The Power of Excitement

Last week, in my non AVID pre-algebra class, I found myself with some time where I could have the students work some quiz review problems or I could teach them about the history of calculus, Newton’s Law of Gravity, and why astronauts float. I chose the latter–I mean after all, what is 25 minutes?

I began my lesson by holding a sheet of paper and a board marker in my hands and asked which would hit the ground first (“The pen!”, they said) and why (“It is heavier”, they argued!) I confirmed the first hypothesis by dropping both (Sadly, no one suggested air resistance for the reason the paper falls slower). I then talked about how we make a piece of paper lighter or heavier (tear it in half to make it lighter; tape a second or third sheet to the first to make it heavier.) So, I held the paper up high again carefully in my left hand in my palm and the marker in my right. I then started to crumple up the paper, very slowly (this is important) and then opened my hand again before the paper was actually crumpled. This always gets a reaction, usually involving frantic shuffling in the seats. This “shuffling” is a sign that the students are excited. The moment I started to look like I would crumple the paper, the students assumed I was “cheating”. They know the crumpled paper will fall faster; they had just hypothesised that heavier objects fall faster than slow; therefore, the crumpled paper is heavier. QED!

When I pointed out that we just agreed that the only way we could make the paper heavier was to tape a second sheet to the first, some students argued that the act of crumpling the paper pushed the atoms closer together thus making the crumpled ball heavier. (This is the point where I really wish I had a good weighing device.) I told the children that they needed to trust me, but the crumpled ball is the same weight as the original paper. When I dropped the crumpled ball and the marker, they fell at the same speed! I told them that gravity always “pulled” objects at the same speed. Everything falls at the same speed in gravity. I needed to beef up the demonstration to really reinforce this idea. That was when I grabbed one of the chairs and the marker and dropped both of them from on high. The chair and the marker hit the ground at the same time. It was loud, the students were shocked, but they all crowded forward (fingers in ears) to see me do it a second time.

After this demonstration, I looked at the question, “Why do astronauts float in the shuttle?” The answer is not obvious–they do not float because of lack of gravity. If you could stand on a building that was 250 miles above the surface of the earth (about the typical altitude of the space shuttle) you would experience about 89% of what you feel on earth. Folks, you cannot float if you weigh 89% of what you weigh on the surface. (1)

The reason that astronauts float is that they are in free fall. Literally, the space shuttle and everything in it are all falling towards the earth. Since everything falls at the same speed in gravity, the astronauts and the space shuttle are all falling towards the earth at the same speed. Consequently,  the astronauts never catch up with the floor of the shuttle and therefore float. The question at this point is, “Why doesn’t the falling shuttle hit the ground?” The reason is that it is moving so fast forward, that it “misses” the ground as it perfectly  follows the curve of the earth. This is more commonly called being in orbit.

(1)Newton showed us that the force of gravity, given two masses, is inversely proportional to the square of the distance between the two masses. The distance is from center of one of the mass to center of the other. This means that if you can double your distance, you get 1/(2*2) or 1/4 the gravity. Since our distance to the center of the earth is 4000 miles, flying a space ship at 250 miles is only an increase of  6%. This becomes 1/(1.0625*1.0625)=.89 or 89%. While it is true that Newtonian theories were superseded by Einstein’s theory of gravity, Newton’s theory works quite fine for ordinary masses.


First week of school

All in all it was a pretty good week in school. Because we spent so much time in class doing what we call a screener test, I was not able to get into some of my strategies. I was able to work some popcorn activites, think-pair-share, groups of four, and some cornell notes.

Popcorn is a cool activity where you throw a problem at the students which has multiple answers or multiple levels of nuance. You want something that will get more than one student response. The students can only talk if they are standing. So you present the problem and when a students wants to answer it they stand and give an answer and explanation then sit down, immediately. Someone else can stand (pop up like popcorn) and give their answer, and so on. It is quick and produces surprisingly cogent answers. It is a neat way to get good participation–the kids love it and they learn very quickly not to talk unless they are up, so it allows pretty good discussion and interaction, much kinesthetic motion, and controlled behavior.

Think-pair-share is pretty straightforward. I present a problem and the students work solo for several minutes writing down their thoughts, then turn to their partners pair, discussing what each has written down, gently critiquing, and looking for some agreement. Students can then move into groups of 4 to develop one answer everyone can agree on. I had the students develop some ideas on how we could work together to make the class a success. I let half the groups suggest what I could do (or avoid doing) to make it work. The students love doing this because they have some definite ideas about what makes good teaching–they have good insight into what teachers can do to screw up a kids love of learning. It went well. Students produced ideas on butcher paper and posted them in the hallway.