More Games with Patterns, Shapes and Symmetry

Exploring patterns can be a lot of fun by making border pattern mats. These mats can be made with construction paper. Have students make patterns made with shapes around the edges of a piece of construction paper.

Then have them make pattern cards using macaroni of different shapes and colors.

Once they are dry, they can be analyzed together for their patterns (ABBABBABB, ABCABCABC, etc.) and then to use other junk box materials (beans, buttons, nature study finds, etc.) to make the same sort of patterns, and then also, new patterns. Can they follow patterns that the others have made? How many new patterns can be created? Can a pattern be made with three colors? Can two different shapes be used to make a pattern? Can a pattern be made with a change in position or one using two sizes? Your job as facilitator in this exercise is to support them in their explorations and if you think they are ready, to help them explore new avenues.

You don't have to confine yourself to lying pattern blocks flat on the table to explore patterns. Stand pattern blocks up into walls in patterns of choice. These patterns can be extended as long as desired. These can also be recorded by drawing and coloring them or with paper shapes on card strips. These cards, once finished, can then be analyzed and identify them with A-B-C. Then as a game, they can use the cards to make each other's patterns.

Fill a shape and fill it well

Just like words that letters spell

Shapes within others

Help everyone see

The beauty of Geometry!

-GEMS Build It!

These activities explore an area of mathematics known as discrete mathematics. This strand of math involves separate, countable quantities and also includes the ways that those quantities can be arranged.

You can buy books (such as Build It! Festival, Mathematics Activities for Grades K—6) that have shapes (star, triangle, hexagon and dodecagon) that can be filled in a variety of ways with the pattern blocks. Students have to fill each shape with a finite, countable number of pattern blocks (the combination of pattern blocks used to fill a particular shape is one discrete solution.) They can discover, however, that different people can fill the same shape in different ways, and along the way discover the relationships among the pattern block shapes, a spatial sense, congruence and equivalence. These multiple solutions are permutations of the combination of blocks. This aspect of discrete math falls under the heading of combinatorics.

(apologies to William Blake)

Kitty, Kitty, leaping light

Through the grassy forest bright

Eyes and ears and whiskery

Such a cheerful symmetry!

GEMS Build It!

In the next activity your student can explore bilateral symmetry as they made designs with pattern blocks using a card that has one-half of a design (which can be found in Build It! Festival, Mathematics Activities for Grades K—6.) They first fill in the half that is on the page and then they complete the other half of the design symmetrically using additional pattern blocks.

sources: 

• Mathematics Their Way, Mary Baratta-Lorton

Build It! Festival, Mathematics Activities for Grades K—6 Written by Philip Gonsalves and Jaine Kopp Weaving mathematics concepts into engaging, hands-on construction activities, this GEMS festival guide includes a wide assortment of classroom learning-station activities that emphasize construction, geometric challenges, and spatial visualization. Introductory activities, such as Architect/Builder, involve students in free exploration of materials and lay the foundation for such mathematical challenges as Create-A-Shape, Dowel Designs, Polyhedra, Symmetry, Tangrams, and What Comes Next? The guide provides geometry background for the teacher, and a list of useful literature connections. Depending on the stations chosen, required materials might include pattern blocks, polyhedra, and wooden cubes. Template patterns for folding and constructing shapes and creating tangrams are provided. Many of the eight main activities connect strongly to the real world and potential careers. For extra dynamics, the unit can culminate in a festival for the entire school!