Patrick Honner’s Moebius Noodles guest post on mathematical paper weaving was very inspiring to me. Mathematical weaving employs one of my favorite making materials – colored paper! It was actually sort of challenging to get started, but after playing around I landed on some solutions which became a nice little unit of paper weaving and grid games with and for young children.
I am imagining that the weaving and the games can be completed in an enjoyable collaboration between adult and child over the course of a day or two. Here are some ideas for setting up the experience and playing the games.
After experimenting a little, a 3/4″ width for vertical and horizontal strips makes a more pleasing final product to my eyes than 1″. To make the vertical strips fold a piece of paper in half and use a paper cutter to cut 3/4″ strips from folded edge to about 3/4″ away from the open edges. Essentially, you are creating a paper warp that is still essentially one piece of paper.
As you can see, below, the horizontal strips weave in very nicely and don’t need any glue or tape to keep them in place if you focus on pushing them gently, but snugly, downward. For the young ones, at least, a basic over/under/over/under weave is challenging enough. Using two horizontal colors creates visual interest and perhaps even a conversation about the patterns you see: alternating colors both vertically, horizontally and diagonally. You can also make a connection to odd and even numbers. Yellow squares in the design show up 2nd, 4th, 6th… places. Green squares are 1st, 3rd, 5th…
The minute I finished the piece above I thought – A GRID! It’s a grid! Over the last couple years I have received mountains of inspiration from the Moebius Noodles blog especially as source of grid games (my favorite so far is Mr. Potato Head is Good at Math). As a result, grids are always in the back of my head. Here are some of the ideas I came up with using a newly woven paper mat/grid and one of my favorite math manipulatives — pennies!
Adult: Oh look! There are three different colors of squares in our woven grid. I’ve got some pennies — I wonder if we could make a square by putting pennies down on only one of the colors?
Adult: That does look like a square. Let’s count and see if there are the same number of little squares (yellow, blue, yellow, blue…) that make up each side? There are! How many little squares are there on each side?
Adult: But, wait! Look what happens when I push a corner penny in toward the center! Yep, it lands on a green square! Let’s do it with the rest of the corners and see what we get. Oh, lovely. A rhombus.
Adult: The corners on the rhombus are on the yellow squares. I wonder what would happen if we pushed them one square toward the middle? Ooooh, look! We have another square. Is it bigger or smaller than our first square? Each side on our first square was six little squares long. This square has sides that are…three little squares long. Cool.
Another exploration, this time growing patterns and a tale of some square numbers who also wanted to get bigger? What little kid doesn’t want to grow up?
And, here’s my favorite. It’s a ‘let’s make a rule’ kind of game. The first penny goes in the bottom left hand corner, and you start counting from there. The first rule here (pennies) was two over, one up. Each time you repeat the rule, you start counting from the last token on the grid.
You’re probably wondering about the buttons? Well, that’s a different rule: one over, one up. Isn’t it cool how they overlap, but not always? Kids can make up their own rules after a little modeling or you can challenge them to guess a rule you made up and keep it going.
And then, of course, the final thing would be to leave the pennies and the paper grid mat out to explore at leisure. Have fun making math!
p.s. After this first foray into mathematical paper weaving, I explored it a little more. Here are more posts on my blog: Weaving Inverse Operations, Multiples and Frieze Patterns – Weaving Fibonacci – Weaving Geometric African Motifs Part 1 and Part 2.