Since I'm teaching two groups of students that I don't know, it was important to me to get to know them as math students as quickly as possible and to be ready to differentiate for them immediately. To prepare, I had each teacher group students into the following descriptors:
* Needs extra support
* Quickly Understands (Above Average)
* First to Finish (will always need something more)
These groups were recorded in a chart in google docs and I printed off multiple copies of it to help me learn student names, know how to group them for lessons, and to take notes on how they were doing with concepts during the week.
Since classes are at different levels and each of us got to different points in teaching multiplying and dividing fractions, I started on Monday with a low-pressure assessment that was also leveled in depth of knowledge demonstration. My students who easily know how to solve fraction equations had to write steps for solving the problem and then explain why they did certain steps. Why do we multiply fractions straight across and not have to find common denominators? :)
This assessment was more interesting than I expected and truly did what a pre-assessment is supposed to do. With the first class, many students completed the first problem by multiplying the numerators and keeping the denominators the same. Then for the second problem, some students began trying to find a common denominator. It was interesting (and nice) to be able to tell them that they were remembering how to add and subtract fractions and I was very proud of them for that. I explained that it is important to have a common denominator when adding/subtracting fractions, but you don't have to have one when multiplying. I tried to convince them that they would love multiplying fractions more because you don't have to have common denominators...they had already learned the harder concept last quarter! For students who knew how to multiply, I was able to see if they would simplify the final answers and turn improper fractions into mixed numbers.
I hope this assessment was able to help students feel confident, rather than like they didn't have any idea what to do. (I was afraid some of them would shut down and not try anything, so I know I'm repeating myself, but I was really glad to be able to say "This is what you do know! I'm so glad you remembered that.")
I also have the same type of worksheet ready for dividing fractions, although I may use it differently with different classes. I haven't talked to my students about dividing fractions yet, so we may use this together to think about WHY flipping the second fraction makes sense. (If you want these, click on the images. I have put the file in my google drive for sharing with you.)