Education Technology

Approximate Areas

Activity Overview

In this activity students determine the approximate area under a curve using a variety of shapes including squares, rectangles (inner and outer rectangles), triangles and trapezia. An optional extension includes the use of the midpoint and Simpson's rule(s).

This activity includes a video tutorial.


The purpose of this lesson is to provide students with an understanding of the approximate area under a curve, including how different shapes can be used and that the limiting case leads to integral calculus. The lesson also helps students become very efficient at using the TI-30XPlus MathPrint calculator.  


  • Inner and Outer Rectangles
  • Left and Right Bound Rectangles
  • Trapezoidal Rule
  • Midpoint Rule (Extension)
  • Simpson's Rule (Extension)

About the Lesson

Students define a range of functions and use the table feature to quickly and efficiently calculate the approximate area under a curve using left and right (inner/outer) bound rectangles, triangles and trapezia. Students can also attempt the extension task which includes the midpoint and Simpson's rules. A teacher Power Point file is also included to help lead students through the activity, plus a video (link below) and a TI-Smartview file that can be loaded into the teacher software. The function pre-defined in the SmartView file is for the Normal distribution combined with Simpson's rule.

Watch the activity tutorial