Yo can show it physically by inflating a balloon or pushing things in a weak cardboard box (or marbles on a table and a cord, if you insist on circles). Intuiti

Yo can show it physically by inflating a balloon or pushing things in a weak cardboard box (or marbles on a table and a cord, if you insist on circles). Intuition building is very useful to build concepts, even perhaps more than proofs. See https://betterexplained.com/articles/adept-method/ https://betterexplained.com/articles/adept-method/ for a discussion of this. You can also introduce the idea of problem decomposition: first identify target shape, then argue how to approach it with 36 fences, then try to derive the formula for the area. At the end of the day, a good teacher will try to do their best with the curriculum, and a bad one will find a way to proselitize wokeness if they chisse to do so; in my opinion the good direction is to empower teachers with resources and curriculum discretion, and in turn require them better results.