A Guy named Pascal and his Triangle

Subject Matter: Math

Grade Level: High School Algebra II

Lesson Objective: 
Learners will demonstrate ability to use Pascal's Triangle to complete binomial expansions.

Subject Matter Content Standard:
CCSS A-ARP-5. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.12 

ISTE Student Standards:
Digital Citizenship - Students recognize the rights, responsibilities and opportunities of living, learning, and working in an interconnected digital world, and they act and model in ways that are safe, legal and ethical. 
2b. Students engage in positive, safe, legal and ethical behavior when using technology, including social interactions online or when using networked devices.

Essential Student Research Question: 
How does Pascal's Triangle make binomial expansion more approachable?

Websites to use as resources: 

Math is Fun - Pascal's Triangle http://www.mathsisfun.com/pascals-triangle.html

Khan Academy - Pascal's Triangle and Binomial Expansion https://www.khanacademy.org/math/algebra2/polynomial-functions/binomial-theorem/v/pascals-triangle-binomial-theorem

Pascal's Triangle and Its Patterns http://ptri1.tripod.com/

Additional Questions:

2. What do the numbers in Pascal's Triangle represent?

3. How did we learn to calculate binomial coefficients previously?

4. Expand (x - y)^5 using Pascal's Triangle.

5. Expand (2m + 3n)^3 using Pascal's Triangle.

6. What did you notice was different between the answers to #4 and #5?

7. What is the 5th term of (5a - 2b)^7 ?

Challenging Questions (Answer in full sentences)

8. Describe how the triangle is constructed in your own words.

9. When Sal Khan is building the triangular structure starting at minute 1:13, what do his "different ways" remind you of? Give one probability example.

10. Pick one special pattern within Pascal's Triangle and explain it in your own words.

1. Now please go back and answer the Essential Student Research Question in your own words!