Mathematics Lesson Plan (Detailed), Summaries of Mathematics

Download Mathematics Lesson Plan (Detailed) and more Summaries Mathematics in PDF only on Docsity! REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS Facilitator: Daniela Marie O. Apelado I. OBJECTIVES A. Content Standard: demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations, and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions. B. Performance Standard: is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions and solve these problems accurately using a variety of strategies. A. C. Learning Competencies: At the end of the discussion, the students should be able to: a. Factors completely different types of polynomials (polynomials with common monomial factor, difference of two squares, sum and difference of two cubes, perfect square trinomials, and general trinomials). Transform a statement into an equivalent if-then statement. II. SUBJECT MATTER Topic: Patterns and Algebra (M8AL-Ia-b-1) A. Topic: Patterns and Algebra B. Materials: Laptop, Presentation, Slide Decks/Visual Aids, LCD Monitor/Projector, Board, Pen or Chalk C. References: 1. Elementary Algebra I. 2000. pp. 200-211* 2. Moving Ahead With Mathematics II. 1999. pp. 194-209 3. NFE Accreditation and Equivalency Learning Material. Special Products and Factoring. 2001. pp. 11-18 4. BEAM I – Module 16: Factoring D. Values Focus: Mutual Respect E. Duration: 45-50 minutes III. METHODLOGY/PROCEDURE Teacher’s Activity Learner’s Activity A. Preparatory Activity REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS I. Daily Routine Good morning class! How are you today? It’s good to hear that. Are you excited for today’s lesson? All right! Before we begin with our discussion, may I request everyone to please stand for a short prayer. You may now take your seats. Is everyone here today? Impressive. II. Review/Apperception Now, as a short recap from our previous lesson, who can give a short overview of the concepts we’ve discussed? Very Good! Let us see how much have you learned from our previous discussion by this activity. Are you ready? Activity: Find My Factors. Direction: Determine the factors of the following quadratic equations. 1. x2+7x+6 2. x2−7 x−8 3. x2+5x+6 4. x2+13x+12 5. x2−10 x−200 Good job class! It seems that you have really mastered our previous lesson. Good morning Sir! We’re doing great Sir. Yes Sir! (A student will lead the prayer.) Yes Sir. Last meeting, we talked about factoring quadratic equations. We determined the factors of the value of C that when added, we will get the value of B in the quadratic equation. We’re ready Sir! (x+6) (x+1) (x+1) (x – 8) (x+3) (x+2) (x+1) (x+12) (x-20) (x+10) REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS x = −b±√b2−4 ac 2a I will sing it twice then it’s your turn after. Am I clear? (sings the formula twice) Now, it’s your turn. Marvelous! You all are great singers! Now we can proceed to the discussion. Yes Sir. (sings until they can sing without looking at the board and memorizes it) D. Explain This morning, we will find the origin of the quadratic formula and it is formed from the quadratic equation to that formula. The quadratic formula where x is isolated at the left and the equation at the right can determine the zeros of the equation was derived from the quadratic equation itself. (ax2+bx+c=0) In finding zeros, we must find the value of x and Mathematicians derived a formula to isolate the x at the left and come up to a formula that can be solved by just substituting the values of A,B and C. First, Start with ax2+bx+c=0 Divide the equation by a REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS Put c/a on other side Add (b/2a)^2 to both sides The left hand side is now in the x^2 + 2dx + d2 format, where "d" is "b/2a" So we can re-write it this way: "Complete the Square" Now Solve For "x" When simplified, REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS x = −b±√b2−4 ac 2a Can you sing the quadratic formula song again? Marvelous! Now everybody sing on my count. That’s great to hear that you can catch up to the lesson. So that’s how Mathematicians come up to isolate the x. Now, we move on to how we can determine the value of A, B, and C. The quadratic equation is in the form ax2+bx+c=0 So, the values of a, b and c are the coefficients and the constant for the value of c. For example: x2+7x+6 A=1 B=7 C=6 Another example: x2−10 x−20 A=1 B= -10 C= -20 Now, can you determine the values of A, B, and C? Let’s test your comprehension. Yes Sir! (sings the quadratic formula) REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS Yes Sir! E. Elaborate I will divide your class into four groups. I will designate leader each group who will pick a fruit from the tree and solve the x values for the equation written on the fruit. 1. x2+14 x+49 2. x2+20x+100 3. 3 x2+11 x+6 4. 5 x2+8x+3 Instruction: Solve for the values of x then report your answer to the class? Use the step we discuss earlier and try to answer without erasures. (start doing their activity) (presenting of activities) F. Evaluate Prepare a sheet of paper. Direction: Read the equations carefully. Write REPUBLIC OF THE PHILIPPINES POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SAN PEDRO CITY CAMPUS the answer by following the steps in solving for the x values using quadratic formula. Solve it in your own. 1. x2+13x+12 2. x2−10 x−200 You have 10 minutes to answer the activity. (After 10 minutes) Pass your papers. Please stand and let’s have a closing prayer. (Closing Prayer)