Do not have them make catapults for your class.
This will take entirely too much time on things unrelated to the standards you are supposed to be teaching. If this is the version of the project you want to do then partner with a shop class or art class where creating the catapult will meet a standard for that teacher. Then use the catapult in your class to create the parabolas. (Hint: You will want to take slow motion video of the bird flying from the catapult so you can project the curve onto paper or poster board.)
Have the students use poster board not paper for the creation of their angry bird course.
Again, have them design the map for their level in art class. Partner with an art teacher. Then when they are complete have them create the flight pattern (parabola) on the map they created in your class.
Remember the important things for your class are...
- Creating the Parabola
- Using the math technology
- Finding all of the following
- Axis of Symmetry
- Height of Parabola
- X intercept (where bird would hit the ground if it hit nothing on the way) and Y intercept (height of catapult)
- Contact point of Bird
- Quadratic Equation & h,k form for vertex
Make the layout of the coordinate plane fit their parabola (flight pattern) you do not want them using awful numbers.
This will slow them down and make the answers to the above hard to grade due to the inconsistent estimates. Make them check with you before they finalize putting it on the coordinate plane. Have them make the entire map and then color it. When they are don't have them use a yard stick to make a line go vertically through the Parabolas Maximum Value. Then have them make another line go horizontally through the same Maximum Value. Then base all other grid lines of the coordinate plane off these two lines.
Here is a sample...