Day 5: "What Is Calculus?"

"What is Calculus?" is the name of the first lesson that I do after I deal with all that summer assignment stuff. The purpose of this lesson is to make calculus less scary and more relatable and to introduce the notation. Some students NEED to be able to see the big picture before they can understand the details. I was definitely one of those students, so this is one of my favorite days of the whole year! ♥

This lesson is available for free here.

The big picture:

Arithmetic: adding, subtracting, multiplying, dividing, exponents

Algebra: solving for and working with variables

Geometry: shape-based math

Pre-Calc/Trig: unit-circle-based math

Calculus: limits, derivatives, integrals

What I basically tell them is:

Limits: f(a) is where you actually plug in a to get the corresponding y-value, but lim x-->a of f(x) is where you plug in a-ish numbers into a function to get the corresponding y-value. Limits are like coordinates in that we give you an x-ish number, and you give us the associated y-value.

Derivatives are a type of SLOPE. The derivative of y = 1 is zero because its slope is zero. The derivative of y = 3x + 4 is three because its slope is three. I explain that we're doing slope with only ONE point, and I show them the power rule for polynomials and notations as well.

Integrals are just area between the function and the x-axis. If you integrate y = 4 from x = 0 to x = 5, then the answer to that integral is 20 because 5 X 4 = 20.

They do limits, derivatives and integrals in today’s lesson, and that makes my heart happy! They read and use the notation. I go ahead and tell them that derivatives are like the opposite of integrals. One year I had a very strong class, and I showed them how to integrate polynomials algebraically because they asked how to undo the power rule. I want them to be as excited about calculus as I am, so I encourage them to ask any questions they have. Also, I give them a few practice problems but not for a grade. I don't like for anything on this day to be threatening or stressful. It's just playing around and getting to know our new medium.

Again, this lesson is available for free in my TPT store, and here's the link.