So. What Can You Do With a SmartBoard?
Introducing ... The Book ...
Title: Apr 26-10:30 PM (1 of 13)

Come write your name ... anyone, c'mon give it a try. It won't hurt ... really ...
Jennifer
Title: Apr 26-11:05 PM (2 of 13)

*
A Sample Lesson ...
... before ...
... during ...
... and after ...
Title: Apr 27-8:56 AM (3 of 13)

The Binomial Theorem
or "one of the ways G-d built the universe" ...
Zhu Shijiei 1261
Pascal 1653
Title: Apr 27-8:51 AM (4 of 13)

ANNOTATE THIS
Title: Apr 27-3:01 PM (5 of 13)

Expand and simplify ...
a+b
Title: Apr 27-8:52 AM (6 of 13)

Find a pattern, add two more rows to the triangle ...
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Title: Apr 27-8:52 AM (7 of 13)

Evaluate each term ...
Title: Apr 27-8:52 AM (8 of 13)

Pascal's Triangle
How many different patterns can you find in the triangle?
SYMMETRY
Counting Numbers
Sum of COUNTING numbers
triangular numbers
Sum of Triangular numbers
Title: Apr 27-8:52 AM (9 of 13)

Pascal's Triangle
How many different patterns can you find in the triangle?
Title: Apr 27-8:52 AM (10 of 13)

Pascal's Triangle
How many different patterns can you find in the triangle?
Title: Apr 27-8:53 AM (11 of 13)

Title: Apr 27-8:53 AM (12 of 13)

The Binomial Theorem ...
Algebraically
Combinatorically
Notice the patterns ...
(1) The coefficient of the term is:
(2) The exponent on a is given by: [n - (i - 1)]
(3) The exponent on b is given by: i
(4) This relation holds for each term in the expansion:
[exponent on a] + [exponent on b] = n
(5) The number of terms in any binomial expansion is: n + 1
Title: Apr 27-8:53 AM (13 of 13)