Algebra 2 Applications Lesson Plan Outline
Lesson Title: Fundamental Counting Principle and Probability: The License Plate Problem
Washington State Algebra 2 Standard Name(s) and Number(s):
State the number and student performance expectation
A2.6.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in
situations arising from two-stage experiments (compound events).
Learning objective:
1. Use the Fundamental Counting Principle to determine the possible number of combinations.
2. Use the Fundamental Counting Principle to calculate the probabilities arising from compound events.
Prerequisite Skills:
1. Represent the sample space of probability experiments in multiple ways including tree diagrams and
organized lists. (7.4.A)
2. Determine the theoretical probability of a particular event and use theoretical probability to predict
experimental outcomes. (7.4.B)
Material for Students:
Small whiteboards and supplies or small posters and supplies
Teaching Aids:
Estimated Time For Completion:
1-2 class periods
References:
I.
PREASSESSMENT:
a. Determine if students understand independent and dependent event.
i. State whether the events are independent or dependent
1. Choosing size and color of a t-shirt.
2. Choosing the winner and runner up at a dog-show.
b. Determine if the students understand theoretical probability.
i. In a class of 30 students, what is the probability that the teacher will call on you?
c. Determine if students can represent a sample space.
i. List the possible outcomes of rolling a white and a black dice.
II.
INTRODUCTION:
a. In small groups, students will use a small whiteboard or poster paper (11” x 17”) to find a
solution to the following question. Give students time to develop solutions. When done,
groups share out their solutions and strategies.
i. You own an ice cream store that has 2 types of cones and 15 different flavors of ice
cream. How many different choices of ice cream cones does your customer have?
You only sell single-scoop cones. Display your solution.
1. How did you decide to display your sample space? Why?
2. How do you know you have all the combinations?
III.
LESSON:
a. Ice Cream Store Problem
i. What would happen if you had choices of 2 cones, 15 ice cream flavors, and 3
toppings? Would the number of possible combinations triple?
1. How did you find the number of combinations? Is there more than one way?
2. Derive a rule for finding the number of possible combinations. (The
Fundamental Counting Principle)
a. If students are struggling with this, have them start with smaller
number of ice cream choices work on building the pattern.(i.e.: 2
cones & 3 flavors then 2 cones & 4 flavors, 2 cones & 5 flavors)
b. Does this rule work for different scenarios? Come up with places
where you could use this. (i.e.: skate boards and trucks, deli
sandwiches, clothing choices, etc.)
ii. What if you decide to sell two-scoop cones? How would the number of combinations
change? Assume you can use the same flavor or different flavors for both scoops.
iii. It is later in the season and you decide to offer fewer choices to your customers to
decrease your inventory. You now offer 2 types of cones (sugar and waffle), 5 types
of ice cream (vanilla, chocolate, strawberry, mint chocolate chip, and mocha almond
fudge) and 2 toppings (chocolate sprinkles and gummy worms).
1. What is the probability of someone ordering vanilla on a sugar cone with
gummy worms?(simple event)
a. Answer: 1/20
2. What is the probability of someone ordering vanilla on a sugar cone with
gummy worms OR chocolate on a sugar cone with gummy worms?
(compound event)
a. P(A or B) = P(A) + P(B)
b. Answer: 1/10
IV.
APPLICATION
a. Now the student gets to practice under the supervision of you the facilitator.
b. Describe what the students do in order to practice or apply what they have learned.
c. Active participation by the students.
d. Collaborative learning activity?
e. License Plate Problem
i. Your state’s automobile license plates have 3 letters followed by 3 numbers. How
many different license plates can they make?
1. Answer: 17,576,000
ii. The state wants to use some specific letters for their own vehicles, so consumers
cannot have the first letter be W, the second letter cannot be S or T, and the third
letter cannot be P. How many license plate combinations are left?
1. Answer: 15,000,000
iii. You really love the number 888. What is the probability of randomly getting a plate
with the number 888? All letters may be used.
1. Answer: 1/1,000
iv. You want your initials for the first three letters of the plate. What is the probability of
randomly getting a plat with your initials? All letters may be used.
1. Answer: 1/17,576
V.
ASSESSMENT
a. Exit Slip – Have students answer the following questions and turn in upon exiting the room.
i. You go to the school cafeteria for a sandwich. There are 4 types of bread, 3 types of
meat, and 2 types of cheese. If you ordered a different sandwich every day, how
many days would you have to eat deli sandwiches to try every one?
ii. What is the probability that the person next to you orders the same sandwich?
VI.
EXTENSIONS
Based on: CURRICULUM GUIDE FOR PROFESSIONAL TECHNICAL COLLEGE INSTRUCTORS
TEACHING & FACILITATING LEARNING - LEVEL I