“fence post” problems

Saw this conversation on Twitter last week:

Once of the most surprising lessons I learned teaching my kids math came from my older son struggling with this type of problem. He has struggled with them for *years* and seemingly no amount of discussion / practice / reading / and etc has made this problems easier.

I’m baffled, but one thing for sure is that I understand that this type of problem can be difficult for kids.

I decided to try out the problem with my kids this morning. My younger son went first and didn’t have too much trouble:


My older son, on the other hand, stumbled a little. In fact, you’ll see that his initial reaction is to label the dots with 1/7ths:


So, I assume that lots of kids will have little trouble with problems like this one, but some kids will struggle. For those kids, this type of problem is far more difficult than you can imagine.

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