Republic of the Philippines
Laguna State Polytechnic University Province of Laguna
COLLEGE OF TEACHER EDUCATION
SEMI-DETAILED SEMI-DETAILED LESSON PLAN IN GRADE 10 MATHEMATICS
PERMUTATIONS AND COMBINATIONS
Prepared by: EUNICE T. DELA TORRE
Checked by: DR. ALBERTO YAZON
May 2017 Content Standard
Showcases the key concepts and skills on Combinations and Permutations counting techniques.
Performance Standards
The learners will be able to integrate knowledge into perceived counting techniques and utilize the available materials properly.
Learning Competencies I. Objectives
At the end of the lesson the students should be able to: a. Differentiate Combinations from Permutations counting techniques. b. Solve and analyze problems with integration of probability and the counting techniques. c. Develop the awareness of its use in our everyday life.
II. Subject Matter A. Topic: Combinations and Permutations
B. References:
Khanacademy Mathisfun.com TEDEx Mathmagic on Youtube C. Materials
Powerpoint presentation Playing cards Unit: picture, candy, question Prize wheel
III. Activity A. Daily Routine
i.
Classroom management
ii.
Prayer
iii.
Greetings
iv.
Checking of attendance
B. Priming
How was the weather today? What could be the weather later? What did you do first when you wake up? Did you think about getting up/ breakfast for the day/ homework to do/ continue your dream this morning? What were the clothes that you thought you would have worn today? Did you watch Meant to be Yours? Who could be Billie’s top 2 from the four boys she had? C. Motivation Math Magic
A deck of playing cards will be shown in the class. The class will be asked to pick any card they want and is to be predicted by drawing one card out of the deck. Two groups of cards of fives of different suits will be shown in class. It will be shuffled and the class will be shown how Math predicts the pairs of the cards. Another 5 pairs of cards will be separated from the deck of card and will be shuffled. As the magic proceeds, Math will separate the suits of the same color from the different.
D. Activity
The Wheel of Your Fortune today
1. Individuals will be called as volunteers to spin the wheel. 2. As it stops to one spot he/she could either win a prize or do a consequence. 3. The individual will choose two out of the 5 things in the prize box. 4. The individual will pick two (1st and 2nd) out of the n people in the consequence box. 5. The individual will pick two out of the 5 tasks and do it. 6. If it stops to the sign, “pick another individua l to spin me”, they will not do anything.
IV.
Analysis
1. How was the game? 2. Did you have a chance to play the game and get the prize? 3. What are the possible prizes that you could get? 4. What combination of prizes did you choose?
5. If it stopped at the laughing face, what were the possible questions to answer? 6. How about the possible consequences that you must do? 7. Who were the people you chose as 1st and 2nd and who re the other people that you might have chosen? 8. What were the tasks you chose, and the other possible tasks you might have chosen? 9. What could be the numbers of the possible combinations to choose from the prizes/ tasks/ people? 10. So from the activity we had, who can guess the lesson for the day?
V.
Abstraction
A. Combination is an arrangement where order does not matter.
=
! ! ( )!
where n is the number of things to choose from,
and we choose r of them
no repetition, order doesn’t matter
Note: combinations are good for groups, teams, piles, or anything that doesn’t matter what order they are placed in to those groups
EXAMPLE 1: We had the game “Wheel of your Fortune Today” wherein you have the chance
to win prizes. If it stops on the happy face you can get two out of 5 candies in the prize box. What are the different candy prizes you can get from the box?
XO
SO
CC
HH
XO SO
SO XO
HHXO
CCXO
XOHH
SO HH
HHSO
CCSO
XOCC
SO CC
HHCC
CCHH
=
!
=
! ( )!
= =
=
! ! ( )! ∙∙∙ ∙∙∙
=
The combination of different prizes are 6: XOSO, XOHH, XOCC, SOHH, SOCC, HHCC.
B. Permutations is an arrangement where order does matter
!
=
( ) !
where n is the number of things to choose from,
and we choose r of them
no repetition, order does matter
Note: Permutations are good for ordered lists, competition results where it matters what order is selected as 1st, 2nd or third.
EXAMPLE2: Since it stopped on the laughing face. You have to answer the question by
choosing the 1st and the 2nd noisiest person among Rhadca, Gillian, Lea, Paul, Joice, and Ramon. What are the different pairs of top 2 noisiest people in the class?
Rhadca
Gillian
Lea
Rhadca xGillian
GillianxRhadca
LeaxRhadca
Rhadcax Lea
GillianxLea
RhadcaxPaul
Paul
Joice
Ramon
PaulxRhadca
JoicexRhadca
RamonxRhadca
LeaxGillian
PaulxGillian
JoicexGillian
RamonxGillian
GillianxPaul
LeaxPaul
PaulxLea
JoicexLea
RamonxLea
RhadcaxJoice
GillianxJoice
LeaxJoice
PaulxJoice
JoicexPaul
RamonxPaul
RhadcaxRamon
GillianxRamon
LeaxRamon
PaulxRamon
JoicexRamon
RamonxJoice
=
! (−)!
=
=
= =
! (−)!
∙∙∙∙∙ ∙∙∙
=
There are 30 possible pairs of top 2 noisiest people in the class!
VI.
Application Group Activity : There will be two groups with different tasks as follows: Group 1: The group wants to take a selfie together but only by 4 persons at a time.
How many ways can they take the picture together?
Group 2: The group wants to join a “Pahabaan ng pag-Aaaaaaah” competition but
only the top three will receive a pad of yellow paper and ballpens. How many possible orders of top three are there for the competition? VII.
Assessment
1. Sir Yazon is throwing a blow out Sem-ender party. He has 24 3rd year students, but only 5 can fit with him in his limo. How many different entourages could Sir Yazon arrive with? 2.
There are 12 snails in a snailshow competition. The top three winning snails receive money. How many possible money winning orders are there for a competition with 12 snails?
VIII. Assignment
Find Combination with repetition and Permutation with repetition. Give two examples.
