Many of you have probably used Robert Kaplinsky and Nanette Johnson’s wonderful Open Middle math problems. There are great problems and resources for running these problems with students on the open middle website and in Robert’s book.
The best ones are on their site, but I have made a few that I shared on my twitter.
The idea I had last week was to think about “playing” this problem against someone else. OPEN MIDDLE VERSUS.
I haven’t tried anything like this with students yet, but I think it could be a fun extra layer. Not only do students need to figure out which digits they need to create a large value for x (9, 8 and 1) but they need to figure out how the numbers play together, and which one is the most important to creating a big value for x. I think the 1 is most important, so maybe this version of this problem would drive a better discussion:
I think it could lead to some fun discussions in class, and you could use this for any type of open middle problem that uses 3 or 4 numbers:
Again, 1 is going to be very important. Is there a reason why?
Cantankchris Math 