Transcript Alliance Class

Alliance Class
April 17, 2012
Probability
Agenda
Development of Probability Concepts
• How Likely Is It?
Exploring the vocabulary of probability
• What are the chances of seeing an elephant a the zoo?
Exploring the meaning of the probability of event A
occurring
• What’s in the Bag?
Experimental probability vs. theoretical probability
WALT
• Use the terms certain, likely, unlikely, and
impossible correctly
• Associate the chances of occurrence of an event
with a position on a probability scale
• Become familiar with the process of randomly
choosing an item from a data set
• Compare fractions by comparing empirical
probabilities (expressed as fractions) and
associate larger (smaller) fractions with events
being more likely (less likely) to occur
CCSSM
7.SP.5 Understand that the probability of a
chance event is a number between 0 and 1
that expresses the likelihood of the event
occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an
unlikely event, a probability around 1/2
indicates an event that is neither unlikely nor
likely, and a probability near 1 indicates a
likely event.
Why is Probability Important?
Everyday we make probabilistic decisions:
Buy a Lottery ticket
Walk outside in a storm
Fly on an airplane
Buy stocks
Medical results
Vocabulary
• What are some events that you would list as
Impossible for you to perform.
What are some events that you would list as
Certain that you could perform?
“In this world nothing can be said to be certain,
except death and taxes.”
BENJAMIN FRANKLIN, letter to Jean Baptiste Le Roy, Nov. 13,
1789
What are some events that you would list that
are between impossible and certain for you to
perform?
Chance Events
• Classify each of these chance events as being impossible to occur,
unlikely to occur, neither unlikely nor likely to occur, likely to occur,
or certain to occur.
a. Our class will watch TV tonight during class.
b. You will use a computer sometime during school tomorrow.
c. Governor Walker will get recalled in the June election.
d. The Brewers will win the Central Division in baseball this year.
e. You will go to the movies during the next month.
f. We will go outside for break tonight.
g. If you were to put the names of all the students in our class in a hat
and draw one name, a boy’s name will be chosen.
h. If I have a bag of 10 blue cubes and one red cube and draw one
cube, the red cube will be drawn.
Impossible
Unlikely
Neither
Unlikely nor
Likely
Likely
Certain
Probability Scale
Directions: Think about each of the following events. Decide where each
event would be located on the scale. Place the letter for each event below
on the appropriate place on the scale.
A. The next roll of a fair number cube will be a 2.
B. You will be successful in four of your next 10 free throw shots.
C. You will meet a dinosaur on your way home from school.
D. You will read at least three books this month.
E. A coin will come up heads five times in a row.
F. A word chosen randomly from this sentence has four letters.
G. It will be sunny tomorrow.
H. You will eat something the color blue today.
I. A spinner with 10 equal parts numbered 1 through 10 will come up a prime
number in the next spin.
J. You will have math homework tonight.
K. If the names of all the teachers at our school are in a hat, my name will be
picked.
CCSSM
• 7.SP.6 Develop a probability model (which
may not be uniform) by observing frequencies
in data generated from a chance process.
A Trip to the Zoo
“If an animal were to be chosen at random from
a bag of zoo animals, which type of animal
would be the most likely or least likely to be
chosen?”
Collecting the Data
Name of Animal
Tally
Frequency
Relative Frequency
Graph
• Bar Graph
Analyze
1. If one “animal” is drawn at random from your
zoo, which animal is the most likely? Least
likely?
2. What is the probability that:
a. The animal is an elephant?
b. The animal is an elephant or a lion?
c. The animal is an elephant and a lion?
Collecting Class Data
Name of Animal
Tally
Frequency
Relative Frequency
Analyze
1. If one “animal” is drawn at random from your
zoo, which animal is the most likely? Least
likely?
2. What is the probability that:
a. The animal is an elephant?
b. The animal is an elephant or a lion?
c. The animal is an elephant and a lion?
Connection to Science
Using the class data, ask what the probability is of
randomly choosing:
1. An animal with four feet?
2. An animal with claws? Hooves?
3. An animal with knees?
4. A meat-eating animal? A pure carnivorous animal?
5. An animal that eats vegetation? A pure herbivorous
animal?
6. An animal that eats both meat and vegetation? A pure
omnivorous animal?
Extensions
Venn diagram
CCSSM
• 7.SP.7 Develop a probability model and use it
to find probabilities of events. Compare
probabilities from a model to observed
frequencies; if the agreement is not good,
explain possible sources of the discrepancy.
What’s in the bag?
Randomly select 20 cubes from the bag. Record
your selection on the recording sheet. After
each selection replace the cube.
Selection Number
1
2
3
Outcome
Organize your data
What do you think is the percent of each of the
following colors in your bag?
Red
Blue
Brown
Summary
7.SP.5 Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood of
the event occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an unlikely event,
a probability around 1/2 indicates an event that is neither
unlikely nor likely, and a probability near 1 indicates a likely
event.
7.SP.6 Develop a probability model (which may not be
uniform) by observing frequencies in data generated from a
chance process.
7.SP.7 Develop a probability model and use it to find
probabilities of events. Compare probabilities from a model
to observed frequencies; if the agreement is not good,
explain possible sources of the discrepancy.
Homework
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Probability Worksheet (Due May 1)
Read “6-8 Statistics and Probability pp. 7 - 10
Make note of the vocabulary and concepts that you are unsure of
Complete video of your class poster presentations (remember to include the
student that your are doing your reflection on). Bring camera and video on May
1st. Chris will help with the editing. May 8th you will share your edited video
with our class
Final reflection on the poster project (Due May 1st)
Your reflection should include:
What struggles did your students have pertaining to the construction of the
poster?
Reflection on the whole poster project – including the strengths and weaknesses
of the project
How does the poster project fit into the CCSS Mathematical Practices?
Resource Binder project (Due May 8th)
Final exam May 15th