# Lesson Plan

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```					                      Lesson Plan
Pascal’s Triangle Activity

1. OBJECTIVE / Intended, Observable Outcomes
 Students will explore the patterns and
relationships throughout Pascal’s Triangle
 Students will find applications of Pascal’s
Triangle to real-life situations

2. MATERIALS / Visual Aids
 Worksheets with group questions on them
 Pizza toppings to tape onto blackboard for
visualization of combinations

3. READINESS / Prior Knowledge and Skills Required
This lesson is geared towards students who may have never
even seen Pascal’s Triangle before. It is intended to be
an introduction lesson.

The students will need to have some ideas about what
series and sequences are and how to look for patterns,
but we have been going through that information for the
last week.

4. MOTIVATION / Anticipatory Set / Advanced Organizers /
Introduction
While the students walk into the room, there will be a
worksheet handed out of Pascal’s Triangle. Underneath of
that will be written: “Please write down what you know

The students will write down everything they know about
the triangle. There will probably be a wide range of
knowledge about it, I expect some will know it’s name and
some applications, and some students in the same class
will have never seen the triangle before.

The papers that the students write on will be discussed
after a few minutes. We will talk together about
Pascal’s Triangle and share some knowledge about it. The
papers are to be kept by the students for referring to
while doing the class activity throughout the hour.
5. PROCEDURE / Instructional Strategies / Activities /
Key Questions
Today is an activity day, so the students will be working
in groups of about 3 or 4. This week, the teacher will
choose groups, since the students got to choose their own
groups last week. So the teacher will split the students
into small groups of 3 or 4. Hand out worksheet #2.

We will discuss these questions together in class. First
the teacher will walk around and make sure that each
group obtained an answer for all the questions. We will
discuss them together, sharing for about 5 minutes how we
came to our conclusions as a class.

When discussing the question on adding the rows together,
the teacher will make the statement that we are going to
call the row that sums to the number two raised to zero
power row zero and the row summing to two raised to the
first power row one and etc.

Following the class discussion, there will be a
transparency with the following problem on it on the
paragraph, another the second, and so on, a small thing
to make sure everyone follows along and it helps the
students practice their reading skills even though they
are in math class.

After reading the problem through, the students will each
receive a worksheet with Pascal’s Triangle on it and some
questions about our problem. The students are to work in
their small groups and try to come up with some
conclusions on Pascal’s Triangle and combinations.

One thing the teacher should try to do is sit in on each
group for at least a one minute span and just talk a
they are working on. Hopefully if the students are on
the wrong track, the teacher will be able to steer them
in the right direction without giving away the answers
that they are supposed to discover on their own.

LAST FIVE MINUTE ACTIVITY
We will end our class period reviewing mathematical
terms. Today we will review the definitions of the
following terms:
Triangle                    Function       Sequence
Formula

6. ASSESSMENT / EVALUATION / Methods of Evaluating
Student Learning
Each group will turn in their worksheets and the work
they used to come up with the solutions. The main method
of evaluation for this class period is simply teacher
observation. The teacher is going to be walking around
the room and seeing how everyone is working together and
problem solving.

Tomorrow we are going to go over some of the findings we
have made on our own, each group will have to stand up
and tell the class what the conclusion is that they came
to for Pascal’s Triangle and finding combinations.

7. SOURCES / References of Ideas
RICHARD G. BROWN
COPYWRITE 1994
WORKSHEET #1

Alone!
WORKSHEET #2

1.   Using the previous row how are the numbers found for
the next row? Find the next row.

2.   What do the sums of each row have in   common?

3.   Draw a line down the center of the triangle, from top
to bottom, what do you notice?

4.   EXTENTION:   Consider some of the patters relating to
our chapter on series and sequences along the
diagonals of the triangle.
WORKSHEET #3
“It’s Friday night and the Pizza Palace is
more crowded than usual. At the counter,
the Pascalini’s are trying to order a large
pizza, but can’t agree on what toppings to
select.

Antonio, behind the counter, says, “I only
have 8 different toppings. It can’t be
that hard to make up your mind. How many
different pizzas could that be?”

“Well, we could get a plain pizza with no
toppings,” says Mr. Pascalini.
“Or we could get a pizza with all 8
toppings,” says Mrs. Pascalini.
“What about a pizza with extra cheese and
“You’re not helping!” Antonio yells at
Pepe. “Get back to work.”

As Pepe starts to clear off the nearest
table, he mumbles to himself, “or a pizza
with anchovies, extra cheese, mushrooms,
and olives.”

Antonio hands an order pad to Mr. Pascalini
and says, “When you decided, write it down
and I’ll make it.” Then he helps the next
people in line, who know that they want: a
large pizza with mushrooms, green peppers,
and tomatoes.

How many different pizzas can be ordered at
the Pizza Palace if a pizza can be selected
with any combination of the following
toppings: anchovies, extra cheese, green
peppers, mushrooms, olives, pepperoni,
sausage, and tomatoes?”
WORKSHEET #4
PASCAL’S TRIANGLE WORKSHEET

1. How many zero-topping pizzas can be made?
2. How many eight topping pizzas can be made?
3. How many one topping pizzas can be made?
Find this number on Pascal’s Triangle and circle it.
State it’s position by row and column.
4. How many seven topping pizzas can be made?
Find this number on Pascal’s Triangle and circle it.
State it’s position by row and column.
5. How are the answers to #3 and #4 related?    Why?
6. How many two-topping pizzas can be made?
Find this number on Pascal’s Triangle and circle it.
State it’s position by row and column.
7. How many six-topping pizzas can be made?
Find this number on Pascal’s Triangle and circle it.
State it’s position by row and column.
8. Are the answers to #6 and #7 related?   If so, why?
9. Use Pascal’s Triangle to predict the number of
possible pizzas with 3-toppings, 4-toppings, and 5-
toppings.
10.    Show by listing that the 3-topping number of
combinations found with Pascal’s Triangle is correct.
Why does this prove the 5-topping possibilities also?
11.    Make a hypothesis about the use of Pascal’s
Triangle when determining possible combination
outcomes.

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