Download Int Math 3 Pacing Guide - UNIT 3

UNIT 3:
Probability
(4 weeks)
GHS Department of Matheπ
πatics
Int. Math 3: Probability
(4 weeks)
I Can . . .
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I can define event and sample space.
I can establish events as subsets of a sample space.
I can define union, intersection, and complement.
I can establish events as subsets of a sample space based on the union, intersection, and/or
complement of other events.
I can define and identify independent events and justify my conclusions.
I can explain and provide an example to illustrate that for two independent events, the probability of the
events occurring together is the product of the probability of each event.
I can calculate the probability of an event.
I can predict if two events are independent, explain my reasoning, and check my statement by
calculating P(A and B) and P(A) x P(B).
I can define dependent events and conditional probability.
I can explain that conditional probability is the probability of an event occurring given the occurrence of
some other event and give examples that illustrate conditional probability.
I can explain that for two events A and B, the probability of event A occurring given the occurrence of
and give examples to show how to use the formula.
event B is
I can explain that A and B are independent events if the occurrence of A does not impact the probability
of B occurring and vice versa.
I can determine when a two-way frequency table is an appropriate display for a set of data.
I can collect data from a random sample.
I can construct a two way frequency table.
I can pose a question for which a two-way frequency is appropriate, use statistical techniques to sample
the population, and design an appropriate product to summarize the process and report the results.
I can illustrate the concept of conditional probability and independence using everyday examples of
dependent and independent events respectively.
I can apply the fundamental counting principle to find the total number of possible outcomes in a sample
space.
I can define factorial, permutation, combination, and compound event.
I can distinguish between situations that require permutations and those that require combinations.
I can apply the permutation formula and the combination formula.
I can compute probabilities of an event.
I can write and solve original problems involving compound events, permutations, and/or combinations.
I can use probability to create a method for making a fair decision.
I can use probability to analyze the results of a process and decide if it resulted in a fair decision.
I can analyze data to determine whether or not the best decision was made.
I can define population and population parameter.
I can explain why randomization is used to draw a sample that represents a population well.
I can recognize that statistics involves drawing conclusions about a population based on the results
obtained from a random sample of the population.
I can choose a probability model for a problem situation.
I can conduct a simulation of the model and determine which results are typical of the model.
Vocabulary
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Event
Sample space
outcome
Subset
Union
Intersection
Complement
Independent events
Dependent events
Probability
Product event
Conditional probability
Two-way frequency
table
Display
Data
random sample
fundamental counting
principle.
Factorial
Permutation
Combination
Simulation
Fair
Theoretical probability
Experimental
probability
model
Common Core State Standards
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.
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.
S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems
S.MD.6 (+) Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing
by lots, using a random number generator).
S.MD.7 (+) Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability
Integrated Math 3 – Unit 3 – Probability
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concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game)
S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random
sample from that population
S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using
simulation. For example, a model says a spinning coin falls head side up with probability 0. 5. Would a result of 5 tails in a row cause
you to question the model?
Standards for Mathematics Practices
Make sense of problems and persevere in solving problems.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Integrated Math 3 – Unit 3 – Probability
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