Transitioning to Iowa Core Mathematics (S-CP #9)
Title: Permutations and Combinations (“Let Me Count the Ways” activity from
SpringBoard Pre-Calc book)
Grade: Alg 2, Pre Calc
Author(s): Erin Hansen, Tony Smith, Evan Haan
Iowa Core Standards for
Mathematical Practices
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1. Making sense of problems *
2. Reason abstractly *
3. Construct viable arguments *
4. Model *
5. Use tools *
6. Attend to precision *
7. Structure *
8. Repeated reasoning *
Place * next to portions of lesson where students
use practice standards.
Student Outcome
I can:
1. Use the multiplication counting principle to
determine the number of ways an event can
occur.
2. Use permutations to determine the number of
ways an event can occur (including
permutations with repetition).
3. Use combinations to determine the number of
ways an event can occur.
4. Determine when to use permutations and
when to use combinations.
Prerequisites:
Students should know factorial notation.
Purpose/ Learning
Goals
Understand that:
1. Determining the number of ways an event can
occur is important to in order to determine
probabilities.
2. Counting and probability are important for
making decisions about the future based on
past patterns.
3. Permutation and combinations is a way of
counting the number of ways an event can
occur in an organized way.
Grouping Strategies
Work with a group of three to complete the task.
LESSON SEQUENCE
(Include plans for adjustments to accommodate all learners)
Launch
Activities
Discuss the purpose and
importance of counting and
probability.
Discuss independent and
dependent events.
Notes
Counting problems are of the
following kind:
How many different 8-letter
passwords are there?
How many possible ways are
there to pick 11 soccer players
out of a 20-player team?
Most importantly, counting is the
basis for computing
probabilities of events.
Ex: What is the probability of
winning the lottery?
Events are independent if one
event does not affect the
other.
Ex: Roll a die two times
Events are dependent if one
Materials
event does affect the other
(one event depends on
another).
Ex: Drawing two names out of a
hat
Explore
Activities
Notes
Materials
Day 1
Complete Part I and II. Students
work with the multiplication
counting principle.
Day 1
The concept of detour-prone and
false detour-prone zip codes
may be challenging for some
students.
“Let Me Count the
Ways” activity
sheet.
Calculator.
Day 2
Complete Part III. Students
explore the concept of
permutations and
indistinguishable
permutations.
Day 2
After students learn the formula
for permutations, show them
how to access permutations
on their calculator.
Guide the students through
#16f,g as a class.
Day 3
Complete Part IV. Students
explore the concept of
combinations and distinguish
between permutations and
combinations.
Day 3
Guide the students through
#19d,e.
After students learn the formula
for combinations, show them
how to access combinations
on their calculator.
Summarize
Activities
Notes
Day 1
Day 1
Have a few groups share their zip How many 5 digit non-detourcode work.
prone zip codes are possible?
Checking for Understanding (CFU):
How did you arrive at this
Give an example of a problem
answer?
that can be solved with the
What are some other possible
multiplication counting
applications of the
principle. Explain how the
multiplication counting
multiplication counting
principle?
principle works for this
example.
Day 2
Discuss permutations as a class.
CFU: There are 10 names on the
ballot for class officers. If all
10 can fill any position, how
many ways can a president,
vice president, secretary, and
treasurer be chosen?
Can a permutation be used to
determine how many ways 4
people can be chosen for a
committee? Explain.
Day 2
When is a permutation used?
Why is it important to be able to
count indistinguishable
permutations?
Day 3
Discuss the difference between
permutations and
combinations.
CFU: Give an example for which a
combination can be used.
Give an example for which a
permutation can be used.
Day 3
When is a combination used?
How is a combination different
from a permutation?
Materials
“Let Me Count the
Ways” activity
sheet.
Calculator.