After the story I assigned The Question where they draw a sketch of the situation and look for information in the story to answer the big question...does the story's hero really have time to carry out his escape plan? On the first day we didn't completely finish the sketches and didn't even start the discussion so we continued it on the 2nd day. We made a list of what we know from the story (especially the items that are mathematicaly relevant). They include the following:
- The ceiling is 30-40 feet high
- The pendulum swings perpendicular with his body
- The pendulum was 3 inches from his body
- He thinks he has 10-12 sweeps or vibrations (back and forth) before it will touch him
- It will take the rats one minute to eat through the rope (yuck!!)
Then we arrived at a "revised question" - How long does it take the pendulum to make 10 swings? We are also going to use the assumption that the ceiling is 30 ft high.
Initial Experiments pg. 201
Okay...the fun part was then asking the students what we needed to know to answer this unit question. I had one boy who instantly said that we needed to know how long it took the pendulum to make one sweep. We had a class discussion about all the things that might effect this time and we narrowed it down to 3 things that we could actually test in class: weight of the bob (end of pendulum), length of pendulum (which is the height of the ceiling in the problem), and the angle of release (amplitude??) of the pendulum. I am not used to using the word amplitude for this type of problem. I keep picturing the perpencicular distance between opposite sides of a parallelogram!
Anyway...the students enjoyed building pendulums. I assigned each group one variable to test but I didn't give them any guidelines other than to test each weight (or length or angle of release) 10 times. Therefore they did 30 total trials. Also they only timed one sweep. After the experiments they decided that the angle of release didn't matter but that the other 2 variables did. Then we discussed issues that may have effected our data like not using the same angle or pendulum length when you were trying to test different weights. Or not using the same pendulum length and weight when testing angle of release. Also, some student held the pendulums in their hands and kind of helped the swing by moving their hand up and down. I look forward to doing more investigations and tying in the statistics as we go!
|Students working on their sketches|
P.S. - Thank you Jim Roebuck for giving us helpful hints on how to best teach this unit!