Rubber Band Cannon Lab (Compiled at Twitter Math Camp 2014

Prior knowledge: Students should be able to

Forms of a quadratic function Know what the graph of a quadratic looks like Be able to identify the features of a quadratic graph Understand and be able to use the 3 methods of solving, 4 if you count take square

root of both sides

Activity: Rubber Band Cannon Lab

The lab written out including how to make the cannon: https://www.flinnsci.com/media/510546/rubber_band_cannon.pdf

Supporting materials: http://danielsmath.pbworks.com/w/file/fetch/62171535/Rubberband%20Cannon%20Lab.pdf

Protractor printable. http://www.math-aids.com/cgi/pdf_viewer_4.cgi?script_name=measurement_protractors.pl&count=1&x=131&y=25

Assessments are attached.

Materials (per group of 3-4 students):

Sturdy, small cardboard box Sturdy ruler with holes or two identical thinner rulers for stability Photocopied protractor 15 rubber bands per group of the same size Pencil (unsharpened) Tape measure Scotch tape Push pin or small dowel pieces approx. 1” long

Rubber Band Cannon Lab

Collecting Data

1. When launching rubber bands, you’ll have to measure the distance the rubber band traveled.

Release angle

Pull-back distance(Always use the same)

Trial 1 Trial 2 Trial 3 Mean of 3 Trials

20

40

50

60

80

2. What do you notice when you change the angle of the launch?

3. Can you make a prediction for the rubber band to hit 150 inches?

I think that the angle is _______ and pull back distance is ______ inches

Test it out. How close did you get to your target?

4. Graph the release angle and average distance below.

5. Write a function to model the data.

6. Sketch the model on the graph above.

7. Label key points and explain their meaning in the context of this situation.

Rubber Band Cannon Assessment

1. Simon launched a rubber band cannon and collected the data below.

Release angle

Pull-back distance

Trial 1 Trial 2 Trial 3 Mean of 3 Trials

10 12 inches 168 192 19620 12 inches 252 228 27630 12 inches 286 290 30045 12 inches 252 262 29460 12 inches 190 191 15670 12 inches 131 106 14480 12 inches 45 46 77

2. Write a function to model the distance the rubber band travels as a function of the release angle.

3. Simon wants to maximize the distance that his rubber band cannon travels. What angle should he use and how far should he expect the rubber band to travel?

4. Simon would like to have his rubber band travel a distance of 200 inches. What release angle should he use?

Rubber Band Cannon Assessment

(data from FlinnSci.com)

1. In the given graph, what is the maximum and what does it represent in the context of launching a rubber band cannon?

2. Based on the model, at a release angle of 60, how far does the rubber band travel before it hits the ground?

3. What does the y-intercept represent in the context of this situation?

4. What are the zeroes of the function? What do they represent in the context of this situation?

5. When the rubber band has traveled a distance of 200 cm, what release angle was used?

Additional Questions: Quadratic Functions

(Teacher should provide students with a graph in order to answer these questions.)

1. In standard form f ( x )=a x2+bx+c , do you believe a > 0 or a < 0? Justify your reasoning.

2. What is the vertex of your parabola? What does this mean?

3. What is the solution to the parabola? What do the solutions mean?

4. Write the equation to the provided graph? (Indicate to students which of the forms you expect.)

5. Write a function in two forms. How can you ensure that both equations are the same?