Tetris and More Worksheet

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K-12: Materials at high school level.


Time-45.svg

Objective: The well known game Tetris is a tessellation game. Here we explore how these shapes are used to tessellate the plane.


Tetrominoes and Tetris

The game pieces used in Tetris are called tetrominoes by mathematicians

Below are the Tetris pieces.

1. Find all the mirror lines for the tetris pieces. The two mirror lines for the very first piece are given. If there are no mirror lines, write NO.

Tetris-pieces-refl.svg

2. There are only 3 pieces that will look exactly the same after you turn them. The pieces with "center" written in them all have so called rotational symmetry. Do they correspond to 2-turns or 4-turns? Write a 2 or a 4 next to the center of the pieces depending on what kind of turns you can do. Tetris-pieces-turn.svg

3. All tetrominoes tessellate the plane. Show a tessellation for each of the tetrominoes below.

A.

Tess-tetris1.svg

B.

Tess-tetris2.svg

C.

Tess-tetris3.svg

D.

Tess-tetris4.svg

E.

Tess-tetris5.svg


Triominoes

What if we wanted to simplify the game? We could look at game pieces made out of three squares.

  • A triomino is a polyomino made from three squares.
  1. There are exactly two triominoes. Draw both of them. (Two triominoes are considered the same if one can be obtained from the other by rotation or reflection).
  2. What kind of symmetry does each of the triominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
  3. Both triominoes tessellate the plane. Show a tessellation for each of the triominoes.

Pentominoes

What if we wanted to playe with larger pieces? Lets think about the pentominoes.

  • A pentomino is a polyomino made from five squares.
  1. There are twelve different pentominoes. Try to find as many of them as you can. (Two pentominoes are considered the same if one can be obtained from the other by rotation or reflection).
  2. Pick five of the pentominoes that you found and for each individual pentomino draw at least one tiling pattern that can be developed with it.
  3. How many different tilings can you create using just the "long pentomino"?
  4. Which of the pentomino shapes can be folded up into a cube? Cut out a copy of a pentomino and try it!


Handin: A sheet with answers to all questions.