Making Math Visible

Workshop Instructions

Lesson Plans

George Hart and Elisabeth Heathfield

Our Workshops.  The activities we offer are designed to make math visible to students and their community.  By working together to build beautiful mathematical objects, students engage directly in mathematical thinking.  Persevering with challenging puzzles and constructions leads students to develop patience and problem solving skills. They realize that precision counts and that collaboration is a valuable ingredient for success.  Students discover that mathematics is much broader than what they may have thought and that there is true joy to be found in the creative solutions to difficult problems.  With renewed success, they become more confident in their own abilities; their relationship to mathematics begins to change.  By displaying their visually engaging work, students are able to take ownership of their learning. They initiate math conversations, changing the math culture in their school and beyond. The classroom becomes a miniature museum of mathematical art that grows throughout the year.

We regularly visit schools to lead classroom workshops.  We also coach teachers in how to use hands-on math activities that tie to the curriculum.  If you are interested in inviting us, contact us.  Here are lesson plans for hands-on math activities that you can try yourself:

Paper Triangle Ball  Students will be challenged to put together colorful geometric constructions from cut-out paper triangless. This will help them deepen their understanding of symmetry and 3D geometry, while providing a fun hands-on activity resulting in intricate sculptures each can take home.

Disc-O-Ball (CD truncated Icosahedron)  As a group, we will build a large truncated icosahedron (otherwise known as a soccer ball) from CDs.  They join together easily using only cable ties through the holes.  Before building it, we will develop the structure on paper, learning about the icosahedron and truncation in general.  For older grades, we will examine perspective and some aspects of symmetry.  The result is a shimmering "disc-o-ball" that can be hung up on display to celebrate the joy of mathematics.

Paper Square Ball  Students will be challenged to put together colorful geometric constructions from cut-out paper squares. This will help them deepen their understanding of symmetry and 3D geometry, while providing a fun hands-on activity resulting in intricate sculptures each can take home.

12-Card Star Each student will make a unique construction using giant playing cards. This take-home sculpture/puzzle encourages abstract thinking, as students realize how the intricate shape they have made is actually isomorphic to a cube.
Super SOMA  SOMA is a cube-based geometric puzzle designed by Piet Hein in the 1930's. In this workshop, students will learn about this classic puzzle by constructing the individual pieces out of wood cubes and solving a progression of problems that lead up to a giant cardboard version which can be displayed and used repeatedly.
Rhombic Triacontahedron Puzzle  The rhombic triacontahedron (RT) is a lovely Archimedean dual polyhedron which can be dissected into 20 rhombohedra. Students will work in groups to build the components from paper and then assemble them into the RT. A coloring aspect will be introduced which adds a second level of interest to the puzzle. Finally, students will create one large cardboard model for the classroom.

Hyperboloid  Using ordinary kabob skewers (or chopsticks) and rubber bands, students will create a fun flexing hyperboloid while learning to internalize and continue an initially challenging geometric pattern. Students will work in pairs to make a model and see from it how a curved surface can be constructed from straight lines.

Domes   Students will become familiar with this classic geometric shape popularized by Buckminster Fuller.  Several variations are presented: an inexpensive paper model and several human-scale cardboard or wood structures.  Teachers can select the most appropriate version depending on their space, budget, and tools.

Catenary Arches  Students will be introduced to the architectural properties of this elegant curve with a choice of three different materials and scales.  Assembling the modules is a fun collaborative challenge that requires patience and balance.  It introduces some mathematical terminology while leading students to develop a physical intuition for the catenary curve.

Rings and Strings  This workshop uses addition and multiplication to lead students in the creation of decorative circular graphs, from small ornaments to large window displays. These two-dimensional artworks are made by following simple algorithmic procedures to thread colored string through numbered holes on a wooden circle.

Polylinks  This is a series of three beautiful constructions made from "craft sticks" (larger popsicle sticks).  They derive from familiar regular polyhedra, but the faces connect by linking instead of joining edge-to-edge.  Students will develop their problem-solving skills as they learn about new types of geometric forms.

Four Geometric Sculptures  Beautify your environment with four geometric sculptures that serve as centerpieces for mathematical conversations.  An additional activity leads students to understand the mathematical principles underlying them and to design their own sculpture.

Cardboard Constructions  Cardboard allows huge long-lasting constructions at very low cost.  These make great focal activities for math festivals and similar events.

Note: These preliminary workshop instructions are in draft form.  We are evolving these and adding more when we find time.  Comments, corrections, and suggestions are welcome. Contact us with any feedback.