Blog Post #3

The above photo is an example of a directly modeled addition problem. I ran this activity during centers with groups of about 4-6 students. I began by stating a story problem, such as "8 bears had a picnic on this bench. Then, they invited 4 more bear friends to join them. How many bears came to the party altogether?". Then, after running through a couple of story problems, I allowed students to make-up their own for the group to solve. This was presented to me as an addition task, but with really advanced groups I created subtraction story problems as well.

The main objective of this task was that students would be able to solve result/whole unknown addition problems through direct modeling and also write the problems out, such as "8+4=12". My own personal goal with running this task was to assess the students' ability to distinguish the difference between addition and subtraction problems. After counting the bears and filling in the first 3 (vertical) boxes, we would complete the bottom row of boxes. At this time, I would ask students if the problem involved addition or subtraction and how they knew. Many students in the class did not have solid definitions of addition and subtraction, so the goal of this task was to create and solidify these definitions as well as correctly write the appropriate symbols (plus, minus and equal signs).

The two possible ways to represent the story problem are both featured on this worksheet. The first, place the number of bears on the top and bottom rows of the pictured picnic table, then count them. The second, write the numbers on the page, include a plus sign and an equal sign between each of the numbers and the answer.

I anticipated that students would place the first number of bears on the top row (write number in first box), the second number of bears on the bottom row (write number in second box), and count the total number of bears in order to write that number in the third box. This could be done in a couple of ways: first, like explained above, students would count the total number of bears after placing each of them on the page. Possible errors could include: students placing the wrong amount of bears on their pages or simply counting incorrectly. Also, they could write the incorrect numbers in boxes.  The second approach is to count on by starting with the first number, then continue counting onwards from that number until each of the bears is counted. I also anticipated that some students wouldn't even use the bears and could do the addition in their head. Again, possible errors could include counting incorrectly.

The student who's work is featured in the photo above used the 'counting on to' approach to solving the story problem. He started by saying the first addend (eight) then counted up to 12, touching each of the four bears one at a time. He was the first student to answer the problem in the group because the remainder of students simply started from zero and counted each of the bears individually. This shows me that the student featured has grasped the concept that addition involves joining two separate groups to find a total. He also knew that it was an addition problem (not subtraction) and used a plus sign, not a minus sign. It is also evident that this student still struggles with not writing his numbers backwards. He has been doing this all year, but when reminded that the numbers are written backwards he laughs, says 'oops!', erases them and writes them correctly without a problem. ((I'm not sure if you can see in the photo, but the '2' in the first '12' was written backwards and he corrected it))

In order to advance his mathematical thinking, I would definitely not use this worksheet again. Writing numbers in the boxes did not assist this student with comprehending how to write-out the addition problem. As you can see, he wrote the number 8 in the 'bears altogether' box at first because he was about to write "8+4=12" in that box. If I had designed this worksheet, I would have written a plus sign between these two boxes and an equal sign before the 'bears altogether' box. I also might move forward to 'change unknown' or 'start unknown' addition problems to continue his growth, considering he mastered the problems provided in this activity.