Objective

Entry Ticket

Performance Task on Profit Selling Smart Forms

Idea Organizer and Written Response

Performance Task: Pulling It Together with Quadratics

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Objective

SWBAT compare different representations of quadratic functions to derive meaning and better understand real-life contexts. SWBAT provide evidence to back up their claims in a clear and cohesive manner.

Big Idea

Students integrate concepts learned about quadratic equations and functions to analyze models and make recommendations for maximizing profit on the sale of smart phones.

Lesson Author

Jason Colombino

Salem, MA

Grade Level

Ninth grade

Subjects

Math

Algebra

Quadratic Equations

quadratic models

modeling

completing the square

quadratic formula

Standards

HSA-SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

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-REI.B.4

Solve quadratic equations in one variable.

HSA-REI.B.4a

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)<sup>2</sup> = q that has the same solutions. Derive the quadratic formula from this form.

HSA-REI.B.4b

Solve quadratic equations by inspection (e.g., for x<sup>2</sup> = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

HSF-IF.A

Understand the concept of a function and use function notation.

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.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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.

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP6

Attend to precision.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Entry Ticket

15 minutes

During today's opening task students practice translating equations using completing the square and solving equations using the quadratic formula. The entry ticket is written on a white board for students to copy:

Complete the square: x^2 +14X + 51
Use the quadratic formula to solve the function: f(x) = 2x^2 -3x -2

I have students complete this entry ticket to practice some of the core skills they will need to be successful in the performance task during today's class.

Performance Task on Profit Selling Smart Forms

60 minutes

During the next hour or so of class students, I will have my students work independently on the Quadratics Performance Task. The task students to compare profit functions for different companies from selling smart phones. The task is designed for students to apply the ideas taught in this unit.

While students are working, I am making rounds, providing cues to students as needed - I try to let most student struggle a bit before providing a cue to help them initiate. This gets at the math practice standard MP.1 as I want students to persevere in problem solving and be able to pause and reflect on what types of strategies and skills they need to navigate a problem.

I also provide some external executive function support for students in terms of time management. After the first 20-minute chunk of the activity I cue students it would be reasonable for them to be done with the first company, and again for each of the next two 20-minute chunks. This helps students pace themselves and also provides some motivation to stay on task.

Idea Organizer and Written Response

15 minutes

To conclude the class, I provide students with an Idea Organizer as a means to organize thier thinking for page 4 of the task (comparing and contrasting the different companies and making decisions about different profit trends). I assign students the homework as writing up the Idea Organizer into a cohesive multi-paragraph response. I chose to make a performance task that values math knowledge and the ability to write because I feel strongly that written expression is a powerful tool to help students better communicate their thinking AND helps them mediate thier thought process and understanding of mathematics.

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