A DETAILED LESSON PLAN.docx

A DETAILED LESSON PLAN IN MATHEMATICS III GEOMETRY I. OBJECTIVES: The students should be able to: a. derive the Pythagorean Theorem; b. apply the Pythagorean Theorem in solving mathematical problems; and, c. appreciate the contribution of Great Mathematician in the field of mathematics. II. SUBJECT MATTER Pythagorean Theorem Reference: Geometry books and internet Materials: cartolina chalk/ board cut outs computer (power point presentation) Values Integration: Appreciation of the contribution of the Great Mathematician in the field of mathematics III. PROCEDURE: Teacher’s Activity

Students’ Activity

A. Preliminary Activities 1. Prayer 2. Recall the Area Addition Postulate

1. Student will be asked to lead a prayer 2. Area Addition Postulate If two or more polygonal regions do not overlap, then the area of their union is equal to the sum of their individual areas.

3. Very good! B. Motivation 1. I have here some cut outs. What are these 1. Sir, you have four congruent triangles and shapes? How many figures do I have? one square. (Students should arrive at this figure out of the cut outs)…

2. Definitely! 3. From these figures you will be having a group activity. The title of the activity is Assemble and Learn. 4. You will be grouped into 5 groups. Each group will choose one representative to present their work afterwards. In doing the activity, the students should follow the following procedures. EXPLORATION Activity: ASSEMBLE AND LEARN POCEDURES: 1. Labels the sides of your triangles like this; b a c 2. Using all the cut outs, form a bigger square.

3. In terms of a and b, what is the length of the side of the inner square? 4. In terms of a and b, what is the area of one of the triangles? 5. What is the area of the inner square? 6. What is the area of the bigger square in terms of c? 7. If you add the area of the four congruent triangles and the area of the inner square, will the sum be equal to the area of the bigger square? Why? 8. Out from the cut outs, form an equation in getting the area of the bigger square. 9. Try to remove the inner square and make an equation indicating the removal of the inner square. 10. The equation should be in its simplest form. C. Lesson Proper 1. What is the simplified form of the equation you’ve derived out from the cut outs? 2. Great answer! That equation is what we call as the Pythagorean Theorem named after Pythagoras. 3. These four triangles are congruent and they are all right triangles. 4. What is a right triangle? 5. Precisely! 6. The longer side, labeled as letter c, is what we call as the hypotenuse, and the 2 remaining sides, labeled as a and b that are shorter are what we call the legs. 7. The Pythagorean Theorem is being used only in a right triangle. 8. Let us try solving a problem using the Pythagorean theorem. Problem 1. 8 6 x Find the value x. Solution: Using the Pythagorean Theorem, c= , c= x, a= 6 and b= 8, by √ substitution, x= √ x= √ x= √ x= 10 Problem 2. Find the perimeter of the square whose diagonal is 5√ cm long. Solution: Since the diagonals of a square bisects each other, 5√ cm will be divided by two.

Let c be the side of the square. a= (5√ )/2 b= (5√ )/2 c= √

√

√

1. The simplified form of the equation we’ve derived out from the cut outs is, c2= a2 + b2 or c= √

4. A right triangle has a right angle and has a measure of 90.

c= √ c= √ c= √ c= √ c= 5

P= 4s P= 4(5) P= 20 cm

D. Application Work by pair to solve the following puzzle. Write the corresponding letter of the item on the space provided at the top of your calculated answer. ___ ___ ___ ___ ___ ___ ___ ___ ___ ____ 3√ 13 15 6 √ 15 12 √ √ 2√ “He is a great mathematician from Samos, Ionia” The following are all right triangles: 1. c= 6, a= 3, what is the value of b? (P) 2. c= 10, a= 3, what is the value of b? (A) 3. b= 12, a= 5, what is the value of c? (Y) 4. c= 13, a= 5, find the value of b? (O) 5. a= 9, b= 12, what is the value of c?(T) 6. c=10, b= 8, what is the value of a? (H) 7. b= 9, c= 11, what is the value of a?(S) 8. a= 10, c= 11, what is the value of b?(R) 9. c= 20, a= 12, what is the value of b?(N) 10. a= 9, b= 12, what is the value of c?(G) E. Generalization 1. What is Pythagorean Theorem?

1. The Pythagorean Theorem In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

2. Very good! 3. What is the essence of the contribution/s 3. The contributions of the Great of the Great Mathematicians in the field of Mathematicians are essential in mathematics because without these contributions mathematics? mathematics would be nothing. Beautiful buildings would not be realized. 4. Great idea! IV. EVALUATION Solve the following problems using the Pythagorean Theorem. 1. Jay- jay left his house and walked 6 km due east and then 8 km due north. How far is he from the starting point? 2. Find the width of the rectangle whose diagonal is 12 cm long and whose base is 4√ cm long. V. ASSIGNMENT 1. Find the area of a rectangle whose diagonal is 15 cm long and whose base is 12 cm long. Prepared by: Mr. Jonel R. Rosete