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.
As students begin to work with Pattern Blocks, they use them primarily to explore spatial relations. Young students have an initial tendency to work with others and to copy one another's designs. Yet even duplicating another's pattern with blocks can expand a student's experience and ability to recognize similarities and differences, and it can also provide a context for developing language related to geometric ideas. Throughout their investigations, students should be encouraged to talk about their constructions. Expressing their thoughts out loud helps students clarify and extend their thinking.
Pattern Blocks help students explore many mathematical topics, including congruence, similarity, symmetry, area, perimeter, patterns, functions, fractions, and graphing. The following are just a few of the possibilities:
- When playing "exchange games" with the various sizes of blocks, students can develop an understanding of relationships between objects with different values such as coins or place-value models.
- When trying to identify which blocks can be put together to make another shape, students can begin to build a base for the concept of fractional pieces. When the blocks are used to completely fill in an outline, the concept of area is developed. If students explore measuring the same area using different blocks they learn about the relationship of the size of the unit and the measure of the area.
- When investigating the perimeter of shapes made with Pattern Blocks, students can discover that shapes with the same area can have different perimeters and that shapes with the same perimeter can have different areas.
- When using Pattern Blocks to cover a flat surface, students can discover that some combinations of corners, or angles, fit together or can be arranged around a point. Knowing that a full circle measures 360° enables students to find the various angle measurements.
- When finding how many blocks of the same color it takes to make a larger shape similar to the original block (which can be done with all but the yellow hexagon), students can discover the square number pattern-1, 4, 9, 16, ...
The use of Pattern Blocks provides a perfect opportunity for authentic assessment. Watching students work with the blocks gives you a sense of how they approach a mathematical problem. Their thinking can be "seen" through their positioning of the Pattern Blocks. When a class breaks up into small working groups, you are able to circulate, listen, and raise questions, all the while focusing on how individual students are thinking.
The challenges that students encounter when working with Pattern Blocks often elicit unexpected abilities from students whose performance in more symbolic, number-oriented tasks may be weak. On the other hand, some students with good memories for numerical relationships may have difficulty with spatial challenges and can more readily learn from freely exploring with Pattern Blocks. By observing students' free exploration, you can get a sense of individual learning styles.
Having students describe their creations and share their strategies and thinking with the whole class gives you another opportunity for observational assessment. As a next step, you may want to gather students' recorded work or invite them to choose pieces to add to their math portfolios.