“Is it a Square?”

In each on-line class that I have taken at Lesley, I have been given investigations and problems that I can use immediately in my classroom. Every week, I anxiously wait to see what problems I will be given to investigate. I am able to select one or more of these problems and give them to my students to explore and solve. I often give one of the problems as a challenge problem. Some of my students have become hooked on these problems and are disappointed if I do not have one for the week. I have been amazed to find some of my students who are not motivated to finish other assignments tackle the challenge problems with enthusiasm. Their passion is contagious. They often want to discuss their progress with me and other students become interested. Soon more students ask for challenge problems to try.
While taking Geometry 1, I was working on a problem for my class. I typically do not give my students a problem until after I have solved it. A copy of the problem was on my desk and another teacher saw it and asked about it. Students overheard our discussion and asked for a copy of the problem so they could try to solve it. I warned them that I had not yet completed the problem, but their curiosity was peaked. It is not often that eighth grade students plead with me to give them a math problem, so how could I say no? I agreed to make copies of the problem during my preparation time. While making copies, two other teachers saw the problem and asked for a copy as well. The problem was simple. There was a diagram of a shape that looked like a square and the question simply was “Is it a square?” It was made up of smaller squares and some additional information was given. Students were also asked to explain their answer. I could see that this was going to be the problem of the day at our school so I solved it during my preparation time. I watched amazed at how engaged students were in trying to figure out this problem. They worked collaboratively and were very creative in their many different approaches. They celebrated when they came up with a solution and were able to prove their answer. They wanted to share their solutions with me and give the problem to their classmates who had not yet seen it. At the end of the day, one of the teachers who had asked for the problem earlier came to my classroom door and simply said, “Is it a square?” I replied, “What do you think?” Our answers matched. I then told him about a student who had solved it in about three minutes which was the record for the day! He shook his head in amazement as he walked away. I am grateful to have a new source of rich problems for my students. These problems bring math alive and help my students practice true problem solving skills. After one of my students solved a challenge problem I was rewarded with her final comment which was, “I think that is the coolest thing I have ever seen in math!”