A Detailed lesson Plan inMathematics 8(Pascal, Fermat)

I. Objectives

At the end of a 60-minute lesson, the students should be able to:

A. define probability;B. determine the number of occurrence of an event;C. solve simple problems involving probability of events; &D. show appreciation on how the likelihood of an event help them in making decisions.

II. Subject MatterA. Topic: Probability of an EventB. References: Grade 8 Mathematics Learner’s Module by Dep.Ed, pp. 562-585.

Learning Probability with Technology & Manipulative from education.brainpop.com

Math User’s Handbook by Creative Publications, pp. 240-251.C. Materials: Printed materials, dices, snake & ladder board game, candies, container,

spinner, flash cards, multi-media presentation, coinsD. Skills to be developed: determining, solving, defining

III. Procedure

Teacher’s Activity Learners’ ActivityA. Daily Routine

1. Customary Greetings

Good morning class Greet your classmates too.

2. Prayer

Kelly, may you lead us to a prayer. Before taking your seat, pick-up the pieces of paper under your desk and arrange your chairs. Class secretary, is there any absent today?

B. Motivation

Now class, are you familiar with the game named Snake & Ladder? And are you also familiar with the movie entitled “Game of Thrones”? So today, we will play Snake and Ladder with

: Good morning ma’am!: Good morning classmates!

: (Kelly will lead a prayer.)

: (The students do as told): None ma’am

: Yes ma’am

: Yes ma’am

the twist of Game of Thrones. When Robert Baratheon, the king of the seven kingdoms died. We have here a chips, this is Daenerys Targaryen and Stannis Baratheon, they want to claim their rights on the throne. They want you to be their armies. They need your help to reach the king’s landing where the throne is. The one who has a fire on their name tags will be the army of Stannis Baratheon and the one who has a dragon on their name tags will be the army of Daenerys Targaryen. This side will be Targaryen’s armies (point to the right) and this side will be Baratheon’s armies (point to the left). Now, go to your respective groups. Settle down class. The mechanics of the game is simple. Would you mind to read, Nemuel?

Thank you, Nemuel. Did you understand class? Are you ready? Let’s see who will win the throne. Now let us start our game. “Shake”… “rattle”… and “roll” Let us clap for ourselves.

C. Presentation of the Lesson

:(The students do as told)

Mechanics:1. Each group is composed of 11 members.2. Each group will be given a die.3. When the teacher says “shake”, one representative of each group will have short quick movements, when the teacher says “rattle”, the representative will have to be ready and steady, and when she says “roll”, the representative will roll the die from each group.4. Another representative will move their chip according to the number shown by the die after rolling it.5.If the chip stops at the foot of the ladder, it means that the chip will move upward following ladder but if the chip stops at the head of snake, the chip will go down to its tail.6. After the 2 representatives from each group, another 2 representatives from each group will do the same.7. The group who will reach the finish line first will be declared as the winner and claim their prize later.

: Yes, ma’am.: Ready

: (The students play the game): (The student do as told)

How did you find the game we played, Karen?

What lessons have you learned?

What did you notice on rolling the dice? Fred?

Excellent! How many faces of the dice do we have? Alvin? Very good. All you’ve said earlier has something to do with our topic today. (The teacher reveals the title). Will you read it, class?

D. Development of the lesson

Suppose we have here two 1-peso coins. What are the possible outcomes we can get in flipping the coins together? Will you give us one? Angelito? Will you show us that outcome using these 2 coins? Very Good, Angelito.

Another outcome, Lorena? Will you show us? That’s right. Another one? Rio? Kindly show us? Rio? Brilliant.

Are there some more? Yes, Marie? Amazing! Is there still any other possible outcome? Now, how many possible outcomes do we have in flipping 2 coins? Joezer? Very Good! What is the probability in getting 2 heads? Roselle? How did you get your answer?

That’s right! Let’s have another problem. In this container there are 15 different colored candies, 3 are red, 7 are blue, and 5 are yellow. Rosemarie wants to pick a red candy from it and she needs our help to know how many chances

: The game was very fun and exciting ma’am.

: Winning the game is only by chance ma’am.

: When rolling the dice, we can only get one result, ma’am.

: 6 faces, ma’am.

:The Probability of an Event

: Head and Tail, ma’am.

: (Angelito do as told)

: Tail & Tail, ma’am.: (Lorena do as told)

: Tail & Head, ma’am.: (Rio do as told)

: Head & Head, ma’am.

: None, ma’am!!

: 4 ma’am.

: 1/4 ma’am.

: Since we have only one chance in getting 2 heads out of 4 outcomes ma’am.

she has to get a red candy. What do you think is her chance of getting red candies? That’s right! But is that already the final answer? Nhorielyn? Why do you say so? Amazing!! How about getting red &yellow candies? Michelle? Very Good!! Now, based on the given problems we can now define if what is probability, who wants to share her/his idea? Abigael?

Nice idea! Now, we have here a definite meaning of Probability. (reveal the definition). Will you read it, Rio?

From the given example a while ago, who wants to compose a formula on getting the probability of an event? Dishelle?

Thank You. Now let’s see if she is correct. (reveal the formula) Wonderful! What a brilliant mind. On getting the P as the event is equal to the number of favorable outcomes over the number of all possible outcomes. Actually this is how we arrived on our answer a while ago.

E. Application Let’s see if you already understand our topic today. Let’s have an activity and we will call it “Play & Spin me correctly” Your group will be seen under your desk.Before you will go to your respective groups, will you read the mechanics, Sharon?

: 3/15 ma’am.

: No ma’am. It should be 1/5.: Because we can still simplify it, ma’am.

: 8/15 ma’am.

: Probability refers to a chance or possibility of getting the possible outcome from an event, ma’am.

:Probability is a branch of mathematics that seeks to study uncertainty in a systematic way. It is a measure or estimate of the likelihood of an event happening.

: Probability of an event is equal to the number of outcomes over the total number of outcomes.

Mechanics:1. As the teacher says “play” she will spin the spinner and get the question on the windows of the palace written on a card depending on the color where the arrow points.2. Color Red is for “House of Lannister”, color yellow is for “House of Baratheon”, color green is for “House of Tyrell”and color Blue is for “House of Stark”.3. The teacher will read the question and students

Now, all who got a card of House Lannister will be the group 1 and go to the left side, while the others who got House Baratheon will be the group 2 and go to the right side, and who got the card of House Tyrell will be the group 3 and they will stay at the back of group 1 while the others who got the card of House Stark will be the group 4 and they will stay at the back of group 2. (the teacher will distribute the flash card and chalk of each group). Are you ready class? Let’s start “Play & Spin me”. “Play”… “Stop”… “Pak Ganern”

Red ( Card of House Lannister)-The probability of getting an 11 when spinning a spinner divided into 12 equal divisions numbered 1 to 12.-The probability of getting an even number from the set of counting numbers.-What is the probability of getting a heart from a deck of cards?-In a class of 24 boys and 15 girls, one student is chosen at random. What is the probability that the student chosen will be a girl? Blue ( Card of House Stark)-The probability of being chosen to do your oral report first if your teacher puts all 25 students in a bag and draws.-The probability of drawing a blue marbles from a bag containing 4 red marbles, 12 green ones, 9 blue marbles and 2 yellow marbles. Green ( Card of House Tyrell)-A card is drawn from a well-shuffled deck of 52

will write the answer on their flashcard given to them.4. As the teacher says “stop”, the students will stop writing.5. As the teacher says “Pak Ganern”, each group will raise their flashcard with their answers written on it. Make sure your answer is in simplified form.6. The group that will not raise their flashcard in the exact time, their answer will not be accepted even if it is correct.7. Whoever gets the correct answer will get 1 point.8. The group who has the highest point will be the winner and claim their prize later.

: (The students do as told)

: Yes, ma’am.

: (The students do the activity)

: 1/2

:1/2

:1/4

:5/13

:1/25

:1/3

cards. What is the probability that the card drawn is an even number?-The probability of getting a blue gumball out of the machine if there are 25 each of green, yellow and blue gumballs.-The probability of getting a prime number in the spinner. Yellow (Card of House Baratheon)-You draw a card from a deck of cards and then put it back, and then you draw another card. What is the probability that you get a spade and then a heart?-If you toss a coin 48 ties and get 26 heads. What is the probability of getting a head?-A spinner is divided equally and numbered as follows: 1, 1,2,3,4,1,1,2. What is the probability that the pointer will stop at an odd number? And the winner is group !!! Let’s clap for them.

F. Valuing

We have here four balloons from your respective kingdoms, you need to pop it out to get the rambled words inside it and arrange them to know what their message to you. Is it clear, class? (distribute the balloons in each group) Ask one representative from your group to post the message that you formed on the board.

Now, Each representative will give at least one sentence about their ideas on the message. Let’s start from group 1, the House of Lannister.

Next is from group 2, the House of Baratheon.

Followed by group 3, the House of Tyrell.

Last but not the least is group 4, the House of Stark.

Excellent! Let’s clap for ourselves. In fact, “Probability is the very guide of life” comes from

:5/13

:1/3

:5/12

:1/6

:13/24

:5/8

: (The student do as told)

: Yes, ma’am.

:(Each representative from each group will post the message they formed on the board at the same time)“Probability is the very guide of life”.

: Probability leads our way in the right direction if we have many choices in life.: Probability can influence us in our life where in choose the options who gets the highest probability for you.: Probability helps us to oversee the chances of a thing, the way we think, it gives us information or hint if we choose it or not.

: Probability is just like a device that assists us on our right destination or rescue us if we are confused.

Cicero. Saying that Probability can help us in making decisions. Consider that option 1 has a lower probability that option 2 but option 3 has the highest probability among them. Therefore, we will choose option 3 which has the highest probability to gain success in your decision.

G. Generalization

Now, from what we discussed a while ago. What is the meaning of Probability again, class? Yes, Kelly.

Excellent! And how about the formula in getting the probability of an event? Yes, Sharon?

Very good. How can probability help us in our daily life? Roselle?

Very good.

IV. Evaluation

It seems that you really understand our lesson today. Then, let’s have some exercises, bring out ¼ sheet of paper and answer the following questions. Make sure your final answer is in lowest term.1. Ma. Visitacion is asked to choose a day from a week. What is the probability of choosing a day which start with S?2. If one letter is chosen at random from the word TRUSTWORTHY, what is the probability that the letter chosen is a consonant?3. The faces of a cube are numbered 11 to 16. If Luring rolled the cube once, what is the probability of rolling a composite number?4. Of the 45 students in a class, 25 are boys. If a student is selected at random for a field trip, what is the probability of selecting a girl?5. What is the probability of getting an 8 from a deck of 52 cards? Let us now check, exchange papers with your seatmate. Count the number of the correct items and pass it forward.

V. Assignment

: Probability is about getting the possible outcome from an event.

: P is equal to the number of favorable outcomes over the number of all possible outcomes.

: It help us in making decision, ma’am.

: 2/7

: 9/11

: 2/3

: 4/9

:1/13

: (The students will do as told)

: (The students will do as told)

Now, bring out your assignment notebook and copy your assignment. Yahtzee is a dice game where 5 dice are thrown

a. What is the probability of rolling a 6 on all five dice?

b. What is the probability of rolling the same number on all five dice?

c. What is the probability of rolling not even one pair with 5 dice?

Goodbye, class.

: P=1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 =1/6^5 =1/7776

: P=6 x 1/6^5 = 1/6^4 =1/1296

P= 6 x 5! =120/1296 =5/54

: Goodbye, ma’am!