Problem Set for Previewing Unit 2

In the second unit of Math I students will be shown the 4 basic operations (addition, subtraction, multiplication and division) when given polynomials. We begin the unit with showing the students to identify monomials, binomials, and trinomials; then we have the students identify the leading coefficient and the degree of the polynomial.

Vocabulary

Monomial Binomial Trinomial Coefficient Degree of a Polynomial Like Terms Distributive Property

Background

To begin we need to develop an understanding of the differences between monomials, binomials, and trinomials. We want to connect this back to the functions that the students learned about in the first preview of unit 1. The function f(x) = x is a monomial, it is written in the form ax where a in this case is 1. If we take this monomial and add to it whether it be a constant or an unlike term we have a binomial (ex 2x+1; x²-2x); thereafter, if we add an additional unlike term we have a trinomial (Ex. x²+x+3; x⁴+x³+3).

Adding and Subtracting Polynomials

Now that the students can identify polynomials, we begin with addition and subtraction. Using various examples and this activity we can show students that addition and subtraction of polynomials is the combination of like terms. We need to make sure that students understand that x and x² or two different terms. Also that even though x is the most commonly used variable we want to make sure students now that any letter may be in place of x.

Multiplying Polynomials

Here we want to begin by multiplying by monomial times a polynomial and have the students understand that this multiplication is using the distributive property. This notes sheet from Henrico School District can help to review distributive property. Once the review is complete we move on to teaching about multiplication of binomials. Here is a PowerPoint presentation to help. We want to make sure that the students understand that the multiplication of any two binomials can be represented as the area of a rectangle. Here is two worksheets representing the multiplication of binomials in both ways students need to understand as the area of a rectangle and using the FOIL method.