This week, we tackled another Math Performance Task. It was about a girl named Beth who had two pockets and five rocks that she kept inside her pockets. The question was: How might the rocks be divided between the two pockets? How many rocks might be in each pocket? This question drew upon our recently acquired knowledge of the number pairs for 5 and challenged us to put this knowledge to use–to see if we could recall the various ways to make five and how to split the whole (5) into parts.
Before we began this task, we actually spent an entire math lesson discussing the question, what was being asked, how to best tackle solving it, and how to communicate our ideas effectively. It’s very important to set the expectations for these sorts of tasks, as students, especially Kindergarten students, don’t automatically know what teachers are looking for in solutions to these more open-ended performance tasks. However, I did not tell them the answers to this task; instead I guided them through the thought process where they discovered possible solutions on their own. My part in this task was to guide their communication so that I could better understand their thoughts and ideas as they worked through the problem.
The next day when I handed over the problem to the students, the results were extraordinary. Every child was able to give me at least one possible solution to this problem of how the rocks may have been divided into Beth’s two pockets. Lots of children gave me more than one possibility and several were able to show me all six possibilities. What makes my heart full and what put a smile on my face was how far the children have come with their ability to communicate their thinking to me since back in the fall when we did a performance task with patterning. Back then the children made a pattern and turned in their work. Very few had any sort of writing, mathematical notations, or explanations of any kind. But on Tuesday, I saw very different thinking and communicating from my class.
Here’s an example of a response that was very well done in terms of communicating ideas and solutions:
This student communicated her ideas with a combination of words, pictures, and mathematical symbols (numbers). I could see from her drawings that she understood the question as she drew Beth, her two pockets (on her pants), and how the rocks could be divided between them. I was also able to see that this student knew that there wasn’t just one way to divide the rocks, but many others, as she drew other sets of pockets on her paper and showed the other divisions that were possible.
Here’s another great example of this performance task:
Again, I could see Beth and the possibilities for the rocks in her pockets as shown by drawings of small rocks and labeled with numerals. This mathematical communication was clear and concise and helped me to understand this child’s thinking in solving this problem.
Students did not need to find all of the possibilities in order to score a 3 on this task (a 3 on a performance task is a VERY good score!). While this child did go on to add more solutions, she began with just one at first.
What makes this response so strong is her communication of ideas using pictures, words, and numbers. And because the task doesn’t expect ALL possible solutions, but simply asks “How many rocks could be in each pocket?” the children only need to give one possibility for a solution to be considered valid. However, the more solutions that are given, the more I know what the child knows.
I’d like to share one more solution to this problem.
This one I share because this child was able to show me, through his pictures, that he already has an understanding of how these part-part-whole solutions are really just basic addition facts–that when we add one part to another part we end up with a whole. While I have not yet taught addition in any form to the students, this child has an understanding of the concept and was able to apply it to the problem. I love these performance tasks because they help me to better understand what the children know and what background knowledge they may already possess.
We have one more performance task slated for the end of April (on patterns). I am anxious and excited to see how the kiddos tackle this problem! If this current task is any indication, I suspect they will do quite well communicating their ideas as they provide a reasonable solution (or solutions) to the task.