Download Grade/Course: Geometry (Second Semester) Instructional Unit 10

Grade/Course: Geometry (Second Semester)
Instructional Unit 10: Understanding Probability
Instructional Schedule: Fourth Nine Weeks (suggested for 15 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Note: The following statistics unit is listed as Algebra 2 curriculum, however it is recommended to be placed in the Geometry sequence of instruction to
alleviate the pressure of the packed Algebra 2 course. There is a possible connection with implementing geometric probability contexts where applicable.
Standards:
Evidence Of Standard:
Prerequisite Knowledge:
Assessment Tools:
(student should be able to…)
(standards linked to content taught in
( formative assessments, quizzes,
previous grades)
mastery tasks/activities)
Understand independence and conditional probability and use them to interpret data. (key content)
(BA 5.3a) 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”).
-Define event, sample space, union,
intersection, and complements as it
relates to probability.
-Describe events as subsets of a
sample space (the set of outcomes)
using characteristics (or categories) of
the outcomes.
-Describe events as unions,
intersections, or complements of
other events (“or”, “and”, “not”).
(BA 5.3b) Understand that two events - I can show why two events A and B
𝐴 and 𝐵 are independent if the
are independent if the probability of A
probability of 𝐴 and 𝐵 occurring
and B occurring together is the
together is the product of their
product of their probabilities with the
probabilities, and use this
equation P(A and B) = P(A) x P(B).
characterization to determine if they
are independent.
(BA 5.3c) Understand the conditional -Explain the conditional probability of
probability of 𝐴 given 𝐵 as
A given B as P(A and B)/P(B), and
𝑃(𝐴 𝑎𝑛𝑑 𝐵)/𝑃(𝐵), and interpret
illustrate this relationship using
independence of 𝐴 and 𝐵 as saying
examples.
that the conditional probability of 𝐴
-Explain that independence of A is the
given 𝐵 is the same as the probability conditional probability of A given B
of 𝐴, and the conditional probability
which is the same as the probability of
of 𝐵 given 𝐴 is the same as the
A, P(A), and the conditional
probability of 𝐴.
probability of B given A is the same as
the probability of B, P(B).
-Distinguish between events that are
independent and those that are not.
(BA 5.3d) Construct and interpret
-Construct and interpret a two-way
two-way frequency tables of data
frequency tables of data when two
when two categories are associated
categories are associated with each
with each object being classified. Use object being classified.
the two-way table as a sample space
-Use a two-way frequency table to
to decide if events are independent
decide if events are independent and
and to approximate conditional
to approximate conditional
probabilities. For example, collect
probabilities.
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 the tenth
grade. Do the same for other subjects
and compare the results.
(BA 5.3e) Recognize and explain the
-Collect data from a random sample
concepts of conditional probability
and determine if events are
and independence in everyday
independent.
language and everyday situations. For -Explain the concepts of conditional
example, compare the chance of
probability and independence in
having lung cancer if you are a smoker everyday language and everyday
with the chance of being a smoker if
situations.
you have lung cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability model. (key content)
(BA 5.3f) 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.
-Understand that the probability of A
given B represents the outcomes
remaining for A to occur once B has
already occurred.
-Understand that this probability is
the fraction of outcomes of B that
also belongs to A.
(BA 5.3g) Apply the Addition Rule,
-Understand and interpret the model
of a situation that the true probability
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) −
𝑃(𝐴 𝑎𝑛𝑑 𝐵), and interpret the answer of an event results from subtracting
in terms of the model.
the number of outcomes shared
between A and B from each
independent probability outcomes.
Note: Any italicized text denotes portions of a given standard that do not apply to identified standard content in this unit.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )