Last week I made a mathematics worksheet for my 8-year-old son, whose school is closed due to the coronavirus pandemic. I’m republishing it here so others can use it for similar purposes.
Figurate numbers and forward differences
There are lots of further directions this could be taken but I’ll leave that to you and your kids. I tried to create something that was conducive to open-ended exploration rather than something that had a single particular goal in mind.
Further reading:
- For the curious: Babbage Difference Engine
- For the intrepid: Concrete Mathematics by Graham, Knuth, and Patashnik, section 2.6 (“Finite and Infinite Calculus”)
Seeing as how we’ve got at least four more weeks of (effectively) homeschooling ahead of us, and probably more than that, in all likelihood I will be making more of these, and I will certainly continue to share them here! If you use any of these with your kids I’d love to hear about your experiences.
The Math Less Traveled 
I tried this with my 7- and 9-year-olds — thank you!
The 7-year-old had a nice “aha” moment when we were looking at the n(n+2) pattern — he said “I see another pattern — it’s always one below a square”. So I showed him how you can move one of the columns of size n, rotate it and put it on top, and you have an (n+1)(n+1) square with one dot missing.
The 9-year-old was able to do it independently and quickly enough that I had him try it with a sequence of cubes next.
I think you definitely hit the mark on “conducive to open-ended exploration.” Very nice.