A good problem is worth a thousand worksheets

I got this problem from openmiddle.com.

All of my students worked on this problem very enthusiastically for most of the class period. It was truly a low floor  high ceiling task because every student in the class was dividing fractions (practicing that skill) and noticing that the quotient was either smaller or larger than previous attempts. Some students used guess and check and were thrilled when they found larger quotients. Other students were more systematice and tried the digits 1,2,3 and 4 and found the largest quotient with these numbers. Others tried 6, 7, 8 and 9 and found the largest quotient with these numbers. And other students noticed that they should use 1, 2, 8 and 9. There was a lot of discussion in the room and students were comparing and discussing their results. Some students noticed that there was more than one way to get a quotient of 36 (or 1/36). And many students were starting to notice and generalize that larger quotients result from larger dividends and/or smaller divisors.

Low floor high ceiling tasks are also sometimes called low threshhold high ceiling or low entry high ceiling tasks. NRICH describes a low threshhold high ceiling task like this:
"A LTHC mathematical activity is one which pretty well everyone in the group can begin, and then work on at their own level of engagement, but which has lots of possibilities for the participatns to do much more challenging mathematics."

I am looking forward to trying this problem with my students now that we are working on ratios: