# Online Algebra Spring 2022 Seminar: Binomial Theorem

## Time & Location

## About the Webinar

If LeBron James is a 78% free throw shooter, what is the probability he makes exactly 18 out of his next 20 free throws? Would you believe the binomial cube holds the secret to answering this question?

In this workshop we’ll look at the binomial cube from the most basic iteration and expand it to it’s most general form - the binomial theorem! This theorem has tremendous applications in algebra, probability, and calculus. In addition, we will explore the Montessori materials used for multiplying binomial expressions, as is done in the Elementary classroom. We’ll then expand this to a more generalized and abstract form, but one which is rooted in the materials. Finally, we will look at applications of the theorem, such as multiplying out binomials and binomial probability distributions.

Schedule: 6-sessions, Meeting Monday and Wednesday on Zoom for 3 weeks for one-hour live sessions with Michael Waski

Cost: $195

**Course length: 3 weeks****Webinar dates: April 2022; All at 7:00pm ET-US**

**Course content: **

**Session 1:**

Binomials in One, Two, and Three Dimensions

Binomial Definition (One Dimension)

Multiplying Binomials (Two Dimensions)

Bead Bars

Binomial Square

Cubing Binomials (Three Dimensions)

The Sensorial Binomial Cube (Primary)

The Numeric Binomial Cube (Elementary)

The Algebraic Binomial Cube

**Session 2:**

Binomials in Four and Five Dimensions

The Fourth Power of a Binomial Material

The Fifth Power of a Binomial Material

**Session 3:**

Pascal’s Triangle and the Binomial Theorem

Pascal’s Triangle - Construction and Patterns

Pascal’s Triangle for Probability

Relating Pascal’s Triangle Binomial Theorem

Expanding Binomials Using Pascal’s Triangle

**Session 4:**

A Combinatoric Approach to the Binomial Theorem

Permutations and Combinations (General)

Relating Permutations to Binomial Expansions

Formalization of the Binomial Theorem

**Session 5:**

Puzzles and Application of the Binomial Theorem

Multiplying Numbers through the Binomial Theorem

Expanding Algebraic Expressions through the Binomial Theorem

Finding Terms or Coefficients without Expanding

Other Applications

**Session 6:**

Binomial Probability Distributions

Probability Tree Diagrams

Solving Binomial Probability Distribution Questions

Technology

**Wish to purchase Teaching Algebra to the Adolescent: A Montessori Approach? Follow this** link**. **

**Certificates of Completion will be emailed to the participants at the conclusion of the workshop (16 hours) **

- Equation Workshop$195$1950$0