##
* *Reflection: Developing a Conceptual Understanding
Playing with Parabolas - Hands on - Section 1: Accessing Prior Knowledge

*Understanding the Approach in this APK Section*

*Developing a Conceptual Understanding: Understanding the Approach in this APK Section*

# Playing with Parabolas - Hands on

Lesson 4 of 7

## Objective: SWBAT use calculators to graph simple quadratic equations and interpret their graphs.

## Big Idea: Students become acquainted with simple quadratic equations! They graph and explore parabolas and gain their first experiences with quadratic function vocabulary and transformations.

*55 minutes*

#### Accessing Prior Knowledge

*10 min*

Before the start of the lesson, I cut out the Symmetry Slips so I can provide one set of slips for each pair of students in the class.

Once students are paired up, I hand each pair a set of slips and ask that together they fold each figure at their "lines of symmetry" or "reflecting lines". I inform the learners that figures may have none, one, or more than one reflecting line.

The activity activates some prior knowledge and sets them up for this introductory lesson on quadratics.

#### Resources

*expand content*

#### New Info

*10 min*

For this lesson I will use this section to introduce vocabulary relevant to the lesson, via a short Vocabulary PowerPoint presentation. I strongly suggest to my students that they not only enter terms in their notebooks, but also add a sketch with features labeled. I include a copy some of the slides of the PowerPoint for printing if desired (see POWERPOINT PRINTS).

*expand content*

#### Activity

*20 min*

Student continue to work with the same partners from the APK section. I hand each student an ACTIVITY SHEET. One student will handle graphing calculator, while the other sketches and writes. In Question 4, I tell students to use the CALC function of their calculator to verify their answer. i demonstrate how they can evaluate any of the equations for any value of x, so they must be carefully identify the equation they want to evaluate.

For this investigation, I like to let students go through each question pretty much on their own. I encourage them to speak to another pair of students for help before they come to me. Some students usually need help with setting their calculator Window values, so I ask students to teach their partners and their neighbors how to set up the viewing Window for their graphs.

#### Resources

*expand content*

#### Generalization

*15 min*

To conclude the lesson I break up the pairs and bring students back to a single group. I proceed to write the equation y = ax^{2} large on the board. I then call on students to answer questions about the graph of this equation. Here are some possible question prompts:

- State the vertex of the graph of a quadratic equation in this form
- State its axis of symmetry
- If the point (-5, -12) is a point on the graph of an equation in this form, name the coordinates of another point on the same graph.
- What roles does "a" play when graphing y = ax
^{2} - Does "a" change the shape of the parabola? Explain.

I will choose questions based on my observations of the students' work on the Activity and make adjustments based on the flow of conversation.

*expand content*

I ask students to complete Homework at home to review today's material and prepare for tomorrow's class.

#### Resources

*expand content*

##### Similar Lessons

Environment: Urban

###### Choosing a Method to Find x-intercepts

*Favorites(3)*

*Resources(12)*

Environment: Urban

###### Seeing Structure in Dot Patterns and Linear Functions

*Favorites(1)*

*Resources(20)*

Environment: Urban

- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
- UNIT 7: Functions
- UNIT 8: Advanced Equations and Functions
- UNIT 9: The Pythagorean Theorem
- UNIT 10: Volumes of Cylinders, Cones, and Spheres
- UNIT 11: Bivariate Data

- LESSON 1: Linear vs Quadratic (Day 1 of 2)
- LESSON 2: Linear vs Quadratic (Day 2 of 2)
- LESSON 3: The Biggest Possible Area
- LESSON 4: Playing with Parabolas - Hands on
- LESSON 5: How long will it take? (Day 1 of 2)
- LESSON 6: How Long Will it Take? (Day 2 of 2)
- LESSON 7: Are Absolute Value Functions Linear?