There are eight different activities on this website, below
you will find challenging tasks for each activity. You can use these to investigate the website.
 
 
Anni’s Triangles

There are many problems that can be posed using the right triangles in a two by two square pattern. In the squares, create all patterns of two right triangles that touch at one point. Two patterns (including the squares) are considered different if one cannot be turned and or flipped to fit exactly on the other. Try to find all the different patterns. The number is between five and fifteen.

 
Same
(A turn to the right)
 
Different
(The triangles at the left
have their corners on the
sides of the big square.
The triangles on the right
have their corners at the
corners of the big square.)
 
Now try to create as many different patterns as you can with three right triangles that touch (point or a side).
You can also try to create as many different patterns as you can with four right triangles whether they touch or not.

 
 
Bowers

Click on the Albers’ Bowers’ button in the upper right of your screen. Choose an eight down by ten across section of one of the Bowers. Try to make this section on your eight by ten grid using three colors of your choice.
Example:

 
 
Square Grid
 
The number of activities that can be done with the square grid is unlimited.
1. Use each shape shown to make a tiling (like tiling a floor). You will have three different tilings. In a tiling, there can be no overlaps and no spaces between the shapes. Your tilings should have repeating patterns. Once you have made one tiling with a shape, you may want to make other tilings with that shape.
 
 
2. Draw a rectangle that contains 16 squares. Now draw a different rectangle that contains 16 squares. Can you draw another? How many can you draw? Now try it with 15 squares. And then with 13 squares. What do you notice?
 
Triangle Grid
 

The number of activities that can be done with the triangle grid is unlimited.

1. Use each shape shown to make a tiling (like tiling a floor). You will have three different tilings. In a tiling, there can be no overlaps and no spaces between the shapes. Your tilings should have repeating patterns. Once you have made one tiling with a shape, you may want to make other tilings with that shape.

 
 
2. Draw a cube. Now draw three cubes in a line. Then draw four cubes that appear to be stacked on top of eachother.
 
 
3. Try making the “T” shown below that looks 3-D. Now draw the “T” from a different viewpoint (there are many possibilities).
 

 
“L’ Tiling

In this activity, you are shown a “L”-like shape. Use this shape to make a tiling. See how many different tilings you can create with the “L” shape. Here are two examples of how the “L” shape can tile. We’ve added color to help create the pattern.

 
 
Multi-tiling (Square Grid)

In the previous activities, each tiling used only one shape. In this activity, you have several shapes to use in making a tiling. Use one, two, three, or four shapes to form your tiling. Remember, in a tiling there are no overlaps or spaces between the shapes. There should be a repeating pattern in your tiling. Use colors to help create your pattern. Make several different tilings and compare them with the tilings made by others.

 
 
Multi-tiling (Triangle Grid)

In the previous activities, each tiling used only one shape. In this activity, you have several shapes to use in making a tiling. Use one, two, three, or four shapes to form your tiling. Remember, in a tiling there are no overlaps or spaces between the shapes. There should be a repeating pattern in your tiling. Use colors to help create your pattern. Make several different tilings and compare them with the tilings made by others.

 
 
Tangrams

Tangrams are an ancient Chinese puzzle. On this page, various shapes are provided. By clicking on a shape at the left, you select as shape to be filled with the Tangram pieces. They start out easy and become more challenging. You could even experiment with making other shapes with the Tangram pieces. Making a square using all seven pieces is challenging.