In my 1st grade classroom, the students are currently working on a variety of ways to understand "greater or less than". Aside from being given just two numbers and deciding what one is greater or less than, the students are working with problems that feature two people with a certain amount of money. One of those people has a significantly larger amount of money than the other, and it is up to the students to decide who has more or less and then to figure out how much more or less the person has.
On this specific page of the math journal/workbook the students were responsible for deciding who had more or less pennies and how much less or more that person had. To do this, students were told to see how many pennies both people had, then count the extra. They were not given a specific model in which to do this, but the student above (let's call them Kay), found her own way to determine which person had more or less pennies than the other. Kay decided it would be best to draw a line from one persons pennies to the next, until they no longer matched up. This allowed her to clearly see who had more or less pennies as well as the amount of pennies that were left over.
In this example, the mathematical objective was to have students determine which person had more or less pennies (depending on what the question asked), then by how many pennies. Based on the 1st grade skills I have observed in the classroom thus far, I anticipated that the students would know be able to see that one row of pennies was longer than the other, but that they would not have any specific methods to figure out how many pennies were left over. I was surprised to see that Kay was able to do this and create her own method (matching) to figure out the given problems.
If I were to encourage this student to move their thinking forward, I would have Kay write out the actual number amount of each row of pennies and have her then determine what number was larger or smaller. This way she would truly understand who had more or less money due to the number amount and not just the length of the row, but regardless, I was very surprised and pleased to see her apply her own method to figure out the problems.
Good analysis...What might this student's method say specifically about what she currently understands about the mathematical concept in question?
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