The Unit Circle Game

Introduction: The Unit Circle Game

About: Studying to become a math teacher. I enjoy making math games on Scratch.

A Parcheesi style board game that can help reinforce trigonometry.

Step 1: Print the Game Board and Pieces

Download this image or the pdf and print it. Use cardstock to increase durability.

Step 2: Cut Out the Pieces 1

Cut out a 3 x 2 rectangle and hand it to your friend.

Cut out another 3 x 2 rectangle and hand it to another friend.

Cut out another 3 x 2 rectangle and hand it to another friend.

You and your friends each pick a color and you each color your six squares the color of your choice.

Step 3: Cut Out Pieces 2

Then cut the rectangles into 12 1 x 2 rectangles.

Step 4: Stand Up Your Pieces

Fold the rectangles at about 25° angle. Now stand them up.

Step 5: Color the Board 1

Each player picks a side of the board and colors the three circles on the x or y axis closest to the origin on their side of the board their color.

Step 6: Color the Board 2

Then color the outside ring of circles on the multiples of π/6 in radians (or 30° in degrees) one color...

Step 7: Color the Board 3

... and the inside ring of circles on the multiples of π/4 a different color.

Step 8: Fill in Information

Fill in what you know about the unit circle. The coordinates (cos, sin), the angles (degrees and/or radians). [If it is π day, use radians] You can find information about the unit circle at

Try to write neater than me.

Step 9: Pretty It Up

Use construction paper or something clever for a frame. Laminate it for extra durability.

Step 10: Find Some Dice

You might have some in a board game or Yahtzee game. If not, you can get them at the Dollar Tree. Or you can find a dice instructable and make your own.

Step 11: Play

Use these rules or make up your own:

  1. Figure out a way to determine who goes first. Be creative. If you cannot think of a fun way, you can just roll a die, and whoever rolls the highest goes first.

  2. Play goes counterclockwise. Move the pieces counterclockwise on the board. The unit circle goes in a counterclockwise direction. For expert players you can add some sort of negative angle rule and go clockwise, since you are free to make up your own rules and encouraged to do so.

  3. You must roll a 5 to move onto the board. You move your piece onto the board at the x or y axis closest to you.

  4. To move a piece on the inside loop, you must roll a 1,2,4 (factors of 4).

  5. To move a piece on the outside loop, you must roll a 1,2,3,6 (factors of 6). This applies to the number on the dice, not to the sum of the dice.

  6. You can split the dice between different pieces, but only the values of the dice. For instance, if you roll two 3s, you can move one piece 6 places or two pieces 3 spaces each, but not one 4 places and the other 2 places.

  7. The only time you can switch loops is at the axis where the two loops overlap.

  8. If two pieces are sitting at the same angle on an axis, they form a blockade and no one can go past them.

  9. At any time, a player can yell out cos or sin of a given angle and the player at that position must say what the sin or cos is. Beginner players may look. Expert players may be restricted from looking.

  10. Players can only look if they less than two pieces in home. (or stairway to the origin - yeah, it’s a weird name, just call it home)

  11. If the player has a blockade, then they cannot look.

  12. If you can move, you have to move. Especially if you’re blocking the way.

  13. Players can enter home after they go 360° around the circle. (or 2π radians).

  14. Players must roll exact to move into home.

  15. Home is not completely safe. If someone yells out cos or sin of your home angle, you must answer or all your pieces at home will be wiped off the board and you will have to start over. Sorry.

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    2 Discussions


    Reply 4 years ago

    Thank you.