##
* *Reflection: Diverse Entry Points
Exploring Quadratic Functions - Section 2: Partner Activity: Investigating Quadratic Functions

I will administer this activity in two different formats, depending on the composition of the class:

- In general, my students should be okay receiving the entire investigation at once. Each pair will work independently through each section in a quiet area of the classroom (or in the hallway). These groups are usually able to stay on task for extended periods of time, and can grapple with challenging material without compromising their own thinking and learning process. With this model, my role as the Teacher will be to probe students with clarifying questions, and to help them develop their own understanding of concepts organically. I will ask students to justify and elaborate on their responses, and to provide counterexamples when possible.
- For some classes, however, the length of the activity may overwhelm students. When I have this concern I re-format the Investigation so that there is only one section visible to students at a time. Students will start with page one, and will receive new sections after a brief check-in with me. This approach gives me the flexibility to withhold specific sections, and to cater the activity to individual student pairs. The activity will still be student-centered, but adapted to provide more Teacher support. I will help students facilitate mathematical conversations, and will insert 2-3 whole group check-ins throughout the course of the period to review prior sections. These check-in's will help students build their confidence, as this small reinforcement becomes a motivator to persevere through the entire investigation.

*Two Possible Approaches to this Investigation*

*Diverse Entry Points: Two Possible Approaches to this Investigation*

# Exploring Quadratic Functions

Lesson 1 of 5

## Objective: SWBAT explore the characteristics of a quadratic function.

## Big Idea: Students will discover the unique characteristics of a parabola through a guided investigation.

*80 minutes*

#### Do-Now

*10 min*

Students will factor 4 trinomial expressions with a > 1 for today's Do Now. After 5 minutes, student volunteers will come to the board to display their responses for the class.

A student will then read the objective, **"SWBAT explore the characteristics of a quadratic function."**

I will ask students if they have heard the word "quadratic" before in a previous math class, and to make a prediction about its meaning by identifying and interpreting its root word.

#### Resources

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We this lesson we begin our Quadratics unit. It will be a smooth transition for my students, as this Unit succeeds their study of Polynomials. My students will be familiar with polynomials and factoring. They will not have seen the graph of a quadratic function in recent lessons.

To begin our study of quadratics, my students will work in homogeneous pairs to complete the Quadratics Investigation. The objective of this activity is to introduce students to the key characteristics of quadratic functions.

Graphing calculators (GDC) are needed to complete the last section of the Investigation. My students have used GDCs in previous classes, but this will be the first time that they will be used in a multi-step problem. Since the GDC is such an important tool for students as they advance into higher level mathematics classes, it is important that they become comfortable with its use in lower grades. Students best develop this GDC intuition through individual practice and troubleshooting, so I will stray away from teacher-led keystrokes. Students will be encouraged to use this Reference Sheet, which will guide them through the execution of a few essential GDC operations.

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#### Closing

*10 min*

With about ten minutes remaining, the class will reconvene as a whole group. I will ask the class to summarize today's activity and to think of examples of parabolas that they have seen in the real world. I will Google search student responses as they say them, so that all students have the opportunity to see more representations of this shape.

Lastly, I will ask students to compare and contrast the use of triangles and parabolas in architecture and construction, and to decide if these structures of this shape are interchangeable.

*expand content*

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- UNIT 1: Welcome Back! - The First Week of School
- UNIT 2: Linear & Absolute Value Functions
- UNIT 3: Numeracy
- UNIT 4: Linear Equations
- UNIT 5: Graphing Linear Functions
- UNIT 6: Systems of Linear Equations
- UNIT 7: Linear Inequalities
- UNIT 8: Polynomials
- UNIT 9: Quadratics
- UNIT 10: Bridge to 10th Grade