Here are some things that I noticed:
1) The students seem to understand the concept of equality. Even though there were many different solutions, all of the students ended up with an equal number of fish in each bowl. I loved seeing how eager the students were to find different ways to solve the same problem.
2) Many students rely on writing addition sentences even when their solution would involve both addition and subtraction. I need to continue to have the students complete math problems that involve both addition and subtraction, and model for the students the need to include both number sentences in the solution.
3) When students solve the same problem in a different way, they often write the same addition and/or subtraction sentence even though their new solution might involve a different one. I need to model for the students how to change the number sentence when the solution changes too. I will do this when completing math problems with the whole class, and then slowly transition the students to doing this on their own.
4) When provided with a paper copy of the fish bowls to use, students often just drew one picture cue, even though more than one picture could be used to show what they were doing. Giving the students just a large, blank piece of paper to complete the problem tends to result in a higher number of picture cues that actually match the various steps in the solutions.
5) While all of the students told me what tool they used to solve this problem (and, in fact, in this case all of them used counters), none of them actually wrote this down. To help get the students in the habit of writing down the tool that they used, I am going to provide a place for them to do so for upcoming math problems. Then I will slowly transition them to automatically including this information in their written work.
6) Sometimes the students have more to share than they are comfortable writing down, and talking to each of the groups showed me just how much they had to say. Using the Livescribe Pen at Math Problem Solving Centres might encourage the students to orally add additional information to what they have written down as well. I will have to give this a try!
Below is a Photopeach Slideshow of the various solutions:
The Great Fish Problem on PhotoPeach
I would love to hear what you notice.
If you would like to try out this math problem with your students too, please feel free to add a comment here letting us know how you solved it. Seeing various solutions and hearing about the process used to solve these problems will definitely help us when we discuss this on Friday.