|We can click together strings of patterns, making winding ribbons of shapes. Try to use a repeating pattern as to how the ribbon is shaped, and what colors we use along the way. We can use a single shape, or combine different shapes, but make sure to follow the same pattern all along the way.|
|Next, click together a string of 6 squares that form a pattern e.g. red, blue, green, red, blue, green. Connect the two ends to make a repeating ring.|
|Now, if we put together 6 squares in the shape of a cross, we can connect the top and bottom of the cross to make a repeating ring, and then close the two sides to make a box. This square box is called a "cube". How is it different from the ring of six squares in the last exercise?|
|Six triangles can be put together to form a regular hexagon. Try putting them together with different color patterns. Try putting the same set of six colored pieces together in different orders, to make different arrangements. For example, you can have three blues on one side, and three yellows on the other, or you can alternating blue and yellow all around, or you can have B,B,Y,Y,B,Y.|
|To make a regular dodecagon (12 sides), we can surround a hexagon with squares and fill in the spaces between the squares with triangles. We can use color patterns to get some variety, and make them more interesting to look at.|
|Make other flat rings, trying different color patterns on the same ring shapes. There are many different arrangements that will work. Feel free to leave open spaces inside the rings if you want. Don't forget to use pentagons in your rings! They can work too, and can lead to some interesting designs.|
|Click the pieces together to make pictures, using shape and color to make it look right. Start off with just triangles, or just squares, then try working with them both together.|
You can make real things, like planes, trees, rockets, cats, the sun, a space station, or anything else you like. Or you can just click them together to make any color design you like, curves, boxes, starbursts, waves, or anything else. Feel free to leave open areas inside your picture. After you make something, see if anyone can guess what it is.
|Make letters and numbers using squares and triangles. Find different ways of making the same letter. Which shapes look most like the letters and numbers you wanted?|
|Make plane figures with just pentagons (there will be gaps between some pentagons), and see if you can form some symmetrical patterns. Look at the empty spaces between the pieces to see what shapes are there. Don't forget to use the colors to show off the pattern. Try making pictures with pentagons. It may take more practice than working with triangles and squares, but you can make some very cool shapes if you try.|
|Create some simple solid shapes such as pyramids, bipyramids and prisms. Try attaching pyramids to prisms, pyramids to pyramids and prisms to prisms in different ways. To attach two models together, take off a matching face and join the models together at this new opening. (see the math page for more info on some of these shapes).|
|Create more simple solid shapes, such as cupolas and cupolas with pyramids or prisms attached. (see the math page for more info on these shapes). Make sure you pick colors that show what parts are the same, and what parts are different. This can make it easier to count the pieces.|
|Using these simple shapes, try counting the faces. Figure out how to count without losing track of where you are! Try counting in "groups" if it helps, you can add up the groups later. For example if you have 3 square pyramids showing 4 traingle faces each, you have 4 + 4 + 4 = 12 triangles, and if you have 4 triangular pyramids showing 3 triangle faces each, you have 3 + 3 + 3 + 3 = 12 more triangles. And if you have 6 triangles making up a hexagon, you can count it either as 1 hexagon or 6 more triangles.|
Thanks also to Melinda Green and Don Hatch for their excellent Tyler Web Application. This free web tool lets you do great flat designs with polygons in just about any arrangement.