Summer Workshops for Math Teachers

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, surface 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.) Also: Shrinky Dinks
• Technology will be used to illustrate concepts.

Most of these lessons were developed for 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.

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.