Now, as a teacher who spent 30 years in public schools and another 11 years after I "retired," operating a tutoring business, I have gone through a lot of pencils with a lot of students. A few weeks ago, as I was explaining some geometry to a student, I used a standard pencil as an example of a hexagon and we walked through the geometry displayed in it. "How many degrees are each angle?" I've also used a pencil to apply ratios and algebra. "What is the ratio of length to width on this pencil?" What percentage of the length is the ferrule?"
I have several things in my tutoring center that play with the mind by using strange proportions. I look for ways to get students to think with a different part of their brain.
I know a man who has a saw mill. He repurposes old power poles. Around here, that means cedar. I asked him to mill some 1/2" boards that were 12' long and 12" wide. Those boards are all bright yellow now.