Here’s a page from a forthcoming pamphlet I’m working on about the geometric truths that underlie–and led to the development of– all our layout tools, including (basically end up at) the sector. If you have kids around the house, you might find it interesting (maybe even enlightening) to put the sector into their hands to show them how they can physically manipulate a tool to illustrate the basic intuitive concept of the fraction.
As you’ll see when I get the pamphlet done, you can use every one of your layout tools to show the reality behind the geometric math they are being injected with at school.
If you don’t have a sector, you can download (for free)a template to make one on the “shop” page of this site. You’ll find a manual for using this three-scale sector on the page as well…for a small fee to help us keep the lights on.