Geo-Crochet = Geometry and Crochet

A fun way to learn geometry is through handwork. Crocheting basic shapes leads to discussions and observations about numbers, patterns, fractions, and so much more!

We started with some lovely alpaca yarn that came straight from Upstream Alpacas. They handspun and dyed the yarns from their own alpacas.

Our 5th grader Wilson then wound each skein into a ball.

We played with geoblocks, figuring out which shapes can be used to form other shapes, such as using 6 triangles to make a hexagon.

Wilson then learned how to crochet granny triangles. He had made granny squares before, so he understood the concept of starting with a circle to create another shape.

The rainbow-colored triangles were done!  Now, time to crochet edging and lay out the triangles.

One thing that we learned, is that the triangle points wanted to curve. Wilson made sure to single crochet three times into each corner.

The triangles were sewn up with leftover yarn.

The 6 triangles, when sewn together, curled up a bit, looking like a circle.

Wilson blocked the triangles using water, a foam board, and push pins to encourage the yarn to hold a hexagonal shape.

The end result is a beautiful, rainbow hexagon! We use it in our homeschooling bookcase and place special calendar gnomes on top.

Spring Flowers and Geometry

We've been inspired by the beautiful daffodils blooming in our yard!  To celebrate this sign of early Spring, we sketched the daffodils for a while when the sun was out....

Daffodils have 6 petals, so we drew 6-pointed stars and hexagons to help us with the symmetry.

Our wonderful neighbor loaned us an amazing Waldorf book that is no longer in print and is all in German.  It features forms and shapes of plants, animals, minerals. 

Next, we drew triangles, squares, 5-pointed stars and 6-pointed stars.  Based on the drawings in the book, we sketched out flowers that follow these 3, 4, 5, and 6-petal/leaf patterns. 

 

Then, it was time to color the flowers.  If the flowers were blooming outside, we observed them (mostly pansies and daffodils right now!).  

Joey

We discussed the color variations of each flower as we drew. 

Ricky

We wrote the numbers in Arabic and Roman numerals and the names of the flowers in English.  Next week, we will add the names in Spanish and German. 

Wilson

The Golden Mean

Come take a peek at Rick's blog post about divine proportion, da vinci, algebra, geometry, and business math...and about our son's 13th birthday rite of passage ceremony: www.thewaldorfway.blogspot.com.

Freehand Artistic Geometry

Ricky, Joey and Mommy have been doing artistic geometry drawings once a week this year. Making shapes out of circles, using a compass and protractor, and measuring with rulers have all been important.

This month, we are trying something new! Instead of using drawing tools, we have been doing our geometry "freehand". First, we started off with drawing angles. After completing our angle examples, we checked with a protractor and realized that we were pretty close! Next, we did some of the drawings from the book Artistic Geometry, such as the Hexagram, and 6 Circles from 1. Next, we will be drawing items from nature, such as shells and leaves.

Artistic Geometry

Geometry is our favorite form of math. Through drawing and building, we experience geometry in different, artistic ways.

The two older kids and Mommy each create a drawing, following the book Artistic Geometry by John Miles. We are learning lines, angles, circles, bi-secting angles, and a variety of polygrams. Shading colors into the angles with our Lyra colored pencils (we purchase these at Great Forest Toys in Fair Oaks, CA) brings the shapes to life!

We tend to stay away from plastic materials, however, we came across two wonderful products at the HSC conference in Sacramento last year. Zometools connect lines into spheres at different angles. We create different polygons and stellations with our Zometools. Here is a picture of Ricky's stellated dodecahedron inside of an icosahedron.

Tubespace are slim tubes that bend and connect into the 5 polyhedra and other shapes. They also glow in the dark!

Folding Circles books are some of our favorite home-learning resources. We fold circles into tetrahedrons, octahedrons and other shapes. Then, we tape or bobby pin shapes together into larger shapes. As the seasons change, we use different colors of circular paper (we buy this at Rudolph Steiner College bookstore) and then our creations become part of our learning environment for a few months. You can see pictures here of our folding circles from autumn hanging from the lamp along with some origami birds, and our current octahedron creations for the winter.

Winter brings snow...or at least in some parts of the world! Although we live about an hour from the snow-capped Sierra mountains, we decided to bring "snow" into our home by making symmetrical snowflakes for our windows out of winter colors. We used kite paper from Rudolph Steiner College bookstore. Gluing smaller versions of the snowflakes onto glass jars, we lit some beeswax candles and watched the beautiful shapes glow in the candlelight!

Speaking of kite paper...one of our latest geometrical adventures is folding window stars. One of our family Christmas gifts was a lovely book, Stars and Flowers Window Transparencies by Frederique Gueret.