## Thursday, February 2, 2012

### Angry Birds and calculus:

First provide the students with a laptop with Geogebra, and the following photo.

Introduce the meaning of Piecewise functions, and how the yellow bird, when clicked, shoots off at a tangent to the curve.

Ask the students to describe what are the two functions that create this curve (Parabola and a line).

Using prior knowledge have students graph the maximum point on the parabola, and use the dot where the yellow bird took off at a tangent (B), to create the equation of the parabola.  Have students graph the parabola in geogabra, overtop the picture, to ensure all calculations have been done correctly.

Next, ask students how to determine the equation of line.

We will need either a) two points or b) a slope and a point.  Both of which is impossible, without the use of the tangent button in Geogabra.  I explained, we can calculate this without that button!

Have students pick another “point on” the parabola (c), and to calculate the slope between B and C.  Ask how do we make this slope more accurate to the slope of the tangent…

Move C closer to B..

Have students move C closer to B, while still staying on the parabola and calculate the new slope.  Eventually move C as close as possible to B.  The slope should be -0.5  Below is a picture of one of the students’ work

Next using the point B and the slope you can create the equation of line.

From here your choice for extensions: I had students graph the piecewise functions on their calculator and got the following image

Lastly, here is a video on how to determine the slope at a point:

1. I think this is great... a nice extension might be to write an equation for a new parabola (as I'm pretty sure they yellow bird just changes speed and is still subject to the gravity of the game) rather than the tangent line.

2. Yes it does, and great idea!!

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4. Now with Angry Birds Space, the birds can fly linearly through space until they reach the atmosphere of the planets (rocks.) I wonder how this activity can be used in that case? Perhaps a discussion of where to ideally enter the atmosphere? Then again, the motion in the atmosphere is not exactly parabolic as the planets are so small.

5. 