Lesson Plan: Integers (Mathematics, Grade 7)

Lesson Plan: Integers (Mathematics, Grade 7)

Chapter Overview

This lesson plan covers the chapter on Integers, focusing on properties of addition, subtraction, multiplication, and division, as outlined in the provided document. The chapter introduces students to integer operations, their properties (closure, commutative, associative, distributive, and identity), and real-world applications. The plan is designed for a Grade 7 mathematics class, spanning approximately 8-10 class periods (45 minutes each).

Learning Objectives

By the end of this chapter, students will be able to:

  1. Understand and apply the properties of addition and subtraction of integers (closure, commutative, associative, and additive identity).

  2. Perform multiplication and division of integers, including positive and negative integers.

  3. Recognize and apply the properties of multiplication (closure, commutative, associative, multiplicative identity, and distributive).

  4. Understand division of integers and its properties, including cases where division is undefined.

  5. Solve real-world problems involving integer operations.

  6. Verify properties using examples and patterns.

Materials Needed

  • Whiteboard or smartboard

  • Markers, erasers

  • Printed worksheets (exercises from the document)

  • Number line posters or manipulatives

  • Dice (blue and red) for Game 1 (Page 9)

  • Game board (-104 to 104) for Game 1

  • Calculators (optional, for checking)

  • Student notebooks

  • Access to online interactive tools (e.g., virtual number lines, if available)

Lesson Structure

Day 1: Introduction to Integers and Closure Property

Objective: Introduce integers and the closure property for addition and subtraction.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Review whole numbers and introduce integers using a number line. Ask: "What happens when we go below zero?"

  2. Direct Instruction (15 min):

    • Define integers (positive, negative, zero).

    • Explain closure under addition (Page 1): The sum of two integers is an integer.

    • Work through table examples: e.g., (-10) + 3, (-75) + 18.

    • Introduce closure under subtraction (Page 2): The difference of two integers is an integer.

    • Discuss why whole numbers differ (subtraction may yield negative numbers).

  3. Guided Practice (15 min):

    • Students complete the addition table (Page 1, statements ii, iii, v, vi, vii).

    • Students complete the subtraction table (Page 2, statements ii, iv, v, vi, vii).

    • Discuss observations: Is the result always an integer?

  4. Closure (10 min):

    • Summarize: Integers are closed under addition and subtraction.

    • Assign "Try These" (Page 4, Question 1a-c) for homework.

Day 2: Commutative and Associative Properties of Addition

Objective: Explore commutative and associative properties of integer addition.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Quick quiz on closure property (e.g., Is (-5) + 7 an integer? Is 8 - 12 an integer?).

  2. Direct Instruction (15 min):

    • Explain commutative property (Page 2): a + b = b + a.

    • Use examples: 5 + (-6) = (-6) + 5.

    • Explain associative property (Page 3): (a + b) + c = a + (b + c).

    • Work through examples: (-5) + [(-3) + (-2)] vs. [(-5) + (-3)] + (-2).

  3. Guided Practice (15 min):

    • Students verify commutative property with pairs (Page 2, statements i-iii).

    • Students verify associative property with examples (Page 3, (-3) + [1 + (-7)]).

    • Group activity: Test five pairs of integers for commutativity.

  4. Closure (10 min):

    • Discuss: Why is subtraction not commutative? (Page 3 example: 5 - (-3) ≠ (-3) - 5).

    • Assign "Try These" (Page 4, Question 1d-e) for homework.

Day 3: Additive Identity and Real-World Applications

Objective: Understand additive identity and apply integer addition/subtraction to problems.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Ask: "What number, when added to any integer, gives the same integer?"

  2. Direct Instruction (10 min):

    • Introduce additive identity (Page 4): a + 0 = 0 + a = a.

    • Work through examples: (-8) + 0, 0 + (-37).

  3. Guided Practice (20 min):

    • Students complete the table (Page 4, statements iii, v, vi, vii, viii).

    • Solve Example 1 (Page 4): Pairs of integers with specific sums/differences.

    • Group work: Create five pairs for "Try These" (Page 4, Question 2).

  4. Closure (10 min):

    • Discuss real-world scenarios (e.g., temperature, bank balances).

    • Assign Exercise 1.1 (Page 5, Questions 1-2) for homework.

Day 4: Multiplication of Integers (Positive and Negative)

Objective: Learn multiplication of a positive and a negative integer.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Review addition as repeated multiplication (e.g., 5 + 5 + 5 = 3 × 5).

  2. Direct Instruction (15 min):

    • Explain multiplication using a number line (Page 5): 3 × (-5) = (-5) + (-5) + (-5) = -15.

    • Introduce method without number line (Page 6): Multiply as whole numbers, add minus sign.

    • Example: 5 × (-4) = -(5 × 4) = -20.

  3. Guided Practice (15 min):

    • Students complete "Try These" (Page 5: 4 × (-8), 8 × (-2), etc.).

    • Work on patterns (Page 6): (-3) × 5, (-4) × 8.

    • Verify: Does (-4) × 8 = 4 × (-8)?

  4. Closure (10 min):

    • Summarize: Positive × Negative = Negative.

    • Assign "Try These" (Page 7, Question 1a-b) for homework.

Day 5: Multiplication of Two Negative Integers

Objective: Understand multiplication of two negative integers.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Quick review: What is 3 × (-5)? What pattern might we expect for (-3) × (-5)?

  2. Direct Instruction (15 min):

    • Use patterns (Page 7): (-3) × 4, (-3) × 3, …, (-3) × (-2).

    • Show: (-3) × (-2) = 6 (positive).

    • Generalize: (-a) × (-b) = a × b.

  3. Guided Practice (15 min):

    • Students complete patterns (Page 7: (-3) × (-3), (-4) × (-3)).

    • Work on "Try These" (Page 8: (-5) × (-6), (-6) × (-7)).

    • Verify: (-31) × (-100), (-25) × (-72).

  4. Closure (10 min):

    • Discuss: Why is the product of two negatives positive?

    • Assign "Try These" (Page 7, Question 1c-d) for homework.

Day 6: Properties of Multiplication

Objective: Explore closure, commutative, and associative properties of multiplication.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Ask: "Is the product of two integers always an integer?"

  2. Direct Instruction (15 min):

    • Closure (Page 10): Complete table ((-30) × 12, (-15) × (-23)).

    • Commutative (Page 10): a × b = b × a (e.g., (-30) × 12 = 12 × (-30)).

    • Associative (Page 12): (a × b) × c = a × (b × c).

  3. Guided Practice (15 min):

    • Students complete tables (Page 10).

    • Verify associativity: [7 × (-6)] × 4 vs. 7 × [(-6) × 4].

    • Group work: Test five pairs for commutativity.

  4. Closure (10 min):

    • Summarize properties.

    • Assign Exercise 1.2 (Page 14, Questions 1a-c) for homework.

Day 7: Multiplicative Identity and Distributive Property

Objective: Understand multiplicative identity and distributive property.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Ask: "What number, when multiplied by any integer, gives the same integer?"

  2. Direct Instruction (15 min):

    • Multiplicative identity (Page 11): a × 1 = 1 × a = a.

    • Multiplication by zero (Page 11): a × 0 = 0.

    • Distributive property (Page 12): a × (b + c) = a × b + a × c.

    • Example: (-2) × (3 + 5) vs. [(-2) × 3] + [(-2) × 5].

  3. Guided Practice (15 min):

    • Complete table (Page 11: (-4) × 1, (-6) × (-1)).

    • Verify distributive property (Page 13: 10 × [6 + (-2)]).

    • Group work: Test five sets for distributive property.

  4. Closure (10 min):

    • Discuss: Why is -1 not a multiplicative identity?

    • Assign Exercise 1.2 (Page 14, Questions 1d-f, 2a) for homework.

Day 8: Division of Integers

Objective: Learn division of integers and its properties.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Review: If 3 × 5 = 15, what are the division statements?

  2. Direct Instruction (15 min):

    • Division as inverse of multiplication (Page 14).

    • Rules:

      • Positive ÷ Negative = Negative.

      • Negative ÷ Positive = Negative.

      • Negative ÷ Negative = Positive.

    • Complete table (Page 14: (-8) × (-9), (-3) × (-7)).

  3. Guided Practice (15 min):

    • Students work on "Try These" (Page 15: (-100) ÷ 5, (-36) ÷ (-4)).

    • Solve Example 2 (Page 17): Test scoring problem.

  4. Closure (10 min):

    • Discuss: Why is division by zero undefined?

    • Assign Exercise 1.3 (Page 18, Questions 1a-c, 3a-b) for homework.

Day 9: Properties of Division and Applications

Objective: Explore properties of division and solve real-world problems.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Quick quiz: What is (-36) ÷ (-9)? Is (-8) ÷ (-4) = (-4) ÷ (-8)?

  2. Direct Instruction (15 min):

    • Properties (Page 15-16):

      • Integers are not closed under division (e.g., (-8) ÷ 3).

      • Division is not commutative or associative.

      • a ÷ 1 = a, a ÷ (-1) = -a.

    • Work through table (Page 16: (-25) ÷ (-1), 13 ÷ (-1)).

  3. Guided Practice (15 min):

    • Solve Example 3 (Page 17): Shopkeeper profit/loss problem.

    • Students complete Exercise 1.3 (Page 18, Questions 4-5).

  4. Closure (10 min):

    • Summarize division properties.

    • Assign Exercise 1.3 (Page 18, Questions 6-7) for homework.

Day 10: Review and Game-Based Assessment

Objective: Review concepts and assess understanding through a game.
Duration: 45 minutes
Activities:

  1. Warm-Up (5 min): Quick review of key properties (closure, commutative, etc.).

  2. Game Activity (25 min):

    • Play Game 1 (Page 8-9): Integer multiplication game with dice and board.

    • Rules: Multiply dice numbers, move counter based on positive/negative product.

    • Groups of 4, monitor for understanding of multiplication rules.

  3. Closure (15 min):

    • Discuss game outcomes: How did multiplication properties help?

    • Review key concepts (Page 19: "What have We Discussed?").

    • Assign a short reflection: "Write one real-world example where integers are used."

Assessment

  • Formative:

    • Class participation in discussions and group activities.

    • Completion of "Try These" and guided practice problems.

    • Homework from Exercises 1.1, 1.2, and 1.3.

  • Summative:

    • Quiz after Day 5: 10 questions on addition, subtraction, and multiplication properties.

    • Final test after Day 10: 20 questions covering all operations and properties, including word problems (e.g., Exercise 1.3, Questions 5-7).

    • Game performance: Assess correct application of multiplication rules.

Differentiation

  • For Struggling Learners:

    • Use physical number lines or manipulatives for visual support.

    • Pair with peers for guided practice.

    • Simplify problems (e.g., smaller integers).

  • For Advanced Learners:

    • Assign additional problems: Create their own word problems.

    • Explore patterns in division (e.g., why a ÷ (-1) = -a).

    • Introduce basic algebraic expressions using integers.

Extensions

  • Cross-Curricular Connection:

    • Science: Use integers to describe temperature changes or elevation (e.g., Exercise 1.3, Question 5).

    • Financial Literacy: Discuss profit/loss scenarios (e.g., Example 3).

  • Technology Integration:

    • Use online tools like Desmos or GeoGebra to visualize integer operations.

    • Create a simple Python program to check integer properties (optional for advanced students).

Reflection

After completing the chapter, ask students to reflect:

  • Which property was easiest/hardest to understand? Why?

  •