Education Technology

Middle Grades Math: The Pentagon Problem

by Texas Instruments


  • Students will use the document to find several non-congruent pentagons having the same area as a given pentagon.
  • Students will solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

About the Lesson

The Pentagon Problem asks students to create a new pentagon from a given one, keeping the area the same. The The_Pentagon_ Problem.tns document was created in response to poor student performance on a 2005 National Assessment of Educational Progress (NAEP) eighth grade test item.


The document provides a simple, virtual "geoboard" that allows students to manipulate the polygon displayed on a unit grid. The grid squares provide a visual means of finding area.


With the .tns file, students can use the concrete picture to help solve the problem and to check their answers to the problem using different methods. They can also use the document to justify conclusions about area, to communicate conclusions to others, and to distinguish correct reasoning from that which is flawed.