Lesson Notes By Weeks and Term v3 - Primary 5
Division
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Division
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Subject: General Mathematics
Class: Primary 5
Term: 1st Term
Week: 4
Theme: Numbers And Numeration
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Watch on YouTubeSee Facebook postdivide numbers by 10 and multiples of 10 up to 90 solve quantitative aptitude problems in volving division of number by 10 and multiples of 10 up to 900 divide numbers by 100 and 200
does not end in two zeros (or any zeros at all), imagine a decimal point at the end of the whole number and move it two places to the left.
Example: 650 ÷ 100 = 6.50 = 6.5
Example: 1,234 ÷ 100 = 12.34 Worked Example 3 (Division by 100): The sum of ₦9,800 was equally distributed among 100 villagers affected by flooding. How much did each villager receive?
Solution: Total sum = ₦9,800 Number of villagers = 100 Amount per villager = ₦9,800 ÷ 100 Using Strategy 1: Remove two zeros from 9,800. ₦9,800 ÷ 100 = ₦98 Therefore, each villager received ₦
9
8. Division by 200: To divide a number by 200: Strategy (Step-by-step): Divide the number first by 100, then divide the result by
2. Example: 4,600 ÷ 200 Step 1: 4,600 ÷ 100 = 46 (remove two zeros).
Step 2: 46 ÷ 2 = 23 So, 4,600 ÷ 200 = 23
Example: 7,000 ÷ 200 Step 1: 7,000 ÷ 100 = 70 Step 2: 70 ÷ 2 = 35 So, 7,000 ÷ 200 = 35 Worked Example 4 (Division by 200): A poultry farmer produced 12,400 eggs in a week. He packs them into crates, with each crate holding 200 eggs. How many crates did he fill?
Solution: Total eggs = 12,400 Eggs per crate = 200 Number of crates = 12,400 ÷ 200 Step 1: Divide by 100: 12,400 ÷ 100 = 124 (remove two zeros).
Step 2: Divide by 2: 124 ÷ 2 =
6
2. Therefore, the farmer filled 62 crates. Quantitative Aptitude Problems involving Division: These problems often present a series of numbers or a pattern where division by 10 or multiples of 10/100/200 is required to find the missing term or complete the sequence. The key is to identify the operation and apply the appropriate division strategy.
Worked Example 5 (Quantitative Aptitude): Complete the sequence: 500, 50, \_\_\_, 0.5 Solution: Observe the pattern: 500 to 50 involves division by 10 (500 ÷ 10 = 50). The next number should be 50 ÷ 10 =
5. Check if 5 ÷ 10 = 0.
5. Yes, it does.
Therefore, the missing number is 5. --- Definition of Division: Division is the process of splitting a number into equal parts or groups. It is the inverse operation of multiplication.
Dividend: The number being divided (the total amount).
Divisor: The number by which the dividend is divided (the number of equal parts or the size of each part).
Quotient: The result of the division.
Remainder: Any amount left over after the division.
Division by 10: To divide a whole number by 10: Strategy 1 (Removing Zero): If the number ends in zero, simply remove one zero from the end of the number. This is equivalent to shifting the decimal point one place to the left.
Example: 450 ÷ 10 = 45 (remove the last zero).
Example: 1,200 ÷ 10 = 120 (remove the last zero).
Strategy 2 (Decimal Point Shift): If the number does not end in zero, imagine a decimal point at the end of the whole number and move it one place to the left.
Example: 75 ÷ 10 = 7.5
Example: 123 ÷ 10 = 12.3 Worked Example 1 (Division by 10): A trader at Onitsha Main Market bought 350 oranges and wants to pack them equally into 10 baskets. How many oranges will be in each basket?
Solution: Number of oranges = 350 Number of baskets = 10 Oranges per basket = 350 ÷ 10 Using Strategy 1: Remove one zero from 350. 350 ÷ 10 = 35 Therefore, there will be 35 oranges in each basket.
Division by Multiples of 10 (up to 90): To divide a number by a multiple of 10 (e.g., 20, 30, 40, ..., 90): Strategy 1 (Step-by-step): Divide the number first by 10, then divide the result by the remaining digit (2, 3, 4, etc.).
Example: 600 ÷ 20 Step 1: 600 ÷ 10 = 60 Step 2: 60 ÷ 2 = 30 So, 600 ÷ 20 = 30
Example: 1,800 ÷ 30 Step 1: 1,800 ÷ 10 = 180 Step 2: 180 ÷ 3 = 60 So, 1,800 ÷ 30 = 60 Strategy 2 (Cancel Zeros): If both the dividend and the divisor end in zeros, cancel out an equal number of zeros from both, then perform the division.
Example: 800 ÷ 40 Cancel one zero from 800 and one zero from
4
0. This simplifies the problem to 80 ÷ 4. 80 ÷ 4 = 20 So, 800 ÷ 40 = 20 Worked Example 2 (Division by Multiples of 10): A farmer harvested 720 tubers of yam and wants to sell them in bundles of 30 tubers each. How many bundles can he make?
Solution: Total tubers of yam = 720 Tubers per bundle = 30 Number of bundles = 720 ÷ 30 Using Strategy 2 (cancel zeros): Cancel one zero from 720 and one zero from
3
0. The problem becomes 72 ÷ 3. 72 ÷ 3 = 24 Therefore, the farmer can make 24 bundles of yam.
Division by 100: To divide a whole number by 100: Strategy 1 (Removing Zeros): If the number ends in two zeros, remove two zeros from the end of the number. This is equivalent to shifting the decimal point two places to the left.
Example: 5,000 ÷ 100 = 50 (remove the last two zeros).
Example: 2,300 ÷ 100 = 23 (remove the last two zeros).
Strategy 2 (Decimal Point Shift): If the number does not end in two zeros (or any zeros at all), imagine a decimal point at the end of the whole number and move it two places to the left.
Example: 650 ÷ 100 = 6.50 = 6.5
Example: 1,234 ÷ 100 = 12.34 Worked Example 3 (Division by 100): The sum of ₦9,800 was equally distributed among 100 villagers affected by flooding. How much did each villager receive?
Solution: Total sum = ₦9,800 Number of villagers = 100 * Amount per villager = ₦9,800 ÷ 100 Teacher Activities: Introduction/Review (10 minutes): Begin by reviewing basic division concepts and terms (dividend, divisor, quotient, remainder) using simple examples (e.g., 20 ÷ 4).
Pose a quick question: "If you have 60 sweets and share them among 10 friends, how many does each friend get?" (Encourage mental calculation or quick method). Introduce the topic of division by 10, multiples of 10, 100, and 200, highlighting its efficiency. Explanation and Demonstration (20 minutes): Division by 10: Explain and demonstrate the "remove zero" and "shift decimal point" methods with examples (e.g., 470 ÷ 10, 85 ÷ 10). Use a place value chart if available to visually show the shift.
Division by Multiples of 10 (up to 90): Explain the "divide by 10 then by the digit" method and the "cancel zeros" method. Demonstrate with examples like 120 ÷ 20, 900 ÷ 30, 2,800 ÷
7
0. Emphasize that canceling zeros is a shortcut for dividing by
1
0. Division by 100: Explain and demonstrate the "remove two zeros" and "shift decimal point two places" methods with examples (e.g., 5,600 ÷ 100, 345 ÷ 100).
Division by 200: Explain the step-by-step method (divide by 100, then by 2). Demonstrate with examples like 6,400 ÷ 200, 10,800 ÷
2
0
0. Quantitative Aptitude: Show an example of a sequence or pattern problem requiring these division skills.
Guided Practice (15 minutes): Provide a few problems for students to solve in pairs or small groups. Circulate to provide support and assess understanding.
Example 1:* If 150 textbooks are to be shared equally among 10 classes, how many will each class get? (Div by 10)
Example 2:* A cooperative society made a profit of ₦2,700 and shared it among 30 members. How much did each member get? (Div by multiples of 10)
Example 3:* A company has ₦45,000 to divide equally among 100 employees. How much does each employee receive? (Div by 100)
Example 4:* 8,600 bags of rice are to be packed into cartons, each holding 200 bags. How many cartons are needed? (Div by 200)
Addressing Misconceptions: Clarify that when canceling zeros, an equal number of zeros must be cancelled from both the dividend and the divisor. Reiterate that for numbers not ending in zeros, decimal point shifting is key.
Student Activities: Participate in Review: Respond to questions during the introduction, sharing prior knowledge.
Active Listening and Note-Taking: Pay close attention to teacher explanations and demonstrations, noting down key strategies and examples.
Collaborative Problem Solving: Work with peers to solve guided practice problems, discussing strategies and solutions.
Questioning: Ask questions when concepts are unclear.
Individual Practice: Attempt independent practice questions. --- Question 1: A community health centre received ₦7,500 to buy drugs for 10 local dispensaries. If the money is shared equally, how much will each dispensary get?
Solution: Total money = ₦7,500 Number of dispensaries = 10 Money per dispensary = ₦7,500 ÷ 10 Using the "remove zero" method: ₦7,500 becomes ₦
7
5
0. Answer: Each dispensary will get ₦
7
5
0. Commentary: This question directly assesses division by 10, using a relevant financial context. The "remove zero" method is the most efficient here.
Question 2: If 4,800 sachets of pure water are to be distributed among 60 street hawkers, how many sachets will each hawker receive?
Solution: Total sachets = 4,800 Number of hawkers = 60 Sachets per hawker = 4,800 ÷ 60 Using the "cancel zeros" method: Cancel one zero from 4,800 and one zero from
6
0. The problem simplifies to 480 ÷ 6. 480 ÷ 6 = 80 Answer: Each hawker will receive 80 sachets of pure water.
Commentary: This problem targets division by a multiple of
1
0. The "cancel zeros" method simplifies the calculation significantly.
Question 3: What is the missing number in the sequence: 9,000, 900, \_\_\_, 9?
Solution: Observe the pattern: 9,000 ÷ 10 = 900 The pattern is division by
1
0. Apply the pattern to the next term: 900 ÷ 10 =
9
0. Check the next term: 90 ÷ 10 =
9. The pattern holds.
Answer: The missing number is
9
0. Commentary: This is a quantitative aptitude problem that requires identifying a pattern involving division by
1
0. Question 4: A cattle ranch produces 15,000 litres of milk monthly. If the milk is packaged into containers of 100 litres each for distribution, how many containers are needed?
Solution: Total milk = 15,000 litres Volume per container = 100 litres Number of containers = 15,000 ÷ 100 Using the "remove two zeros" method: 15,000 becomes
1
5
0. Answer: 150 containers are needed.
Commentary: This question assesses division by
1
0
0. It's a direct application of removing two zeros for efficient calculation.
Question 5: A large consignment of 28,000 kilograms of fertiliser needs to be repackaged into bags of 200 kilograms each for sale to farmers. How many bags of fertiliser will there be?
Solution: Total fertiliser = 28,000 kg Weight per bag = 200 kg Number of bags = 28,000 ÷ 200 Step 1 (Divide by 100): 28,000 ÷ 100 = 280 (remove two zeros).
Step 2 (Divide by 2): 280 ÷ 2 =
1
4
0. Answer: There will be 140 bags of fertiliser.
Commentary: This problem assesses division by 200, requiring a two-step approach: dividing by 100, then by 2. ---
Market Price Calculation: Students can practice calculating unit prices. If 50 kilogrammes of garri costs ₦10,000 at the market, a buyer might want to know the price per kilogramme (₦10,000 ÷ 50 = ₦200 per kg). This helps them make informed purchasing decisions and identify fair prices.
Community Resource Allocation: Imagine a community receives 3,000 doses of a vaccine, and there are 20 primary health centres to distribute them to. Students can calculate how many doses each centre receives (3,000 ÷ 20 = 150 doses). This demonstrates fair distribution and resource management.
School/Classroom Organisation: If a school has 1,200 pupils and wants to divide them into 40 classes, students can calculate the number of pupils per class (1,200 ÷ 40 = 30 pupils per class). This helps in understanding classroom planning and student-teacher ratios. ---