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# Performance Task: Pulling It Together with Quadratics

Lesson 11 of 13

## 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.

*90 minutes*

#### Entry Ticket

*15 min*

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.

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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.

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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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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Introduction to Quadratic Functions
- LESSON 2: Interpreting and Graphing Quadratic Functions
- LESSON 3: Rate of Change & Comparing Representations of Quadratic Functions
- LESSON 4: Rearranging and Graphing Quadratics
- LESSON 5: Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)
- LESSON 6: Building Quadratic Functions: f(x), kf(x) and f(kx)
- LESSON 7: Factoring and Completing the Square to Find Zeros
- LESSON 8: Forming Quadratics: Math Assessment Project Classroom Challenge
- LESSON 9: The Three Musketeers: Simplifying the Quadratic Formula
- LESSON 10: Quadratic Quandaries: Modeling with Quadratic Functions
- LESSON 11: Performance Task: Pulling It Together with Quadratics
- LESSON 12: Study Session for Unit Test on Quadratics
- LESSON 13: Unit Assessment: Quadratic Functions and Equations