Patterns
with “Pentagonal” Triangles
Click
on the pentagon for a template you can copy and print out. ·
Let children play around
with sets of the “pentagonal” triangles and discover for themselves what
kinds of shapes can be made. ·
Show children examples of
the finished stars. Challenge them to work out which triangles have been
used, and how they have been put together. Challenge children to create a
finished star themselves. ·
When they have made the
stars let them identify all the new shapes that emerge when the stars are
put against the light. In each case
within the star smaller examples of
two kinds of “pentagonal star will emerge which are similar
to the originals. or ·
Challenge children to
make the patterns by following the instructions as given below.
Ideas for activities with children
Patterns with “Pentagonal” Triangle 1 (72,72,36)
The first set of patterns all use a triangle
with angles of 72,72, and 36 degrees.
Click here for
some outlines you can print off and use to make the stars below.
Some hints on paper to
use and how to glue the triangles. Use thin coloured paper to start with. If you become more expert then try tissue paper but
this can be hard to handle Arrange all the triangles
in place first to make sure they make the complete shape. If you glue the
first pair straight away you may find that the last
triangle is way out. When you have all
triangles in place, adjust them to create the final pattern.
Hold the first pair in place with pressure from your fingertip. Lift the
flap of the upper triangle and spread a
little glue ( I use a glue stick) on the triangle underneath. Let the upper
triangle fall back into place a press to
fix.
Pentagon
and Nesting Star
Overlap 5 triangles
to create a pentagon.
Discover a nested 5 pointed star
when you put the pentagon on the window. Hold the pattern in place with clear
plastic. (Book covering film works well. Rub it with a sock or soft toy to
generate a static charge which will hold it in place)
Can you recognize the
triangles that appear?
Pentagonal
Star
Once again use 5 triangles but overlap as shown
here.
Put the star on the window and discover a 5
pointed star nested inside.
Hollow
Pentagonal Star
Another method of creating a star using 5 of
the triangles is shown here. It is not quite as easy as the previous methods
but creates a very elegant window star.
Hollow Pentagonal Star
Variable Overlap Star
You can decide to overlap the triangles any
amount you like, as long as it is the same for each pair.
Here they are overlapped so that the mid points
coincide. 
Here
they were overlapped a smaller amount.
Patterns
with “Pentagonal” Triangle 2
Use this triangle for all the patterns below.
It is triangle with angles
of 36,
36, and 108 degrees.
Click here for
an outline you can copy and print out.
Hollow
Pentagon
Overlap 
and glue in place like this
When
you place the Hollow Pentagon
against
the light a pentagonal star
appears
inside the pentagon.
Hollow
Pentagonal Star (1)
Use 10 triangles and combine in pairs. Then
overlap them to create a star.
Against the light
Hollow
Pentagonal Star (2)
The same star pattern can be created using only 5 triangles but the
placing is
slightly more difficult.
Against
the light a nested 5 pointed star appears!
Hollow
Pentagonal Star (3)
Use 10 triangles and first combine them in pairs like this.
Then overlap the pairs to create a star with a
larger hollow pentagon at the centre.
A
pattern like this emerges against the light.
Ten
Pointed Star
Overlap 5 triangles to create this rather
unusual star. Notice how the bases of the triangles are in a straight line but
do not overlap.
