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 3D. 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.




Multitiling
(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.




Multitiling
(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.
