I like to use old AMC problem as a way of challenging the kids. These old contest problems cover all sorts of topics and most of the problems are pretty clever, too, so the challenges are also fun.
When we cover these problems I ask the kids to pick a year at random and work through some problems from that year’s test. Right now my younger son works through some of the first 10 problems on the AMC 8 and my older son works through some of the problems from 10 to 20 on the AMC 10. After they are done working we review problems that gave them a hard time.
Because there aren’t too many old AMC exams (and also because the kids probably aren’t great random number generators!) they end up working through the same problems fairly often. Today my older son was working on a question that gives him problem every time. More on that one later. First, though, a geometry question that my younger son initially struggled with:
Now the problem my older son struggled with – it is a more difficult problem, but the struggle seems to come from the arithmetic rather than from the more difficult ideas required to solve the problem. I feel that my biggest struggle working with they boys has been helping them learn to work carefully. The two videos below illustrate the point well when the arithmetic mistakes cause a great deal of difficulty for him and also prove to be extremely challenging for him to find.