Most groups determined their surface area by the end of the class period, but none of the groups were able to decide upon a formula. We continued the next day, and while some groups were able to write a formula that reflected a correct understanding of the concept (though not written correctly "variable-wise"), others were stumped. Even though they were stumped about writing a formula, the "stumped groups" were able to explain to me HOW they had found their surface area. Most of them explained that they found the front and multiplied by 2 because the back is the same, and that they found the top and multiplied by 2 because the bottom was the same, (and the same idea for the sides), and then they added those three sums together. Other groups found the area of all six surfaces and added them all. One group found the area of the 3 different sides, added them and then multiplied by 2. Based on our conversations, I know that they all had a correct way to find the surface area, but writing a formula was difficult. Some groups were very close with their formulas, but had to be guided toward naming the length, width, and height with different variables.
One group actually finished fairly quickly (correct formula and all!), so they then worked on determining the surface area of a triangular prism (I had a Toblerone box on hand to use)....they found that surface area fairly quickly too!
In the end, several groups wrote good formulas, which were shared and discussed with the class. The students really seemed to enjoy this activity - it was challenging but achievable:) Giving the students the chance to explore the concept and to construct a formula based upon their understanding of surface area was a great use of class time!