Berger- Student work week 6

The student sample that I brought had to do with the same topic that I wrote about for the noticing blog. The specific problem that the student did was 3 1/4 - 2 3/8. This was an exit slip problem, and we had been going over this topic for a few days. The student recognized that he had to find a common denominator so they ended up with 3 2/8 - 2 3/8. From there the student got the final answer to be 1 1/8. This student work sample reveals that the student is on the right track, he understands the first few steps needed to subtract fractions. I definitely plan on asking the students to explain their thinking, in order to see what their understanding is. It was interesting because it wasn't just this one student who didn't realize that 2-3 was a negative number. Over 1/4 of the class had the same answer and had either gone through the problem too quickly or simply forgot how to borrow. I would advance this student's mathematical understanding by holding up two fingers and asking him if there is any way that I can take away three. If that doesn't get through to him, I could use other materials such as pennies or pencils to show him how you can't subtract 3 from 2 or in that case any larger number from a smaller number. Once we get past that concept, I would ask him how he thinks he could solve this problem if he doesn't have enough numbers in that fraction right now. I would let him think for a bit and come up with a solution. Hopefully, it would be that he needs to borrow, but if not I would demonstrate how you could borrow from the whole number in front of the fraction. Once we borrow I would explain how you then need to add the new fraction (that equals one whole) with the previous fraction (2/8) in order to subtract the 3/8 from the fraction. We would then get our final answer and see if we could reduce it any further to get it to the simplest form. Another way that I could advance his thinking would be to take each step separately. For example, first look at simple subtraction, 2-3 and figure together that this equation is not possible, without having negative numbers. Next, we could look at a simple subtraction problem, for example 43-18. We could look at how you can't subtract 8 from 3, so you need to borrow from the 4. This may help the student realize the use of borrowing. From there we could look at our fraction subtraction problem and see if we can plug those similar methods in to solve this equation. The student could work with a few different types of fraction subtraction problems, ranging levels from easy such as 4/8 -2/8 to a little more difficult 3/5-1/6 and then get into mixed numbers and keep building on the facts that he has learned.