An open box is to be made by cutting a square from each corner of a 12-in by 12-in piece of metal and then folding up the sides. What size square should be cut from each corner to produce a box of maximum volume?
Source: Calculus with Applications, Lial, Greenwell and Ritchey, 2008. Shared by Stephanie Piantedosi, Mathematics Teacher at Newton North High School.
Back to 3 Reads Tasks
Comments are closed.
Stephanie,
Thank you for sharing this Three Reads task. I am curious how your high schoolers read and interpreted it. Please share.
This was the second problem/task we did this year and we did the 3-reads to help students understand the problem before trying to solve it. This is a typical optimization problem and although does not require a lot of reading, students in the past, while solving, tend to not focus on the idea and just write down such things as 30*70. The students have been responding well to the 3 reads. They close their eyes for the 1st read and visualize the problem, and then they have done a great job rephrasing the question for the second read. Some ways they rephrased the question are: “How can we create a box to hold the most things?” and “What size should we cut to make up a box with the most space?” They struggled a bit with the third read, where they identified the important quantities. They stated things such as “volume formula, what are we putting in the box, shape of the box.” Overall, the 3-read strategy helped the students enter the problem more slowly focusing on the “story” rather than on “how do we get the answer.”