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Family fun with Fractiles

Here are some fun games you can enjoy with your Fractiles sets.

Mirror-Your-Friend Game

Players: 2 or more
Materials: one Large (192-pc.) or one Travel (96-pc.) set
Teaches: reflection symmetry and cooperation

Set up: Place any two tiles, edges together, near the center of the board.

Game Play:

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 which mirrors that move.
Player 2 places a tile that mirrors the last player’s move, and then adds a tile of their own for the next player to mirror.
Continue in this manner, adding a third or fourth player and/or alternating turns. Have fun seeing the cooperative designs that emerge!

Symmetry Groups Activities

Ages: 7 and up
Teaches: basic symmetry groups

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

Symmetry Groups Activity #1

Materials: one Large (192-pc.) or one Travel (96-pc.) set

How to Play:

Give each person at least seven tiles of each color.
Have each person 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. Hint: Some objects belong to more than one symmetry group.
Ask the children to name examples of both manmade (e.g., a checkerboard = translation symmetry) and natural (e.g., the human face = reflection symmetry; a daisy = rotational symmetry) forms.

Symmetry Groups Activity #2

Materials: Magazines with lots of colored pictures, scissors, paste, scrapbook.

How to Play:

Have the children select and cut out magazine pictures that are examples of the different symmetry groups about which they have learned.
Use the pictures to begin a symmetry scrapbook with separate pages or chapters for each symmetry group.
Encourage each child to explain in their own words why each picture belongs to a particular symmetry group (or groups).

Small Circles Activity

Ages: 7 and up
Materials: one Large (192-pc.) or one Travel (96-pc.) set
Teaches: symmetry, areas, and angle combinations
Time: at least 15 minutes

Optional: To aid in understanding this activity, refer to packaging illustrations of 21-piece circles. It will be more challenging if an example is not shown.

How to Play:

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.
Working independently, each person forms a circle using all of their 21 tiles.
Each person will discover their own unique style of tiling the same circular area with their 21 tiles.
Compare the various circles you have made and describe the similarities and differences.
If you can, describe what types of symmetries have emerged. Do any of the circles have translation symmetry? rotation? reflection? more than one kind of symmetry? no symmetry?

Stars Activity

Ages: 8 and up
Players: 1 or teams
Materials: one Large (192-pc.) or one Travel (96-pc.) set
Teaches: awareness of spatial relationships and angle combinations
Time: at least 15 minutes

Optional: To aid in understanding this activity, refer to package instructions section "Why the Tiles Fit Together So Many Ways."

How to Play:

Give each person at least 14 red tiles, 7 yellow tiles, and 7 blue tiles.
Each person will make a star using the 7 yellow tiles. Help the children answer this question: What fraction of 360 degrees (a full circle) is one yellow tile? (answer: 1/7th)
Use a calculator with as many decimal places as possible to see how many degrees there are in a single yellow tile. (answer: 360 divided by 7)
Next, each person will make a star with the 14 red tiles. What fraction of 360 degrees is one red tile’s angle? (answer: 1/14th)
Again use the calculator to see how many degrees there are in a single red tile. (answer: 360 divided by 14)
Calculate all the angles of the tiles (six angles in all) - 1/14 of 360, 2/14 of 360, on up to 6/14. Ask the children whether they notice anything strange about the resulting numbers.
Next, have everyone try to make a star using only the 7 blue tiles. Can anyone make a blue star in the same way as they made a yellow or red star? Discuss with the children: Why or why not?
Now have everyone make another star, but this time use more than one color of tile. This star will look uneven or nonsymmetrical compared to the stars you made using only one color.
After everyone has made this star, each person can try trading some of the tiles in their star for different tiles. For instance, two red tiles can fit in place of one yellow tile. Try other combinations. Discuss with the children: What does this tell you about the relationships of the angles?

Four Plus Stars Game

Ages: 7 and up
Players: 2 or more
Materials: one Large (192-pc.) or one Travel (96-pc.) set
Teaches: awareness of spatial relationships and angle combinations
Time: at least 15 minutes

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

Note: 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 that add up to 360 degrees.

Set up: Place one tile near the center of the board.

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

Rules:

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

Happy tiling!

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