MFM2P - Day 51: Shell Matching Activity, Continued

I thought today's warm-up would be quick, but we spent a little while digging deeper. This was the Always-Sometimes-Never statement and what they came up:

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.

Once they completed that, they got back into the same groups as yesterday and contined to work on the Shell matching activity. I circulated helping each group understand what to do with the tables of values. I picked one of the expressions and we worked out the table together then found the matching piece. In most cases I chose 2n + 6. I then explained that some of the expressions were equivalent to others, like 2(n +3) is to 2n + 6 so they share a table and an area model. A couple of groups almost finished:

I normally have them figure out the equivalent expressions before they start gluing anything down, but instead they drew lines to make the connections. I need to think about how to make this activity work better. I think I need to make sure they have an entire period to do it - perhaps have them cut up the pieces the day before, even. I think I would also encourage them to organize them into "linear" and "quadratic" and work out the equivalent expressions as a first step so that they are making clusters, instead of lines of matching pieces.

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.