Pascal’s Triangle
Introduction Task Process Resources Evaluation Conclusion
Introduction
Pascal's Triangle was originally developed by the ancient Chinese, but Blaise Pascal was the first person to discover the importance of all of the patterns it contained. Blaise Pascal (1623 - 1662) was a French mathematician. His surname is used as the unit of pressure. He is most famous for the triangle named after him, Pascal's Triangle. It's not a geometrical triangle, but a triangle of numbers. Each row begins and ends with the number 1. Each other number is the sum of the two numbers above it.
You are to investigate number patterns in Pascal’s triangle and present the
findings to the class with a
poster, overhead transparencies, and/or
power point. You will design a brief lesson (with
handouts) for the class to
practice number patterns.
1.
Print
the template.
a.
Complete
row 5 through row 9 following the pattern.
b.
Find
the sum of the numbers in each row.
Examine the sums.
What pattern do you see in the sums?
c.
Predict
the sum of the numbers in row 10. Then
check your answer by finding row 10 of Pascal’s triangle and finding its sum.
d.
Want
more practice?
2.
The
figure below shows how to find the sum of the diagonals
of Pascal’s triangle.
a. Describe
the pattern in the sums of the diagonals.
b.
Predict
the sum of the next two diagonals.
c.
The
sums are called the Fibonacci numbers.
1
1
2 3
5
For more examples, click
here.
3. Everyday investigation
Suppose the grid represents
all of the streets between you house
and your grandmother’s house.
You will be begin your route at your house and
move down the grid to get to your grandmother’s house.
Activity:
I. Print
the grid. Fill in each circle with
a letter from A-P. Start
with
A at the top (row 0), Fill in B then C (on row 1), D then E then F ( on
row 2), and so forth. (See
Mrs. Papizan if you don’t understand.)
II. How many
different routes are there between each pair of points listed below?
Write your answer on the
grid.
a.
A
and B
b.
A
and C
c.
A
and D
d.
A
and E
e.
A
and F
f.
A
and G
g.
A
and H
h.
A
and I
III. Explain
how Pascal’s triangle is related to the numbers on the grid.
IV. Extend
the pattern to find how many different routes there are.
4.
Investigate
more patters of Pascal’s triangle by coloring certain patterns of numbers. Try the online
practice (read this page then play the
game!)
5. Prepare a 5 –10 minute presentation about Pascal’s
triangle. Teach the class some of the
basics of what you have learned and design a quick worksheet for them to
practice. (DO NOT READ BORING
PARAGRAPHS TO THE CLASS! Discuss it
like you know what you are talking about!)
Use several visual aids to help the class understand the topic.
Scroll down
this site to the section on combinations.
Evaluation
Web Quest Evaluation Rubric
Presentation |
||||
|
|
70 |
80 |
90 |
100 |
|
Were the presenters enthusiastic about this presentation? |
Presenters may as well been asleep they were so boring. |
Presenters were faking their enthusiasm or could have been more lively. |
Presenters were reasonably excited about their topic. |
Presenters were excited enough to make the audience want to know more. |
|
Did the presenters make eye contact or just read to the
class? |
Read to the class long boring paragraphs |
Some reading with a small bit of eye contact |
Maintained eye contact throughout at least half the presentation |
Great eye contact for most of the presentation. Made the listener feel that they were part of the presentation. |
|
Did the presentation flow well or were there long
pauses of silence? |
Several long pauses of silence, very unorganized |
Some pauses of silence, unorganized in parts |
Very few pauses of silence, 1 part unorganized |
No pauses; presentation flowed well |
|
Did all team members have a role in delivering the
presentation? |
One person gave the entire presentation. |
One person gave most of the presentation. |
Both persons had equal speaking parts but they did not seem to function as a team. |
Both persons had equal speaking parts and functioned well as a team. |
Project Design 70 80 90 100
|
Did the project address all necessary information? |
Left off several items |
Left off a 2-3 of items |
Left off one item |
All required items included |
|
Did the project have an interesting look? |
Plain, no color, 1 picture |
A little color, 2-3 small pictures |
Colorful, a few pictures, but not very pleasing |
Very interesting, pleasing look, good pictures |
|
Did the visual aids offer variety and maintain
interest? |
Aids were uninteresting and did not pertain to subject. |
Aids were too small to see but were appropriate. |
Aids were interesting but were all the same type. |
Interesting visual aids that were large enough to see. |
|
How much effort seemed to be put into this project? |
Looked and sounded like it was all done last night. |
A little effort was put into the poster but none into the presentation (or vise-versa) |
A respectable amount of work was obvious. |
An outstanding job that Mrs. Papizan will show for future reference. |
Presentation Avg: Project Avg: Overall Score:
Now that you have completed this web quest, you
should have a stronger understanding for Pascal’s triangle. If you enjoyed this study, you may want to
consider further research in the careers involving predictions and
combinations.