Get an intuitive understanding of how the slope of a tangent can be approximated with a secant...
Play with the Desmos file by opening it in the Desmos web app.
Why is Calculus only taught in Grade 12? Students need to have the algebra background to be able to calculate "difference quotients" and manipulate limits.
But do you need to be proficient in algebra to understand Calculus? Nope. You just need a basic understanding of rate of change.
"Slope Puzzles" have students predict the graph of the derivative of a piecewise function. The answer is revealed by sliding the black point to the right...
Link to Slope Puzzle 1 Desmos
I believe there is way too much emphasis on algebra in the high school math curriculum. Not enough time is spent building a deep understanding of the concepts.
Even though it's saved for the end of Grade 12, as a rite of passage to mathematical prowess, differential calculus isn't a difficult concept! Even my Grade 9's could solve this puzzle after some practice.
Link to Slope Puzzle 2 Desmos
Solving these puzzles builds an intuitive understanding of differentiation without having to perform any algebra at all. I plan on using these puzzles in my Calculus class from the first day of the semester to help build that intuition.
I also plan on having Calculus students create their own Slope Puzzles in Desmos as a way to test their understanding of piecewise functions and function continuity.