Student Work #4

 The students have been placing a dot in each of these charts everyday of school. The charts are split into sets of 10 (5 dots on the top, 5 on the bottom)

 Mrs. Wilson had an entire day's lesson prepared for us for 100's day. Unfortunately, there was a snow day on the 99th day of school, so when we were there on Monday it was still only day #99. However, she still threw together this mini lesson which enabled the students to practice their addition skills.

The teacher drew the same type of chart on the white board and placed red, dot magnets within the chart. This task was designed as a way to practice addition and subtraction. This will elicit students to begin thinking of numbers in terms of sets of ten, which later down the road may make subtraction simpler.  Here, Mrs. Wilson placed 7 magnets in the chart then asked the students to raise their hands when they knew how many were in the chart. She called on different students to explain how they got their answers. I anticipated that students would simply count the number of dots on the board. I also anticipated that some of the more advanced students would add the top row to the bottom row (5 + 2 = 7).

Some students simply counted the numbers (either in their head or on their fingers), while others added 4+3 (look at how you can group the dots), and lastly one student explained that he counted the empty squares and subtracted that number from ten. Evidently, the class has a wide variety of ways in which they think about solving problems, which also shows that there is a wide range of proficiency in the class in terms of their abilities to add and subtract numbers below 10. Like exemplified above, two ways to approach this task would be to count, add, or even subtract the number of missing dots to the total number of boxes.

The students that counted the number of dots on their fingers are still at the stage in which they need to directly model what they are adding, while students that counted the number in their heads still used direct modeling (by looking at the dots), but are a bit more advanced. The one student that thought of this representation as a subtraction problem leads me to believe that the student has advanced beyond simple addition and is ready to continue advancing to larger number problems.

In order to advance student thinking, I would suggest to write the problem numerically on the board as the student explain their answers. For example, the students that split the problem into four plus 3, write 4 + 3 = 7 on the board so that students will continue to connect the pictures they see with numbers. The same would go for the subtraction problem (10 - 3 = 7). Another way to advance their thinking would be to use more than one chart. Even in there were only 4 dots in one chart and 5 in the other, it would scaffold students into thinking of numbers in terms of addition, not just counting.