In my 1st grade placement classroom, the students are currently working on "skip counting". Among just given a timeline and told to count up the students were taught a couple of different ways to "skip count". However, in this picture the student was given a timeline to 20 and was instructed to count by 2's until they reached 20.The task is wanting students will use the number line to assist in reaching the number 20. The picture of the students work shows they used a variety of approaches to work on these problems.
On this specific page in the students math workbook they were asked to "skip count" by 2's, 5's, and 10's and students were responsible for figuring out the proper way to count to 20. To do this the teacher reviewed with the students what it meant to "skip count". Then she brought up a number line on the SmartBoard and they skip counted by 3's together as a class. While the class was counting up by 3's the teacher was using the pen to jump from 0 to 3 to 6 to 9 etc. on the number line. When released on their own Todd (picture above) used a couple of different methods to skip count. The first one asked him to count by two and he used the jumping process starting at 0 and going up by 2's. Todd also, crossed out the numbers that would not be used when counting by 2's. He was the only one in class that did this. When asked why he crossed them out he responded that it was easier for him to see the numbers that are used when counting by 2's. He correct accomplished this task as shown in the picture. In question 2, he did the same process of jump counting. When I asked him by did he think of circling the numbers you "land on' when skip counting by 5's he said because he started at 0 and counted up 5 in his head and then he just circled it. I then asked him why he used the "jumping" process and he responded with he was checking his work.
In these questions the mathematical objective was for students to start at 0 and count by the given number up to 22 or where the time line ends. The time line was given to the students as a key to help them to allow them to visually see how to start at one number and count up by a given number. The process of teaching students skip counting is to help the development of their fluency in calculation, number sense, and a basis of multiplication and division. This worksheet is assisting in boarding students range of numbers with which they can skip count. The use of the number line was to prompt students thinking about counting up.
Since this student displayed that he has mastered counting up by using a number line the next step could be asking him to show his knowledge of this task different ways. The student maybe presented with a worksheet that shows numbers counting up by 3's, 5's, 9's and have blanks in the process. For example, the student could be given something like this 0, ___, 6, 9, ____, 15,... the student will then have to apply his knowledge in order to figure out the missing numbers. This will apply higher thinking of this task.
This is a great analysis. What is really great is how you incorporate specific questions that you asked the student throughout the task; thus, you are not just relying on a worksheet, but were able to actually see the student engage in the mathematical work and were able to derive further insights from that. Also excellent is how in your suggestions of how to advance the student's understanding, you create a problem with specific numbers chosen in order to accomplish your objective for the task.
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