Cosmas Student Work

This piece of student work is from one of my first grade students and is a practice sheet about nickels and pennies.  The side of the sheet I will focus on is the side about nickels.  The students were given this practice during their independent math work time and had to count by 5’s to write the amount of nickels shown.  There is a small blank box with a cent symbol next to it for students to record their answers.   In the first problem, there are 3 nickels with a blank box, and the lines to “count ___, ___, ___” are already filled in (5, 10, 15).  This student wrote “20” in the blank box.  This leads me to believe that the student thought she was supposed to fill in the next number that comes in that sequence of counting by 5’s.  Several other students in the class did the same.  If there were 4 nickels they wrote 25 instead of 20.  When asked about this, one student said they thought they were supposed to count the box too even though it isn’t pictured as a nickel.  I would imagine this was a common thought throughout.

              However, this student only followed this “pattern” on the first example.  On all the rest, she simply counted the number of nickels present and put that in the blank box as “2 cents” or “5 cents”.  Interestingly enough though, on the lines where she was supposed to count up by 5’s, she counted sometimes by 2’s or 5’s depending on what number she put in the box.  For example, the box where she put a 7 (because of the 7 nickels pictured) she started counting “7, 9, 12, 14, 16, 18, 20”.  Though this isn’t a correct sequence of counting by 2’s, she still thought she was supposed start counting at 7.  This tells me first, that she didn’t understand that she was supposed to count each nickel as its own entity equaling 5 instead of counting how many nickels were pictured.  She may understand that a nickel is worth 5, but not that when we see multiple nickels we are to count them by 5’s to determine the worth of that grouping. 

              My second thought on this child’s work is that she may have been confused by the picture of whether this was a nickel or a penny.  I do not typically like to give sheets about money money because the student can be easily confused (especially when they are first learning the coins) which coin is pictured.  Manipulative coins will be extremely beneficial to getting this student to explain her thinking.  She may see the way a nickel looks and feel the way it feels as a 3-D coin and have no trouble counting them by 5’s.  it is possible she thought she was counting pennies, in which case the “count __, __,” lines would be confusing.  If I thought they were pennies I would be confused what to count by as well.  It is possible she did this and just counted by 2’s or 5’s depending on the number she placed in the box.

 In addition to manipulative coins, another thing that I think would help gain insight into this child’s thinking would be to have her use pennies and nickels in this case to set out, for example, 40 cents.  I would then be able to observe how she approaches the coins.  She may make a decision that counting by 5’s and using all nickels is the best way to arrive at 40 proving that she understands how much a nickel is worth.  This student may also not know how to approach these coins and I would be able to learn about the sense she makes of them blindly.