Baseball Jerseys

Yesterday I gave my students this problem to work on.  Baseball Jerseys.  I tried to not be helpful and they were not liking it (at first).  I monitored groups and asked questions as I walked around to point them in the right direction.  I loosely followed the 5 practices for mathematical discussion for this activity and the discussions were fantastic!

Here are the images I used (in order) to lead the class discussion.

I picked this one, because this is where most groups started, they picked a number and determined the price to each company just to see what would happen.  Unfortunately, I couldn't get this group to go beyond this one example, even though I keep asking them "Which company should I pick if I have 10 people on the team?"

After most group picked a few random numbers to try, they decided to organize their work in a table (some took some convincing).  

Part of the assignment was to give advice.  The group that created the table about stopped with the table, they did not give advice.  I picked this work next to show how nice this sums up everything.  BTW: this group only had the advice and no work.  *Sigh*

I included this one next because this group has a table (I wish they had gone beyond 15) AND the advice below.

Finally, I showed the class this one because the group wrote expressions for each company, but then plugged numbers in.  I wish they had gone further and set the expressions equal to each other.  When I mentioned that to the class, they said they did do that but they thought it was wrong.  DON'T BE AFRAID TO BE WRONG!!