Head-Royce Summer Institute


Hands-On Geometry (grades 6-10)/ Transformational Geometry (grades 8-11)


June 26-30, 2017

Hands-On Geometry

with Henri Picciotto

Monday-Tuesday, June 26-27
9:00 a.m. to 3:30 p.m. (lunch provided)

In this two-day workshop for teachers in grades 6-10, I will present kinesthetic and manipulative activities. This hands-on curriculum is intended to complement related work in paper-pencil environments: it serves to preview, review or extend key concepts in geometry. The activities can be used to enrich and enliven the high school geometry course, or to lay the groundwork for it.

  • Topics include angles, triangles, quadrilaterals, area, the Pythagorean theorem, congruence, similarity, "soccer angles", and tiling.
  • Tools include manipulatives (such as pattern blocks and geoboards) and puzzles (such as tangrams and pentominoes.)
  • Technology will be used to illustrate concepts.

These lessons were developed in somewhat heterogeneous classes, and reach a wide range of students. They provide support for the less visual by complementing the drawing and studying of figures, and enrichment for the more talented by offering deep and challenging problems.

This workshop does not overlap with Transformational Geometry.

Register here (*note we are pleased to be able to offer 80% scholarships to a handful of public school teachers, thanks to the generosity of an anonymous donor. Don't miss out!)

Transformational Geometry

with Henri Picciotto

Wednesday-Friday, June 28-30
9:00 a.m. to 3:30 p.m. (lunch provided)

The Common Core State Standards call for a complete rethinking of geometry in grades 8-11. Instead of basing everything on congruence and similarity postulates, as is traditional, the idea is to build on a foundation of geometric transformations: translation, rotation, reflection, and dilation.

In order to teach this effectively, it is important to have a solid understanding of the underlying math, as well as ideas for rich activities for students. I have been teaching transformational geometry for twenty years, and have a lot to share. This three-day workshop will cover:

  • The implications for the teaching of proof.
  • Composition of transformations -- the four isometries and their fundamental properties.
  • Symmetry in depth -- around a point, along a strip, in the plane. Connections to art and design.
  • Computing geometric transformations with the help of complex numbers at first, then matrices -- this is the mathematics that underlies all computer graphics.
  • Transforming graphs: all parabolas are similar
  • Intelligent use of technology to support all this, including a highly motivating unit on geometric construction.

This workshop does not overlap with Hands-On Geometry.

Register here (*note we are pleased to be able to offer 80% scholarships to a handful of public school teachers, thanks to the generosity of an anonymous donor. Don't miss out!)


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