Lesson Notes By Weeks and Term v3 - Primary 6
Addition and Subtraction
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Addition and Subtraction
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Subject: General Mathematics
Class: Primary 6
Term: 2nd Term
Week: 4
Theme: Basic Operations
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Add any set of numbers; Solve problems on subtraction of whole numbers; Solve word problems in volving addition and subtraction of whole numbers.
money is remaining?
Solution Steps:
1. Align by Place Value: Write the numbers vertically, ensuring digits of the same place value are in the same column. ``` 7,500,000 - 3,875,420 ------------ ```
2. Subtract the Units Column: 0 - 0 =
0. Write 0. ``` 7,500,000 - 3,875,420 ------------ 0 ```
3. Subtract the Tens Column: 0 -
2. Cannot subtract. Borrow from the next non-zero digit to the left. The nearest non-zero digit is 5 in the hundred thousands place. Borrow 1 from 5 (making it 4). This 1 becomes 10 in the ten thousands place. Borrow 1 from 10 (making it 9). This 1 becomes 10 in the thousands place. Borrow 1 from 10 (making it 9). This 1 becomes 10 in the hundreds place. Borrow 1 from 10 (making it 9). This 1 becomes 10 in the tens place. Now, the top number effectively becomes: 7,499,9(10)00. ``` 7,4 999 (10)00 - 3,875,420 ------------ ``` Now, 10 - 2 =
8. Write 8. ``` 7,4 999 (10)00 - 3,875,420 ------------ 80 ```
4. Subtract the Hundreds Column: 9 - 4 =
5. Write 5. ``` 7,4 999 (10)00 - 3,875,420 ------------ 580 ```
5. Subtract the Thousands Column: 9 - 5 =
4. Write 4. ``` 7,4 999 (10)00 - 3,875,420 ------------ 4,580 ```
6. Subtract the Ten Thousands Column: 9 - 7 =
2. Write 2. ``` 7,4 999 (10)00 - 3,875,420 ------------ 24,580 ```
7. Subtract the Hundred Thousands Column: 4 -
8. Cannot subtract. Borrow 1 from 7 in the millions place (making it 6). The 1 becomes 10, adding to 4 makes it 14. ``` 6 14 7,4 999 (10)00 - 3,875,420 ------------ ``` Now, 14 - 8 =
6. Write 6. ``` 6 14 7,4 999 (10)00 - 3,875,420 ------------ 624,580 ```
8. Subtract the Millions Column: 6 - 3 =
3. Write 3. ``` 6 14 7,4 999 (10)00 - 3,875,420 ------------ 3,624,580 ``` Answer: The remaining money for road construction is ₦3,624,
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0. C. Solving Word Problems Involving Addition and Subtraction Strategy for Word Problems:
1. Read and Understand: Read the problem carefully, multiple times if necessary. Identify what information is given and what needs to be found.
2. Identify Keywords: Look for words that indicate addition (e.g., total, sum, in all, altogether, increased by, combined) or subtraction (e.g., difference, remaining, how many left, decreased by, how much more/less).
3. Plan the Steps: For multi-step problems, break them down into smaller, manageable parts. Determine the order of operations.
4. Perform Operations: Execute the addition and/or subtraction accurately.
5. Check and State Answer: Review the calculation and ensure the answer makes sense in the context of the problem. State the final answer clearly with appropriate units.
Worked Example 3: Word Problem (Addition and Subtraction)
Problem: A farmer harvested 4,500 tubers of yam in the first season and 3,870 tubers in the second season. He sold 6,250 tubers in total. How many tubers of yam are left with the farmer?
Solution Steps:
1. Step 1: Find the total number of yams harvested (Addition).
Yams from first season: 4,500 Yams from second season: 3,870 Total harvested = 4,500 + 3,870 ``` 4,500 + 3,870 ---------- 8,370 ``` Total yams harvested = 8,370 tubers.
2. Step 2: Find the number of yams remaining after selling (Subtraction).
Total harvested: 8,370 Yams sold: 6,250 * Yams left = 8,370 - 6,250 ``` 8,370 - 6,250 ---------- 2,120 ``` Answer: The farmer has 2,120 tubers of yam left. This section provides a detailed explanation of the core concepts, methods, and strategies for teaching addition and subtraction of whole numbers, including worked examples relevant to the Nigerian context.
A. Addition of Whole Numbers Definition: Addition is the process of combining two or more numbers (addends) to find their total sum. It represents an increase or accumulation.
Terms: Addends: The numbers being added together.
Sum/Total: The result obtained after adding the numbers.
Key Principle: Addition is performed by aligning numbers according to their place value (units under units, tens under tens, hundreds under hundreds, etc.) and adding from right to left (from the least significant digit to the most significant).
Carrying Over (Regrouping): When the sum of digits in a particular place value column exceeds 9, the 'tens' part of the sum is carried over (regrouped) to the next higher place value column.
Worked Example 1: Addition of Large Numbers Problem: A community raised ₦1,452,385 for a borehole project and later received a grant of ₦975,
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0. What is the total amount of money raised for the project?
Solution Steps:
1. Align by Place Value: Write the numbers vertically, ensuring digits of the same place value are in the same column. ``` 1,452,385 + 975,860 ------------ ```
2. Add the Units Column: 5 + 0 =
5. Write 5 in the units column. ``` 1,452,385 + 975,860 ------------ 5 ```
3. Add the Tens Column: 8 + 6 =
1
4. Write 4 in the tens column and carry over 1 to the hundreds column. ``` 1 1,452,385 + 975,860 ------------ 45 ```
4. Add the Hundreds Column (including carry-over): 3 + 8 + 1 (carry-over) =
1
2. Write 2 in the hundreds column and carry over 1 to the thousands column. ``` 11 1,452,385 + 975,860 ------------ 245 ```
5. Add the Thousands Column (including carry-over): 2 + 5 + 1 (carry-over) =
8. Write 8 in the thousands column. ``` 11 1,452,385 + 975,860 ------------ 8,245 ```
6. Add the Ten Thousands Column: 5 + 7 =
1
2. Write 2 in the ten thousands column and carry over 1 to the hundred thousands column. ``` 111 1,452,385 + 975,860 ------------ 28,245 ```
7. Add the Hundred Thousands Column (including carry-over): 4 + 9 + 1 (carry-over) =
1
4. Write 4 in the hundred thousands column and carry over 1 to the millions column. ``` 1111 1,452,385 + 975,860 ------------ 428,245 ```
8. Add the Millions Column (including carry-over): 1 + 1 (carry-over) =
2. Write 2 in the millions column. ``` 1111 1,452,385 + 975,860 ------------ 2,428,245 ``` Answer: The total amount of money raised is ₦2,428,
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5. B.
Subtraction of Whole Numbers Definition: Subtraction is the process of finding the difference between two numbers. It represents a decrease, taking away, or comparing quantities.
Terms: Minuend: The number from which another number is subtracted (the larger number).
Subtrahend: The number being subtracted (the smaller number).
Difference: The result obtained after subtracting one number from another.
Key Principle: Subtraction is performed by aligning numbers according to their place value and subtracting from right to left.
Borrowing (Regrouping): When a digit in the minuend is smaller than the corresponding digit in the subtrahend, it is necessary to 'borrow' or 'regroup' from the next higher place value column. This involves decreasing the digit in the higher place value by 1 and increasing the current digit by
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0. Worked Example 2: Subtraction of Large Numbers Problem: A state government budgeted ₦7,500,000 for road construction. If ₦3,875,420 has already been spent, how much money is remaining?
Solution Steps:
1. Align by Place Value: Write the numbers vertically, ensuring digits of the same place value are in the same column. ``` 7,500,000 - 3,875,420 ------------ ```
2. Subtract the Units Column: 0 - 0 =
0. Write 0. ``` 7,500,000 - 3,875,420 ------------ 0 ```
3. Subtract the Tens Column: 0 -
2. Cannot subtract. Borrow from the next non-zero digit to the left. The nearest non-zero digit is 5 in the hundred thousands place. Borrow 1 from 5 (making it 4). This 1 becomes This section outlines practical activities for effective delivery of the lesson.
A. Teacher Activities: Review and Introduction: Begin by reviewing students' prior knowledge of place value and basic addition/subtraction of smaller numbers (up to thousands). Introduce the topic by presenting a relatable problem, e.g., "If a market woman buys goods worth ₦50,000 and sells for ₦75,000, how much profit did she make? Then she spent ₦10,000 on transport. How much is left?" State the learning objectives clearly (using the learner-friendly versions). Concept Explanation and Demonstration (Refer to Section 2): Use a large chalkboard or whiteboard to demonstrate column addition and subtraction with large numbers step-by-step, explicitly showing carrying and borrowing procedures. Employ place value charts or visual aids to illustrate the concept of regrouping (carrying/borrowing). Use local currency notes or bundles of sticks to represent place values if available.
Highlight key vocabulary: addends, sum, minuend, subtrahend, difference.
Guided Practice (Refer to Section 4): Work through several examples together as a class, encouraging student participation in each step. For word problems, guide students to identify keywords and plan the solution steps before calculating.
Facilitation and Monitoring: Organize students into small groups for collaborative problem-solving. Circulate around the classroom, providing support, checking for understanding, and correcting misconceptions. Encourage peer-teaching and discussion among students.
Feedback and Review: Provide constructive feedback on students' work. Address common errors observed during practice sessions. Summarize key learning points at the end of the lesson.
B. Student Activities: Active Participation: Participate in warm-up exercises and quick mental arithmetic. Engage in discussions by answering questions and contributing ideas during concept explanation.
Individual and Group Practice: Solve addition and subtraction problems individually in their notebooks. Work collaboratively in groups to solve assigned problems, especially word problems, discussing strategies and solutions. Present their solutions on the board and explain their reasoning to the class.
Problem Solving: Analyze word problems, identify the necessary operations, and plan their solution steps. Apply the learned column methods for addition and subtraction.
Self-Correction and Peer Assessment: Check their own work and correct errors based on teacher feedback or peer review. Provide constructive feedback to classmates during group activities.
Real-world Connections: Discuss how addition and subtraction are used in their daily lives or within their local community (e.g., market transactions, community budgeting, counting livestock). This section provides scaffolded practice questions for the teacher to work through with students.
Question 1 (Addition): A local government council constructed two new primary schools. The first school cost ₦12,580,340 and the second school cost ₦9,756,
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5. What is the total cost of building both schools?
Solution: To find the total cost, add the costs of the two schools. ``` 111111 12,580,340 (Cost of first school) + 9,756,895 (Cost of second school) 22,337,235 ```
Commentary: Emphasize careful alignment of place values and managing carry-overs, especially across the millions digit.
Question 2 (Subtraction): The population of a city in Nigeria was 5,234,700 people. Due to migration, 1,859,325 people moved out of the city. What is the current population of the city?
Solution: To find the current population, subtract the number of people who moved out from the original population. ``` 4 11 12 14 6 9 10 5,234,700 (Original population) 1,859,325 (People who moved out) 3,375,375 ```
Commentary: This example requires multiple borrowing steps. Guide students to clearly mark changes to digits when borrowing. Question 3 (Word Problem - Mixed Operations): A farmer harvested 3,500 bags of maize and 2,850 bags of guinea corn. He sold 4,100 bags of maize and 1,980 bags of guinea corn. How many bags of crops does he have left in total?
Solution: Step 1: Calculate total maize harvested and sold (Maize remaining).
Harvested maize: 3,500 bags Sold maize: 4,100 bags (This scenario suggests the farmer sold more than harvested, or the question implies selling from a previous stock. For simplicity and to fit the problem scope, let's assume the question meant he had 3500 bags and sold 2850 bags of maize. Let's rephrase for clarity or adjust calculation).
Self-correction: The problem implies "he sold 4,100 bags of maize" which is more than harvested. This is an error in the question phrasing for a typical P6 problem where stock is created by harvest then reduced by sale. Let's assume the question meant "he sold 2,850 bags of maize and 1,980 bags of guinea corn from his total harvest of 3,500 bags of maize and 2,850 bags of guinea corn." This makes more sense. Revised Question 3 (Word Problem - Mixed Operations): A farmer harvested 3,500 bags of maize and 2,850 bags of guinea corn. He sold 2,800 bags of maize and 1,900 bags of guinea corn. How many bags of crops does he have left in total?
Solution (Revised Q3): Step 1: Calculate remaining maize.
Maize harvested: 3,500 bags Maize sold: 2,800 bags Maize left = 3,500 - 2,800 = 700 bags Step 2: Calculate remaining guinea corn.
Guinea corn harvested: 2,850 bags Guinea corn sold: 1,900 bags Guinea corn left = 2,850 - 1,900 = 950 bags Step 3: Calculate total bags of crops left. Total left = Maize left + Guinea corn left Total left = 700 + 950 = 1,650 bags
Commentary: Guide students to break down the problem into logical steps: first calculate remaining quantities of each item, then add them up for the final total. Emphasize carefully reading the question to avoid misinterpretation of quantities (as I just did!).
This topic is highly applicable to various aspects of Nigerian life, fostering practical numeracy skills.
Market Transactions and Personal Finance: Application: Students can calculate the total cost of goods purchased at a local market (e.g., adding the prices of yam, rice, and vegetables). They can also calculate the change received after a purchase, or determine if they have enough money for several items.
Local Context: A parent sends a child to buy items from the 'keke' shop. The child needs to calculate the total cost of bread, milk, and sugar, and then subtract from the money given to know the change. This directly applies addition and subtraction of money.
Community Development and Budgeting: Application: Understanding community project finances. For example, a Community Development Association (CDA) collecting levies for a project (e.g., street lights, waste disposal).
Local Context: The CDA collects ₦1,500,000 from residents. They spend ₦800,000 on poles and wires. Later, they receive a grant of ₦500,
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0. Students can calculate the total funds received and the remaining balance after expenses. This teaches financial accountability and planning.
Population and Demographics: Application: Analyzing changes in population figures for states, cities, or even school enrollment.
Local Context: Students can use population data from the National Population Commission (NPC) to compare the total population of two states (e.g., Kano and Lagos) or calculate the increase/decrease in a town's population over a decade by adding births and subtracting deaths/emigration. This integrates mathematics with social studies.