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Detailed Lesson Plan

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Detailed Lesson Plan
I.
OBJECTIVES:
At the end of one hour, 95% of Grade 9 students of section Rizal will be able to:
1. Define concepts on angle of elevation and angle of depression.
2. Identify the segment that represents the line of sight.
3. Identify the angle that represent the angle of elevation or angle of depression.
4. Cite important application of angle of elevation and depression in real life.
II.
SUBJECT MATTER
Topic: Angles of Elevation and Angles of Depression
Reference/s: High School 'Grades 9 & 10 - Math (John Kelliher, 2012, page 355-363)
Mathematics 9 (DepEd, 2014, page 457-462)
DEVICES AND MATERIALS
 Tape Measure
 Manila Paper
 Printed Animals
 Cartolina
 Pentel Pen
III.
IV.
PROCEDURE
Teacher’s Activities
A. Routinary Matters
Good morning, Class!
Student`s Activities
Good morning ma`am!
Class please stand for our prayer. Marvin, In the name of the father….
please lead the prayer.
Amen.
Before you take your seats, please pick up the
pieces of paper under your chair and kindly throw
those in a proper place.
Yes, ma`am.
Is there any absent for today class?
No, ma`am.
Very Good! Give yourselves a round of (Class Applause)
applause!
B. Review
Class, do you remember our past lesson last Yes, ma`am.
week?
And what was that lesson?
Ma`am!
Yes, Roel.
Our previous lesson was all about
trigonometric ratios ma’am.
Yes, very good Roel.
Now, who can
trigonometric ratios?
explain
further
about Ma`am!
Yes, James!
The trigonometric ratios are special
measurements of a right triangle. The two
sides of a right triangle which form the
right angle are called the legs, and the
third side, opposite the right angle is
called the hypotenuse.
Good job James! Any addition?
Yes, Jhango!
Ma’am.
A way of remembering how to compute
the sine, cosine, and tangent of an angle
is to memorize the word SOHCAHTOA.
SOH stands for Sine equals Opposite
over Hypotenuse. CAH stands for Cosine
equals Adjacent over Hypotenuse. TOA
stands for Tangent equals Opposite over
Adjacent..
Impressive Roel! Thank you very much!
C. Motivation
This morning, we will have a new lesson, but Yes, Maam!
before that we will have a game called “FDP”. Are
you ready class?
Now, listen carefully for the instructions. Form
yourselves into 3 groups; you can choose your
group mates.
Are you done already with the grouping?
Yes, Ma`am.
So, here are the mechanics of the game.
Yes, ma`am.
Problem #1:
Catherine is a pet lover. She has three (3) birds and
two (2) dogs. One week after one (1) of her dog
died. Her father bought three (3) chicks as a
replacement for her dog. How many birds, dogs and
chicks does Catherine already have?
Answers:
Birds= 3
Dog=1
Chicks =3
Problem #2:
Once upon a time in a far away kingdom there lived
four (4) gorgeous chicks and three (3) chubby
snakes. They became happier when their family Snakes =3
grew with the addition of two (2) sweet dogs. How Chicks = 4
many snakes, chicks and dogs are in the kingdom? Dogs = 2
Problem #3:
Babe is an all pig group of four (4) pabebe pigs. But
a year after, two (2) members of pabebe pigs
died because of car accident. The management
decided to form another group including remaining Pigs= 2
pabebe pigs and the newly discovered talents, the Birds= 2
Chick=1
two (2) birds and one (1) chick. How many pigs,
bird and chicks are there in the group?
Problem #4:
The four (4) singing birds serenade the two (3) cute
dogs in the park. Two (2) snakes who were also in
the park that time fell in love with the sweet voices
of the birds. Even the three (3) chicks fell in love
with their music but the three (3) pigs found it
boring and walked away. How many birds, dogs,
snakes, chicks and pig stayed in the park?
Birds = 4
Dogs = 3
Snakes = 2
Chicks = 3
Pigs = 0
Problem #5:
The two (2) chicks who were clever once was lost
in the meadows one afternoon. They were very
afraid when they saw three (3) snakes. They ran Chicks = 2
for their lives and unexpectedly three (3) dogs Dogs = 3
showed up and protected them from the enemies.
So the three (3) snakes walked away and left the
two (2) chicks. How many chicks, dogs and snakes
were left?
Give yourselves a round of applause! Did you
have fun??
Yes, ma`am.
Alright!
D. Presentation
Our lesson for today is all about Angle of
Elevation and Angle of Depression.
E. Explanations
But first, we must know what is a line of sight is.?
Who has an idea based on our activity and from the
world itself?
Ma’am!
Yes, Jessica!
Very well said, Jessica!
The line of sight is a straight line along
which an observer observes an object. It is
an imaginary line that stretches between
observer's eye and the object that he is
looking at.
Now, what is an angle of elevation? Any Idea? Ma’am!
From the word elevate.
Yes, James!
Ma`am!
The angle of elevation is an angle
between the horizontal and the line from
the object to the line of sight.
Yes, Very Good James!
Angle of Elevation is the angle above horizontal
line that an observer must look to see an object that
is higher than the observer..
What about the Angle of Depression?
Ma`am!
Yes, Mary Joy!
If the object is below the level of the
observer, then the angle between the
horizontal and the observer's line of sight
is called the angle of depression.
Excellent, Mary Joy!
The angle of depression is actually congruent to the Yes, Ma’am!
angle of elevation. Do you notice it?
Now, we will learn how to identify the
segment that represents the line of sight and the
angle that represent the angle of elevation or angle
of depression. Look at the picture I have posted on
the board. If you will notice, there are lines and
letters on it. On that picture, you can now identify
the line of sight and the angle of elevation or
depression. On the right side of the board is the
table which you will fill in. You put on the box what
segment the line of sight is and the name of the
angle of elevation or depression.
Angle of
Elevation
Angle of
Depression
Line of
Sight
Ma`am!
Zero pair is a pair of opposite term.
Very good! Nice observation.
So, now we can now proceed to the addition of
polynomials.
Example # 1 (2x2-3x+4) + (3x2+2x-3)
(2x2-3x+4)
+
(3x2+2x-3)
5x2-x+1
Example # 2 (2x3+1) + (x2-x-1)
(2x3 +1)
+
(x2-x-1)
2x3+x2+x
Example # 3 (4x2+4x-5) + (-4x2+2x-1)
4x2+4x-5
+
-4x+2x-1
6x-6
Is everything clear now in addition and
subtraction of Polynomials class? Is there any No ma`am.
question or clarification?
Lets have proceeddc now to the subtraction
of polynomials who can still remember the rule in Ma`am!
subtracting integers? Anyone?
Yes, Ellen
The rule in subtracting integers are,
first change the sign of the subtrahend and
change the operation to addition.
Very good Ellen! Good job! That’s corect class!
Why did I ask that question? This is beacause we
will apply or use that rules in subtratcion of integer
in subtracting polynomials. Lets have an example:
Example # 1: (3x3-x2+x-5) – (x3-x2+x+3)
3x3-x2+x-5
+
-x3+x2-x-3
2x3 -8
Example # 2: (2x2-x+1)-(-x-3)
2x2-x+1
+
x+3
2x2 + 4
Example # 3: (5x3-3x+1)-(x3+4x2-2)
5x3-3x+1
+
-x3-4x2+2
4x3-4x2-3x+3
You`re doing great class! And do you still have
any questions? Or any clarification?
No ma`am.
F. Generalization
As an overview, what is a line of sight?
Ma’am!
Yes, Jhango!
who can tell to the class what is an angle of
elevation?
Yes, Jessica!
Excellent Jessica!
Then, what about the angle of depression?
Yes! Other hands please!
Yes, Ashley!
Very Good Ashley, Thank you!
Class, cite an imporatant application of angle of
elevation and depression in real life?
The line of sight is a straight line along
which an observer observes an object. It
is an imaginary line that stretches
between observer's eye and the object
that he is looking at.
Ma`am!
The angle of elevation is an angle
between the horizontal and the line from
the object to the line of sight..
Ma`am!
If the object is below the level of the
observer, then the angle between the
horizontal and the observer's line of sight
is called the angle of depression.
Ma`am!
Yes, Arjune!
Ma’am,
One of the important application of angle
of elevation and depression in real life is
determination of height and distances of
distant objects that are not directly
measurable.
Excellent, Arjune!
G. Drill
Now lets check if you really understood our
lesson today. We will call this activity “Angle-lo
Gulo!”
We will have the same grouping.
H. Evaluation (10 minutes)
Please get ¼ sheet of paper and answer the
following:
(2x3 + 7x2 + x) + (2x2 - 4x - 12)
(6x3 - 4x2 + x - 9) - (3x2 + 7x + 3)
(2x2 + 1) + (x2 - 2x + 1)
(54x3+23) – (57x3-38x2+6x+5)
(12x2 + 17x - 4) + (9x2 – 13x + 3)
(5x3-6x+10) + (x3+10x-9)
(34x3+43x2-63) – (23x3+13x2+12)
(8x3-6x+10) – (x3+13x-36)
(45x3-62x2-77) + (86x3-13x2+12)
10. (24x3-12x2+53) + (65x3+13x2+16)
1.
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8.
9.
I. Assignment
Answers
1. 2x3+9x2-3x-12
2. 6x3-7x2-6x-12
3. 3x2-2x+2
4. 3x3+38x2-6x+18
5. 21x+4x-1
6. 6x3+4x+1
7. 11x3+30x2-75
8. 7x3-19x+46
9. 131x3-75x2-65
10. 89x3+x2+69
Read in advance chapter 8 in your algebra
book from page 418-425 the Multiplication and
Division of Polynomials lesson.
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