Operations on Integers
Performing Operations on Integers (Addition, Subtraction, Multiplication, Division)
Learning Standards
Content Standard
The learner demonstrates understanding of key concepts of numbers and number operations
Performance Standard
The learner is able to formulate real-life problems involving integers and solve these with understanding
Learning Competency
Perform operations on integers using different methods
Code: M7NS-Ia-1
Complete Lesson Plan
Learning Objectives
- •
Review the concept of integers and number line
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Add and subtract integers correctly
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Multiply and divide integers using rules
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Solve real-life problems involving integers
Lesson Procedures
motivation
Real-life scenario: 'The temperature was 5°C in the morning. It dropped by 8°C in the evening. What is the new temperature?' Show how integers help us solve this.
presentation
- •
ADDITION OF INTEGERS
Rule 1: Same signs
- Add the absolute values
- Keep the common sign
- Examples:
- (+5) + (+3) = +8
- (-5) + (-3) = -8
- •
Rule 2: Different signs
- Subtract the smaller absolute value from the larger
- Use the sign of the number with larger absolute value
- Examples:
- (+8) + (-3) = +5
- (-8) + (+3) = -5
- (+5) + (-9) = -4
- •
SUBTRACTION OF INTEGERS
Rule: Add the opposite (KCC - Keep, Change, Change)
- Keep the first number
- Change subtraction to addition
- Change the sign of the second number
Examples:
- (+7) - (+3) = (+7) + (-3) = +4
- (+5) - (-2) = (+5) + (+2) = +7
- (-6) - (+4) = (-6) + (-4) = -10
- (-8) - (-3) = (-8) + (+3) = -5
- •
MULTIPLICATION OF INTEGERS
Rules:
- Same signs → Positive result
- (+)(+) = +
- (-)(-) = +
- Different signs → Negative result
- (+)(-) = -
- (-)(+) = -
Examples:
- (+4) × (+3) = +12
- (-4) × (-3) = +12
- (+4) × (-3) = -12
- (-4) × (+3) = -12
- Same signs → Positive result
- •
DIVISION OF INTEGERS
Rules: (Same as multiplication)
- Same signs → Positive
- Different signs → Negative
Examples:
- (+12) ÷ (+3) = +4
- (-12) ÷ (-3) = +4
- (+12) ÷ (-3) = -4
- (-12) ÷ (+3) = -4
generalization
Questions:
- What are integers?
- What are the rules for adding integers?
- How do we subtract integers?
- What are the rules for multiplying/dividing integers?
- When do we use integers in real life?
guided practice
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Solve together using number line and rules:
Addition:
- (-7) + (+10) = ?
- (-5) + (-8) = ?
Subtraction: 3. (+9) - (+15) = ? 4. (-4) - (-6) = ?
Multiplication: 5. (-6) × (+5) = ? 6. (-7) × (-4) = ?
Division: 7. (+20) ÷ (-4) = ? 8. (-36) ÷ (-9) = ?
- •
Use counters to model operations visually
- •
Practice with real-world problems:
- 'A diver is 15 meters below sea level (-15). He dives down 8 more meters. What is his new depth?'
- 'The temperature dropped 3°C each hour for 5 hours. What is the total change?'
independent practice
- •
Activity 1: Perform the operations:
- (+15) + (-22) = ____
- (-18) + (-7) = ____
- (+25) - (-13) = ____
- (-30) - (+12) = ____
- (-8) × (+6) = ____
- (-9) × (-7) = ____
- (+48) ÷ (-8) = ____
- (-56) ÷ (-7) = ____
- •
Activity 2: Word Problems:
- A submarine is at -120 meters. It rises 45 meters. What is its new position?
- The temperature is -5°C. It drops by 8°C. What is the new temperature?
- A business lost ₱500 per day for 7 days. What is the total loss?
- •
Activity 3: Fill in the missing number:
- (-12) + ___ = -5
- ___ - (+8) = -15
- (-4) × ___ = +28
preliminary activities
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Prayer and greetings
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Review: Positive and negative numbers
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Quick drill: Identify integers on number line
Assessment
answers
- -7
- -23
- +56
- -5
- -150 meters (150 meters below sea level) Bonus: -5 + 8 - 6 = -3
evaluation
- •
Solve:
- (+18) + (-25) = ____
- (-14) - (+9) = ____
- (-7) × (-8) = ____
- (+45) ÷ (-9) = ____
- Problem: A hiker starts at 200m above sea level (+200). He descends 350 meters. What is his new elevation?
Bonus: Evaluate: (-5) + (+8) - (-3) × (-2)
Materials & Resources
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Large number line for classroom
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Integer cards (positive and negative)
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Two-color counters
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Manila paper and markers
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Calculators
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Worksheets with practice problems
assignment
Homework:
- Practice operations: Create 5 problems each for addition, subtraction, multiplication, division
- Solve word problems from textbook pages ___
- Research: How are negative numbers used in banking?
Remarks:
- Use number line consistently for visual learners
- Provide extra practice for students struggling with sign rules
subject matter
Topic: Operations on Integers
Key Concepts:
- Integers include positive numbers, negative numbers, and zero: {...-3, -2, -1, 0, 1, 2, 3...}
- Number line helps visualize integer operations
- Rules for operations:
- Addition: Same signs → add and keep the sign; Different signs → subtract and use sign of larger number
- Subtraction: Add the opposite (change to addition)
- Multiplication/Division: Same signs → positive result; Different signs → negative result
Materials:
- Number line (large classroom version)
- Integer cards (+/- numbers)
- Counters (two colors for positive/negative)
- Manila paper and markers
- Calculators