Lesson Plan: General Term in the Binomial Theorem | Nagwa Lesson Plan: General Term in the Binomial Theorem | Nagwa

Lesson Plan: General Term in the Binomial Theorem Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find a specific term inside a binomial expansion and find the relation between two consecutive terms.

Objectives

Students will be able to

  • recall the formula for a general term in a binomial expansion, (𝑥+𝑦),
  • use the formula for a general term in a binomial expansion, (𝑥+𝑦), to find a specific term (or its coefficient) for
    • a given exponent 𝑥,
    • the highest or lowest power of 𝑥 in the expansion,
    • the middle term(s) in the expansion,
    • a given position when terms are arranged by ascending or descending powers of 𝑥,
    • a specified coefficient,
    • two or more terms with the same coefficient as each other,
  • understand the relationship between consecutive terms of a binomial expansion,
  • use the relationship between consecutive terms in a binomial expansion (and their coefficients) to find
    • the ratio between two terms,
    • the largest or smallest term,
  • find an unknown in a binomial when given information about one or more specific terms.

Prerequisites

Students should already be familiar with

  • the binomial theorem,
  • combinations and associated notation,
  • simplifying factorials.

Exclusions

Students will not cover

  • methods involving Pascal’s triangle.

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