1. Topic-
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| Pascal's Triangle and Combinations |
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2. Content-
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This lesson is about Pascal's Triangle and how it is related to
combinations. This lesson is about Blaise Pascal and Pascal's Triangle.
Other topics to be discussed with this would be Chu Shih-chieh's Precious
Mirror of the Four Elements and Omar Khayyam.
Vocabulary:
Combination-an arrangement, or listing, of objects in which order
is NOT important.
Equation: nCr |
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3. Goals: Aims/Outcomes-
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1. The importance of this lesson is for the students to determine
a combination, given a word problem.
2. I want to show the students where they may use this in real life.
The book lists an example.
3. The importance of this lesson is for the students to explore one
specific person related to Pascal's Triangle
4. The students will have to find a brief history on their topic and
also the contributions towards the triangle.
5. The students will work cooperatively with a partner or 2 group
members to create a short presentation based on the information they
find. |
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4. Objectives-
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1. Students will be able to use the combination formula to complete
word problems.
2. Students will be able to find the number of combinations of a set
of objects.
3. Students will be able to develop a view on Pascal's Triangle.
4. Students will explore both the Internet and the library to find
information.
5. Students will be able to prepare a 3 to 5 minute presentation based
on their findings in class. |
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5. Materials and Aids-
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| chalkboard, chalk, book, pencil, paper, index cards, computer, library |
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6. Procedures/Methods-
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A. Introduction-
1. Students will have pre-assigned partners, upon entering the classroom
they will be asked for one student to open their textbook to page
386. They will follow the first two steps and answer the five questions.
2.Have the students break into their groups.
3. Distribute the specifications sheet for the information the students
need to present. |
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B. Development-
1. I will ask the students what they found by doing the opening
activity. After discussing these questions, I will begin my lesson.
2. First, I will state the definition of a combination and show the
formula derived to go with it.
3. We will review permutations, then go over a combination example.
4. Next, I will help the students determine whether a situation is
a combination or permutation.
5. I will show the students how combinations are related to Pascal's
Triangle, by using the chart from one of my sources.
6. Students will go to the computer lab to research on their topics.
7. If needed, I will dismiss one group at a time to report to the
library to find information. |
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C. Practice-
1. As a class, we will go over the skills and concept check section
in the book.
2. The students will then return with their partner to work on the
guided practice section or the book, problems 4,5,& 6. As a class,
we will then go over the answers for these three problems.
3. Once the students research their topic, they will be able to answer
the questions given.
4. The students should attempt to go over their presentation one time
during this class. |
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D. Independent Practice-
1. I will assign problems 7, 10, 11, 13, 15, and 17 for homework.
The remaining class time can be used to begin the homework.
2. If the students decide they want to use a visual aid, they may
make this.
3. Although this is not a requirement, it is a great addition to the
project. |
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E. Accommodations (Differentiated Instruction)-
1. I will provide a sheet with both permutation and combination
formulas.
2. I will assign groups so that the students who do not understand
how to do the problems work with students who are behind.
3. Handouts will be provided to those who need them. |
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F. Checking for understanding-
1. Most of the class, I will be using student input. I will call
on different students for each question I ask.
2. Also, while the students are working on the exercises with a partner,
I will be walking around the room.
3. The presentation will be my assessment for these two days. They
will have the rubric which I will be grading them from, so they know
what is expected. |
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G. Closure-
1. I will remind the students about their homework problems. and
also tell them we will spend another day discussing combinations and
their relation to Pascal's Triangle.
2. Explain to the students their presentations will be due 10 minutes
after class starts, they will be given the beginning of class to practice
one more time. I will remind them if they want a visual aid this should
be completed for tomorrow (Wednesday).
3. Ask for any questions on the project. |
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7. Evaluation-
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1. I will quickly look over their homework the next day, then as
a class we will discuss the homework problems assigned.
2. By student input and the amount of work done, I will be able to
determine what specific areas of combinations I need to discuss in
greater detail.
3. I will walk around the room to make sure the students are on task
and speaking with other group members researching their specific topic.
4. Check to see if anyone is doing any further activities that night
to go along with their project. |
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