Katelyn McCormick Student Work Week 5

                The sample of math that I received this week is a worksheet that included writing numbers more than and less than a given number and skip counting.  The first question asked the student to write the number before and after 1, 3, and 5.  The student correctly wrote the numbers that come before and after the given numbers.  The next question asked students to count by 1s: 0, 1, 2, _, _, _; count by 2s: 0, 2, 4, _, _, _; count by 5s: 0,  5, 10, _, _, _.  The student filled in the blanks correctly for counting by 1s.  The student wrote 5, 6, 7 for the blanks in counting by 2s.  The student wrote 11, 12, 13 for the blanks in counting by 5s. 

                This sample reveals a great deal about this student's current mathematical understanding.  The student was able to write the numbers that directly precede and proceed a given number.   This means that they understand the concept of more than and less than because they could write the number before and after.  The student also understands clearly how to count by 1s and write those numbers in order.             This also reveals that the student has a gap in their mathematical understanding of skip counting.   The student was unable to write the numbers for counting by 2s and counting by 5s.  This could be because they did not see the directions that told them to count  by 2s and 5s, but it could also be that the student does not know how to skip count.  The student looked at the third number in each set and began counting up by 1s from that number.  This child can not yet demonstrate how to skip count by 2s and 5s.

                A way that I might advance this student's thinking is to ask them what skip counting is and why we use it.  This would get the child to think about their knowledge of skip counting and how we could use skip counting.  If the child did not know what skip counting was, I would simply explain to them that skip counting skips some of the numbers so that you can count quickly up to a given number.  I may ask the student if they know of any places that we skip count.  I might add that we can skip count on a clock as we count by 5s.  Another way that I might advance this student's thinking is to have the student show me how to count by 2s or 5s using objects.  This way the student could work independently to attempt the problem and make a clear distinction as to why we might use skip counting.  If I were able to ask this student a question, I might ask what they know about skip counting.

                This student would benefit from practice with skip counting using a variety of objects.  This way the student could see different representations of the same process.  I could also suggest that the student count the people in the room by 2s and 5s.  The student could see which way was a faster way of counting.