The task began by forming seven groups of three or four students based on where they were already sitting in the room. For reference, on the anticipation chart, I only referred to one student from each group by name. I gave the students the task and told them to individually read through the problem and to start working on the problem independently for five minutes before starting to work on the task in their groups. At the end of the time allotted, the groups should have some sort of solution with justification and be ready to present their results if called upon whether right or wrong.
The groups began working slowly as this the type of task was slightly different than what they were ...view middle of the document...
Quinn’s group was another that I specifically talked with while the groups were working. This group easily recognized that they were finding a new area from the original rectangle but their approach was really unorganized. The members of this group were, what I would call, button smashing on their calculators and it only appeared that they were just trying to guess and check answers as quickly as possible so that they could be finished. Guessing and checking is a viable solution method, however, it lacks the mathematical connections that the task was selected to make. While they were working I asked them if there was a way that they could organize their work to keep track of what each person was trying or be more systematic about instead of just punching in possible numbers into their calculator to see if the values would work. I also reminded them that answers are great but I was really wanting to see the how and why behind their answers. They started to organize their information from all the people in their group so I moved on to see what the other groups were doing.
The other five groups were working well and more strategic in their pursuits on one of the three methods that I had intended on students to be able to produce. Two groups, Kayla’s and Hunter’s, had organized their work in tables to come up with their solution. Both of these groups were done with the task early so I challenged them to see if they could come up with another, possibly more algebraic method, before I brought the class back together.
Three groups were on track with writing a quadratic equation and attempting to solve it by factoring. There were a few mistakes in the factoring aspect like forgetting that the equation had to equal zero before factoring to solve for the unknown. To point the one group, Mariah’s, in the right direction with this I asked them how the quadratic equation should look before you can solve it using factoring. The other two groups, Miranda’s and Vicky’s, were completing the task as I had intended per my objective so I let them continue to work in their groups until I brought everyone back together.
Based on my monitoring chart, the intended order of how I planned to have students share their solutions would have been the group or groups that created a table to organize their information followed by writing a quadratic equation and then graph. The third group to share would have been any group that made the mistake of adding 50% to each dimension instead of trying to increase the overall area by 50%. I wanted to question students to specifically see that by adding 50% to each dimension, they are not meeting the conditions of the problem since they are not increasing each dimension by the same amount. The last group or groups that I planned on having share would be the ones whose solution was the intended solution which was writing a quadratic equation and solve it by factoring.
After seeing the groups working on the...