This was the warm up assignment given to the students. The questions were on the overhead, but they asked that the students find the basic facts and then solve the problem. By this, the teacher was hoping they would understand that all they must do is to multiply the number that are not zero together, and then count up how many zeros in each number there are, and add those to the end of the answer.
As I watched this student solve the problems, he did just that. For example, in number 1, the student multiplied 9 and 8, then wrote 72 on his paper. Then he counted 4 zeros and wrote those after 72. This shows me that this student understands place value, and knows how to manipulate a large multiplication problem to make it more simple to solve.
The students could have used an array to help figure out 9 times 8, and then just add up the zeros and put them at the end of the number they counted in the array. A student would use this approach if they had trouble with the multiplying the basic facts. Another possible way, is to just multiply it all out. Eventually, the student would realize that it is a waste of time to multiply all of the zeros together and then cut right to the basic fact, and add the zeros.
The way that this student solved it shows his understanding of multiplication and the zero property. This student knows that zero times zero will always be zero, and therefore they only worry about the basic fact. I also noticed that this student did not write down the basic fact. I noticed that many of the students did, which makes me feel that this students work is more advanced. He knew the basic fact and multiplied in his head, which also shows me that he knows all of his basic multiplication facts, which many of the other students are struggling with.
I, personally, find it helpful to write everything out, so I think it would be beneficial for the student and their future with math, if they get in the habit of writing everything out. I would ask that they practice write their process out, beginning with the basic fact. Now that this student shows a clear understanding of how to use basic facts and the zero property with multiplication, I think it is time to have them work on division with basic facts and multiplication.
A good analysis, especially in light of having the opportunity to watch the student do the problem in real time (and comparing this to what you saw other students do), which led to an interesting and enlightening analysis. I would encourage you to think about what you might ask the student next (before having him move on to another topic). What type of problem might advance his thinking more within this mathematical topic? What about this mathematical topic might he still not yet understand, or what other potential connections might he be able to make to other mathematical concepts?
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