Having this new knowledge really brought us on track with what we're supposed to do. We started out measuring 75 meters. Alice secured several loops of string around the Barbie's feet to make sure she would slip out, and then attached the rubber bands. We decided that we would measure how many rubber bands it took the Barbie at one height, then increase half a meter and measure with that height and so on until we've found a pattern. We saw Parker's group doing this by marking the heights on the whiteboard, attaching a string and then away from the wall, dropping the Barbie at the string. It was very effective, and much better than our attempts that left the Barbie crashing against the wall, so we did that. We measure first 1 meter, then 1.5 meters, then 2 meters until we reached 3 meters. When it came time to do 2.5 and 3, we went outside on the staircase so we could measure it with more accuracy and didn't have to precariously stand on chairs to get the measurement.
With 1 meter, we first tried with 6 rubber bands, but her head hit the ground. We then tried with 5, but it was too close for comfort. We ended up using 4 rubber bands. This was the general process for measuring; using lots of rubber bands and then reducing until we found the right amount.
At first, we thought we saw a pattern. We used 4 rubber bands in 1 meter, and then 8 in 1.5 meters and then we thought we used 12 in 2 meters! We thought it increased by four. But, in 2.5 we got 15 rubber bands, and in 3 meters we got 19 rubber bands. The pattern was gone. We returned to the class room and contemplated the board. How were we supposed to turn this into an equation?
Denise told us it was slope; the rate at which the rubber bands increase over time. The number of rubber bands was y, so on the vertical side, and the height was x, on horizontal line. We already had our coordinates; 1 meter with 4 rubber bands was (1, 4). We tried out different graphs and tried to find different slopes, all by hand, but none of them would work! This is what the board ended up looking like:
By this time, class was over. So, I headed onto the Math Help Center thinking that we would never find the equation. I entered the information, using a scatterplot, but there wasn't a consistent slope. I went to Mr. Osksness and asked him about it. He told me that in this case, we should use the most linear line we could draw on the plot and use the slope of that. He told me it didn't have to be exact, which made this project a million times less stressful. Not even ten minutes later, Alice runs in and told me she found the equation. She had entered the coordinates into a graphing calculator and told the calculator to find the slope. She put that into the equation with our y-intercept of 0 since there's where our graph starts and we have our equation! Now, to test it out in class...