Using the Geoboard


Henri Picciotto

The geoboard provides a nicely constrained environment for mathematical exploration, and lends itself to many activities where students can discover, review, or apply important ideas in the K-12 curriculum. This page is a hopefully comprehensive list of links to geoboard activities on this site and on my blog.

All activities I link to below can be done on the CircleTrig Geoboard, a two-sided manipulative I designed. On one side, an 11 by 11 traditional geoboard. On the other side, a circle geoboard, with radius 10 cm, and a 360° protractor. It is available from Nasco. (However, most can be done on traditional 11 by 11 geoboards, or traditional circle geoboards.)

In my experience, "virtual manipulatives" do not work as well to generate student discussion, but they are useful if you don't have the physical version, and also to discuss solutions on the projector or to get images for use in worksheets or student reports. I created this Virtual Geoboard and Virtual Circle Geoboard for those uses, and for distance learning situations.

Compact introduction to the geoboard for teachers: one page | two pages


11 by 11 Geoboard

Geometry Labs (free download)

Area: Labs 8.4-8.6
Distance, Pythagoras, Radicals: Labs 9.1-9.4, 9.6
Similarity, Slope: Labs 10.1, 10.2

Algebra: Themes, Tools, Concepts (free download)

(Some of these lessons overlap and complement the ones in Geometry Labs)
Area: Lessons 1.12, 2.12, 4.12, 6.12, 11.A
Distance, Square Roots Lessons 6.12, 7.12, 9.1-9.4, 9.A, 9.9, 9.C,
Similarity, Slope: Lessons 3.12, 8.3, 11.3

Also on this site

Virtual Geoboard
Proving Pick's Formula
Dot Papers
Connect the Dots: lattice problems and puzzles for teachers (and students)
Connecting the Dots! (presentation slides): html | PDF | Keynote
A debate about the geoboard

Blog posts

Geoboard Triangles
Inscribing Geoboard Squares in Polyominoes
No Three on a Line
Heilbronn's Triangle
Ariadne's String
Geoboard Problems for Teachers
Geoboards and Dot Paper

Circle Geoboard

Virtual Circle Geoboard

Geometry Labs (free download)

Angles: Labs 1.7-1.9
Symmetry: Lab 5.5
Area: Labs 9.5, 11.7
Basic trig: Labs 11.1-11.7
(All but the trig activities can be done on any circle geoboard. The trig activities require the CircleTrig geoboard.)

Also on this site

(excerpts from Geometry Labs)
The 10cm Circle
10-cm circle paper