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Rationalizing the Denominator Lesson

Description: 

In this lesson, students will learn how to rationalize the denominator and will be re-introduced to the idea of a conjugate and also imaginary numbers. By the end of the lesson, they should be able to rationalize a denominator even if it contains complex or imaginary numbers.

Learning Targets: 
Students will be able to rationalize a denominator containing real numbers
Students will be able to rationalize a denominator containing complex and imaginary numbers
Students will be able to multiply by the conjugate in order to rationalize a denominator with real and complex numbers
Link: 
Rationalizing Denominator Extra Help
https://www.youtube.com/watch
AttachmentSize
PDF icon Rationalizing Denominators DO-NOW.pdf216.49 KB
PDF icon Rationalizing the Denominator Fixed Notes.PDF68.68 KB
PDF icon Rationalizing the Denominator WORKSHEET-KEY.pdf244.7 KB
Author: 
davesarkipato
Content Area: 
Mathematics
Pre-Calc and Calculus
Language: 
English
Resource Type: 
Lesson
Licensing: 
Creative Commons Licence
Grade: 
11
12
Common Core Math
Common Core Math: 
CCSS.MATH.CONTENT.HSN.CN.3
CCSS.MATH.CONTENT.HSN.RN.2
CCSS.MATH.CONTENT.HSA.REI.4b
Tags: 
Rationalizing the Denominator
Complex Numbers
Imaginary Numbers
Real Numbers
Conjugate
Multiplying by the Conjugate

How are the standards/objectives assessed?

Exit ticket: http://www.regentsprep.org/regents/math/algtrig/ato3/ratdenprac.htm

Student prerequisite skills and knowledge

Students should have learned about complex and imaginary numbers in Algebra 2. They should also have learned how to multiply by the conjugate to rationalize a denominator. Today's lesson will take what they have learned and go just a bit further.

How is the concept or procedure explained or demonstrated?

It fits into the context of this lesson and the unit because students will have rationalize a denominator anytime there is a radical or imaginary numbers. We will soon be graphing polynomials and they may be required to rationalize the denominator first before they can graph.

What concepts or procedures are being explained or demonstrated in this lesson object?

The procedure requires students to analyze the example and determine if they need to find the conjugate or if the denominator can be rationalized without doing so.

What was your experience, both successes and challenges, using this lesson object with your students?

Successes - many students remembered this concept from Algebra 2 and only need a few reminders on how to solve the problems. Once they completed a few examples using the conjugate they were off and running. Challenges - a couple of the students struggled with foiling and multiplying radials together. If you teach this lesson, you may want to go over a few ""reminder"" examples on how to multiply two radicals and also how to foil with radicals.