Geometry Labs


by Henri Picciotto

Geometry Labs is a book of hands-on activities that use manipulatives to teach important ideas in geometry. These 78 activities have enough depth to provide excellent opportunities for discussion and reflection in both middle school and high school classrooms.

  • Middle school teachers will find many labs that help prepare students for high school geometry by getting them to think visually and become familiar with fundamental concepts, figures, and vocabulary.
  • Teachers of high school geometry —whether traditional, inductive, or technology-based— will find many labs that approach key topics in their curriculum from a different point of view. In some cases, the labs in this book can replace corresponding lessons in your textbook. Other labs can be used to preview or review material that you teach in more traditional ways.
  • Trigonometry teachers will find a new approach, using the CircleTrig geoboard, to introduce basic right-triangle and unit-circle trigonometry concepts. This approach also makes trigonometry accessible to younger students.

You may download the whole book or individual sections for your non-commercial use.

For a preview of some labs from the book, see:

The book uses tangrams, pattern blocks, cubes, mirrors, plus two manipulatives I designed, the CircleTrig Geoboard, and the Geometry Labs Template.

See below for revisions, extensions, connections, and corrections.


CircleTrig Geoboard

On one side, an 11 by 11 geoboard. Useful for many things, especially activities about slope, area, distance, the Pythagorean theorem, and simplifying radicals. On the other side, a circle geoboard, with radius 10 cm, and a 360° protractor. Useful for activities leading to the inscribed angle theorem, and to introduce basic trig, both on the unit circle (the unit being the decimeter) and in right triangles. Most of these activities of course can be done on paper, but it's more fun to start on the geoboard.

Geoboard Activities

(Where to get it.)


Geometry Labs Template

Eight different triangles, ten different quadrilaterals, seven different regular polygons, and all the pattern blocks — shapes you need for basic geometry activities. The template is great for exploring the Archimedean tilings. It also includes centimeter and inch rulers, plus a numberless protractor. You can keep it in a 3-ring binder. See it as a PDF.

The template is also useful in introducing translations, reflections, and rotations. See this worksheet.

(Where to get it.)

Connections, Corrections, Extensions, and Revisions

You are welcome to contribute to this page. Send me e-mail.

Special papers:
10cm Circle (PDF), to work on Chapter 11 on paper.
10cm Circle in Cabri, and Sketchpad. (The latter contributed by Roger Gemberling.)
For the classroom:
Possible intro to Lab 1.7, by Michael Pershan.
Consider doing Lab 1.10 before Lab 1.7, as suggested by Alex Wilson.
Extension of Lab 1.10: Soccer Angles, using interactive geometry software.
Slight edit of Lab 5.6: Symmetry, an attempt to make the table headings easier to understand.
Extension to Lab 5.6: Cover the Big Dodecagon with pattern blocks, + connections.
Lab 6.1: Use patty paper! Have students share the work and report what they discover.
John Golden's GeoGebra version of Lab 6.4: Making Quadrilaterals from Triangles
Connection to Lab 8.4 or 8.6: Heilbronn's Triangle
Extension to Lab 8.5: Inscribing Geoboard Squares in Polyominoes
Revision and extension of Labs 9.1 and 9.6: Taxicab Geometry
Preview or review of Lab 9.2: Pythagorean Theorem home page
Desmos version of Labs 9.3 and 9.4, by Liz Caffrey
Extension to Lab 9.4: Ariadne's String
Extension to Lab 10.2, #4: Include "tilted" rectangles in your search.
Connection to Lab 10.2, #5: No Three on a Line
Different version of Lab 10.4: Rep-Tiles, including an extension.
Extension to Section 10: Shrinky Dinks, by Rachel Chou (requires cm grid paper)
Trig intro: I now do 11.2 with the 10-cm circle before 11.1, and 11.5 before 11.4.
Connection and slides for Lab 11.8: π for circles, π for polygons?
For teachers:
Correction to the Lab 3.9 solution, by Austin Shapiro and his students at Proof School, SF
Extension to Lab 8.6: Proof of Pick's Formula


Related pages on this site:
Pattern Blocks
Geometric Puzzles
Middle School
Geometric Transformations