Here is the modified task my students saw on my television as well as their computers...
I knew this would happen because I have done this task before, but right away I had many students thinking the answer to the first question was 10 minutes/15 minutes/20 minutes. This makes sense if you are thinking 5 minutes for every 4 inches, but as we discussed a little deeper, the students realized that more than just one side of the bubble wrap is being popped. We also had a discussion about what the area answer would mean in this case...square inches of bubble wrap of number of bubbles.
I enjoyed the layout of this task because it had one situation where you could get right to the number of square inches through repeated addition, and one where you had to find a reduced down version of the ratio first. This gave the students a few different viewpoints and for the most part didn't allow them to do the same thing twice.
I am a big fan of letting students discover shortcuts through actual mathematical understanding, and this task also allows for those types of transitions. I had one group who did a ratio table and went from 5 square inches in 2 minutes all the way up to 625 square inches. Sounds crazy? I don't think so. The students were able analyze their work and find quicker ways without me specifically telling them something. The understanding is owned by the student.
Question two was interesting after the students found the amount of square inches. Once 384 square inches was found and I asked them to find the side lengths of that square, many students put half of 384 or a quarter of 384 not really thinking what that answer would mean. This is a great situation to walk away as a teacher and make sure students get time to think about their decision.
Below is a list of the standards I tied to this task as well as student work and my discussion help sheet. Enjoy!
|My Discussion Help Sheet|