A set of Pattern Blocks consists of blocks in 6 geometric, color-coded shapes: green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons. The relationships among the side measures and the angle measures make it very easy to fit the blocks together to make tiling patterns that completely cover a flat surface. The blocks are designed so that all the sides of the shapes are 1 inch except the longer side of the trapezoid, which is 2 inches, or twice as long as the other sides. Except for the tan rhombus, which has 2 angles that measure 150°, all the shapes have angles whose measures are divisors of 360-120°, 90°, 60°, and 30°. Yet even the 150° angles of the tan rhombus relate to the other angles, since 150° is the sum of 90° and 60°.
These features of Pattern Blocks encourage investigation of relationships among the shapes. One special aspect of the shapes is that the yellow block can be covered exactly by putting together 2 red blocks, or 3 blue blocks, or 6 green blocks. This is a natural lead-in to the consideration of how fractional parts relate to a whole - the yellow block. When students work only with the yellow, red, blue, and green blocks and the yellow block is chosen as the unit, then a red block represents 1/2, a blue block represents 1/3, and a green block represents 1/6. Within this small world of fractions, students can develop hands-on familiarity and intuition about comparing fractions, finding equivalent fractions, and changing improper fractions to mixed numbers. They can also model addition, subtraction, division, and multiplication of fractions.
Pattern Blocks provide a visual image which is essential for real understanding of fraction algorithms. Many students learn to do examples such as "3 1/2 = ?/2," "1/2 x 1/3 = ?" or 4 / 1/3 = ?" at a purely symbolic level. If they forget the procedure, they are at a total loss. Yet students who have many presymbolic experiences solving problems such as "Find how many red blocks fit over 3 yellows and a red," "Find half of the blue block," or "Find how many blue blocks cover 4 yellow blocks" will have a solid intuitive foundation to build these skills on and to fall back on if memory fails them.
Students do need ample time to experiment freely with Pattern Blocks before they begin more serious investigations. Most students can begin without additional direction, but some may need suggestions. Asking students to find the different shapes, sizes, and colors of Pattern Blocks, or asking them to cover their desktops with the blocks or to find which blocks can be used to build straight roads, might be good for starters.