What a kid learning math can look like – understand equations

This morning a problem from Art of Problem Solving’s Algebra book gave my son  some trouble.  I wouldn’t have picked it as a tough one ahead of time, but he was stuck and we decided to talk through it.

Here’s the problem and his initial thoughts – the idea of turning the words into an equation is what was giving him trouble:


Next we moved on to the 2nd part of the problem -> writing a new equation once we’ve removed 84 pennies. This step goes relatively smoothly after having worked through the problem in the first step:


The last step was to solve the equations. Ahead of time I would have guessed that this would have been the most difficult step, but it turned out that the mechanical steps required here went pretty well:


So, an interesting problem and also interesting to see where the difficulty was. I sometimes (actually quite often) do a pretty bad job of guessing where the difficulty in problems will be. This problem was a nice reminder that turning words into math is something that takes a little practice and a little getting used to.