Monday, September 30, 2013
Objective:
Students will construct Venn diagrams and determine probabilities of
compound events to make decisions about the risks involved in the situation while
completing SAS 2.A.1.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
Compound event, Venn diagram, probability, random
Opening:
Venn diagram
Students have studied probability have likely seen Venn diagrams before.
New concepts to be introduced are:
How to read a Venn diagram.
Worktime:
Students will start SAS 2.A.1.
Questions to redirect and facilitate learning:
How do you determine which numbers to put in which parts of the Venn diagram?
What do overlapping circles mean? What about numbers outside all of the circles?
Closing:
Have students present their solutions to questions 1-5.
Evidence of student Learning:
Students will be able to construct a Venn diagram needed to answer questions 6-10
tomorrow.
Tuesday, October 1, 2013
Objective:
Students will construct Venn diagrams and determine probabilities of
compound events to make decisions about the risks involved in the situation while
completing SAS 2.A.1.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
Compound event, Venn diagram, probability, random
Opening:
Venn diagram
Students have studied probability have likely seen Venn diagrams before. Yesterday
we went over how to read a Venn diagram.
New concepts to be introduced are:
How to construct a Venn diagram.
Worktime:
Students will finish SAS 2.A.1.
Questions to redirect and facilitate learning:
How do you determine which numbers to put in which parts of the Venn diagram?
What do overlapping circles mean? What about a number outside all of the circles?
What does the sum of all of the parts of the Venn diagram need to equal?
Closing:
Have students present their solutions to questions 6-10.
Evidence of student Learning:
Students will be able to construct a Venn diagram to model a situation that they create.
Wednesday, October 2, 2013
Objective:
Students will use tree diagrams to explore dependent and independent
events and calculate probabilities by completing SAS 2.A.2
.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
.
Academic Vocabulary:
Dependent event, independent event, tree diagram,
conditional probability
Opening:
Students have previously been introduced to dependent and independent events and seen tree
diagrams.
Make a tree diagram from the pumpkin patch example together as a class.
New concepts to be introduced are:
Being able to calculate probabilities using tree diagrams.
Worktime:
Students will work in pairs on SAS 2.A.2 1-7.
Questions to redirect and facilitate learning:
What methods can help you visualize situations that have multistage events with a
variety of pathways? How can you represent those different pathways?
How are stages of an event shown on a tree diagram?
How do you read a tree diagram?
Closing:
Have students present questions 1-7.
Emphasize: How the number of choices in each outcome affect the number of total outcomes.
Evidence of student Learning:
Students will be able to explain what happens when we eliminate one bread choice.
Thursday, October 3, 2013
Objective:
Students will use tree diagrams to explore dependent and independent
events and calculate probabilities by completing SAS 2.A.2
.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
.
Academic Vocabulary:
Dependent event, independent event, tree diagram,
conditional probability, equally likely
Opening:
Students have previously been introduced to dependent and independent events and seen tree
diagrams. Yesterday they used tree diagrams to determine probabilities of events.
New concepts to be introduced are:
Students will be introduced to the concept of equally likely.
Worktime:
Students will work in pairs on SAS 2.A.2 8-14.
Questions to redirect and facilitate learning:
How are stages of an event shown on a tree diagram?
How do you read a tree diagram?
Closing:
Have students present questions 8-14.
Emphasize: Question #10. Are all outcomes equally likely?
Evidence of student Learning:
Students will be able to explain when outcomes are equally likely while using a tree
diagram.
Friday, October 4, 2013
Objective:
Students will use area models to find probabilities of successive events
while starting SAS 2.A.3.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
Area model, tree diagram, probability
Opening:
Students are familiar with area and fractions.
Make rectangle and ask them fraction of the rectangle is shaded.
New concepts to be introduced are:
How to use a rectangle and area to determine probability.
Worktime:
Students will work in pairs on SAS 2.A.3 1-4.
Questions to redirect and facilitate learning:
How can you determine which portion of the area model to shade?
How does the area correspond to the probability of events?
Closing:
Have students present questions 1-4.
Emphasize: #3 – how to construct an area model for this situation
Evidence of student Learning:
Students will be able to construct an area model for #3.
Monday, October 7, 2013
Objective:
Students will construct and use area models to find probabilities of
successive events while finishing SAS 2.A.3.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
Area model, tree diagram, probability
Opening:
Students are familiar with area and fractions. Yesterday they were introduced to area models.
New concepts to be introduced are:
Use the area models to answer questions about payoff/expected value.
Worktime:
Students will work in pairs on SAS 2.A.3 5-8.
Questions to redirect and facilitate learning:
How can you determine which portion of the area model to shade?
How does the area correspond to the probability of events?
How do you use area models to determine expected value?
Closing:
Have students present questions 5-9.
Emphasize: #5 and 6 – how do you use the area model to determine expected payoff?
Evidence of student Learning:
Students will be able to correctly answer #8 on finding probability using a given area
model.
Tuesday, October 8, 2013
Objective:
Students will use weighted tree diagrams to find probabilities of
successive events working starting SAS 2.A.4.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
weighted tree diagram, probability, compound event
Opening:
Students are familiar with tree diagrams when dealing with equally likely events.
Ask them them to make a tree diagram of flipping a quarter twice. What would happen if it was
a trick quarter and you were twice as likely to flip a heads as you were a tails?
New concepts to be introduced are:
How to use a weighted tree diagram to determine probabilities.
Worktime:
Students will work in pairs on SAS 2.A.4.
Questions to redirect and facilitate learning:
What do the probabilities for each sample space add up to?
How do you use the probabilities listed on each tree branches to determine the
probability of a compound event?
Closing:
Have students present questions 1-6.
Emphasize: #2c – what is the sum of the probabilities for each sample space? And #5 –
probability that it is NOT…
Evidence of student Learning:
Students will be correctly answer #4 – finding a probability using the given weighted
tree diagram.
Wednesday, October 9, 2013
Objective:
Students will review using Venn diagrams, tree diagrams and area
models to determine probabilities and make predictions.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
weighted tree diagram, tree diagram, area diagram, Venn
diagram, equally likely, probability, compound event
Opening:
Students are familiar with all of these concepts. Remind them that there is a test tomorrow!
New concepts to be introduced are:
Accuracy.
Worktime:
Students will work in pairs on the review.
Questions to redirect and facilitate learning:
How do you construct a tree diagram? Venn diagram? Area model?
What do the numbers in each area of the Venn diagram tell you?
How can you use the branches on the tree diagram to determine probability?
Closing:
Have students present answers to the review.
Emphasize: Anything that they are still struggling with.
Evidence of student Learning:
Students will do well on the test tomorrow.
Thursday, October 9, 2013
Objective:
TEST
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Friday, October 10, 2013 (ER day!) (Two day activity)
Objective:
Students will choose using Venn diagrams, tree diagrams or area models
to determine probabilities and make predictions.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
weighted tree diagram, tree diagram, area diagram, Venn
diagram, equally likely, probability, compound event
Opening:
Students are familiar with all of these concepts. Remind them that there is a test tomorrow!
New concepts to be introduced are:
Being able to present a solution to a problem to the class and communicate how they solved it.
Worktime:
Students will work in pairs on one of the following: SAS 2.A.4 #8, SAS 2.A.2 #14, or SAS
2.A.3 #9.
Questions to redirect and facilitate learning:
How do you construct a tree diagram? Venn diagram? Area model?
What do the numbers in each area of the Venn diagram tell you?
How can you use the branches on the tree diagram to determine probability?
Closing:
Evidence of student Learning:
Students will be accurately solving the problems that they are going to present to the
class on Tuesday.
Tuesday, October 15, 2013 (Continued from Friday - Two day activity)
Objective:
Students will choose using Venn diagrams, tree diagrams or area models
to determine probabilities and make predictions.
TEKS: (3) The student analyzes and evaluates risk and return in the context of real-world
problems. The student is expected to:
(A) determine and interpret conditional probabilities and probabilities of compound events by
constructing and analyzing representations, including tree diagrams, Venn diagrams, and
area models, to make decisions in problem situations;
(B) use probabilities to make and justify decisions about risks in everyday life; and
(C) calculate expected value to analyze mathematical fairness, payoff, and risk.
Academic Vocabulary:
weighted tree diagram, tree diagram, area diagram, Venn
diagram, equally likely, probability, compound event
Opening:
Students are familiar with all of these concepts. Remind them that there is a test tomorrow!
New concepts to be introduced are:
Being able to present a solution to a problem to the class and communicate how they solved it.
Worktime:
Students will work in pairs on one of the following: SAS 2.A.4 #8, SAS 2.A.2 #14, or SAS
2.A.3 #9.
Questions to redirect and facilitate learning:
How do you construct a tree diagram? Venn diagram? Area model?
What do the numbers in each area of the Venn diagram tell you?
How can you use the branches on the tree diagram to determine probability?
Closing:
Students will present their solutions to the above problems.
Evidence of student Learning:
Students will be able to clearly explain how they solved their probability problems.