Geometric themes are the latest trend in classroom decor. I personally love the sleek look of straight lines and angles, it's neat, crisp, and orderly. The more abstract ones remind me of color-by-number worksheets! As long as the design in simple and not too busy, it would look amazing in a classroom. The simple rule to follow it to stay away from patterns that have a million tiny shapes all over it. Always choose larger shapes with larger color blocks so that the design is soothing to look at. As examples, you can look at the examples below. I made sure to choose ones that are more cost-effective but still of good quality.
Modern Squares Multi Geometric Area Rug: The colors are bright and cheerful and the quality will hold up to the wear. This gets bonus points for being half the price of other similar rugs.
Art Deco Geometric Area Rug: This rug is beautiful, plush, bright, and well made. Also at a good price and comes in different sizes.
Contemporary Modern Boxes Area Rug: This is a soft, great quality rug that actually comes in different colors and sizes. Also within a good price range.
Scandinavian Triangles Geometric Rug: It is extremely affordable. Rugs of this size can cost a few hundred dollars, which is just unrealistic and unnecessary for a classroom. The designs great for a neutral theme.
If you'd like to see some classroom decor printables with a geometric theme, see my growing collection here.