Manipulatives

# Pattern Blocks

in middle school and high school

Henri Picciotto

Pattern blocks are ubiquitous in elementary schools, but they're not commonly seen in middle school or high school. Yet, they do offer plenty of interesting curricular opportunities. (And yes, they're fun!)

### On This Site

Pattern blocks are featured in my book Geometry Labs, a free download on this site. In fact, they are used in the first and the last lesson in the book! Here is an index of the labs that use pattern blocks:
Angles: 1.1, 1.2, 1.4
Polygons: 3.3, 3.6
Symmetry: 5.4, 5.6
Tiling: 7.2
Measurement: 9.5, 11.8
Similarity: 10.4

Symmetry with Pattern Blocks: cover a regular triangle, hexagon, and dodecagon with pattern blocks, and analyze the symmetries. (This an online applet for Geometry Labs 5.6)

Dodecagons:A classic activity is to cover a 1-inch-side dodecagon with pattern blocks. This provides a great context to discuss symmetry (see Geometry Labs 5.6.) An extension: cover the 2-inch-side big dodecagon with pattern blocks: examples, activity, and discussion.

Wallpapers Catalog: From the point of view of symmetry, there are exactly 17 different wallpaper designs. I made a catalog of those, illustrating each one with an example using pattern blocks.

Wallpaper Starters is a challenging puzzle-like activity which combines symmetry and tiling. The idea is to extend the given pattern, using the given mirror lines as the only guide.
If you create more pattern block wallpaper starters, I will post them here and credit you.

This presentation (PDF | Keynote) is mostly about pattern blocks, but it does include some work using the Geometry Labs template. The Keynote version features some fun animations. You can watch me making the presentation in a condensed 90-minute video version of a three-hour workshop here And here is a K-8 version of the talk: PDF | Keynote.

Pattern Block Trains is a rich activity about rate of change, which starts easy, and gets quite challenging.

If you use SmartBoards, here is a pattern block Notebook gallery item.
If you create pattern block files for other platforms, I will post them here and credit you.

### Elsewhere

NCTM has a nice online pattern block applet, as does the Math Learning Center. The latter is particularly well suited for tiling, as it makes it easy to duplicate blocks. Jen Silverman created a good one in Geogebra. Computers are great to create and record figures, but if you have access to them, using actual pattern blocks is by far preferable in the classroom or for your own explorations.

### History

Pattern blocks were invented by Edward Prenowitz in 1963, as part of the Elementary Science Study (ESS) at the Education Development Center (EDC) in Newton MA. He was proud of the design, particularly the fact that each shape had its own color (not unlike Cuisenaire blocks and Zome), and that one could do so much with just six shapes.

My own teaching was very much influenced by the ESS units (Tangrams, Mirror Cards, Peas and Particles, Where Is the Moon?, Daytime Astronomy, Pendulums, Mystery Powders, Optics, and probably others.) Alas they're out of print and hard to find.