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Binomial Mastery: Pascal’s Triangle, Theorem, and Probability
Class Experience
US Grade 9 - 12
Intermediate Level
This course is intended to give students an opportunity to learn about the concepts of Pascal's Triangle and the Binomial Theorem, as well as their properties, applications, and connections to probability. It is intended to be an introduction to these topics, so no prior understanding of them is required. However, it will be helpful for a learner to have an understanding of how to expand binomials and some basic probability. Although we will have a set amount of content to cover each class,...
6 lessons//3 Weeks
Week 1Lesson 1Intro to Binomial Expansion and Pascal's TriangleIn this lesson, students will explore the patterns that exist in binomial expansions and how those patterns relate to Pascal's Triangle.Lesson 2More with Binomial Expansion and Pascal's TriangleIn this lesson, we will expand on what was covered in the previous class and learn how to create full and partial expansions of binomials using Pascal's Triangle.Week 2Lesson 3The Binomial TheoremIn this lesson, we will define and analyze the Binomial Theorem, show how it connects to Pascal's Triangle and practice using it in a variety of problems.Lesson 4Challenge Problems with Binomial TheoremIn this lesson, we will work on solidifying and extending our understanding of the Binomial Theorem by tackling a variety of challenging, abstract problems related to the theorem and binomial expansion.Week 3Lesson 5The Binomial Theorem and ProbabilityIn this lesson, we will make the connection between the terms of a binomial expansion and the outcomes of a binomial probability.Lesson 6Applications of Binomial ProbabilityIn this lesson, we will expand on what was covered in the previous lesson and explore some of the applications of binomial probability, including coin flips, dice rolls, test taking, decision making, etc.
- Students will understand how Pascal's Triangle can be used as a tool for binomial expansion.
- Students will make connections among Pascal's Triangle, binomial expansion, and the Binomial Theorem.
- Students will improve their understanding of the Binomial Theorem by applying it and its properties to binomial probability.
- Students will solidify their understanding of the Binomial Theorem and binomial probability by exploring some of the many applications that exist in the real world.
Since learning about them in high school, Pascal's Triangle, the Binomial Theorem, and binomial probability have been one of my (many) favorite topics in math. As a student, I noticed that these topics seemed to appear in a wide variety of math courses and were often very challenging for students to understand and utilize effectively. As a teacher, I noticed that every year, this topic was listed as the most difficult by a majority of the students, so I've made it a goal to "demystify" this set of concepts. In addition to my understanding of the importance of these topics and their value to a variety of areas of study, I have the following qualifications: -B.A. in Mathematics from Rice University -M.A in Mathematics from University of Houston -Texas Teaching Certificate -almost 15 years teaching and tutoring courses that teach and/or use these concepts
1 - 2 hours per week outside of class
Homework
Frequency: 1-2 per weekFeedback: available upon requestDetails: Students will be given optional extra practice homework assignments after each class, so that they can check their own understanding of the topics prior to the next class period. Answer keys will be provided and questions will be addressed in the next class.
Students should have completed at least an Algebra 1 course and be familiar with basic probability and binomial expansion.
Paper Pen or Pencil a graphing calculator (I will be using the Numworks in class, but students can use what they have)
Teacher expertise and credentials
Texas Teaching Certificate in Mathematics
Master's Degree in Mathematics from University of Houston
Hi, I’m Erin! I graduated magna cum laude from Rice University in 2008 with a B.A. in both Mathematics and Psychology, as well as obtaining a teaching certificate for grades 7-12. I then went on to get a M.A. in Mathematics from the University of...
Group Class
$40
weekly or $120 for 6 classes2x per week, 3 weeks
45 min
Live video meetings
Ages: 13-17
4-12 learners per class