Monday, November 14, 2016

2 Day Paper Airplane Statistics

All credit for this lesson goes to Julie Reulbach who posted her favorite middle school lessons on twitter and this statistics lesson was one of her examples.

I showed students the video and then asked them what I should do first. I made sure they noticed that after each step the step number appeared next to the crease. Then we went into our cafeteria where earlier my colleague Mr Rodinsky and I had marked off 1 meter increments in 3 columns to a little beyond half court of a basketball court. It went to about 15 meters.

Students paired up and flew their plane. Then they helped each other measure it. Some measured in meters, other measured in centimeters.

Upon returning to class, I asked students how we could represent our 3 trials accurately. Some students suggested getting the mean average, by adding the flight distances and dividing by the number of trials, 3. Other suggested the median. Others suggested the mode. Most students did not have a mode. We also discussed converting back and forth between meters and centimeters.

Some students threw it backwards on accident. As you can see in the picture below, students reasoned that the minimum flight, -300, would be subtracted from the maximum flight 1035, which results in subtracting a negative, which is equivalent to adding a positive.

In math support we did the border problem (you can find it on the functions unit on youcubed.org or just google it). A 10 by 10 square with just the border shaded in. How many squares without counting 1 by 1? After 2 explanations of 40, one student realized the whole thing is 10 by 10, or 100 squares. He wanted to subtract out the middle square, which he said was 8 by 8. That resulted in 36. Students revised their thinking with 40 and said subtract 4. They couldn't say why, but they realized it was overlapping. Other answers were 32 and 28.

I then did a second example with a 6 by 6 square. Answers there were 20, 22, 24, and 26. They reasoned it would be 6+6 and 4+4.

I made sure my colleague knew the nuance of histograms. a bar here represents all values 100 or greater, but less than 200.

On day 2 I had students finish getting their mean and median. I wanted to compile a class list, so first each student shared their 3 flight distances. Then they shared either their mean or median, because as we saw, you wanted to share the bigger number, especially if your mean got much lower with a negative number. Medians would disregard a low outlier.

After composing a class list with a number being the mean or median from each student, I asked what we should do next. They said put it in order, it'd be easier to look at and to find the median.

I then asked students if they remembered what a histogram was. Many said a bar graph, but there were ranges of numbers. I added that the bars are next to each other, and have no space between them. They said to number the y axis by 1's to see how tall it would be.

After constructing this as a class, I asked what else we could do. They said a box plot. I reminded them that they needed 5 important numbers to construct it. They told me: minimum, lower quartile, median, upper quartile, and maximum.

I said that they should discuss in their group those 5 numbers. After a few minutes, they reported the results out. Then we constructed the box plot as a combination with the histogram because the x axis was already scaled. This also allows you to have 2 representations at once. Clearly below, 1st period was skewed left.