Online Algebra 2022 Seminar: Binomial Theorem

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.

The workshop includes 6-sessions with Michael Waski. The sessions will be pre-recorded and you will be able to access these recordings starting April 5th. The workshop access link will be sent to you.

Cost: $195

• Course length: 6, 1-hour sessions
• Dates: Access link available starting April 5th    

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)