Mathematics - Junior Secondary 3 - Multiplication and Division of Numbers in Base 2 Numerals

Multiplication and Division of Numbers in Base 2 Numerals

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TERM: 1ST TERM

WEEK 5

Class: Junior Secondary School 3

Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Multiplication and Division of Numbers in Base 2 Numerals
Focus: Multiplication of Two 2-Digit Binary Numbers, Division of Two to 3-Digit Binary Numbers
SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Perform multiplication of two 2-digit binary numbers.
  2. Understand and apply the rules for binary multiplication.
  3. Perform division of binary numbers with up to 3 digits.
  4. Understand and apply the division algorithm in binary numbers.
  5. Apply multiplication and division of binary numbers in real-life contexts.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Problem-solving exercises
• Real-life application

INSTRUCTIONAL MATERIALS:
• Flashcards with binary numbers
• Worksheets
• Whiteboard and marker

 

PERIOD 1 & 2: Multiplication of Two 2-Digit Binary Numbers

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces multiplication of binary numbers and the rules (e.g., 0 × 1 = 0, 1 × 1 = 1, carry-over rules).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates binary multiplication with examples, e.g., 11 × 10.

Pupils observe and follow the steps.

Step 3 - Demonstration

Solves examples of binary multiplication step by step.

Pupils solve problems with teacher’s guidance.

Step 4 - Note Taking

Teacher writes down the multiplication rules and examples.

Pupils copy the rules and practice.

NOTE ON BOARD:
• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 1 = 1

EVALUATION (5 exercises):

  1. Multiply: 11 × 10
  2. Multiply: 101 × 11
  3. Multiply: 110 × 101
  4. Multiply: 1001 × 110
  5. Multiply: 111 × 101

CLASSWORK (5 questions):

  1. Multiply: 101 × 11
  2. Multiply: 110 × 100
  3. Multiply: 111 × 10
  4. Multiply: 1001 × 101
  5. Multiply: 111 × 100

ASSIGNMENT (5 tasks):

  1. Multiply: 100 × 101
  2. Multiply: 1110 × 110
  3. Multiply: 1011 × 101
  4. Multiply: 10000 × 111
  5. Multiply: 1101 × 100

 

PERIOD 3 & 4: Division of Two to 3-Digit Binary Numbers

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the concept of dividing binary numbers (e.g., 101 ÷ 11).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates division of binary numbers step by step (similar to long division).

Pupils observe and follow the steps.

Step 3 - Demonstration

Solves examples of binary division with up to 3-digit numbers.

Pupils solve problems with teacher’s guidance.

Step 4 - Note Taking

Teacher writes down division examples and steps.

Pupils copy notes and practice.

NOTE ON BOARD:
• 101 ÷ 11 = 11
• Division steps: First, divide the first digit of the dividend by the divisor, then move to the next digit, and repeat.

EVALUATION (5 exercises):

  1. Divide: 101 ÷ 11
  2. Divide: 1111 ÷ 101
  3. Divide: 10010 ÷ 110
  4. Divide: 1101 ÷ 11
  5. Divide: 10001 ÷ 100

CLASSWORK (5 questions):

  1. Divide: 1001 ÷ 11
  2. Divide: 10110 ÷ 100
  3. Divide: 1111 ÷ 11
  4. Divide: 11001 ÷ 100
  5. Divide: 10001 ÷ 101

ASSIGNMENT (5 tasks):

  1. Divide: 10010 ÷ 101
  2. Divide: 11100 ÷ 110
  3. Divide: 101010 ÷ 111
  4. Divide: 11011 ÷ 100
  5. Divide: 101010 ÷ 1001

 

PERIOD 5: Application to Real Life

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces real-life examples where binary operations are used, such as in computer science, coding, and data storage.

Pupils listen and ask questions.

Step 2 - Examples

Shows how binary operations are used in computing and data systems.

Pupils identify numbers and explain.

Step 3 - Drill

Pupils solve real-life application problems involving binary numbers.

Pupils work on the problems and discuss results.

EVALUATION (5 questions):

  1. How do computers use binary numbers for calculations?
  2. Explain how the division of binary numbers is used in data storage.
  3. What is the benefit of multiplying binary numbers in computer systems?
  4. Apply binary multiplication in determining the size of memory storage in a computer.
  5. Solve: 1101 (data size) × 101 (storage units)

CLASSWORK (5 tasks):

  1. Find the binary product of two 2-digit binary numbers and explain how it can be used in computing.
  2. Apply binary division to calculate the storage units required for a file with 11001 binary digits.
  3. Compare the binary results of a multiplication operation in a computer system.
  4. Write a problem involving binary multiplication in real life.
  5. Write a division problem for a computer system using 3-digit binary numbers.

ASSIGNMENT (5 tasks):

  1. Research the use of binary numbers in video game development.
  2. Write a paragraph on how binary multiplication affects data transmission speed.
  3. Apply binary division to calculate the storage space for different file formats.
  4. Create a binary multiplication problem based on a real-life scenario.

Use the concept of binary division to calculate the data rate in a binary data transfer system.