I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed her the other day where we counted up how many ways there were of getting between two points in a city without actually counting them all up.
I think the thing she really liked about it was that we had a picture in front of us (a roadmap for a madeup town with ridiculously few roads) and could use some simple math to conclude things about it.
Are there any other visual problems like this that you guys recommend that only involve arithmetic skills (not required but if it involves fractions or decimals all the better)? Or is there a website or book that has several of these types of problems? Thanks in advance!
I know this is obviously late, but just in case: I would suggest some basic combinatorial math that you could use almost any visual to assist in. This would be doubly visual because it opens up use of the visual tool of Pascal's Triangle, and therefore all the creative uses for it one could find.
One off the top of my head example:
Let's say you want to have a variety of sandwiches for lunch and you want to see how many days you can go without repeating the exact sandwich, with a limited amount of ingredients, but you are not too opinionated on what "defines" a sandwich; in this case, just that there should always be bread.
The ingredients you have are only one kind of bread, mayo, mustard, lettuce, onions, turkey, swiss cheese and cheddar cheese.
There is a formula that you could use to determine that you could have 127 different sandwiches before repeating, or you could use Pascal's Triangle, which could also tell you how many 1 ingredient sandwiches you would have, how many 2 ingredient and so on, by going down the "line" at 7.
http://gofiguremath.org/wp-content/uploads/2013/12/Rows-0-10-and-beyond-cropped.png
This particular example is also "useful" in real life with things such as the never ending pasta bowl and "endless" burger combinations at friendly restaurants etc...
If your student is interested in these kinds of things, you can introduce other basic systems such as fibonacci numbers etc.
I hope you are still working at this kind of thing and this provides some ideas.