Once we had learned about the basics of fractions- denominators and numerators - I wanted to give my students a chance to put their learning to the test and use it in a problem solving situation. My school has been focusing on problem based learning in Math for quite some time now and even though I still considered myself a math newbie I try to integrate this as much as possible.
This problem was modified from a problem given to me by a colleague and I am very proud of how of turned out! Click on the picture below to see the original problem given to the students. I choose to have my students complete this problem independently, even though I usually have them work in pairs, so I could see their understanding and use this as a formative assessment piece.
Here are some examples of how my students chose to solve the problem. I left it very open-ended (no real correct answer) and you can see my feedback written in green ink. The students who also have a sticky on their sheet were told to be prepared to present their solution to the class.
I think it's important to give students an opportunity to practice before they speak in front of their peers whenever possible.
Once the students finished the first part of the problem I gave my students this second problem to extend their thinking about fractions.
Here are some student examples.
Once again, you can see my feedback in red ink. I gave my students their work back and asked that they answer any questions I asked in green or red ink and be prepared to talk about the problem the next day in class. One by one I called the students up and displayed their work on the document camera. What I liked most about this problem is that all my students were able to solve the problem and no answer was wrong! How empowering is that?
After we had discussed the different answers and fractions used by my students to solve this problem we switched gears to comparing fractions according to the benchmarks of 0, 1/2, and 1. Since the students used such a wide variety of fractions (from 3/3 to 3/16) to "cut" their pieces this was a fantastic end to the lesson.
This was our previous lesson/anchor chart on fraction benchmarks...
And this is what we created using the pizza fractions from my student's solutions. We ranked them in order from closer to0, closer to 1/2 and closer to 1 and then discussed which pizza party we would rather be at!
All in all, I am pretty proud of how it all turned out....especially for a math newbie!