Materials needed: poster board, marker / colored pencils, meter sticks or tape measures, a variety of ropes or string.
Working in pairs (or groups of three if needed), groups chose one type of rope (or string) and cut a piece that was at least 100 cm long. (More about the length in a minute.)
Students measured the length of the rope and recorded the length. (It was helpful to have tape measures instead of meter sticks or rulers.) Then students tied one knot in the rope and re-measured the length. They repeated this process until 10 knots had been tied.
I provided groups a table to organize their data.
Groups then made a scatterplot of their data on the poster board. I asked that groups be sure to include their data table on the poster.
To finish the first day, students reflected on the following questions:
A) Looking at your graph and table of
values, what trends do you see?
B) Suppose you were to tie three more knots
in your string. How long do you think
the string would measure? Explain how
you arrived at your estimate.
To prepare for the second day, I chose three groups that used different rope and had started with different lengths of rope. I created a Desmos graph that included the data from three groups. I calculated the linear regression equation for each set of data. (https://www.desmos.com/calculator/it3v9a0efu). I also hung three posters on my board, along with the rope they used.
When students entered the room, they naturally started looking at the board and making observations. I asked students to individually write down "What do you notice? What do you wonder?" After two minutes of individual thinking, students engaged in a large group discussion. I let their observations and wonders drive the discussion.
Here is a partial list of things students noticed, discussed, and analyzed:
- The y-intercepts of the graphs are the initial length of rope.
- The slope for each line is different; the slope for the thickest rope is steeper than than the slope for the thinnest string.
- The data is fairly linear, but not perfectly linear for any of the graphs. We discussed why that is the case.
One tip with the initial length of the rope: The rope must be long enough to be able to tie 10 knots in it. If the rope is too short, the knots end up knotting together and the data becomes a lot more variable. I had a group that chose a very thick piece of rope and by the 7th knot, their rope was just one huge chunk of knot that was impossible to measure. That group had to restart with a longer piece of rope.
