www.MathEdPage.org/angles
Adapted from Geometry Labs, by Henri Picciotto
Angles Around a Point
Equipment: Pattern Blocks
Place pattern blocks around a point, so that a vertex (corner) of each block touches the point, and no space is left between the blocks. The angles around the point should add up to exactly 360°.
For example, with two colors and three blocks you can make this figure:
Use the chart below to keep track of your findings.
 Every time you find a new combination, circle the appropriate number on the list below.
 Cross out any number you know is impossible.
 If you find a possible number that is not on the list, add it.
Since the twocolors, threeblocks solution is shown above, circle that one first.
Colors 
How many blocks you used 
all blue 

all green 

all orange


all red 

all tan 

all yellow 

two colors 

three colors 

four colors 

five colors 

six colors 

How many solutions are there altogether? __________
Discussion
 Which blocks offer only a unique solution? Why?
 Why are the tan block solutions only multiples of 4?
 Explain why the blue and red blocks are interchangeable for the purposes of this activity.
 Describe any systematic ways you came up with to fill in the bottom half of the chart.
 How do you know that you have found every possible solution?
 Which two and threecolor puzzles are impossible, and why?
 Which fourcolor puzzles are impossible, and why?
 Why is the fivecolor, eightblock puzzle impossible?
 Which sixcolor puzzles are impossible, and why?