Polynomial Functions Review Day 2

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Objective

Students will review solving and graphing polynomial functions and equations.

Big Idea

Students reinforce their knowledge of polynomial functions while increasing their ability to successfully prepare for a summative assessment.

Lesson Author

Amelia Jamison

Caldwell, ID

Grade Level

Eleventh grade

Subjects

Math

polynomial functions

Standards

HSA-SSE.A.1

Interpret expressions that represent a quantity in terms of its context.*

HSA-APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

HSA-APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

HSA-APR.D.6

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.C.7c

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MP3

Construct viable arguments and critique the reasoning of others.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Polynomial Function Review Day 2 which asks students to prove the accuracy of a graphically solved polynomial. This warm up was inspired by a problem from EngageNY.

I also use this time to correct and record the previous day's Homework.

Review Activity

35 minutes

I begin this lesson by passing back the quiz from the previous day. This quiz will give the students some indication of their preparedness for many of the concepts covered on the unit test. Also, I ask that they correct their mistakes as this will help them avoid making the same mistakes again.

This remainder of this lesson is a continuation from the previous day. They will again get white boards and we will finish the PowerPoint. I may also add problems given the results of yesterday's exit ticket.