These lessons do not contain much "math" so I don't understand why you say their intent is to get students to "think about math". They seem very much like Clyde's lessons, intended to not get students to think at all, and appeal to their common sense instead. If this is all there is then all the student has learned is that a function is like a formula, suitable to be parroted in a video I suppose. Ask the student how a function is like a line or a set and they will be lost. If your lessons all stop at the limit of common sense then are you even teaching anything? The first part of this lesson, a function as a formula, is useable as an introduction, but the rest of the lesson involving inverses, composition, and the reference to calculus is misplaced. There is no value in this form of mimicry where you seem to be trying to "plant" notions in their head. After the "function as a formula" introduction, the students then need to then gain familiarity with functions in practice. This and guidance will eventually enhance their senses beyond the discreteness of arithmetic and the "function as a formula" toddler definition that you start with will be replaced with a more complete "function as a function" notion. What do I mean by a more complete notion? Well, for starters, they will begin to picture ranges as projections of the domains. They won't use the word "mapping" but they will think in the ways of a mapping. They will associate individual points in the range with the corresponding points in the domain. They will sense that a sequencing of sorts is maintained (function v relation) and they will sense that this projection is continuous (because they will mostly be working with continuous domains and continuous functions). They will sense that there a definite connection between parts of the domain and the range and they will begin to sense the nature of that connection. If we limit ourselves to a portion of the domain then we also limit ourselves to a very well defined portion of the range as well. So many things th they couldn't have sensed before, will now be plainly visible. I am not saying that you must teach functions, but if you do, this is the only possible reason to do it. There is no other use case for "functions" other than to know them.