If you would like to play the game in full screen, you can hit the little icon on the top-right corner of the game, that looks like a building with 4 columns. This will take you to a the site where you play it in full screen, but do not click on anything else on that page. I cannot control what appears on that website, so don't follow any links on that page.
If the game doesn't work due to school firewalls (which is funny because it's a state sponsored website) you can use this link to a different site: https://classicreload.com/oregon-trail.html. As with the other site, don't click on any links on that page, as the whole website as not been vetted.