Module 4 Grade 9 Mathematics (RADICALS)
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Transcript of Module 4 Grade 9 Mathematics (RADICALS)
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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
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Module 4
Rational Exponents and
Radicals
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Lessons: 1. Zero, Negative Integral and Rational Exponents
2. Radicals 3. Solving Radical Equations
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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?
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Recall: Laws of Exponents
= 1, if m= nZero Exponent = 1
Negative Exponent = 1/
1 =
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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
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Simplify
8.
9.
10. 10 -3 + 10 -2 + 10 1 + 10 0 + 10 -1 + 10 - 2
= x4 z2
= 11, 121 1000
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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.
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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
=
=
=
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Change the following into exponential form
1. 3 2. 3.
= 3 ( 2x3 ) 1/2
= (4r2 s3 t4 ) 2/5
=
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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.
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Simplify the following
a. b. c. d.
= 10x
= 2xy3z5=
= - 4 x2
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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
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Multiplication of radicals
= 42
=
= 5 + 3
1.
2. ( 2 + ) ( 5 - )
3.
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Division of radicals
=
= 2
= 3
1. 4
2. 3 )
3. 6
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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
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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:
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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
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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?
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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.
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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.
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THANK YOU!!!!
GOD BLESS US ALL