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- 1. I. Objectives At the end of the lesson students should be able to: a. Define rational equation b. Simplify rational expression c. Apply the procedure on how to simplify rational expression II. Subject Matter Topic: Equations Involving Rational Expression References: Oronce, O.A and Medoza, M.O www.purplemath.com Materials: PowerPoint presentation, LCD, activity sheets, metacards, and cartolina Time: one hour Strategies: Guided-Discovery Learning, Exposition and Cooperative Learning III. Lesson Proper Teachers Activity Student’s Activity Daily Routine May I request everyone to stand up and start our day with a prayer. Everybody, let’s recite our mathematical prayer. Good morning, Class! Before you take your seats please pick up the pieces of paper under your chairs and arrange your chairs as well. You may now take your seat. Chloe, may I know who are absent today? Kindly give us your report. Thank you, Chloe. Review Last time, we discussed about what is a complex fraction and we learned that there are two methods used in simplifying complex fraction. Let’s see if you really understood the lesson by recalling some concepts about our previous lesson. Let’s do our review in the form of Music and Learning is Fun. Students will recite the prayer Good afternoon, Miss Pagaduan! Students will pick up the pieces of paper and arrange their chairs Students will take their seat I’m glad to tell you nobody is absent today.
- 2. To play this game, When the music starts I will give the ball in the class and it will be passed around. Pass the ball to your classmate next to you. When the music stops, the students with the ball will answer the question. Is my instruction clear, Class? So let’s start. (Music plays then stop) It is a fraction that has a rational expression either in the numerator, denominator or both. How many methods were used in simplifying complex fraction? In method one, in simplifying complex fraction you have to invert the denominator to its what? In method two I simplifying complex fraction, we multiply the numerator and denominator to its what? What is the LCD of x+4 and x-6? Motivation Before we proceed to our new lesson, remember that during Grade 7 you discussed about how to find x, right? Let’s play a short game again. It is called “Find your X”. I will choose 10 representatives from the class .Each representative will be given a metacards. The metacards consists of an equation to find x and the answer. Everybody will be scattered around the room and when the music starts you must find your x by greeting to each other and solving the equation if it matches to yours. When the music stops, you must already found your partner and tell to the class how come you arrive in that pairing. Is it clear? Yes, Ma’am Complex fraction Two methods Reciprocal We multiply it by the LCD (x+4)(x-6) Yes, Ma’am! (The class will choose a representative) Yes, Ma’am!
- 3. So, let’s begin! (Music starts) (Music stops) Since you already found your pairing, will you tell now to the class why you arrive with that pairing? Very good! You may now take your seats. Today, we’re going to discuss about Equations Involving Rational Expression and it involves how to find x. A. Activity Our activity before I discuss our topic is that you’re going to complete the table first. (Showing the cartolina with a table to fill). The first and second column are the values of a and b. The third and fourth column, you have to multiply the values of a and b and simplify it. You will be given 7 minutes to finish the task. Afterwards, I will randomly call some of you to fill the columns. a b a˙b Simplified form 5 x+ 1 5 12 m- 1 12 3x 4 𝑥 +4 10a 1 2𝑎 + 3 5𝑎 Let me answer number one for you. What is the value of a and b? In the third column, we have to multiply the value of a and b? What does it look like if we multiply a and b? If we multiply it the simplified form of number one is what? Students will mix around the room to find their match (Students will explain why they come up with such paring) The representatives will take their seat The value of a and b are 5 and x+ 1 5 . 5(x+ 1 5 ) 5x+1
- 4. Do you understand what are you going to do now? Ok, you may now begin. (After 7 minutes) Ok, time’s up. Let’s answer the activity. (The teacher will randomly call to fill the columns) Very good! How about if we’re now going to find x? (Showing another set of rational expressions) Rational Expression LCD x 𝑥 5 + 1 4 = 𝑥 2 3(𝑥+3) 𝑥+1 +2 = 3𝑥+1 𝑥+1 2 𝑥−3𝑥+2 + 3 𝑥−2 = 4 𝑥−1 𝑥 9 - 2 5 = 1 3 B. Analysis Observe our denominators first. What do you notice in our denominators? Since they are dissimilar fractions, what are you going to find? In number 1, what is the LCD of our denominators? Next thing, we’re going to multiply both sides by 20 then simplify. What is now our new equation? Yes, ma’am Students will start answering the activity a b a˙b Simplified form 5 x+ 1 5 5(x+ 1 5 ) 5x+1 12 m- 1 12 12(m- 1 12 ) 12m – 1 3x 4 x +4 3x( 4 x +4) 24 10a 1 2a + 3 5a 10a( 1 2a + 3 5a ) 11 They are dissimilar fractions We’re going to find the LCD The LCD of 5, 4 and 2 is 20. 4x+5= 10x
- 5. That’s right! Our new equation is 4x+5= 10x. What are we going to do next to find x? Very good! What is x? Excellent! To see if x is 5 6 we will only substitute the value of x to our equation to see if our answer is correct. (Showing the checking to the class) So we have the correct answer. In number two, what is our LCD? Since our LCD is x+1, what are we going to do next? Are we going to multiply first or cancel out the common factors? After we cancel out and multiply we can now combine like terms. So what is our new equation? So what is x? Let’s see if our x is equal to -5. Let’s substitute -5 to our x. (Showing the checking) Therefore, the value of x is indeed -5. What if our x didn’t match in our checking? How are you going to write the solution if it is false? Very good! If our equation doesn’t have any solution it is called extraneous solution. C. Application Will you try to solve the remaining items? I will be giving you 7 minutes to complete the task. Then after 7 minutes, we’re going to check. Is that clear, Class? (After 7 minutes)Okay, time’s up! Finish or not finish, let’s check. (Checking of Apply the subtraction property and divide both by 6. x is 5 6 The LCD is x+1 We will cancel out the common term then we multiply. The new equation is 5x+11=3x+1 x is -5 The equation has no solution
- 6. activity) D. Abstraction Based on the two activities we have, can you described to me rational equation? Or what is a rational equation? How do we simplify rational equation? What is an extraneous solution again, class? Do you have any question, class? Do you understand now how to solve rational equation? IV. Evaluation Let’s have one last activity. I’ll be grouping you into three groups. I will call the three leaders of the group to come in front and get the list of your members and the activity sheet. I will be giving you another 10 minutes to complete the task then we will check. Is it clear, class? (The teacher will call the leaders and give the activity sheet) (After 10 minutes) Ok, time’s up. Finish or not finish, let’s check.(Randomly calling students for the checking of activity) Are you done checking, Class? Please pass your paper to the center aisle then to the front. Rational equation is an equation that contains one or more rational expressions. Rational equation is an equation that contains in which one or more terms is a fractional one. To simplify rational equation we must eliminate the rational expressions in the equation by multiplying both sides of the equation by the LCD. Solve the equation then check. Extraneous solution is an apparent solution that does not solve its equation. None, ma’am Yes, ma’am Yes, Ma’am Students will pass the papers to the center aisle then to the front
- 7. V. Assignment For your assignment, answer page135 nos. 2, 3, 21, 27 and 28. Show your solution. Put it in your notebook. Prepared by: Eileen M. Pagaduan Practice Teacher Approved by: Mr. Jeffrey S. San Juan Cooperating Teacher Ms. Nenita S. Juvida Vice Principal Ms. Claribel S. Verdadero Principal SGD Felicidad O. Rodelas Practice Teaching Supervisor High School

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