They were quite sure we were done and then I asked about 1/2 squared. Reluctantly, they figured it out and noticed that the result was smaller than the number squared. Hmmm. We tried 3/2. That one was bigger. So I asked them to try any fraction and see what they got. Two ideas came out of that: the result is smaller if
- the number is less than one
- the numerator of the fraction is less than the denominator.
We explored these ideas and refined the first one a little and agreed that they both represented the same thing.
I really liked the thinking and noticing involved in this A-S-N.
Next, they glued two factoring examples in their exercise books. Here is the file. One required them to add some zero pairs.
As it turned out we spent the entire week doing factoring and this matching activity. Longer than I had planned, but that is the nice thing about spiraling. I can adjust the timing as needed and tailor it to my current students' needs.