Student Work #3

The question for this task is, "I had 5 dimes. I lost 1. How many dimes were left?". The purpose of this task is to see the student’s level of understanding in how she solves simple subtraction problems. This follows under the common core standard “N.MR.00.08 Describe and make drawings to represent situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting”. It is designed to elicit student thinking because it is a high level task, requiring the student to decide how she is going to solve it. It isn’t just a subtraction sentence asking for the answer, but a story problem that allows her to use her own method to solve. Through observing how she solved the problem and asking her to explain her thinking of how she did it, the teacher would be able to get a better understanding of her strengths as well as some misconceptions she might have about solving problems such as this one.

When approaching this task, the student could use a drawing to represent the dimes. She could also use objects (such as the classroom bean counters) to represent the dimes, putting out 5 and then taking away 1. She could use either of the counting strategies (counting up from larger, counting on from first) either in her head or on her fingers. I anticipate that *Sandy’s current mathematical thinking will result in her being able to solve the problem and that she will use the bean manipulative to do so. My reasoning for this is that *Sandy scores at an average level for the class, and while she is able to solve problems, she usually relies on looking at concrete images. I don’t anticipate her counting in her head, as she might mix up numbers. Possible errors she might come across are adding instead of subtracting, taking out too many bean counters to begin with, and then only taking away one, and counting in her head and taking away too many.

The steps taken by *Sandy to approach/solve the problem:

 Me: “Can you tell me what you did to solve this problem?”

Sandy: “Uhm, well, the girl (pause), I had 5 dimes but then I crossed one out because I lost one. And then I wrote the number sentence because I thought it was a good idea.”

Me: “That was a good idea, why did you think it was a good idea?”

Sandy: “Because it shows I taked away 1 from 5. 5-1=4.”

Me: “Why did you circle the 5 and the 1 in the question?”

Sandy: “Uhm, because those are the important parts. Those numbers are what it asks about.”

            Based on mathematical content knowledge, I hypothesize that: *Sandy can solve subtraction word problems for totals up to 10 by using object counting. I could also hypothesize that: *Sandy can represent her mathematical thinking through writing simple subtraction sentences for numbers totaling 10. While this wasn’t in the directions for students to do, *Sandy chose to write the number sentence. This showed me that she understands how the drawing she made represents actual numbers. For kindergarteners, I don’t think all of them understand this concept yet, so it showed me she has made an important connection. This concept goes along with the common core standard, “N.MR.00.09 Record mathematical thinking by writing simple addition and subtraction sentences, e.g., 7 + 2 = 9, 10 - 8 = 2”.

            To advance her thinking, I might add some more information to the problem that is not important, to see if she can still pick out the important parts. I might also ask her if there are other ways/things she can do to solve this question. This would allow her to explore other ways to solve problems, expanding her knowledge on why it works the way it does.