Students playing with Buscher Blocks are immersed in mathematical beauty, because all the "dimensions" of the blocks are mathematically related. Each dimension is a whole-number multiple of the slot width and depth.

Play may be free or directed.

The teacher can learn something about the personalities of the students by watching them engage in free play. Some students play alone and others play in teams. Some students build towers, others build walled citadels, and others build graceful temples. For examples, see the "Kid Pix" page.

The teacher may wish to supplement free play with directed play, in order to teach certain lessons. I suggest the following exercises as starting points for directed play. The exercises are devised for students having a wide range of capabilities. They are ordered by degree of difficulty. I hope that teachers, students, and others will devise additional exercises, and that they will share their exercises with me.

Exercise 1. Disassemble a fancy cube.

Invite the students to disassemble a fancy cube. In doing so, they will discover an inner structure like that revealed by a biological dissection. Invite the students to sort the disassembled blocks by shape. In doing so, they will see that intricate and stable structures can be constructed from a relatively small set of simple shapes.

Exercise 2. Make 2D designs with the flat blocks.

Give each student all the blocks of a particular shape. Since there are twenty-four cee blocks, you may want to divide them into two sets of twelve, or three sets of eight. Invite the students to make two-dimensional designs with their blocks.

Exercise 3. Make 3D structures with the flat blocks.

Invite the students to construct three-dimensional forms with the flat blocks. They can copy forms shown here or in the "Instruction Book"; or they can build their own forms.

Exercise 4. Decorate a slot block.

Give each student a slot block. Invite them to decorate the slot blocks with flat blocks.

Exercise 5. Copy 2D designs to graph paper.

Give each student a sheet of quarter-inch graph paper. Invite each student to align a flat block with the lines on the graph paper. Point out that the smallest dimension of a flat block - "S", the slot width - corresponds to two units on the graph paper. Invite the students to copy the designs they made in Exercise 2 onto the graph paper at various scales: "S" = 1 unit, "S" = 2 units, etc.

Exercise 6. Build a simple span.

Invite the students to build spans, using slot blocks and cee blocks. The simplest span is a line of joined slot blocks supported at each end by a single slot block. Because the fit between blocks is a little loose, such a span will sag if it is too long. One or more intermediate supports will eliminate the sag.

Exercise 7. Build an arch.

A longer span can be constructed in the shape of an arch. Sag is prevented because the two sides of the arch lean together, compressing the blocks. The stress gets transferred, however, to the two base blocks at the bottom of the arch. These blocks will tend to slide apart.

This sliding can be prevented by tying the base blocks together, with a string or a chain of rubber bands. Adding a tension member to the assembly converts it to a truss, a basic part of many roof structures.

Another way to prevent sliding is to place a buttress beside each base block. The buttress can be a book or a rock. One advantage of using buttresses is that the space under the arch remains open.

Exercise 8. Add flying buttresses.

To make more space under the arch, the arch can be raised onto pillars. Now, the stresses in the arch will tend to push the tops of the pillars apart.

These stresses can be balanced by flying buttresses.

Exercise 9. Draw an oblique projection.

Explain oblique projections: two axes are perpendicular to each other, and the third goes off at a forty-five degree angle (for example) to the other two. A face aligned with the perpendicular axes has the same shape as the corresponding face of the model. The other two faces are skewed. Invite each student to draw an oblique projection of a slot block or of a structure that he or she has built. Graph paper is very helpful for this exercise - a slot width can be represented by two horizontal or vertical units, or by a single diagonal unit.

Exercise 10. Draw an isometric projection.

Explain isometric projections: three axes make sixty-degree angles with each other. Distances along all three axes have the same ("iso" means "same") ratio to the to the corresponding distances on the model. Invite each student to draw an isometric projection of a slot block. For this exercise, graph paper is of little help; the student must know how to use a compass and straight-edge. A right-angle drafting triangle would help the student to draw parallel lines more quickly.