Download Geometry Mathematics Curriculum Guide – Unit 8 Probability

Geometry Mathematics Curriculum Guide – Unit 8 Probability
Unit 8: Probability
2016 – 2017
Time Frame: 7 days
Primary Focus
Students will understand independence and conditional probability and use them to interpret data. Students will be able to compute probabilities of
independent, dependent, and compound events.
Common Core State Standards for Mathematical Practice
Standards for Mathematical Practice
MP4 - Model with mathematics.
MP5 - Use appropriate tools strategically.
MP6 - Attend to precision.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated
reasoning.
Unit 8
How It Applies to this Topic…
Use a variety of methods to model, represent, and solve real-world problems.
Select and use appropriate tools to best model/solve problems.
Transform figures efficiently and accurately and label them appropriately.
Use patterns or structure to make sense of mathematics and connect prior knowledge to
similar situations and extend to new situations.
Generalize the process to create a shortcut which may lead to developing rules or creating a
formula.
Clover Park School District 2016-2017
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Geometry Mathematics Curriculum Guide – Unit 8 Probability
2016 – 2017
Stage 1 Desired Results
Transfer Goals
Students will be able to independently use their learning to…
Experience the strong connection between statistics and probability; using data to select values for probability models.
Meaning Goals
UNDERSTANDINGS
ESSENTIAL QUESTIONS
Students will understand that…
How can an event be described as a subset of outcomes using correct set
Events can be described as a subset of a sample space.
notation?
The probability of two events occurring together is the product of their
How are probabilities, including joint probabilities, of independent events
probabilities, if and only if then the events are independent.
calculated?
The probability of two events can be conditional on each other and the
How are probabilities of independent events compared to their joint
interpretation of that probability.
probability?
Two-way frequency tables can be used to decide if events are independent and How does conditional probability apply to real-life events?
to find conditional probabilities.
How are two-way frequency tables used to model real-life data?
Conditional probability and independence are applied to everyday situations.
How are conditional probabilities and independence interpreted in relation to a
Conditional probability of A given B can be found and interpreted in context.
situation?
The addition rule can be applied and the resulting probability can be
What is the difference between compound and conditional probabilities?
interpreted in context.
How is the probability of event (A or B) found?
Acquisition Goals
Students will know and will be skilled at…
The definition of event, sample space, union, intersection, and complement.
How to identify independent events.
The definition of dependent events and conditional probability.
Establish events as subsets of sample space based on the union, intersection, and/or complement of other events.
Calculate the probability of an event.
Determine if two events are independent with justification.
Calculate the conditional probability of A given B.
Use the concept of conditional probability and independence using real life examples.
Calculate the probability of the intersection of two events.
Calculate the conditional probability of A given B.
Determine the probability of the union of two events using the Addition Rule.
Pose an original question, prepare a solution, and interpret the result.
Investigate the relationships between P(A∩ B) , P(A∪ B), P(A | B), and P(A | B) using tree diagrams and Bayes Theorem.
Unit 8
Clover Park School District 2016-2017
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Geometry Mathematics Curriculum Guide – Unit 8 Probability
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Cluster: Standard(s)
Understand independence and conditional probability and use them to interpret data
S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or
complements of other events (“or,” “and,” “not”).
S.CP.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this
characterization to determine if they are independent.
S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability
of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.4 - Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as
a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in
your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor
science given that the student is in tenth grade. Do the same for other subjects and compare the results.
S.CP.5 - Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare
the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Explanations, Examples, and Comments
Stage 3
Build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop understanding of
MATERIALS BY STANDARD(S):
conditional probability and independence.
CCGPS Analytic Geometry: Unit 7: Applications of Probability
Other Resources
MVP Course 2: Module 9 Probability Teacher – Student
Cluster: Standard(s)
Use the rules of probability to compute probabilities of compound events in a uniform probability model
S-CP.6 - Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
S-CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
S-CP.8 - Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the
model.
Explanations, Examples, and Comments
Stage 3
MATERIALS BY STANDARD(S):
Teacher should use assessment data to determine which of the
materials below best meet student instructional needs. All materials
listed may not be needed.
CCGPS Analytic Geometry: Unit 7: Applications of Probability
Unit 8
Clover Park School District 2016-2017
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Geometry Mathematics Curriculum Guide – Unit 8 Probability
2016 – 2017
Use probability to evaluate outcomes of decisions.
S-MD.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
S-MD.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Explanations, Examples, and Comments
Stage 3
This unit sets the stage for work in Algebra II, where the ideas of statistical inference are
MATERIALS BY STANDARD(S):
Teacher should use assessment data to determine which of the
introduced. Evaluating the risks associated with conclusions drawn from sample data (i.e.
materials below best meet student instructional needs. All materials
incomplete information) requires an understanding of probability concepts.
listed may not be needed.
CCGPS Analytic Geometry: Unit 7: Applications of Probability
Stage 2 - Evidence
Evaluative Criteria/Assessment Level
Descriptors (ALDs):
Claim 1 Clusters:
Sample Assessment Evidence
Concepts and Procedures
NONE
Claim 2 Clusters:
Understand independence and conditional
probability and use them to interpret data
Problem Solving
Level 3 students should be able to map, display, and identify relationships, use appropriate tools strategically, and
apply mathematics accurately in everyday life, society, and the workplace. They should be able to interpret
information and results in the context of an unfamiliar situation.
Claim 3 Clusters:
Level 4 students should be able to analyze and interpret the context of an unfamiliar situation for problems of
increasing complexity and solve problems with optimal solutions.
Communicating Reasoning
NONE
Go here for Sample SBAC items
Go here for more information about the Achievement Level Descriptors for Mathematics
Common Assessment
See Sample Assessments for Geometry Units.
Unit 8
Clover Park School District 2016-2017
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Geometry Mathematics Curriculum Guide – Unit 8 Probability
2016 – 2017
Stage 3 – Learning Plan: Sample
Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning
LEARNING ACTIVITIES:
Suggested Sequence of the Unit (See NOTES section for more detail for Extended Geometry.)
NOTES:
Students have previous exposure to Probability in 7th
grade. See standards 7.SP.1 to 7.SP.8
Use CCGPS Analytic Geometry: Unit 7: Applications of Probability for this unit.
Extended Geometry classes should select two or three
of the MVP lessons from the link below to support
student success in the core curriculum.
Common Assessment
Daily Lesson Components
Learning Target
Warm-up
Activities
•
Whole Group:
•
Small Group/Guided/Collaborative/Independent:
•
Whole Group:
Checking for Understanding (before, during and after):
Assessments
Unit 8
Clover Park School District 2016-2017
MVP Course 2: Module 9 Probability Teacher – Student
Page 5