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**MIRROR
YOUR FRIEND GAME**

Ages
5 and up, two or more players

Materials needed: one large or one travel set

Teaches reflection symmetry, cooperation

First set up the game by placing any two tiles,
edges together, near the center of the board.

Player #1 places a third tile adjacent to one
of the tiles on the board so that the three tiles
together form a design with reflection (mirror
image) symmetry.

Player #1 then selects a fourth tile and adds
it to the design making sure that the next player
will be able to place a tile that mirrors that
move.

Player #2 places a tile that mirrors the last
player’s move, and then adds a tile of her
own for the next player to mirror.

Continuing in this manner, it is fun to see the
cooperative designs that emerge. This is an easy
game to play with young children.

**SYMMETRY
GROUPS**

Ages 7 and up

Materials needed: one large or one travel set

Teaches basic symmetry groups

**Symmetry Groups, Activity # 1**

Optional: Review the section "Fractiles and
Symmetry" printed on the inside cover of
the Fractiles-7 package for illustrations and
definitions of symmetry groups.

Next, make some simple designs that are examples
of each symmetry group.

Give each child at least seven tiles of each color.
Have each child use their tiles to create one
or more simple designs for one or more of the
symmetry groups.

Have a discussion asking the children to think
of some everyday objects belonging to each of
the symmetry groups. Ask them to name some examples
that are man-made and some that are natural forms.
Examples might include the human face as reflection
symmetry, a daisy as rotational symmetry, or a
checkerboard as translation symmetry. Hint - some
objects have more that one kind of symmetry.

**Symmetry
Groups, Activity # 2 **

Materials needed: Magazines with lots of colored
pictures, scissors, paste, scrap book.

Look through the magazines, select and cut out
pictures that are examples of the different symmetry
groups you have learned about. Use the pictures
to begin a symmetry scrapbook with separate pages
or chapters for each symmetry group. Explain in
your own words why each picture belongs to a particular
symmetry group.

**MAKING
SMALL CIRCLES**

Ages 7 and up

Teaches symmetry, areas, angle combinations

Materials needed: one large or one travel set

*Allow at least 15 minutes*

Divide the tiles into smaller sets of 21 tiles
- 7 of each color. Give each person one of these
smaller sets and a Fractiles board or other suitable
steel based playing surface.

Each person works independently to form a circle
using all their 21 tiles. It will be easier if
you refer to packaging illustrations of 21 piece
circles. It will be more challenging if an example
is not shown.

Discover your own unique style of tiling the same
circular area with your 21 tiles.

Compare the various circles you have made and
describe the similarities and differences. If
you can, describe what symmetries have emerged?
Do any of the circles have translation symmetry?
rotation? reflection? or more than one kind of
symmetry? no symmetry?

**STAR
MAKING**

Ages 8 and up

Work individually or as a team

Develops awareness of spatial relationships, and
angle combinations.

Materials needed: one large or one travel set

*Allow at least 15 minutes*

If desired, you can refer to package instructions
section "Why the Tiles Fit Together So Many
Ways". This will be more challenging if you
do not read the material first.

1. Give each person at least 14 red tiles, 7 yellow
tiles, and 7 blue tiles.

2. Make a yellow star, using 7 yellow tiles. A
full circle has 360 degrees, so what fraction
of 360 degrees is one yellow tile (answer: 1/7th)

3. Next make a star with red tiles (14 red tiles).
What fraction of 360 degrees is one red tile’s
angle (answer: 1/14th)

4. Use a calculator with as many decimal places
as possible to see how many degrees are there
in a single red tile. (answer: 360 divided by
14)

5. Again use the calculator to see how many degrees
are there in a single red tile. (answer: 360 divided
by 14)

6. Calculate all the angles of the tiles (six
angles in all) - 1/14 of 360, 2/14 of 360, on
up to 6/14. Did you notice anything weird about
the numbers you got?

7. Next try to make a star using only blue tiles.
Can you make a blue star in the same way as you
made a yellow or red star? Why or why not?

8. Now make another star, but this time use more
than one kind of tile. This star will look uneven
or nonsymmetrical compared to the stars you made
using only one color. After you have made this
star, try trading some of the tiles in your star
for different tiles. For instance, two red tiles
can fit in place of one yellow tile. Try other
combinations. What does this tell you about the
relationships of the angles?

**FOUR
PLUS STARS GAME**

Ages 7 and up, for 2 or more players

Develops awareness of spatial relationships and
angle combinations.

Materials needed: one large or one travel set

*Allow 15 minutes or more*

**Object of the game: **

Be the first player to complete a star composed
of 4 or more tiles.

A star in this game is made of 4 or more tiles
whose corners meet in the middle. Together these
tiles close the circle. In other words, their
adjacent corners have angles which add up to 360
degrees.

**How to Play:**

Set up the game by placing one tile near the center
of the board.

Players take turns placing one tile at a time
on the board.

The tile being placed must have at least one of
its edges adjacent to the edge of a tile that
is already on the board.

Tiles may not hang over the edge of the board
or overlap other tiles.

You are not allowed to make a star with only 3
tiles as this is too easy and the game would end
quickly.