I.
Objectives
a. Cognitive domain Know the definition and formula of probability. b. Affective domain Relate probability in real-life situations through a short skit. c. Psychomotor domain Perform knowledge skills related to probability in problem solving.
II.
Subject Matter
Mathematics (Probability) Sources: Math Time [Workbook for third year students] http://www.mathgoodies.com/lessons/vol6/intro_probability.html III.
Materials to be used
spinner/wheel with four colors (yellow, blue, green and red) jar with different colors of marbles 6-sided die
IV. Energizer A. Activity Pass the Prop B. Procedure Supplies: a prop (a paper cup, a scarf, a piece of rope, a book) 1. Have students stand in a circle. 2. The teacher will define “prop” as any moveable item used on the set of a play or handled by an actor. She will instruct students that the object of this game is to change the prop she is holding into something it is not. They must use it as if it is that object. There is no sound in this game. 3. The teacher will hold the prop in her hands and demonstrate. For example: she will pretend it is a telephone, she will hold it to her ear and mouth words as if she is talking into it; pretend it is a shoe and she is slipping it on her foot; pretend it is a fork and uses it to eat.
4. Students are to call out what they think you have turned the object into. When they call out the correct answer, the teacher will pass the prop to the student to the right. That learner is to do the same. The teacher will tell learners there are no “repeaters” allowed. If someone chooses the same object as you, you must come up with a different object to change the prop into. 5. Continue the game until everyone has had one turn.
V.
Discussion with Matrix
1. Matrix
1st outcome (1st event)
Probability
Experiment
2nd outcome (2nd event)
3rd outcome (3rd event)
2. Discussion First, without discussing the formula in getting the probability, the teacher will state a problem. Problem: A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red? The teacher will move the spinner and let the students know the answer. Answer: The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth. The teacher will then introduce to the students the meaning of probability and other terms associated to it. She will relate this to the activity earlier. Then the formula will also be discussed. An experiment is a situation involving chance or probability that leads to results called outcomes. In the activity, the experiment is spinning the spinner. An outcome is the result of a single trial of an experiment. The possible outcomes are landing on yellow, blue, green or red. An event is one or more outcomes of an experiment. One event of this experiment is landing on blue. Probability is the measure of how likely an event is. The probability of landing on blue is one fourth.
P(A) =
The Number Of Ways Event A Can Occur The total number Of Possible Outcomes
The teacher will apply the formula using the earlier activity. Problem 1: A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on each color? Outcomes: The possible outcomes of this experiment are yellow, blue, green, and red.
Probabilities: 1
# of ways to land on yellow P(yellow)
=
P(blue)
= total # of colors
4
# of ways to land on blue
1
=
P(green)
= total # of colors
4
# of ways to land on green
1
=
P(red)
= total # of colors
4
# of ways to land on red
1
=
=
4
total # of colors
The teacher will then generalize the solution to the problem. In Problem 1, the probability of each outcome is always the same. They spinner has equal chances for the colors to land. The probability of landing on each color of the spinner is always one fourth. The teacher will provide another problem. Problem 2: A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? of rolling an odd number? Outcomes:
The possible outcomes of this experiment are 1, 2, 3, 4, 5 and 6.
Probabilities:
# of ways to roll a 1 P(1)
=
1 =
total # of sides
6
# of ways to roll a 2 P(2)
P(3)
=
1 =
total # of sides
6
# of ways to roll a 3
1
=
= total # of sides
6
# of ways to roll a 4 P(4)
=
1 =
total # of sides
6
# of ways to roll a 5 P(5)
P(6)
=
1 =
total # of sides
6
# of ways to roll a 6
1
=
= total # of sides
6
# ways to roll an even number P(even)
=
3 =
total # of sides
6
# ways to roll an odd number P(odd)
=
2
3 =
total # of sides
1 =
1 =
6
2
The teacher will elaborate the solution in the problem. Problem 2 illustrates the difference between an outcome and an event. A single outcome of this experiment is rolling a 1, or rolling a 2, or rolling a 3, etc. Rolling an even number (2, 4 or 6) is an event, and rolling an odd number (1, 3 or 5) is also an event.
VI. Activity A. Activity Groupings (skit and correct sentence formation) B. Procedure: 1. After the teacher has discussed probability, she will group the students into five and will let them solve and discuss the next problem with one another. Problem: A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble? 2. She will let them use this sentence pattern: The probability of choosing a red marble is _____ out of _______. The probability of choosing a green marble is _____ out of _______. The probability of choosing a blue marble is _____ out of _______. The probability of choosing a yellow marble is _____ out of _______. 3. Teacher facilitates groups and listens as students share structured responses with one another.One student per group will then write their solutions on the board. Using these sentences, the student will discuss it using key vocabulary including the terms probability, experiment, event and outcome. Students will also relate the activity in real life by doing a short skit. Teacher evaluates student responses using these criteria: •
Use of complete sentences
•
Concept expressed using academic vocabulary terms
Relevance and impact of the skit in probability
VII.
Generalization
The probability of an event is the measure of the chance that the event will occur as a result of an experiment. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes. The probability of an event A, symbolized by P(A), is a number between 0 and 1, inclusive, that measures the likelihood of an event in the following way:
If P(A) > P(B) then event A is more likely to occur than event B. If P(A) = P(B) then events A and B are equally likely to occur. VIII. Evaluation Name__________________________________ Section_________________________________
Directions: Read each question below. Encircle the letter of the correct answer.
1. Which of the following is an experiment? a. Tossing a coin.
c. Choosing a marble from a jar.
b. Rolling a single 6-sided die.
d. All of the above.
2. Which of the following is an outcome? a. Rolling a pair of dice.
c. Choosing 2 marbles from a jar.
b. Landing on red.
d. None of the above.
3. Which of the following experiments does NOT have equally likely outcomes? a. Choose a number at random from 1 to 7.
c. Choose a letter at random from the word SCHOOL.
b. Toss a coin. d. None of the above.
4. What is the probability of choosing a vowel from the alphabet? a. 21/26 b. 5/26
c. 1/21 d. none of the above
5. A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number? a.
1/11
c. 6/11
b. 5/11
d. none of the above
6. A pair of dice is rolled and the resulting number is odd. Which of the following events is the complement of this event?
a. A number greater than 8 is rolled
c. A number less than 5 is rolled
b. An even number is rolled
d. A multiple of 5 is rolled
7. You roll two dice. The first die shows a ONE and the other die rolls under the table and you cannot see it. Now, what is the probability that both die show ONE? a. 1:3
b. 1:6
c. 1:36
d. 9:36
8. From a standard deck of cards, one card is drawn. What is the probability that the card is black and a jack? a. 1/2
b. 1/13
c. 1/26
d. 1/52
9. A piggybank contains 2 quarters, 3 dimes, 4 nickels, and 5 pennies. One coin is removed at random. What is the probability that the coin is a dime or a nickel? a. 3/14
b. 4/14
c. 7/14
d. 1/7
10. A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased? a. 1
b. 3
c. 9
d. 27
IX.
Assignment
Problem Solving: 1. A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond. 2. A card is drawn at random from a deck of cards. Find the probability of getting a queen. 3. The blood groups of 200 people are distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?
Philippine Normal University National Center for Teacher Education College of Teacher Development
Educational Psychology
Semi-detailed Lesson Plan on Mathematics: (Probability)
Submitted to: Professor ArminaMangaoil
Submitted by: Rosellnica L. Balasoto II-9 BS Psychology
Submitted on: October 11, 2013
