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Five Times The Fun

Five Times The Fun. A power point presentation on Polyominoes and Pentominoes. Polyominoes. Made with adjacent squares that share a common edge. 1 square = Monomino, 2 = Domino, 3 = Triomino, 4 = Tetromino, 5 = Pentomino, … Mainly used for recreational purposes.

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Five Times The Fun

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  1. Five Times The Fun A power point presentation on Polyominoes and Pentominoes

  2. Polyominoes • Made with adjacent squares that share a common edge. • 1 square = Monomino, 2 = Domino, 3 = Triomino, 4 = Tetromino, 5 = Pentomino, … • Mainly used for recreational purposes. • We will focus on Pentominoes

  3. PENTOMINO MANIA • Pentominoes are made of 5 squares, each sharing at least 1 common edge with another square. • Each arrangement of squares is labled with the letter it looks like. • They became famous in the 1950’s and have kept mathematicians busy as they continually find new things they can do.

  4. Fun With Pentominoes • There are many challenging puzzles that can be done with pentominoes. • There are over 2,339 ways to arrange the petominoes in a 6x10 grid. • This is one way 

  5. What is so special about these squares? • 60 squares in a set of Pentominoes. • The set has the ability to completely cover a square with out any overlap or holes. • If there is a cube with that has an edge of 10 units, Pentominoes can cover it completely with only one of each piece. • If we “bend” the pieces, it is even possible to fit all 12 pieces onto a sphere with out any overlap. • If you are looking for formulas on polyominoes and pentominoes, then this is the site to check out!

  6. Pentominoes make the Cube!

  7. Applications??? • Pentominoes are not all fun and games. • Art and Design are a major area where polyominoes and pentaminoes are used. • When laying tile on a floor or wall, different patterns of polyominoes are also used.

  8. Why are they important? • Pentominoes should be taught in school for a couple of very important reasons. • Pentominoes are fairly new, only being discovered in 1953, but they are a fun way to get students to think spatially and develop the ability to do mental flips and rotations in their heads. • They also show kids that just because you have a different answer, it is not necessarily wrong. • Teaching pentominoes can easily tie into other areas of math like perimeter, area, symmetry, and tessalations.

  9. What Next? • As of now, most of what Pentominoes are is simply puzzles. • However, these puzzles can come to reveal patterns that apply to more than just these suqares. • Research on Pentominoes and Polyominoes is ongoing. • Mathematicians and scientists are exploring more ways that these unique sets of squares affect our lives.

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