Today my students completed part two of the three part math problem. Both the Grade 1 and Grade 2 students had to work in partners to solve a problem involving fish. There were different numbers for each grade. Right away, the children applied what was asked in this problem to what was asked in our **Great Smartie Problem** completed on Monday. Connecting the two problems, many of them chose to solve this problem in a similar way. They quickly figured out that some of the ways to solve the *Smartie Problem* may not apply here: no one wanted to eat any real fish.:) The students were creative though. One discussed putting the fish all into one bowl and moving one over at a time until there was an equal number in both bowls, and one even suggested going out to buy more fish. Someone said that she was going to “put some of the fish into the pond,” but her solution changed when she started working with her partner. I’ll be interested in hearing what the students think of their solutions as they discuss them tomorrow.

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:

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.

Aviva

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Aviva,

Great observations on your part & good student participation and problem solving. I think many students are far more comfortable with adding than subtracting which is something you noticed. I liked that you see the need for an explanation as to how the problem was solved. This is so necessary as time goes on. I always enjoy your postings and your class is truly lucky to have you as their teacher.

JoAnn

Thanks JoAnn! I really appreciate all of your support! I think that students are more comfortable with adding too, and hopefully, with more modelling, they will continue to get more comfortable subtracting as well.

Thanks again for your comment!

Aviva