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"Let us strive to make each moment beautiful."
Saint Francis DeSales
painting by Katie Bergenholtz

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 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!

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 the same book.) 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.

source: Mathematics Their Way, Mary Baratta-Lorton

3 comments:

  1. Hmmm...another fun book to check out!

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  2. I like how this opens up the idea of patterning to all sorts of things! I love the idea of using buttons and beans or other found objects. Our daughter likes to talk about ABAB or AABB patterns with our sleeping arrangements. It's nice when they start applying what they learn in real life settings! Thanks for linking up with another wonderful activity!

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  3. I really like your math posts. So many ideas for various pattern games. Interestingly, my daughter really picks up on word patterns and understands patterns in general, but not interested in making patterns. Oh, she will do them once in a while, but only on her own terms :)

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