap (5 minutes) The teacher summarizes the key concepts covered: division by sharing/grouping, repeated subtraction, factors, multiples, and finding missing factors. The teacher poses quick revision questions to check understanding.
Materials: Bottle tops, stones, beans, chalk, chalkboard, flashcards with multiplication facts, rectangular grids or squared paper.
A. Introduction (10 minutes)
1. Recall Multiplication: The teacher displays flashcards of basic multiplication facts (e.g., 4 x 5 = ?, 6 x 3 = ?). Students chorally or individually state the answers.
2. Link to Division: The teacher explains that division is the opposite of multiplication. If 4 x 5 = 20, then 20 ÷ 5 = 4 and 20 ÷ 4 = 5.
3. Real-Life Context: The teacher asks students about situations where they share things (sweets, kolanuts, money, textbooks). This initiates the idea of fair sharing, which is division.
B. Activity 1: Division by Sharing/Grouping (20 minutes)
Teacher Activity: Demonstrates sharing using concrete objects. For example, "I have 12 bottle tops and I want to share them equally among 3 groups." The teacher physically distributes the bottle tops, one by one, into three designated areas.
Demonstrates grouping: "I have 15 beans. I want to put them into groups of
5. How many groups can I make?" The teacher counts out groups of 5 beans. Explains how to record this on the board (e.g., 12 ÷ 3 = 4).
Student Activity: Students work in small groups with their own sets of manipulatives (stones, beans). Teacher provides various division problems (not exceeding 48, by 2, 3, 4, 5, 6). "Share 18 stones equally among 3 friends." "Make groups of 4 from 24 beans. How many groups?" Students physically perform the sharing/grouping and state their answers.
C. Activity 2: Division by Repeated Subtraction (15 minutes)
Teacher Activity: Explains division as taking away equal groups repeatedly until none are left. Demonstrates on the chalkboard with an example like 20 ÷ 4. 20 - 4 = 16 16 - 4 = 12 12 - 4 = 8 8 - 4 = 4 4 - 4 = 0 (Counted 5 subtractions, so 20 ÷ 4 = 5).
Student Activity: Students practice 2-3 examples on their exercise books using repeated subtraction. "Divide 27 by 3 using repeated subtraction." "Calculate 36 ÷ 6 using repeated subtraction."
D. Activity 3: Expressing Numbers as Products of Factors (15 minutes)
Teacher Activity: Introduces the term "factor." Explains that factors are numbers that multiply together to give another number (the product). Demonstrates using a rectangular pattern on the chalkboard or grid paper. For example, for 12: 1 row of 12 (1 x 12) 2 rows of 6 (2 x 6) 3 rows of 4 (3 x 4) Lists the factors of 12 (1, 2, 3, 4, 6, 12). Provides examples within 48, asking "What numbers can we multiply to get 24?" Student Activity: Students work in pairs. Each pair is given a number (e.g., 18, 30, 40) and asked to draw rectangular patterns on grid paper or identify factor pairs using multiplication knowledge. Students list the factors for their assigned number.
E. Activity 4: Finding Missing Factors (10 minutes)
Teacher Activity: Explains that if we know the total (product) and one part (factor), we can find the missing part by dividing.
Presents problems like: "4 x ? = 28". Explains that this is asking "28 divided by 4 is what?".
Demonstrates how to solve: ? = 28 ÷ 4 =
7. Student Activity: Students solve various missing factor problems provided by the teacher on the chalkboard or as a quick quiz. 3 x ? = 21 ? x 5 = 45 6 x ? = 42
F. Activity 5: Distinguishing Between Factors and Multiples (10 minutes)
Teacher Activity: Clearly defines and contrasts factors and multiples using simple language and examples already covered. "Remember, factors divide a number. Multiples are what you get when you multiply a number." Gives examples: "Is 4 a factor of 12 or a multiple of 12?" "Is 20 a factor of 5 or a multiple of 5?" Student Activity: Students respond to teacher's
Sharing Food and Resources: In many Nigerian homes and communities, division is used daily for sharing food items like rice, garri, or yams among family members or during community events. Students can relate to sharing biscuits with siblings or distributing water sachets during a hot day.
Example: A mother has 18 boiled eggs and wants to share them equally among her 3 children for breakfast. Division helps her determine that each child gets 6 eggs (18 ÷ 3 = 6).
Market Activities and Costing: When buying items in bulk or calculating unit prices, division is crucial. Market women often divide a large sack of beans or rice into smaller, equal portions for sale.
Example: If 5 tubers of yam cost N1500, how much does one tuber cost? (N1500 ÷ 5 = N300). This helps a buyer know the fair price of a single yam.
Organizing and Grouping Items: In schools, churches, or community gatherings, items like chairs, books, or sports equipment often need to be arranged in equal groups or rows.
Example: If a teacher has 30 exercise books and wants to put them into piles of 6 for each group, division tells her she will have 5 piles (30 ÷ 6 = 5).