Further Mathematics - Senior Secondary 1 - Surds

Surds

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TERM: 1ST TERM

WEEK 8

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Surds
Focus:
i. Definition of surds
ii. Rules for manipulating surds
iii. Rationalization of the denominators of surds

SPECIFIC OBJECTIVES:

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

  1. Define and identify surds.
  2. State and apply the rules for simplifying and manipulating surds.
  3. Rationalize the denominators of simple surds.

INSTRUCTIONAL TECHNIQUES:

  • Guided discussion
  • Question and answer
  • Step-by-step demonstration
  • Practice exercises

Step 3 - More Examples

Expands to more examples: 3/√5, 2/√3, and combinations with simplification.

Students follow along and ask questions.

Step 4 - Guided Practice

Provides rationalization exercises for class practice with support.

Students work through examples in groups or pairs.

NOTE ON BOARD

Steps for rationalizing the denominator:

  

NOTE ON BOARD Steps for rationalizing the denominator:

  1. Multiply top and bottom by the surd in the denominator.
  2. Simplify numerator and denominator.
    Examples: 1/√3 = √3/3 | Students copy the steps and examples. |

 

EVALUATION (5 exercises):

  1. Rationalize: 1/√2
  2. Rationalize: 3/√5
  3. Rationalize: 4/√3
  4. Rationalize: 2/(√2)
  5. Simplify and rationalize: 5/(2√3)

 

CLASSWORK (5 questions):

  1. Rationalize: 2/√7
  2. Rationalize: 7/√11
  3. Rationalize: 5/(√5)
  4. Rationalize and simplify: 9/(2√2)
  5. Rationalize and simplify: 3/√6

 

ASSIGNMENT (5 tasks):

  1. Rationalize: 6/√2
  2. Rationalize: 4/√8
  3. Rationalize and simplify: 10/(2√5)
  4. Write the steps to rationalize 1/√x.
  5. Explain why we rationalize denominators.