The Tales of Nerdy Norm

Objective: TSWBAT understand how a change in "a" or "c" in the standard form of a quadratic equation ax^2 + bx + c changes the graph of the resulting function.

Prerequisite Knowledge/Concepts: Understanding what standard form of a quadratic equation is; Basic understanding of the idea of a transformation to a graph; Understanding that the basic shape of a quadratic function is a parabola; Ability to graph a set of ordered pairs on a graph; Ability to create a table of values from a given function

Procedures:
1) Introduce the project concept. Students will be telling the story of "Nerdy Norm the Normal Parabola." Nerdy Norm is a parabola whose equation is y = x^2 on a typical/usual day. However, Norm's equation changes when his moods and/or location changes. Provide students with examples of Norm's various "moods" and their corresponding equations. For example, "High Nerdy Norm" could be the equation y = x^2 + 7 and "Nerdy Norm Flipped" could be the equation y = -x^2.
2) Have students take the various "moods" you give them and show graphically what happens. For each equation you give them (around 10 total), have students create a table of values (I suggest from x = -5 to x = 5 at a minimum). Then have students plot the ordered pairs to create a graph of the equations on one large coordinate plane. [It will be helpful for students to use different colors and create a key to their graph.]
3) Next, students should use the graph they created to write a story that details how and why Nerdy Norm's graph changed as his mood changed. You can have students write a story in paragraph form first or have students work directly with a storyboard format. Make it clear that the story should match what happens on the graph!
4) Students will use clay to create a model of Nerdy Norm - i.e. students will model the shape of a parabola out of clay.
5) Students will use a video camera to record "stop motion" shots of their parabola in each of the various transformations they graphed. Then, students will use stop motion animation software to create a video from these shots.
6) Students will create voice-over narration recordings of the stories they wrote detailing Nerdy Norm's various moods. Students will use video editing software to add their voice narration to their stop-motion video.
7) Students will present their video projects to the class.