Probability
STEM-Centric Lesson
Author: Hannah Knisely
Background Information
Subject:
Identify the course the lesson will be
implemented in.
Grade Band:
Identify the appropriate grade band for the
lesson.
Duration:
Identify the time frame for the lesson.
Overview:
Provide a concise summary of what students
will learn in the lesson. It explains the lesson’s
focus, connection to content, and real world
connection.
Algebra I
9-10
90 Minutes
This lesson is an introduction to probability. Students will conduct experiments in order to determine the
likelihood or probability of conceiving a girl versus a boy. A STEM Specialist will help students interpret
their results and engage students in hands-on learning experiences that demonstrate how probabilities
are used and incorporated by STEM professionals. Students will begin to explore real-life applications
for finding the probability of an event occurring.
Teachers will need to understand the basics of probability. They will need to familiarize themselves with
independent and dependent events as well as mutually exclusive events; and the difference between
“and” and “or” probabilities.
Background Information:
Identify information or resources that will help
teachers understand and facilitate the
challenge.
Definition
Example
An experiment is a situation involving chance or
probability that leads to results called outcomes.
In the problem above, the experiment
is spinning the spinner.
An outcome is the result of a single trial of an
experiment.
The possible outcomes are landing on
yellow, blue, green or red.
An event is one or more outcomes of an experiment.
One event of this experiment is
landing on blue.
Probability is the measure of how likely an event is.
The probability of landing on blue is
one fourth.
In order to measure probabilities, mathematicians have devised the following formula for finding
the probability of an event.
Probability Of An Event
P(A) =
The Number Of Favorable Outcomes
Total Possible Outcomes
Page 1 of 9
Probability
STEM-Centric Lesson
STEM Specialist Connection:
Describe how a STEM Specialist may be used
to enhance the learning experience. STEM
Specialist may be found at
http://www.thestemnet.com/
Enduring Understanding:
Identify discrete facts or skills to focus on larger
concepts, principles, or processes. They are
transferable - applicable to new situations within
or beyond the subject.
Essential Questions:
Identify several open-ended questions to
provoke inquiry about the core ideas for the
lesson. They are grade-level appropriate
questions that prompt intellectual exploration of
a topic.
Student Outcomes:
Identify the transferable knowledge and skills
that students should understand and be able to
do when the lesson is completed. Outcomes
must align with but not limited to Maryland State
Curriculum and/or national standards.
Product, Process, Action, Performance, etc.:
Identify what students will produce to
demonstrate that they have met the challenge,
learned content, and employed 21st century
skills. Additionally, identify the audience they will
present what they have produced to.
Background Information
Visit khanacademy.org for videos and practice problems to familiarize yourself with Probability basics.
https://www.khanacademy.org/math/trigonometry/prob_comb/basic_prob_precalc/v/basic-probability
STEM Specialists would be incredibly beneficial in this probability lesson. They can provide better
insight as to how probability and statistics are used in STEM careers. Some examples of careers that
use probability and statistics on a daily basis include, but are not limited to, medical decision making,
actuarial sciences, bio-mathematicians, biomedical sciences, environmental and ecological sciences,
government services, finances, engineering, nursing, pharmaceuticals, public policy, quality
improvement, risk analysis, survey researchers, marketing, etc.


The probability of an event happening is equivalent to the number of favorable outcomes
divided by the total possible outcomes.
Probability and statistics are tools that can be used to inform decisions.


How can probability be used to inform decisions?
What careers incorporate the use of probability and statistics for decision making?
Students will be able to:
 calculate the probability of an event occurring.
 determine which decision is best given the probability of success.
 apply probability to real-world situations, including careers in STEM that use probability and
statistics for decision making.
Students will work in pairs (or individually) to conduct an experiment simulating
the outcome of gender in children. This experiment will help with their overall
understanding of how experimental probability is related to theoretical
probability and why a simulation would be used rather than conducting a full
experiment in the case of gender outcome. Students will have the goal of being
able to describe what probability is, how it is used in the real world, and what
careers incorporate the use of probability in decision making.
Audience:
☒Peers
☒Experts /
Practitioners
☒Teacher(s)
☐School Community
☐Online Community
☐Other______
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Probability
STEM-Centric Lesson
Standards Addressed in the Lesson:
Suggested Materials and Resources:
Identify materials needed to complete the
lesson. This includes but is not limited to
websites, equipment, PowerPoints, rubrics,
worksheets, and answer keys.
Background Information
S-MD.B.5.a Weigh the possible outcomes of a decision by assigning probabilities to pay off values and
finding expected values.
S-MD.B.6 Use probabilities to make fair decisions
S-MD.B.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical
testing, pulling a hockey goalie at the end of a game).
S-CP.A.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.A.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.A.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.A.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.B.6 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.B.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.B.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.
Equipment:
 Projector
 Computer
 Calculator
 Coins (enough for each student in the class to have one)
 Pencil/Pen
Websites (must be accessible to all stakeholders):
The following resources are not directly used in this lesson but could be used for
review/research/extension of the topic.
 http://www.ma.utexas.edu/users/mks/statund/careers.html
 http://www.myplan.com/majors/mathematical-statistics-and-probability/related-careers27.0502.html
Page 3 of 9
Probability
STEM-Centric Lesson
Background Information
People, Facilities:
 Teacher
 STEM specialist
Materials (rubrics, worksheets, PowerPoints, answer keys, etc.):
 Gender Simulation Record Sheet
 Probability PowerPoint
 Things to Consider… (Classwork)
 Supplemental homework assignments (candy, dice, spinners)
Consider having the students create their own homework assignment (students create
probability questions and provide the answers with the assignment to validate their
understanding)
Page 4 of 9
Probability
STEM-Centric Lesson
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model is
not linear.
☒Engagement
☐Exploration
☐Explanation
☐Extension
☐Evaluation
Details
Standards for Mathematical
Practice
Materials:
 Projector
 Computer
 Probability PowerPoint
 Gender Simulation Record Sheet
 Coins (enough for each student in the class to have one)
☐Make sense of problems and
persevere in solving them.
Preparation:
 Use the PowerPoint as a guide throughout the lesson.
 Provide each student with a copy of the Gender Simulation Record Sheet
and a coin to flip.
☒Construct viable arguments
and critique the reasoning of
others.
Facilitation of Learning Experience:
 Began the class with a discussion about probability. Specifically, open with
where students have heard the word “probability” or “statistics” before.
 Discuss the idea of a simulation—the act of imitating an actual event,
condition, or situation for the use of computing probability of an event
occurring.
 Lead students into a discussion of gender in children. Ask them if a
simulation would be an appropriate means to determine if a couple will have
a boy or girl.
 Have the students conduct their own simulations using a coin to represent
the two different genders—boy=heads, girl=tails. The results from each of
their coin tosses should be recorded in the Gender Simulation Record Sheet.
 When the class is done with their individual simulations open the classroom
back up to discussion.
 As a class discuss the following questions:
1. How many families had three male children? Female children?
2. How many of your families had the same order of male and female
children?
3. How many different combinations of offspring are possible in this
simulation?
4. Did anyone else in the class have exactly the same simulation results
as you?
☐Reason abstractly and
quantitatively.
☒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.
Page 5 of 9
Probability
STEM-Centric Lesson
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model is
not linear.
Details
Standards for Mathematical
Practice
5. Why is the gender of each child an independent event?
Sample Answers to these questions include:
1. Two families; one family
2. Two families
3. 8
4. It is possible, but not common.
5. The gender of each child does not depend on the gender of any other
child.
Transition:
Collect the coins, as well as the gender simulation record sheet. If the questions
posed for analysis were written down (teacher discretion) then those answers should
be passed forward as well.

☐Engagement
☐Exploration
☒Explanation
☐Extension
☐Evaluation
Materials:
 Projector
 Computer
 Probability PowerPoint
Preparation:
 Use the PowerPoint as a guide throughout the lesson.
Facilitation of Learning Experience:
 Slowly go through the Probability PowerPoint with students.
 Discuss the difference between independent and dependent events.
 Show that probability is a number between 0 and 1. This number can be
represented as a fraction, decimal, or percent.
 Next, discuss the difference between experimental and theoretical
probability.
 After that, explain the difference between unions and intersections—“or” vs
“and” respectively.
 Walk students through the basic examples provided on how to calculate
probability.
 Be sure to break down what it means for two events to be mutually exclusive.
☐Make sense of problems and
persevere in solving them.
☒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.
Page 6 of 9
Probability
STEM-Centric Lesson
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model is
not linear.
Details
Transition:
Now that students have been exposed to what it means to calculate probability apply
this concept to everyday events the students can relate to.
☐Engagement
☒Exploration
☐Explanation
☐Extension
☐Evaluation
Materials:
 Projector
 Computer
 Probability PowerPoint
Facilitation of Learning Experience:
 Ask students for their input when it comes to applying the idea of probability
to everyday events. The PowerPoint highlights four simple applications:
traffic patterns, dressing for the weather, gambling, and where to eat to avoid
food poisoning. Be sure to expand this through class discussion. Discussions
will vary so application answers will vary with it.
 Next, expand that discussion to include careers that incorporate the use of
probability. The PowerPoint presentation gives several examples of careers
(specifically STEM careers) that incorporate the use of probability for
decision making, but again, feel free to expand the list.
Transition:
Now that the students have been exposed to the concept of probability and how it is
used/incorporated into everyday life, the students should be asked to apply that
knowledge to their own decision making strategies, using probability.
Standards for Mathematical
Practice
☐ Look for and express regularity
in repeated reasoning.
☐Make sense of problems and
persevere in solving them.
☒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.
Page 7 of 9
Probability
STEM-Centric Lesson
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model is
not linear.
☐Engagement
☐Exploration
☐Explanation
☐Extension
☒Evaluation
Details
Materials:
 Things to Consider handout
Preparation:
 Review questions in Things to Consider handout in advance.
 Prepare copies of Things to Consider handout for students.
Facilitation of Learning Experience:
 Students should work independently (or with a partner) and read through the
scenarios posed. Each scenario paints a picture of a situation with statistics
provided. Students will read through the situation, analyze, and make a
decision using the statistics given to justify their answer.
 This process should be done independently (or with a partner) to start but
could end in a class discussion of decisions made.
Transition:
Students should demonstrate their new-found knowledge of probability through
practice problems in the form of examples. To expand the incorporation of real-world
examples, have the students create their own homework assignment. They should
come up with 5-10 questions on their own, applying probability to the real world.
Once finished, they should make an answer key, indicating each step of the equation
to prove their understanding of the material. Additional homework assignments are
included with the lesson.
Standards for Mathematical
Practice
☒Make sense of problems and
persevere in solving them.
☒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.
Page 8 of 9
Probability
STEM-Centric Lesson
Supporting Information
Struggling Learners
Provide guided notes that follow along with the PowerPoint presentation. These notes could
include the definitions, example problems, etc. and simply leave blank spaces for the students
to fill in as the notes are discussed in class.
For the Things to Consider… assignment, students can be guided into the right direction by
discussing the options with the teacher or the STEM specialist weighing out the consequences
for decisions made, based on the situation given.
English Language Learners
Incorporate supporting materials as discussed under the “Struggling Learners” section.
Interventions/Enrichments
Identify interventions and enrichments for diverse
learners.
Provide a word bank with definitions/translations for students to better understand the
terminology.
Incorporate real-world examples from the student(s) native country (if different from American
usage).
Gifted and Talented
Have students determine different scenarios in which probability would be used to make difficult
decisions. Allow students to use computers or Mobile Learning Devices (Phones, Tables,
iPods, etc.) to research situations in which knowing the probability/statistics prior to decision
making is vital.
Page 9 of 9