Permutation

Grade 9 · Mathematics

Semester 2 | Period 6 | Week 34

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Subject: Mathematics

Semester: 2

Period: 6

Week: 34

WEEK 34

Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Permutation
Focus: Arrangements Using Permutation

SPECIFIC OBJECTIVES:

By the end of the lesson, pupils should be able to:

  1. Explain the counting principle (multiplication principle).
  2. Define permutation and its importance in arranging objects.
  3. Use the formula nPr= n!    to calculate permutations.

      (n−r)!

  1. Solve practical problems involving arrangements of letters, digits, and people.
  2. Apply permutation in real-life scenarios (e.g., seating arrangements, race positions).

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Group exercises
  • Practical arrangement tasks
  • Class discussions

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and marker
  • Flashcards with letters or numbers
  • Worksheets with permutation problems
  • Chart showing factorial values
  • Calculator (optional)

 

PERIOD 1 & 2: Counting Principle and Definition of Permutation

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation (Warm-up)

Teacher asks: “If you have 3 shirts and 2 trousers, how many outfits can you make?”

Pupils suggest answers; teacher highlights the multiplication principle.

Step 2 – Building Knowledge (Explanation)

Explains counting principle (multiplication principle): If one event can occur in m ways and another independent event in n ways, total ways = m × n.

Pupils take notes and give examples.

Step 3 – Introduction of Permutation

Defines permutation: “An arrangement of objects in a specific order.” Explains that order matters.

Pupils listen and take notes.

Step 4 – Demonstration

Example: Arrange 3 letters A, B, C. Total arrangements = 3! = 6. Lists all: ABC, ACB, BAC, BCA, CAB, CBA.

Pupils observe and copy arrangements.

NOTE ON BOARD:

  • Counting principle: multiply choices at each stage.
  • Permutation formula: nPr= n!

                                                (n−r)!

  • Factorial: n!=n×(n−1)×…×1

EVALUATION (5 exercises):

  1. Arrange letters A, B, C, D in all possible orders.
  2. Find the number of ways to choose 2 students from 5 for president and vice president.
  3. Calculate 5P3 using the formula.
  4. Arrange 4 books on a shelf.
  5. Find the number of 3-digit numbers that can be formed from 1, 2, 3, 4, 5 without repetition.

CLASSWORK (5 questions):

  1. Arrange letters X, Y, Z. How many ways?
  2. Calculate 6P2.
  3. Arrange 3 students from a group of 5 for a line-up.
  4. Find number of ways to seat 4 friends in 4 chairs.
  5. Arrange 5 letters P, Q, R, S, T in 3-letter codes.

ASSIGNMENT (5 tasks):

  1. Find all arrangements of letters M, N, O.
  2. Calculate 7P3.
  3. Find the number of ways to assign 2 prizes to 6 participants.
  4. Arrange 4 books labeled A, B, C, D on a shelf.
  5. Create a real-life problem requiring permutation and solve it.

 

PERIOD 3 & 4: Applying Permutation Formula

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation

Teacher asks: “In a race with 5 runners, how many ways can gold, silver, and bronze be awarded?”

Pupils suggest answers; teacher relates to permutation formula.

Step 2 – Building Knowledge

Shows formula nPr= n!

                                (n−r)!

and explains each term (n = total items, r = items to arrange).

Pupils copy formula and ask clarifying questions.

Step 3 – Demonstration

Example: 5 runners, 1st, 2nd, 3rd positions: 5P3 = 5 × 4 × 3 = 60 ways.

Pupils solve similar examples alongside teacher.

Step 4 – Guided Practice

Additional examples:

  
  • Arrange 6 books on a shelf taking 3 at a time.
  • Arrange 4 students from 7 for positions. | Pupils work in pairs or groups to solve.

EVALUATION (5 exercises):

  1. 8P2 = ?
  2. Number of ways to choose president and vice president from 6 students.
  3. Find 7P4.
  4. Arrange 5 letters from A, B, C, D, E in 3-letter codes.
  5. Number of 3-digit numbers from 1, 2, 3, 4, 5, 6 without repetition.

CLASSWORK (5 questions):

  1. Find 6P3.
  2. Number of ways to award 1st and 2nd prizes to 4 students.
  3. Arrange 5 books taking 3 at a time.
  4. Find 9P2.
  5. Number of ways to seat 5 people in 5 chairs.

ASSIGNMENT (5 tasks):

  1. Find 10P3.
  2. Arrange 4 letters from W, X, Y, Z.
  3. Number of 3-digit numbers from 1–6 without repetition.
  4. Create a real-life problem involving permutation and solve it.
  5. Arrange 6 students for 3 positions in a group.

 

PERIOD 5: Practical Classroom Activity and Applications

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Anticipation

Ask pupils to form a line for class photos. How many ways?

Pupils suggest ways and count possible arrangements.

Step 2 – Explanation

Teacher links scenario to permutation formula.

Pupils follow explanation.

Step 3 – Practical Task

Use flashcards or letters. Pupils form arrangements and calculate using formula.

Pupils arrange objects and verify results.

Step 4 – Discussion

Discuss applications: seating plans, race positions, arranging books, password codes.

Pupils provide examples from daily life.

EVALUATION (5 exercises):

  1. Arrange 5 friends in 5 chairs.
  2. Find 4P2.
  3. Number of ways to choose 3 committee members from 5 for specific roles.
  4. Arrange letters A, B, C, D in codes of 2 letters.
  5. 6 runners, 1st, 2nd, 3rd prizes. Find total arrangements.

CLASSWORK (5 questions):

  1. Find 5P3.
  2. Number of ways to arrange 4 books on a shelf.
  3. Arrange 3 students from 6 for positions.
  4. Find 7P2.
  5. Number of ways to seat 5 people in a row.

ASSIGNMENT (5 tasks):

  1. 8 students for 3 positions: calculate arrangements.
  2. Arrange letters X, Y, Z, W in 3-letter codes.
  3. Create a real-life permutation problem and solve it.
  4. Find 9P3.
  5. Arrange 6 students for 4 specific roles.