Further Mathematics - Senior Secondary 1 - Binary operations

Binary operations

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TERM: 3RD TERM

WEEK 8
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Binary Operations I
Focus: Definition of Binary Operation, Laws of Binary Operation (Associative Law, Commutative Law, Distributive Law)
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define binary operations.
  2. Explain and apply the associative law of binary operations.
  3. Explain and apply the commutative law of binary operations.
  4. Explain and apply the distributive law of binary operations.

INSTRUCTIONAL TECHNIQUES:

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

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating binary operations
  • Flashcards with examples of binary operations
  • Worksheets for practice

PERIOD 1 & 2: Introduction to Binary Operations
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of binary operations. Explains that a binary operation involves two operands from a set and produces another element from the set.

Students listen attentively and ask clarifying questions.

Step 2 - Definition

Defines binary operation and gives examples using basic operations like addition and multiplication on sets.

Students observe and take notes.

Step 3 - Types of Binary Operations

Explains different types of binary operations on sets such as addition, subtraction, multiplication, and division. Discusses how these operations can be applied to numbers and other sets.

Students ask questions about the different types of operations.

Step 4 - Laws of Binary Operations

Introduces the laws governing binary operations: Associative, Commutative, and Distributive. Explains each law with examples.

Students take notes and ask questions about the laws.

NOTE ON BOARD:

Binary Operation: An operation that combines two elements of a set to form another element of the set. Examples: +, -, ×, ÷.

Students copy the definition and examples.

EVALUATION (5 exercises):

  1. What is a binary operation?
  2. Give an example of a binary operation on the set of integers.
  3. What does the commutative law state?
  4. Explain the associative law with an example.
  5. What is the distributive law in binary operations?

CLASSWORK (5 questions):

  1. Identify whether the operation of addition on integers is a binary operation.
  2. State whether multiplication is commutative or not with an example.
  3. State the associative law for addition with an example.
  4. State the distributive law of multiplication over addition.
  5. Provide an example of a binary operation in real life.

ASSIGNMENT (5 tasks):

  1. Write a definition of a binary operation.
  2. Provide an example of the distributive law using multiplication and addition.
  3. Explain the associative law using the operation of subtraction.
  4. Find a real-life example of a binary operation.
  5. State the commutative law using an example of division.

PERIOD 3 & 4: Laws of Binary Operations: Associative, Commutative, and Distributive
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Associative Law

Explains the associative law: (a * b) * c = a * (b * c). Uses examples with addition and multiplication.

Students take notes and practice with examples.

Step 2 - Commutative Law

Explains the commutative law: a * b = b * a. Demonstrates with examples using addition and multiplication.

Students work with examples and ask questions.

Step 3 - Distributive Law

Explains the distributive law: a * (b + c) = a * b + a * c. Provides examples and non-examples.

Students practice solving examples based on the distributive law.

Step 4 - Guided Practice

Provides several problems for students to apply the laws of binary operations in different scenarios. Encourages collaboration with peers.

Students work together in pairs and solve problems based on the laws of binary operations.

NOTE ON BOARD:

Associative Law: (a * b) * c = a * (b * c)

Commutative Law: a * b = b * a

EVALUATION (5 exercises):

  1. Apply the associative law of addition to the numbers 4, 5, and 6.
  2. Demonstrate the commutative law of multiplication with the numbers 7 and 9.
  3. Show the distributive law using multiplication and subtraction.
  4. Using the numbers 2, 3, and 5, apply the distributive law.
  5. Check if the operation of subtraction follows the associative law.

CLASSWORK (5 questions):

  1. Prove that multiplication is commutative using the numbers 3 and 8.
  2. Use the associative law to simplify the expression (4 + 6) + 7.
  3. Simplify the expression 2 * (3 + 5) using the distributive law.
  4. Using addition, show the associative law with the numbers 3, 4, and 5.
  5. Apply the distributive law with division over subtraction.

ASSIGNMENT (5 tasks):

  1. Apply the commutative law to the operation of addition using 12 and 15.
  2. Show that subtraction does not follow the commutative law.
  3. Prove the distributive law using multiplication over addition.
  4. Find an example of a real-world application of binary operations.

Solve a set of problems applying the associative law to both addition and multiplication.