Cosmas Student Work

This piece of student work was an in-class assignment done by a second grade student.  The first part of the page deals with money equivalencies which my MT has been working with students on a lot.  The bottom portion of the page deals with using three digits to make the smallest and largest number possible.  First, this student does something interesting on the top portion of the page.  Number 2 asks for how many pennies are equal to 1 quarter (25).  This student puts 23.  At first glance this leads me to believe she has some misconception about how much a quarter is worth OR the 1 to 1 correspondence that pennies represent.  However, what’s interesting is that in numbers 3 and 5 she proves me wrong.  In number 3 she correctly identifies that the equivalency of 2 quarter is 10 nickels.  Here she demonstrates that she understands 2 quarters equals 50 cents and that 10 nickels is another way to arrive at 50 cents.  Then, in number 5 she correctly identifies that it takes 75 pennies to equal 3 quarters.  Taking numbers 3 and 5 into account makes it difficult to support my initial claims about her performance on number 2.  This student may struggle with the 1 to 1 correspondence of a penny, but she was able to conduct it easily when the question was about 3 quarters.  This student also may struggle with how much a quarter is worth, but she answers correctly when asked to put this in nickels so that leads me to believe my assumption would be false again.  This makes me think that her response for number 2 may have just been a careless mistake and needs revisiting. 

              I also noticed some mistakes on the bottom portion of this assignment.  The first two examples she completes correctly with the smallest and largest numbers, but the next two she answers incorrectly.  One example has the digits 5, 3, 8 and she writes the smallest number as 538 and the largest as 583.  This is puzzling to me because my MT has been working on place value with these students extensively lately.  In the two previous examples though, she starts with the smallest number in the hundreds and the largest number in the hundreds when appropriate.  This leaves me wondering why she used the 5 as the digit in the hundreds place for both the smallest and largest number.  She does make a smaller and larger number in the 500’s but not the largest number she could’ve made.   The student does something similar in the next example as well.  The digits are 7, 6, 9 and she creates the smallest number correctly 679, but as the largest number she writes 796 failing to recognize that the largest number would begin with 9 in the hundreds place not 7.  Though she made a larger number than 679, it is not the largest.  This is interesting because in the second example, the largest number requires a 9 in the hundreds place and she does so correctly.  So why did she not recognize that here?  Her performance on these two examples leads me to wonder if: 1. She didn’t understand the task was to create the largest number possible, or 2. If she wasn’t sure how to construct the largest number beginning with the hundreds place.  I would assume that she understood the assignment due to her performance in-class as well as on the first two examples, but I can’t be sure.  From my observations I believe that she understands which digits are larger but did not fully comprehend how to construct them in a manner that would make the largest number.  In the last example, since 7 and 9 are only one number apart, she most likely chose 7 to use first and then made the largest number in the 700’s that she could.