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. 2. 3. 4. 5. 6. 7. 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.
