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Taft Avenue, Manila

Department of Mathematics

A Detailed Lesson Plan in Grade 7 Mathematics on

Angle-Sum Theorem of Polygons

Submitted By:

Kevin Emmanuel S. Deniega

III- 34 BSE Mathematics

Submitted to:

Dr.Gladys Nivera

February 5, 2013

Original Copy

I. Objectives: At the end of a 30-minute period class the students should be able to:

A. Explain how to get the sum of the interior angles of a convex polygon. B. Solve for the sum of the interior angles of an n-sided convex polygon. C. Determine the number of sides of a polygon based on the given sum of all the interior angles. D. Foster cooperation with his group mates in accomplishing the task assigned to their group. E. Present to the class the output of their group activity. F. Develop the act of helping his/her classmates in some of their difficulties in answering some problems. G. Respond to the questions of his/her classmates with regards to the question that he/she is answering.

II. Subject Matter:

Topic: Angle Sum Theorem of Polygons

Materials: Puzzle, chart, worksheets, protractor

References:

Nivera, Gladys C. (2012).Patterns and Practicalities (K-12).Grade 7 Mathematics.

Makati City: Don Bosco Press.

Jose-Dilao, S. & Bernabe, J. (2002). Geometry.

Quezon City: SD Publications.

III. Instructional Strategies:

A. Preparatory Activities 1. Prayer 2. Greetings 3. Checking of attendance

B. Developmental Activities

Teacher’s Activities

1. Review and Motivation. The class will be divided into four groups. Each group will be provided with a jigsaw puzzle (the puzzles are shown at the last page of this lesson plan). After they formed the puzzle they will found several illustrations of polygons (from triangle to octagon). They need to identify each polygon and they need to recall the sum of the interior angles of a triangle. They will be provided with a magic pen that will help them to decode the hidden message at the back of the puzzle. The hidden message will lead to a new activity that will launch the lesson for the day.

2. Lesson Proper After they found the device they will find out the following instruction: 1. Count the number of sides of each polygon. 2. Draw all the possible diagonals that can be formed from one vertex of the polygon to another vertex of that same polygon. 3. Count the number of triangles that can be formed after drawing all the diagonals. 4. Using a protractor, find the sum of all the measurement of the interior angles of each polygon. 5. Record your data on the chart that will be given to you by the teacher. (the example of the chart is shown at the last page of this lesson plan)

Student’s Activities

All of the group will post there chart on the board.

Can you please compare the number of triangles formed by the diagonals with the number of sides of the polygon? What is the sum of the interior angles of a triangle?

What can you say about the sum of the interior angles of a triangle and a quadrilateral? How about a quadrilateral and a pentagon?

How can you relate the sum of the interior angles of each polygon with respect to the number of triangles that can be formed by the diagonals?

C. Generalization How can we obtain the number of triangles that can be formed by an n-sided polygon or n-gon? What is the sum of the interior angles of an n-gon?

How can we identify the number of sides of a polygon if the only given information is about the sum of the interior angles of that polygon?

The number of triangles formed is two (2) less than the number of sides of the polygon.

The sum of the interior angles of a triangle is equal to 1800.

The difference between the sum of the interior angles of a triangle and a quadrilateral is equal to 1800.

The difference between the sum of the interior angles of a quadrilateral and a pentagon is equal to 1800.

The quotient between the sum of the interior angles of each polygon and the number of triangles formed is equal to 1800.

The number of triangles can be formed with an n-gon is two less than the number of sides of polygon or n-2. The sum of the interior angles of an n-gon is equal to the product of the number of triangles formed and 1800 or (n-2)1800 We can identify the number of sides of a polygon if we have the sum of the interior angles. Solve for the quotient of the given sum of interior angles and 1800. Just add two (2) to the quotient. In mathematical symbol we have this as: Sum of the interior angles180°+2

4. Application

Look for a partner. It can be your seatmate or anyone from the class, seat beside each other. There will be two worksheets; you must see to it that you are holding different worksheet. For those who are holding the worksheet 1 you will act as the first doer then those who are holding worksheet 2 you will act as the helper. The doer will answer the question and the helper will be the one to check the answer of the doer. If the doer has a question, the helper must answer it and the helper must guide the doer in answering. After the doer answered the first question, you will switch role. Remember that you are going to switch role after each question. Please see to it that your partner do not see the solutions that is also provided in you worksheet, you can fold the worksheet if you want. You can start doing the activity.

Worksheet 1 Worksheet A | Answer to Worksheet B | 1. What is the sum of the measurement of the interior angles of a Dodecagon? | 1. Using the formula to get for the no. of sides of a polygon: Sum ofinterior angles180° +2 5580°180°+2 24+2 33 The polygon has 33 sides | 2. How many side does a polygon has if the sum of the measurement of all its interior angles is equal to 43200? | 2. Using the formula: (n-2)1800 For decagon: (10-2) 1800 (8) 1800 14400 For quadrilateral: (4-2) 1800 (2) 1800 3600 So, 14400 – 3600= 10800 10800 is the difference. | 3. Get the difference between the sum of interior angles of an octagon and a pentagon. | 3. Pentadecagon has 15 sides. Using the formula: (n-2)1800 (15-2) 1800 (13) 1800 23400 The sum of the interior angles of a pentadecagon is equal to 23400 |

Worksheet 2 Worksheet B | Answer to Worksheet A | 1. How many side does a polygon has if the sum of the measurement of all its interior angles is equal to 55800? | 1. Dodecagon has 12 sides. Using the formula: (n-2)1800 (12-2) 1800 (10) 1800 18000 The sum of the interior angles of a dodecagon is 18000 | 2. Get the difference between the sum of interior angles of a decagon and a heptagon. | 2. Using the formula to get for the no. of sides of a polygon: Sum ofinterior angles180° +2 4320°180°+2 24+2 26 The polygon has 26 sides | 3. What is the sum of the measurement of the interior angles of a pentadecagon? | 3. Using the formula: (n-2)1800 For pentagon: (5-2) 1800 (3) 1800 5400 For Octagon: (8-2) 1800 (6) 1800 10800 So, 10800 – 5400= 5400 5400 is the difference. |

5. Evaluation On a one-half sheet of paper, answer the following. I. Find the sum of all the interior angles of the following: 1. Triskaidecagon (13 sides) 2. Hexakaidecagon (16 sides) 3. Enneadecagon (19 sides) 4. Hectagon (100 sides) 5. Chiliagon (1000 sides) II. Find the number of sides of a polygon based on the following given sum of the interior angles. 1. 27000 2. 34200 3. 54000 4. 70200 5. 93600

Key to correction: I. II. 1. 19800 1. 17 sides 2. 25200 2. 21 sides 3. 30600 3. 32 sides 4. 176400 4. 41 sides 5. 1796400 5. 54 sides

Attachments: After the students solve the puzzle, the puzzle will look like this: Note: All groups have the same set of puzzle.

The chart that will be used by the students in doing the activity: Polygon | Number of Sides | Number of Triangles | Sum of the measure of interior angles | triangle | | | | quadrilateral | | | | pentagon | | | | hexagon | | | | heptagon | | | | octagon | | | |

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