Pascal's Triangle Web Quest Project - Hannelore Hauke

Introduction:

Pascal's Triangle is an interesting set of numbers that are related to other number sets and patterns throughout mathematics. This project will familiarize you with the working of Pascal's Triangle and also enable you to use the knowledge you acquire to answer questions about this special triangle. You will also discover the origins of Pascal's Triangle and who originally came up with the ideas behind it.

Pennsylvania State Standard for Mathematics

• 2.8.8.C which states that students will be able to 'Find the missing elements and recognize, describe and extend patterns to include linear, exponential, and simple quadratic equations.'

Task:

The following questions about the history of Algebra and Pascal's Triangle should be answered through your research:

• Where did the use of Algebra start? What country?
• Algebra can be broken down into several different categories. Name three (3) difference types of Algebra and give a short description of each.
• When was the Rhind Papyrus written by the Egyptians?
• In what period of time did the Babylonians contribute to our knowledge of Algebra (looking for answer in years)?
• Diophantine Algebra was lead by the Greek mathematician, Diophantus. Briefly describe "Diophantine Equations".
• According to record, Hindu influence on mathematics dates back to what year?
• Even though we know Pascal's Triangle by the given name, it was not Blaise Pascal who originally found the pattern in the numbers. There are two groups of people who studied the numbers which Pascal developed many applications for. Name the two groups or people who originally studied the number patterns.
• The Chinese do not refer to the pattern as Pascal's Triangle, but by the name of another mathematician. What do the Chinese call Pascal's Triangle?
• Briefly describe the following: How Pascal's Triangle is Constructed, The Sum of the Rows, Prime Numbers, Hockey Stick Patterns , and Magic 11's

The following chart shows the different powers of the binomial (a+b), and compares the expanded form with Pascal's Triangle.

1) Start with the expanded form of (a+b)^2, and multiply by a+b. What is the result?

2) Do the same with the expanded forms of (a+b)^3 and (a+b)^4. What is the result?

3) How does the number of terms in each row of the expanded for compare with the exponent in the power of the binomial?

4) How many terms would you expect to be in the expansion of (a+b)^7?

5) Extend Pascal's Triangle through row 10.

6) Write the coefficients of each term in the expansion of (a+b)^7.

Process:

Use the information you find at the following web sites to answer the questions above.

Pascal's Triangle and It's Parts
Wikipedia: Pascal's Triangle
History of Algebra
Wikipedia: Algebra
The History of Algebra

Projects must be presented to the class. Presentations can include PowerPoint Presentations, Flip-Charts, and Drawings of Pascal's Triangle.

Other useful resources for Information:

Math Forum: Pascal's Triangle
Ask Dr. Math
Printable Triangle to Fill In
Google
Yahoo
Ask
Dogpile

Evaluation:

Rubric

• Students spoke clearly during presentation of findings: ___Yes ___No
• All group members participated in oral presentation: ___Yes ___No
• Students had good use of visuals during presentation: ___Yes ___No
• All nine questions about the history of Algebra and Pascal's Triangle were answered correctly: ___Yes ___No (___/9)
• All six math problems relating the Pascal's Triangle were answered correctly: ___Yes ___No (___/6)
• Each group member turned in a conclusion paragraph: ___Yes ___No

In most cases, group members will all receive the same grade. In the event that certain students do not contribute to the research, do not help answer questions, do not participate in the oral presentation, and/or do not turn in a conclusion paragraph, grades will be affected accordingly.

Conclusion:

I hope you enjoyed discovering the wonders of Pascal's Triangle. Each student is required to write their own paragraph explaining something fun and/or interesting that you found out about Pascal's triangle that was not included in this project. Have you come to any conclusions about the Triangle that you did not come across in your research? If so, include your theories in your conclusion.

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