Binomial Mastery: Pascal’s Triangle, Theorem, and Probability
In this 3-week course, students will learn the structure and meaning of the Binomial Theorem and explore its connections to Binomial Expansion, Pascal's Triangle and Binomial Probability,
Erin Townley
Average rating:
5.0
Number of reviews:(1)
What's included
6 live meetings
4 hrs 30 mins in-class hoursHomework
1-2 hours per week. 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.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, the class dynamics and procedures will be tailored to the unique make-up of each group. Larger groups will have more opportunity to work with partners and small group dynamics, while smaller groups will have more individual check-ins with me. The class will meet twice a week, and each meeting is 45 min to allow for ample time to explore, discuss, and practice the concepts presented. I encourage my students to be active learners by asking and answering questions, offering explanations, etc., as this enriches the experience and the learning for all students. There will be no required homework assigned in this class, but optional homework assignments/extra practice will be provided after each class meeting for students to complete when needed.
Learning Goals
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.
Syllabus
6 Lessons
over 3 WeeksLesson 1:
Intro to Binomial Expansion and Pascal's Triangle
In this lesson, students will explore the patterns that exist in binomial expansions and how those patterns relate to Pascal's Triangle. 45 mins online live lesson
Lesson 2:
More with Binomial Expansion and Pascal's Triangle
In 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. 45 mins online live lesson
Lesson 3:
The Binomial Theorem
In 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. 45 mins online live lesson
Lesson 4:
Challenge Problems with Binomial Theorem
In 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. 45 mins online live lesson
Other Details
Pre-Requisites
Students should have completed at least an Algebra 1 course and be familiar with basic probability and binomial expansion.
Supply List
Paper Pen or Pencil a graphing calculator (I will be using the Numworks in class, but students can use what they have)
External Resources
Learners will not need to use any apps or websites beyond the standard Outschool tools.
Joined June, 2024
5.0
1reviews
Teacher expertise and credentials
Texas Teaching Certificate in Mathematics
Master's Degree in Mathematics from University of Houston
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 conceptsReviews
Live Group Course
$40
weekly or $120 for 6 classes2x per week, 3 weeks
45 min
Live video meetings
Ages: 13-17
4-12 learners per class
