module 4 grade 9 mathematics (radicals)

ALVIN O. INSORIOPacita Complex National High School

2014 DIVISION MID-YEAR INSET ON CONTENT AND PEDAGOGY FOR

SECONDARY MATHEMATICS EDUCATION

DAYAP NATIONAL HIGH SCHOOL

CALAUAN, LAGUNA

Module 4

Rational Exponents and

Radicals

Lessons: 1. Zero, Negative Integral and Rational Exponents

2. Radicals 3. Solving Radical Equations

Priming

1. Have you ever wondered about how to identify the side lengths of a square lot if you know its area?

2. Have you tried solving for the length of any side of a right triangle?

3. Has it come to your mind how you can find the radius of a cylindrical water tank given its volume?

Recall: Laws of Exponents

= 1, if m= nZero Exponent = 1

Negative Exponent = 1/

1 =

Drill

1) 3x0

2) ( - 3x ) 0

3) ( 3x 3m y 2n ) 3

4) ( 2x y z -3 ) ( - 4x 3y z5 )5) (2m ½)( - 3m 2/3 )6) 3 2 . 4 0 + 1 ½ . 5 0

7) 64 . 8127 . 216

Simplify using laws of exponents= 3= 1= 27x 9m y 6n

= - 8x 4y z 2

= - 6m 7/6

= 10= 8/9

Simplify

8.

9.

10. 10 -3 + 10 -2 + 10 1 + 10 0 + 10 -1 + 10 - 2

= x4 z2

= 11, 121 1000

Radical Expression

A radical expression or radical is an expression containing the symbol which is called radical sign. In symbols , n is called index or order and am is called the radicand.

Change the following into radical form

1. 5x ½

2. ( 3 mn2 ) 2/3

3. ( 2n2 ) ¾

4. ( x2 + 3 ) 1/3

( x2 – 3 ) – 1/3

= 5

=

=

=

Change the following into exponential form

1. 3 2. 3.

= 3 ( 2x3 ) 1/2

= (4r2 s3 t4 ) 2/5

=

Laws of Radicals

The simplified form of radical expression would require;• No prime factors of a radicand has an exponent

equal or greater than the index.• No radicand contains a fraction• No denominator contains a radical sign.

Simplify the following

a. b. c. d.

= 10x

= 2xy3z5=

= - 4 x2

Addition and subtraction of radicals

We add or subtract by combining the similar/like radicals

1. 5

2. 20 10

3. 2

= 6

=15

= 10

Multiplication of radicals

= 42

=

= 5 + 3

1.

2. ( 2 + ) ( 5 - )

3.

Division of radicals

=

= 2

= 3

1. 4

2. 3 )

3. 6

Radical Equation

It is an equation in which the variable appears in a radicand.

Solve for x

1. x – 6 =

2. 4 + = x

3. 3 = 2

= 9 is the only solution4 is extraneous root

= 6 is the only solution 3 is extraneous root= - 19/27

Problem Solving

A woman walks 5 meters to the east going to school and then walks 9 meters northward going to the church. How far is she from the starting point which is her house? Express your answer in radical form.

Answer:

Group Activity:20 minute brainstorming

Content Area/Lesson

Critical content areas from the

teacher's perspective

Critical content areas

from the learner's

perspective

Recommended Teaching/learning,

strategies/activities

Lesson 1: Zero, Negative Integral and Rational Exponents

Lesson 2: Radicals

Lesson 3: Solving Radical Equations

Analysis1. From the activity, what are the content areas teachers

do find most easy to teach? most difficult to teach?2. What are the common difficulties encountered by the

teachers in teaching the concepts of rational exponents and radicals?

3. Which of the content/s is/are most challenging for the students to learn? most difficult to comprehend?

4. What are the insights you have gained from this activity?5. Are the recommended strategies/activities practical and

appropriate in eliminating the perceived difficulty?

Abstraction

1. Explain the identified critical content areas based on the perception and prior experience of the teachers and the learners.

2. Discuss appropriate teaching strategies and learning activities that can be used in the classroom.

3. Share best practices in teaching variations.

Application

1. Create a scenario of the task in paragraph form about variation incorporating GRASPS format. Create a rubric for the grading of this activity.

2. Present the output to the class.

THANK YOU!!!!

GOD BLESS US ALL