Objective

Warm-Up and Priority-Setting

Review Workshop

Final Questions and Assignment

Review Workshop: Polynomial Functions and Expressions

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Objective

SWBAT begin pulling together everything they have learned so far about polynomial functions and expressions in preparation for tomorrow's unit test.

Big Idea

Tomorrow is the unit test on polynomial functions and expressions. In this lesson, we do more practice with word problems, solving equations, graphing parabolas, and rewriting quadratic functions.

Lesson Author

Colleen Werner

Ipswich, MA

Grade Level

Eleventh grade

Subjects

quadratic functions

Math

completing the square

Standards

HSA-SSE.B.3a

Factor a quadratic expression to reveal the zeros of the function it defines.

HSA-SSE.B.3b

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

HSA-APR.A.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.

HSA-REI.B.4

Solve quadratic equations in one variable.

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

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.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

HSF-IF.C.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF-IF.C.8a

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

HSF-IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Warm-Up and Priority-Setting

30 minutes

Helping Students Self-Assess

Today is a review day for tomorrow's test on polynomial functions and expressions. The previous night, students were given a set of application problems. I start class by checking these problems with the homework rubric and project solutions to the problems on the board. The unit test is tomorrow, and I take time to review any requested problems, even if this portion of the lesson takes a little longer than anticipated.

After discussing the homework, we synthesize the major concepts of the unit by completing the Polynomial Functions and Expressions Unit Checklist. This checklist has a set of "I can" statements that students use to assess their understanding of the concepts and skills presented in the unit. Students rate each item on the list according to the following scale:

A = I understand this so well that I could teach it to someone else.

B = I get this but I should review a bit

C = I don’t get this – I better study my notes and/or get help

D = I don’t remember anything about this

There is also a space on the unit checklist for students to write down where they can find practice on any item they need to study.

Review Workshop

40 minutes

The Review for Unit Test on Polynomial Functions and Expressions is a collection of exercises from this unit. Students work in table groups to complete these exercises or something else that they have identified as a priority on their checklist. As students review for the test, I make the answer key available at my desk for anyone who wants to check their work. As they review I circulate and answer questions that come up.

EXTRA HELP: I put together a set of videos, Blendspace Review - Polynomial Functions and Expressions, that students can use if they need remediation on a particular skill. This is especially useful for students that may have had absences during the unit. I discuss my rationale for providing this resource in the video Blendspace for Review.

Final Questions and Assignment

20 minutes

Students complete the Review for Unit Test on Polynomial Functions and Expressions as needed for homework. I remind students that the answers to the homework will be available on Edmodo and that they should check their answers online in preparation for the following day's unit exam.

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