Sarah Lilly
AFDA: Permutations and Combinations
Phoebus High Mathematics Department
Course:
AFDA
Teacher:
Ms. Lilly
Date(s):
2 day
SOL:
ALGEBRA, FUNCTIONS AND DATA ANALYSIS
STANDARD AFDA.6
The student will calculate probabilities. Key concepts include:
a) conditional probability;
b) dependent and independent events;
c) addition and multiplication rules;
d) counting techniques (permutations and combinations); and
e) Law of Large Numbers.
Objective(s):
The student will compare and contrast permutations and combinations, calculate the number of permutations
of n objects taken r at a time, calculate the number of combinations of n objects taken r at a time, and
determine how to use permutations and combinations as counting techniques to solve real-world problems.
Daily Essential Question:
When should I use a permutation versus a combination?
Materials Needed: Permutations Activity Worksheet, Combinations Activity Sheet, Permutation or
Combination? Sheet, Exit Ticket, Permutations and Combinations Test, Test Closure Questions
Classification
Part I: Warm-up
Suggested time:
5 minutes
Part II: Anticipatory
Set
Intro. to the lesson
Suggested time:
25 minutes
Part III:
Teaching the Lesson
Suggested time:
Day 1:
GP: 15 minutes
IP: 35 minutes
Closure: 5 minutes
Day 2:
Test: 40 minutes
Procedures
Notes
Day 1: Students receive their graded Probability Quiz (the
correct solutions have already been reviewed with the
students).
Day 2: Students list their questions/confusion regarding
permutations and combinations.
Day 1: When does order matter? Students come up with
example situations where order would matter and would
not matter. These situations will then be used for Ms. Lilly
to construct their Permutations and Combinations Quiz.
Day 2: Class review of permutations and combinations in
small groups and large group.
Vocabulary: permutation, factorial, combination
Procedures:
Day 1:
1. Define permutation and combination formulas.
2. Model how to use the formulas.
3. Define factorial and explain its relationship to
permutations.
4. Demonstrate the use of calculators to find permutations
and combinations.
5. Students will work in small groups to complete the
Whole group, small
group
Scripted Questions:
1. When can we use
either permutations or
combinations?
2. When should you use
the formula versus
typing it into your
Sarah Lilly
AFDA: Permutations and Combinations
Test Review:
20 minutes
Permutations Activity Worksheet as Ms. Lilly circulates.
6. Students will work in small groups to complete the
Combinations Activity Worksheet as Ms. Lilly circulates.
7. Students will correctly determine as a class whether
permutations or combinations should be used as Ms. Lilly
reads the examples on the Permutations or Combinations?
Worksheet. The students must also offer an explanation as
to why they choose their technique.
8. Ms. Lilly will explain any situations that seem unclear
and the class will brainstorm how to identify which
technique to use in difficult situations (key words, etc).
Day 2:
1. Students demonstrate their understanding of
permutations and combinations on the Permutations and
Combinations Test.
2. Class discussion to go over the test so that students can
give themselves immediate feedback on how they did.
calculator?
Important Reminders:
1. Remind students to
work on the problems
with each other instead
of dividing the work.
They must communicate
with each other and
worth through the
problems with each
student.
Closure:
Day 1: Permutations and Combinations Exit Ticket: Briefly
(in 5 – 7 sentences) compare and contrast permutations
and combinations to someone who has never before heard
of them. Also explain when you use each and how using
one or the other affects the outcome.
Part IV:
Evaluating the
Lesson
Part V:
Re-teaching the
lesson
Part VI:
Applying the Lesson
Suggested time: 5
minutes
Part VII:
Extending the
Lesson
Day 2: Read through the Test Closure questions with the
students.
Student progress will be monitored through observation,
class discussion, guided practice, independent practice and
the closure activity.
The teacher will analyze what aspect of the task the
student struggle to complete. The same task will be reassessed, but with different values.
Students will complete the following for homework:
Day 1: Students will identify 5 situations in their lives
where permutations should be used and 5 situations
where combinations should be used. They will explain why
they believe a permutation vs. a combination should be
used and offer an example of numbers, the formula, and
their solution for each.
Day 2: Students will answer the Test Closure questions.
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