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* *Reflection: Student Led Inquiry
Quadratic Quandaries: Modeling with Quadratic Functions - Section 4: Collaborative Work Time: Performance Task - Quadratic Quandaries

Having students create their own problems and work can lead to powerful engagement and motivation.

For the Quadratic Quandaries Performance Task, I find that students love the flexibility and creative room that the performance task allows. Although it can be difficult, I try to reach a good balance of clear expectations and flexibility for this task.

Student work shows the variety of not only topics, from **Football Functions **to **Flappy Bird Rage**, but also in terms of depth of understanding. Many projects had relatively straight forward quandaries (when does an object hit the ground, what is the maximum or minimum height that the object reaches, etc.), but some had complex questions, like the **Volleyball Complex Question **where the group found an interesting application of quadratic functions.

An important note to the student work in this reflection is it is a mix of groups from my advanced honors section and groups from my fundamentals section. I am continuing to try and design and implement more engaging and open-ended tasks like the Quadratic Quandaries Performance Task for ALL students.

*Student Led Inquiry: Performance Tasks and Collaborative Work*

# Quadratic Quandaries: Modeling with Quadratic Functions

Lesson 10 of 13

## Objective: SWBAT apply key features of quadratics and methods for solving quadratics to solve real life problems. SWBAT create equations that model real-life scenarios using quadratic functions. SWBAT read, write, think and speak to demonstrate understanding of the lesson objectives.

#### Entry Ticket

*10 min*

For the **Entry Ticket: Quadratic Quandaries** students practice creating equations and differentiating between linear, exponential and quadratic functions.

The reason I have students complete this exercise is twofold. First, I want students to review how to create equations to model real-life scenarios because part of today's lesson is a performance task that asks students to do just that. Second, I want to help frame the unit on quadratics to students by asking questions that not only have them think about what quadratics are, but how quadratic functions are different from linear and exponential functions.

#### Resources

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After the entry ticket, the class turns to a brief focus lesson, where I model different applications of quadratic functions. During this time, the **Class Notes: Quadratic Quandaries **are projected on the Smart Board and students are actively taking two column notes, using the **Guided Notes: Modeling Motion with Quadratics.**

It is important to remind/preview with students that they will be asked to create their own problem that can be modeled with quadratic functions later in the lesson to point out the relevance and importance of the class notes.

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In this section I lay out the expectations and grading components for the Quadratic Quandaries Performance Task/Project. I hand out a copy of the **Performance Task Checklist and Rubric: Quadratic Quandaries** to each student and give students a few minutes to silently review the assignment before discussing it.

I then go through the overall intent of the project as well as the different components. I also review logistics (materials and where they are in the classroom, expectations around positive behavior during group work, etc..).

Time for questions is then provided and students dive into working on the project! It also is a good idea to explicitly remind students that they already have made excellent headway with the project through the work they did on their entry ticket in today's class.

This project is geared to give students an opportunity to further develop the Math Practice standards **MP3 **and** MP4**. Students have time to create arguments and critique the perspective of their peers in a setting that encourages students to make connections of how exponential functions can be used to model situations and better understand real-world phenomena.

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After the focus lesson on modeling with quadratics, students begin working on the **Quadratic Quandary Performance Task** in small groups.

I like having students work on performance tasks like the **Quadratic Quandaries Performance Task** because it provides a nice balance of structure and flexibility/choice for students.

During this time my role is that of a facilitator. I begin the time by making sure all of the groups have chosen a topic to model with a quadratic function. I ask reflective questions to help students monitor their progress and also to encourage the group to converse and collaborate with each other.

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#### Exit Ticket and Homework

*5 min*

To conclude the lesson, I spend a few minutes recapping the intent of the task as well as expectations and where students can find them (**Performance Task Checklist and Rubric: Quadratic Quandaries**).

For homework, each group of students needs to complete the project outside of class. As an Exit Ticket, I have each group of students reflect on the following prompts:

- What did your group do well on?
- What can your group improve upon for next time? What concrete suggestions do you have for how your group can make those improvements a reality?

Before ending class, I ask each group to tell me what their plan is to complete the project. This closing activity helps students break down the steps needed to complete the project. I push them to articulate a plan for completing the project and monitoring their progress as they do so. My goal here is to promote a skill that is important as they continue with their secondary and post-secondary education.

Next class, when students turn in their projects, I will take the time to display all of the presentations and wonderful work that students have created. I also try to invite school administrators and other teachers to see the work and, again, start the year on a positive note of high expectations, challenge with just the right balance of support.

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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