Further Mathematics - Senior Secondary 1 - Binary operations III

Binary operations III

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TERM: 3RD TERM

WEEK 10
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Binary Operation III
Focus: Multiplication Tables of Binary Operations
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Understand binary operations and the concept of multiplication tables in binary.
  2. Draw and complete multiplication tables for binary operations.
  3. Apply binary multiplication tables to solve problems.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practice exercises
  • Discussion
  • Analogy and real-life connections

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts of multiplication tables
  • Flashcards with examples of binary operations
  • Worksheets for practice on binary multiplication

 

PERIOD 1 & 2: Introduction to Binary Operations and Multiplication Tables

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of binary operations and their importance in computing. Explains the operation of multiplication in binary (using 0 and 1).

Students listen attentively and ask clarifying questions.

Step 2 - Binary Multiplication

Demonstrates the multiplication table of binary numbers (0 × 0, 0 × 1, 1 × 0, 1 × 1) on the board. Example: 1 × 1 = 1, 1 × 0 = 0, etc.

Students observe and take notes on the multiplication process.

Step 3 - Drawing Multiplication Tables

Guides students to draw the multiplication table for binary numbers (0, 1). Students are instructed to fill in the table based on the binary multiplication rules.

Students actively participate in drawing and filling in the binary multiplication table.

Step 4 - Practice with Examples

Teacher provides additional binary multiplication problems for students to solve using the multiplication table. Example: Multiply 1 × 1, 0 × 1, etc.

Students practice and complete the given multiplication problems using the table.

NOTE ON BOARD:
Binary Multiplication Table

×

0

1

0

0

0

1

0

1

Students copy the table into their notebooks.

 

PERIOD 3 & 4: Applying Binary Multiplication Tables

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Recap of Binary Multiplication

Recaps the binary multiplication table and emphasizes its importance in performing binary arithmetic.

Students revise the multiplication table in their notebooks.

Step 2 - Solving Problems with Multiplication Table

Teacher provides complex binary multiplication examples (e.g., 101 × 11) and guides students step-by-step on how to use the table to solve them.

Students observe and participate in solving the problems using the table.

Step 3 - Group Practice

In pairs or small groups, students practice solving more binary multiplication problems. Teacher walks around to provide assistance.

Students work in pairs or groups, solving the problems and asking for help when needed.

Step 4 - Independent Practice

Teacher assigns independent tasks where students must solve binary multiplication problems on their own. Example: Multiply 101 by 10, 110 by 11.

Students complete the multiplication tasks on their own, applying the table.

NOTE ON BOARD:
Example:
Multiplying 101 × 11

  1. First, multiply 101 × 1 = 101.
  2. Next, multiply 101 × 1 (shifted one place to the left) = 1010.
  3. Add both results:
    101
  • 1010
    ———
    1111 (binary result).

 

EVALUATION (5 exercises):

  1. What is the product of 1 × 1 in binary?
  2. What is the product of 0 × 1 in binary?
  3. Multiply 110 by 10.
  4. Multiply 101 by 11.
  5. What is the binary product of 1 × 0?

 

CLASSWORK (5 questions):

  1. Multiply 111 by 10.
  2. Multiply 100 by 11.
  3. Multiply 101 by 01.
  4. Multiply 011 by 10.
  5. What is the binary multiplication of 1 × 1?

 

ASSIGNMENT (5 tasks):

  1. Complete the binary multiplication table for numbers 0, 1, 2, and 3.
  2. Solve the following binary multiplication: 110 × 101.
  3. Multiply 111 by 111 in binary.
  4. Research the application of binary multiplication in computer science.

Think of a real-life scenario where binary multiplication would be used.