What is the best method to make new Settlers like tiles
If you have access to a die-cutting press, as many teachers might, one can buy a hexagon press die.

Google Sizzix/Westminster Bigz Dies  Hexagon and you find several sizes.

They make a block of 6x 3/4" and 1" hexes (suitable for counters), and one of 4x 2" hexes, and one which does 2.5" hexes.

Check your local craft stores and school supply stores.

The presses run from $50 to several hundred dollars, and the dies $20 to $50 apiece, so this is not an inexpensive solution. Nor is it efficient; you'll need to manually line up the graphic. It will, however, allow for leather, magnet, chipboard, and other non-paper samples to be easily made in a regular size.

Using them without a suitable press requires a firm hand, a smooth hard surface, and a rolling pin that can take your weight...