|Explore patterns for tiling the plane (covering a flat surface with tiles). Find repeating sets of tiles that can be used, and different ways they can be arranged. Use colors to identify hexagons or dodecagons, or use colors to change how a pattern looks.|
|Find more tilings of the plane by using different shaped tiles. Build bigger tiles with unusual shapes by using multiple pieces with the same color. Use these bigger tiles in a repeated pattern.|
It is ok if you end up with empty spaces in your patterns. Not every tile will work to fill the whole plane, but you won't know until you try them. And don't forget, if your tiling doesn't work the first time, try arranging the tiles a different way. Maybe a different order might just work.
|Explore the Platonic Solids. Notice that each one is made with every face being the same shape, and every corner having the same number of faces. Identify how many faces, edges and corners each figure has. Make a table, with all three counts for each of the 5 figures. Notice any similarities between some of the numbers? This is not just a coincidence, there are interesting relationships between these models.|
|Examine the Archimedean Solids that can be made with Jovo. There are a few Archimedean solids that require octagons or decagons, but we can build all the rest, and get an idea of what they are all about.|
Notice that although there are more than one kind of face shape in each model, each corner has the same arrangement of faces (same number of pieces, in the same order). Identify how many faces, edges and corners each figure has. Notice the left-handed and right-handed snub polyhedra (each one "twists" a different way). See the math page for more info on these shapes to make sure you see all of them.
|Starting with a net of a figure and a picture of what it should look like, assemble that figure. A "net" is a flat configuration of all the pieces, that can then be folded up. Sometimes there is more than one way to fold up a net, so it is helpful to have a picture of the final result to get an idea. Let me know if you want the net of any model, and I will send it to you.|
|Make the polyhedra above using different coloring patterns, such as making an octahedron with two alternating colors. Make a dodecahedron using three, four or six colors. Try to find more than one way to use the same number of colors.|
|Try drawing some of the polyhedra. Sit it down on a table and look at it carefully as you draw. Draw the edges that you see, at the angles that you see. Try not to draw the shapes you know are there, since a square won't look like a square when you have it turned sideways. Turn the polyhedron around and draw it from a different direction.|
|Try drawing a ‘landscape’ of several different polyhedra, such as a few buildings arranged on a table. Move around and look at the scene before picking a spot to draw from. Once you have completed your drawing, compare it with someone else's, and try to figure out which direction theirs was drawn from.|
|Use strips of pieces to explore multiplication and division. Use colors to help keep track of what pieces go together. Practice some of the properties of multiplication and addition by demonstrating them with pieces.|
Four goups of five squares is the same count as five groups of four squares (commutative property of multiplication)
Three groups of four squares plus three groups of two squares is the same as three groups of four + two squares (distributive property of multiplication)
|Use flat figures to work with fractions and percentages.|
Divide a hexagon figure into 2, 3, or 6 equal shares, so that you can represent 1/2, 2/3 and 5/6. Simplify the fraction 4/6.
Using strips of 10 or 20 pieces, try to figure out some percentages. Four pieces out of twenty is what percent?
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.