Student Work Blog #2

          The purpose of this activity is to see the student’s level of understanding in regards to counting by 2’s and 5’s. This learning task follows the common core standard: “N.ME.00.05 Count orally to 100 by ones. Count to 30 by 2’s, 5’s and10’s using grouped objects as needed.” This task is designed to elicit student thinking because the student is given a question orally and then asked to explain how and why she came to the answer. The student can think about the question being asked and give reasoning for her answer in her own way. The question/directions do not give a specific way the student is supposed to solve it.

In this activity, I wrote a number on a dry-erase board and asked the student, “Will you land on this number if you count by 2’s?”. The student would then answer and I would follow with, “How do you know that?”, giving her the opportunity to explain how she came to that answer. A blank 100’s chart was provided for the student to reference if needed.

The student could approach this task by guessing if the number would be landed on and then checking by using the 100’s chart. The student could go right into using the 100’s chart to count by 2’s. If the student knows how to count by 2’s in her head, she might do that as well. For counting by 5’s the previous possibilities for approaching the problems are possible, as well as using the “5’s song” her class learned. The student could also count the numbers on the chart and every 5^th one mark off.

I anticipate *Sally will solve the questions that ask her to count by 5’s more easily than the questions asking to count by 2’s. I anticipate she will use the “5’s song” to determine whether a number will be landed on. For 2’s, I think she will give an answer right away (guessing), and then go back to the 100’s chart to count. I think possible errors that might come up are that *Sally will count by 1’s at some point. I also anticipate that *Sally will have a difficult time explaining how she got to the right answer (if in fact she is right).

Our conversation (steps taken to approach the given problems):

Me: (Writes the number 12 on the board) “Will you land on this number if you count by 2’s?”

Sally: “Yes.”

Me: “How do you know that?”

Sally: “Because it’s here (points to the 12 on the 100’s chart).”

Me: “So how does that tell you if you’re counting by 2’s you will land on it?”

Sally: “Because 2, 4, 6, 8, 10, 12 (Using her finger to skip count on the 100’s chart). See, I stopped on the 12.”

Me: (Writes the number 21 on the board) “Will you land on this number if you count by 2’s?”

Sally: “No”

Me: “Why not? How do you know you won’t stop on it?”

Sally: “Because you would do 20, 22, 24, 26…and that means you passed 21. See, it’s back here (points to the 21).”

Me: “Ok, now I’m going to give you a number and I want to know if you will land on it if you count by 5’s.” (Writes the number 10 on the board)

Sally: “10. Ok…uhm…yes because 5, 10, 15, 20.”

Me: “What about this number (writes 12 on the board)?”

Sally: “Yes! Wait…(whisper singing the 5’s song)…no, it doesn’t.”

My: “Why not? Why did you change your mind?”

Sally: “Because (singing) 5, 10, 15, 20, 25…12 is skipped.”

            As with many of the other students in this Kindergarten class, *Sally had a hard time verbally expressing how she came to the right answers. She knew the answers, but has a harder time putting her thoughts into words. However, based on the way she solved them, I can hypothesize that *Sally’s mathematical understanding of this concept is at grade level, because she answered the questions correctly and used strategies she has learned to solve them (such as the song). I could also hypothesize that *Sally is able to count to 30 by 2’s and 5’s using a 100’s chart.

            To advance *Sally’s thinking, I could take away the 100’s chart and ask her similar questions, to see if she can do this skip counting without the visual. It would be possible to ask her if the number 32 would be landed on if counting by 2’s. This would advance her thinking because they have only gone up to 30 with counting by 2’s, so this would be a challenge to see if she understands the “pattern” of counting by 2’s. I might also ask her to count by 10’s, since they have been introduced to this concept.