–Updated April 2, 2021 to remove the Wet Phone task published originally in Middle Grades Geometry and Measurement (Steele, 2006). Our apologies to the author Michael Steele for posting your intellectual property.–
Cynthia started today’s meeting by saying that she would be sharing a problem from a recent workshop she attended on multiple solution tasks (MSTs). These problems are designed so that there are multiple correct solutions. In our math circle, we have grown accustomed to seeing multiple strategies for solving a problem, but usually there is one correct solution. Even after we saw different solutions later on, there was something nagging at me. Are they both equally correct? Really?
Cynthia shared a main problem and an extension. The problem was called the Wet Phone Task and is described in the publication Middle Grades Geometry and Measurement (Steele, 2006).
We started by looking at the problem individually, then started to work together in pairs and trios. Some of us starting drawing pictures. Others used tiles to model the situation.
After we had worked in groups for a while, Cynthia gave us chart paper and asked us to prepare ourselves to Publish and Defend our ideas.
Tim, Linda and Nicholas shared a solution which was similar to Tamika and mine. They also decided that 112 phones had to go back.
Are these the only two solutions? If you want to send few phones back, is there a way of packing phones that will result in fewer than 112 being sent back?
Once we were all satisfied that Tamika and Stephen defended their solutions adequately, Cynthia asked us to design a crate with twice the volume of the original crate, so that fewer phones are damaged.
This caused a lot of discussion. To get twice the volume, can we just double dimensions of the original crate? Or should we just double the number of Iphones? Or double the number of cubic inches? How do we know what possible dimensions will get the new doubled volume?
They used the original crate dimensions (36″ x 18″ x 32″) and doubled one dimension (18″ –> 36″) to get twice the volume. They decided that this would hold 288 Iphones. Then the question was, how many would get wet?
The new volume of larger crate was 20,736 cubic inches or 288 Iphones. There are various dimensions that would allow for this volume.
P.S. If you like this problem, Mark and I wrote a very similar problem for the NYSED/CUNY Manufacturing CareerKit called Packing a Shipping Container.
In Attendance: Cynthia, Eric, Gregory, Linda, Nicholas, Stephen, Tamika,
Tim
Programs Represented: Literacy Assistance Center, CUNY Adult Literacy/HSE Program, CUNY Start, DOE, Brooklyn Public Library, ParentJobNet, Bard Prison Initiative, Brooklyn Public Library
Respectfully submitted by Eric
