Permutation - Manugas

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A Lesson Plan in Mathematics IV Prepared by: Eunice L. Manugas January 31, 2010

I.

OBJECTIVES At 1. 2. 3.

II.

the end of the lesson, the students should be able to Explore permutation Find the number of linear permutation of n things taken n or r at a time.

Find the number of circular permutation of n different things

SUBJECT MATTER Topic Reference Materials Needed Values Integrated

III.

: Permutation : Interactive Mathematics IV by Santos pp 473-481 : Manila Paper, textbooks, bond papers, photo copies : participation, promptness, open-mindedness, active thinking

TEACHING STATEGIES (4As) TEACHER’S ACTIVITY

STUDENTS’ ACTIVITY

a. OPENING ACTIVITY Let the students do the routinary activities - Opening prayer - Arranging of the seats - Checking of attendance and Uniforms

(Students are performing their daily tasks)

b. PRESENTATION Motivation Write the letters L, O, V, E in the board. I have a treasure box that contain a password having the letters L, O, V, and E. Unscramble the letters in as many as you can without repetitions. Write your answers in any sheet of paper. You have ten minutes to do it.

(Students are writing their guesses)

Now, how many guesses have you made?

Janice: 12 Shanice: 8 Dennice: 24

Detailed Lesson Plan on PROBABILITY |

Prepared By: Eunice L. Manugas

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Submitted to: Mr. Steven Razonable UNIVERSITY OF CEBU – Graduate School Sanciangko St., Cebu City (032) 255 7777

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TEACHER’S ACTIVITY


Great, now let us have an activity. Activity Group the students into four and provide a piece of manila paper. Instruct them to make a tree diagram. Let them work the diagram for 15 minutes. Allow them to present their work in the class.

(Students readily go to their group and start making a tree diagram) (Each group presents their tree diagram to the class)

Analysis An arrangement of objects or events similar to the activity in the exploration in which the order is important is called permutation. To find the total number of passwords that the hidden treasure has, we can use a list or a tree diagram.

John: That is great, Ms. Manugas. Jason: I understand now, by using the tree diagram, I get the 24 possible password of the treasure

Indeed, and please take note that it does Ericka: I see, so that means that not allow repetition. Hence we can say arrangement or the order is that 4 * 3 * 2 * 1 = 24 really important in permutation In general if n is a positive integer, then n factorial denoted by n! is the product of all positive integers less than or equal to n. Abstraction 1. How can we get the permutation of n things taken n at a time?

Michelle: We can use the Formula nPn

Yes, we can use that formula. We may also use the formula nPr which means the number of permutations that can be made with n things taken r things at a time. nPr

= n(n-1)(n-2) * … * (n-r+1)



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TEACHER’S ACTIVITY


Let us try to solve this. What are we going to do if we are looking for the numbers of permutations of 6 things taken 3 at a time? What formula do we use? Please come in front Nilo.

Nilo: We use the formula nPr ; n=6 and r=3 thus nPr = 6P3 = 6 * 5 *4 = 120

Very well, Nilo. WE may also use the formula nPr

= (n!) / (n-r)!

There is also a special case of permutation where the arrangements of things are in a circular pattern. We call it circular permutation. When people are seated around a circular Eugene: So that means that when a tube, we cannot say that one is seated person moves his position by one in the first seat as what we have on place clockwise or counter linear permutations. In general, there clockwise the relative positions is no first in the arrangements of things in does not change. circular pattern, Yes, you are absolutely correct, Eugene. Remember that the number of circular Permutations of n different things are (n-1)! = (n-1)(n-2) * … * (2)(1)

Application On your workbook, answer pages 479-480.



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IV.

EVALUATION On your math activity notebook, answer the following. 1. In how many ways can 9 different books be arranged on a shelf? 2. The SBO Club organizes a car race in which four cars A, B, C, and D are entered. a. In how many ways can the race be finished if there are no ties? b. In how many ways can the first two positions come if there are no ties?

V.

ENRICHMENT Do this at home 1. In how many ways can 5 persons be seated around a circular table? 2. In how many ways can 9 people be seated at a round table?



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Permutation - Manugas

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