Download IM7 - Unit 9 Probability.docx

Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit 9 - Probability
Unit Title: Probability
Course: Integrated 7
Brief Summary of Unit: Students will learn to determine probabilities of both simple and compound events, and why
the theoretically calculated probability does not always equal the actual experimental probability.
Textbook Correlation: Glencoe Math Course 2 Chapter 9 EXCEPT 9-6 (including all labs)
Time Frame: 3.5 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
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How accurate do I need to be?
When is estimating the best solution to a
problem?
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strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
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Make predictions about given situations.
Mathematically determine the chances of a favorable outcome.
Meaning
Essential Questions
Understandings
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How can you predict the outcome of future
events?
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Why (experimentally) do you not always get
what you (theoretically) should?
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How can finding the probability of a simulation
help form inferences about real-world events?
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How can you determine if an event is fair or
unfair?
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What is the best method for finding the
probability of simple and compound events?
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Probability of a chance event is a number
between 0 and 1, written as a fraction,
decimal, and/or percent.
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What should happen (theoretical probability)
is not always what does happen
(experimental probability).
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Probabilities of simple events can be
combined to form the probability of a
compound event.
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Lists, tables, tree diagrams, and simulations
can be used to represent compound events
in order to draw inferences about the event.
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Probability experiments can be used to
determine if an event’s outcome is fair or
unfair.
Acquisition
Key Knowledge
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complementary events
compound event
dependent events
Key Skills
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Use informal descriptions to describe the
probability of events
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experimental probability
fair
Fundamental Counting Principle
independent events
outcome
permutation
probability
random
relative frequency
sample space
simple event
simulation
theoretical probability
tree diagram
uniform probability model
unfair
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Find and interpret the probability of a simple
event.
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Use an experiment to determine relative
frequency.
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Find and compare experimental and
theoretical probabilities.
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Use experimental and theoretical probabilities
to decide whether a game is fair or unfair.
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Find probabilities of compound events.
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Perform probability simulations to model realworld situations involving uncertainty.
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Use a simulation to generate frequencies for a
compound event.
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Use multiplication to count outcomes and find
probabilities.
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Explore the probability of independent and
dependent events.
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Find the probability of independent and
dependent events.
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Use a list, table, tree diagram, or the
Fundamental Counting Principle to find out
how many items are in the sample space of a
compound event
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Use a simulation to discover the experimental
probability of an event and compare it to the
theoretical probability of the same event (M&M
lab).
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Design a simulation to represent an event and
use it to find the probabilities of various
outcomes.
Standards Alignment
MISSOURI LEARNING STANDARDS
Investigate chance processes and develop, use and evaluate probability models.
(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) Approximate the probability of a chance event by collecting data on the chance process that produces
it and observing its long-run relative frequency, and predict the approximate relative frequency given the
probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly
200 times, but probably not exactly 200 times.
(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.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the
model to determine probabilities of events. For example, if a student is selected at random from a class,
find the probability that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated
from a chance process. For example, find the approximate probability that a spinning penny will land
heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny
appear to be equally likely based on the observed frequencies?
Investigate chance processes and develop, use and evaluate probability models.
(7.SP.8) Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a compound event is the fraction of
outcomes in the sample space for which the compound event occurs.
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree
diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the
outcomes in the sample space which compose the event.
c. Design and use a simulation to generate frequencies for compound events. For example, use random
digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A
blood, what is the probability that it will take at least 4 donors to find one with type A blood?
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goals:
1.1, 1.4, 1.5, 1.6, 1.7, 1.8
2.2, 2.3, 2.7
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
4.1, 4.4, 4.5, 4.6
Performance:
Math 1, 3, 5