Lesson 1: Polynomials

what is the difference between the different types of polynomials?

What is a leading coefficient?
What is a degree?
What is a constant term?

Polynomial
Monomial
Binomial
Trinomial
Leading term
Leading Coefficient
Constant Term
Degree

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Lesson Description This lesson focuses on identifying, classifying, and simplifying expressions known as polynomials. Students will learn the "anatomy" of these expressions, including: The Definition of a Polynomial: Understanding that polynomials consist of terms with whole-number exponents (no negative exponents or variables in denominators).Anatomy of a Term: Identifying the coefficient, the variable, and the degree (exponent) of individual terms. Classification by Terms: Learning to name expressions based on the number of terms they contain: Monomial (1 term)Binomial (2 terms)Trinomial (3 terms)Degree of a Polynomial: Determining the overall degree by finding the highest exponent in the expression. Standard Form: Learning to write polynomials in descending order of their exponents (e.g., 3x^2 + 5x - 2).
Purpose The purpose of Section 13.1 is to establish mathematical literacy. Before students can perform complex operations like factoring or solving quadratic equations, they must be able to speak the language. This section ensures that when a professor says, "Look at the leading coefficient of the trinomial," the student knows exactly where to look. It also introduces the concept of Standard Form, which is the universal "filing system" for algebra that prevents errors during addition and subtraction.
Depth of Knowledge (DOK) Level
DOK Level 1
Level 1 (Recall & Reproduction): This section is primarily about classification and definition. Students are asked to recall rules for naming (Monomial vs. Binomial) and identify specific parts of an expression (like the degree). While it involves some organization (Standard Form), it is fundamentally about identifying the properties of mathematical objects rather than solving complex problems.

present a variety of polynomials and have the students determine what the different aspects of each polynomial is and how are they different from each other

"you try" on pg 302 and practice problem #1 on page 317