Intro to Integrals (Calculus)

At a glance:

Topics: Riemann sums, integration, calculus

Grades: 10-12

Standards: LIM‑5.A.1,3 (EK)

Duration to complete: 10-15 minutes

Learning outcome: Students will learn what an integral is conceptually and how they can be estimated by summing the areas of many columns that model the curve.

Intro for students: What exactly is an integral? In simple terms, it’s just the area of a graph. In this experience, you’ll explore integrals of simple functions and graphs you draw yourself. And now you know Calculus!

What makes this topic challenging for kids?

Students often learn how to perform integral math without first understanding conceptually what an integral is. They do not understand it as the area under a curve and therefore have no frame of reference for why they are learning the math.

What’s our approach?

We explain integrals with some help from another concept -- Riemann sums. By drawing a curve and viewing the rectangles that make up the Riemann sum, students will first understand what the purpose of an integral is -- to find the area underneath a curve. Riemann sums provide a tangible illustration that can easily be built upon to explain integrals.

Intro to Integrals provides a helpful mental model for students to use as a springboard for more complicated studies in integrals.