This task had to do with making the number 4 in 4 different ways. The students were given squares of different colors they they had to cut and paste into the boxes. The color squares must match their math problem. For example: 2+2=4, the student has two blacks and two purples making 4. This is to show that there are two separate groups of numbers equalling 4. I would say that this is a higher level task because it forces the students to come up with different ways to make a certain number on their own. They are the ones making the problem, and they also have to work with manipulative that match their equation. The manipulative can solve as a guide to help them visually see objects to represent numbers, but the worksheet also has them write out the standard equation so they are getting that exposure as well. The teacher also provided unifex cubes for the students to work with before cutting and pasting the squares. The particular student said he used unifex cubes, his fingers, and guess/check to help him figure out 4 ways to make the number 4. This shows me that he was using the materials provided for him to him guide his thinking, but he has not mastered this skill yet.
Three questions I have are:
1. Why did the teacher choose the number 4?
2. Did the teacher teach them to that flipping the equation would give the same answer (i.e. 1+3 and 3+1 both equal 4).
3. How many numbers does the teacher plan on doing this sort of worksheet for?
To find out the answers to 1 and 3, I would ask my teacher. I have no idea why the number 4 was something she chose and I also have not seen this type of worksheet done before, so I would have to ask her to find out if she does this for more numbers or just the number 4. For number 2, I do not think she taught the students this property. I am making this guess because when working with the students on this worksheet, the ones who struggled were ones that did not realize that the problem can be flipped. I explained that concept to them, so I feel like she has not formally taught that yet, but again, to be sure I would have to ask.
I think you have the right idea by asking your cooperating teacher about these different questions that you have...by generating these questions, you can think of the pointed questions to ask, and your CT's answers to these questions can give you insight not only into mathematics instruction but also into the "teacher thinking" that goes on in the classroom.
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