A couple of years ago I decided to make a Geoboard when I saw the price of them in the educational catalogs. We just so happened to have a wooden cutting board from a local discount store. This wooden board had already been an artist canvas at one point and now would be turned into a homemade Geoboard!
How to Make Your Own Homemade Geoboard:
Get a thick piece of wood that is square and well sanded.
Gather some small finishing nails, ruler, pencil, and hammer. (I tried to use thumb tacks like I saw on Mama Jenna but they just broke to pieces so I switched to nails.)
Mark your grid on the piece of wood. You can measure out your marks or print a Geoboard Pattern.
We used fabric hairbands but you could easily use loom bands or small rubber bands depending on what you have on hand or can buy cheap locally.
How to Play with your Homemade Geoboard:
The first time I showed my kids our homemade geoboard they made a lot of free form designs which I would consider ART more then MATH but I am totally fine with this idea as well.
You can show your child a shape and see if they can recreate it or a letter or a number. You could ask them to make a design with only orange bands. You could ask your child to make a pattern with two colors for a different game.
Just be sure that whatever you do you allow the child to explore and have fun!
If you do not have time to make your own geoboard you can buy one from Amazon.
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If you are wanting even more math ideas check out Cool Maths for Cool Kids for 31 days of awesome ideas!