Lesson Notes By Weeks and Term v3 - Primary 1
Subtraction II
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Subtraction II
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Subject: General Mathematics
Class: Primary 1
Term: 1st Term
Week: 10
Theme: Basic Operations
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find missing numbers in a statement; cross-check the correctness of subtraction in everyday life.
Basic Operations buying items. For example, if they pay ₦20 for an item that costs ₦15, they expect ₦5 change. They can cross-check this by adding the cost of the item to the change received (₦15 + ₦5 = ₦20) to ensure it matches the money paid. This is a common and important skill in Nigerian markets.
2. Sharing and Distribution within the Household/Community: This skill is useful when sharing items like food (e.g., groundnuts, fruits) or resources (e.g., pencils, books) among siblings or friends. If there are 10 oranges and 4 are eaten, the child can find how many are left, and also cross-check if the number stated as "eaten" plus "left" equals the original total.
3. Resource Management (Home/School): Children can use subtraction to keep track of supplies. For instance, if a carton contains 12 sachets of water and 5 have been used, they can calculate how many are left. They can also use cross-checking to confirm inventory counts.
4. Traditional Games: Some traditional Nigerian games involve counting and removing items, like "Ayo" (though more complex, the principle of taking away and checking remains).
8. Differentiation, Remediation and Extension
A. Differentiation Strategies: Remediation (for struggling learners):
1. Concrete Manipulatives: Provide an abundance of physical objects (counting sticks, bottle tops, pebbles, beads) for all problems. Allow extended time for them to physically model the subtraction and addition processes to find missing numbers and cross-check.
2. Number Line: Encourage the use of a number line for visual support in counting back (for `Total - ? = Left`) and counting forward (for `? - Taken Away = Left`).
3. Simpler Numbers: Start with smaller numbers (within 5 or 10) for extra practice before progressing to larger numbers (up to 20).
4. Buddy System: Pair struggling learners with more capable peers for peer support and guided practice.
5. Teacher Support: Provide one-on-one or small group instruction, explicitly guiding them through each step with patient questioning.
Extension (for high-achieving learners):
1. Increased Number Range: Challenge them with slightly larger numbers (e.g., within 20 or 30, depending on individual readiness) in their problems.
2. Create Word Problems: Task them with creating their own real-life word problems involving missing numbers or cross-checking, set in Nigerian contexts. They can then swap and solve each other's problems.
3. Multi-Step Problems: Introduce simple two-step problems that involve both addition and subtraction, e.g., "A tailor had 15 buttons. He used 6 for a shirt, then bought 3 more. How many buttons does he have now? Check your first subtraction."
4. Explain to Peers: Have them act as "junior teachers" to explain the concepts to a small group of struggling learners, reinforcing their own understanding.
Subtraction II Term: 1st Term Week: 10 ---
1. Overview and Learning Objectives This topic, Subtraction II, builds upon learners' foundational understanding of subtraction by introducing more complex problem-solving scenarios. It focuses on developing the critical thinking skills required to identify unknown quantities within subtraction statements and to verify the accuracy of subtraction calculations. Mastery of these concepts is crucial for everyday numerical literacy in Nigerian contexts, from verifying change at the market to managing small household budgets. Upon completion of this lesson, students will be able to: Find a missing number in a given subtraction problem (e.g., "If I have 8 oranges and give some away, and now I have 3 left, how many did I give away?"). Check if a subtraction calculation is correct, especially when dealing with transactions or sharing items in daily life (e.g., "When Daddy gives me ₦10 and I buy biscuit for ₦4, the shopkeeper should give me ₦6 change. Is that correct?"). These objectives connect directly to practical real-world applications in Nigeria such as counting change received after purchases, sharing food or items among siblings, keeping track of items consumed from a stock, or verifying simple calculations made by others.
2. Key Concepts and Explanations A. Review of Subtraction Subtraction is the process of taking away a number from another number. It helps to find "how many are left," "how many more/less," or "the difference between" two numbers. The result of subtraction is called the difference. For Primary 1, subtraction is generally introduced with numbers up to 10 or 20, using concrete objects. B. Finding Missing Numbers in Subtraction Statements This concept requires learners to understand the relationship between the numbers in a subtraction problem. There are two main types of missing number problems at this level: Type 1: Missing number is the amount taken away.
Structure: `Total Number - ? = Remaining Number`
Example: `8 - ? = 3` Explanation: The learner knows the starting amount (Total Number) and the ending amount (Remaining Number). To find the missing number (the amount taken away), they can either:
1. Count Back: Start from the Total Number and count back until they reach the Remaining Number, counting how many steps they took.
Illustration: To solve `8 - ? = 3`: Start with 8 objects. Remove objects one by one until 3 are left. Count how many were removed. (8 -> 7 -> 6 -> 5 -> 4 ->
3. Removed: 1, 2, 3, 4, 5). So, `? = 5`.
2. Count Up (from remaining to total): Start from the Remaining Number and count up to the Total Number, counting how many steps were taken.
Illustration: To solve `8 - ? = 3`: Start at
3. Count up to 8: (3 -> 4, 5, 6, 7, 8).
Count the steps: 1, 2, 3, 4,
5. So, `? = 5`.
3. Inverse Operation (more advanced, but can be visualised): Think `Total Number - Remaining Number = Amount Taken Away`.
Illustration: `8 - 3 = 5`.
Worked Example 1 (Type 1): Problem: Musa had 7 mangoes. He ate some and now has 2 mangoes left. How many mangoes did Musa eat? (`7 - ? = 2`)
Step-by-step Solution:
1. Understand: Musa started with 7, ended with
2. The unknown is what he ate.
2. Visualise/Manipulate: Provide 7 physical objects (e.g., bottle tops).
3. Action: Remove objects one by one until 2 are left. Start with 7 bottle tops. Remove 1, 6 left. Remove 1, 5 left. Remove 1, 4 left. Remove 1, 3 left. Remove 1, 2 left.
4. Count: Count how many bottle tops were removed (5 bottle tops).
5. Conclusion: Musa ate 5 mangoes. (`7 - 5 = 2`)
Type 2: Missing number is the original total.
Structure: `? - Amount Taken Away = Remaining Number`
Example: `? - 4 = 5` Explanation: The learner knows how much was taken away and how much is left. To find the original total, they can:
1. Combine (Add): Add the amount taken away to the remaining number. This is the 3 left. Remove 1, 2 left.
4. Count: Count how many bottle tops were removed (5 bottle tops).
5. Conclusion: Musa ate 5 mangoes. (`7 - 5 = 2`)
Type 2: Missing number is the original total.
Structure: `? - Amount Taken Away = Remaining Number`
Example: `? - 4 = 5` Explanation: The learner knows how much was taken away and how much is left. To find the original total, they can:
1. Combine (Add): Add the amount taken away to the remaining number. This is the inverse operation.
Illustration: To solve `? - 4 = 5`: Imagine you have 5 objects left. You know 4 were taken away. If you put those 4 back, you'll get the original total. So, `5 + 4 = 9`.
Using physical objects: Put 5 objects in one group (what's left). Put 4 objects in another group (what was taken away). Combine both groups and count the total.
Worked Example 2 (Type 2): Problem: A tailor had some buttons. He used 3 buttons for a dress and now has 6 buttons left. How many buttons did he have at first? (`? - 3 = 6`)
Step-by-step Solution:
1. Understand: The tailor used 3, and 6 are left. The unknown is the starting number.
2. Visualise/Manipulate: Provide 6 physical objects (what's left) and 3 physical objects (what was used).
3. Action: Combine the two groups of objects. Put 6 stones in one pile. Put 3 stones in another pile. Push the piles together.
4. Count: Count the total number of stones (6 + 3 = 9).
5. Conclusion: The tailor had 9 buttons at first. (`9 - 3 = 6`) C. Cross-checking the Correctness of Subtraction Cross-checking (or verifying) a subtraction means ensuring the answer (difference) is correct. The fundamental principle is that addition is the inverse (opposite) operation of subtraction.
Rule: If `A - B = C`, then `C + B = A`. `A` = Original Total (Minuend) `B` = Amount Taken Away (Subtrahend) `C` = Remaining Amount (Difference)
How to Cross-check:
1. Take the answer (the difference).
2. Add it to the number that was taken away (the subtrahend).
3. If this sum equals the original total (the minuend), then the subtraction is correct.
Worked Example 3 (Cross-checking): Problem: Aisha calculated `10 - 4 = 6`. Is her answer correct?
Step-by-step Solution:
1. Identify: Original Total (A) = 10, Amount Taken Away (B) = 4, Aisha's Answer (C) = 6.
2. Apply Rule: Add Aisha's answer (6) to the amount taken away (4).
3. Calculation: `6 + 4 = 10`.
4. Compare: Does the sum (10) match the original total (10)? Yes, it does.
5. Conclusion: Aisha's subtraction is correct.
Nigerian Context: This is vital for verifying change received at the market, confirming quantities when sharing food at home, or ensuring fairness in distributions within the community. For example, if a seller gives change, a child can add the change to the cost of the item to see if it equals the money they paid.
3. Teaching and Learning Activities
A. Teacher Activities
1. Introduction (10 minutes): Begin with an oral warm-up: quick mental subtraction problems (e.g., "10 minus 3?", "8 minus 5?"). Introduce the concept of "mystery numbers" in subtraction through a simple story problem using concrete objects (e.g., "I had 9 pens. I gave some to a student and now I have 5 pens left. How many pens did I give away?"). Do not reveal the answer yet. Explain that today, students will learn how to find these missing numbers and how to check if their subtraction answers are correct.
2. Demonstration: Finding Missing Numbers (15 minutes): Use physical manipulatives (bottle tops, pebbles, counting sticks) to demonstrate "Type 1" problems (`Total - ? = Left`).
Example: `7 - ? = 3`. Place 7 bottle tops. Ask students to observe as the teacher removes tops one by one until 3 are left. Count the removed tops. * Demonstrate "Type 2" problems (`? - Taken Away = Left`).