“Gather round every body! This is awesome. Come here, gather round and check this out.” I wait until everyone is zoned in on what is about to happen. I lift the fuzzy, bright green tennis ball into the air and let go. The ball speeds up and hits the floor with rubbery “pop.” Just as the ball bounces back up to it’s new top height, I catch it mid air.
“How high was that? Does anyone know?” They usually make guesses.
“But how do you know for sure? Could we find it exactly?” They agree a meter stick would help. So I have a student hold the iPad camera on the meter stick and the class watches as the ball bounces back up. We disagree on an exact height, but agree it’s within one centimeter.
“Find a way to predict… from which height to drop the ball so that it bounces back up to a certain height that I will give you.”
I give them whiteboards, markers, rags, a meter stick, and a ball (golf, tennis, or racquet). I tell them I will give them a bounce back height in 14 minutes and start the timer. I give them no further direction. What will they come up with?
I saw just two data points and proportional reasoning. That group called it good after 2 minutes. Haha (and they ended up doing pretty well!) One group also took two data points and found an equation of line of best fit on their graphing calculator and scribbled… alot. I liked that one group dropped the ball and found 3 different bounce back heights and took the average. Then another group went all out and did four rounds of dropping at ten different heights and took averages. Another group found percentage (bounce back / drop height) and then wrote every “sciencey” equation they knew. They also drew me a flux capacitor and Dr. Who police box. Completely unexpected, one group used the board as a recording tool for each drop and bounce! So cool!
I told everyone the height I wanted it to bounce back. Something like 77cm. Some groups had that as a data point already, some did proportional reasoning, others had equations, and some groups plain old guessed. I wasn’t super strict on bounce back, but wanted them to see how close they were.
Afterwards, we all gathered around with white boards and had our first… wait for it… board meeting. They laughed at my first pun, this could be a good year. I asked, “Which groups were successful (pretty close)? What do we see in common on those boards.” I get responses like, “Uhh, there’s numbers.” I really have to lead them this early in the year. “Those numbers are data points. How many data points did everyone have?” We hear everything from 1 to 50. “What was the bare minimum for successful bounce back?” The class agrees 10 data points is pretty good.
“When you have data, how do you make sense of it?” Now we really get going.
One student replies, “Well we tried to find a pattern.” I’m not supposed to have favorites, but I’m really glad she said that! “What were good ways to find a pattern?” They really think for a bit. Then things really get rolling. “Well you could graph it?” “Yes! You can graph and where can we go from there?” “Well if there’s a pattern, we could probably find an equation?” “YES!”
At this point, I’m stunned this conversation is actually happening. Am I dreaming? Also at this point, the students are scared because I just yelled, “YES,” at the top of my lungs…
“So, we need 10 data points, a graph, an equation, and some calculations. Let’s try this again with a new type of ball and a new bounce back height. Ready? Go!”
Amazingly significant improvement. It should also be noted that I have 9th – 12th grade students from Algebra to Calculus. When I see high math students explaining how to find a line of best fit for data to lower level math students, I nearly giggle with excitement.
I tried to video tape these with slow motion app Ubersense, but I don’t have my iPad mini lab up and running for everyone to use. Next year?
As a end of class challenge. I tell them we should drop the balls from the school balcony in the commons to see if we can calculate the bounce back height. We measure the height at 588cm and everyone does calculations. None of the drops bounce back to the calculated height (golf balls were close). In the little time left in class, I asked why. Partly because I didn’t know, but mostly because we should always ask why. I figured it out pretty quickly (before we made it back to the room). I’m excited to get to conservation of energy later this Fall to talk about it again.
I mentioned last week I started teaching sig figs and unit conversion and how much I regret doing it. The regret is still there, but what’s started should be finished. So, I did my best to make it fun and use physical examples. Standing in front of class, I slip my show off my foot with out them noticing. I tell them, “Today we invent a new unit and we call it…,” kick shoe in the air and catch, “the SHOE.” They’re all impressed because they didn’t expect it. Then I spend a couple minutes trying to catch the shoe behind my back from kicking it off my foot.
“Everyone take off a shoe and measure (use your partner if you need to) your heigh in SHOEs. Then measure the length of your shoe in centimeters and find how tall you are in meters. This takes a bit of time, but they get the hang of it.
“Everyone there? Okay, good. I want you to find the volume of the room in SHOEs. Choose one pair of shoes in the group.” We usually have to talk about how to find volume (must have been a long brain-rotting summer). They start climbing and crawling all over the room.
My design for the work/note sheet ended up better than I expected. I definitely didn’t intend for this pleasant problem to pop up, but I’m glad it did.
I had students find length, width, and height in SHOEs. Then convert each of those into meters. They found the volume in SHOEs^3 by multiplying down the first column. A lot of students then found volume in meters^3 by converting from SHOEs^3, but this didn’t match their value for multiplying down the third column.
We ended up with a great discussion about unit conversion. They didn’t see that they had to convert each dimension of SHOE to meters in the last conversion. Many were upset when values didn’t match and the table didn’t sync. But, when we figured out the problem and all was good in the world, they were happy life made sense again.
I gather the classes attention again.
“Johnny, how tall are you in SHOEs?”
“Umm, seven and a half SHOEs tall.”
“Lisa, how many SHOEs tall are you?”
“Well, I’m seven and half SHOEs too”
“How does it make sense that Johnny and Lisa are the same SHOE height when Johnny could be a starting center in basketball and Lisa could be the basketball?” I didn’t really phrase it this way, but wanted to. The students talked about how the shoes weren’t the same length even though they had the same name. We discussed the importance of communication. Imagine what it was like way back in history. I also told them the story about the NASA teams that one used inches and the other centimeters (I don’t know the real story, but I made up a good one!).
“What values did everyone end up with for volumes?” We agree to use meters while talking now, so everyone is on the same page. Those values were ranging quite a bit. “So, what’s going on. The volume of this room isn’t fluctuating. Shouldn’t there be an exact value?” Then we talk about rounding and how the room isn’t exactly perfect box.
My take home for this week. Me asking questions is good. Me shutting up and letting them ask/answer the classes questions is better! LIFTL = Learning is for the Learners.