Info On Pentomino Puzzles A paper on pentominoes. A really nifty 8 by 8 java Pentomino Solver. David Eppstein s geometry Junkyard entry on polyominoes and other Animals. http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html
Extractions: A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges. Up to isomorphism (rotating and flipping), there are 12 possible shapes, which are illustrated below. Each piece is labelled by the letter that most accurately reflects its shape. V T W X U Z F P I N Y L The problem is to fit the 12 pentomino pieces into various shapes, often rectangles. The rectangle shapes that fit all 60 squares are of sizes 3x20, 4x15, 5x12, and 6x10. Here's a solution to the 6 by 10 puzzle using the letter encoding. NFVVVYYYYI NFFFVLLYZI NNFXVLZZZI PNXXXLZWTI PPUXULWWTI PPUUUWWTTT Much better looking is the same solution using tables and gifs. The algorithm used by COS is a clever backtracking algorithm, as described in the upcoming book "Combinatorial Generation." Here is a page of more solutions to various pentomino puzzles. The may get stale with time. Please send us any updated addresses or new ones that should be included. The T.I.D. Ronse School Pentominos Page
Geometry geometry. Activity 1 Pentominos. Learning Objectives related to Curriculum Plane back. geometry. Activity 2 Newt Tessellations. Learning http://mathcentral.uregina.ca/RR/database/RR.09.99/sawatzky1/teachnotes-geo.html
Extractions: Geometry Activity 1: Pentominos Learning Objectives related to Curriculum: Plane, spatial awareness: Construction of two dimensional objects using pentominos G-16, G-25 Number of Students: 1 or 2 Resources/Materials: Pentomino Grid Pentomino Figure Patterns Pentominos - make your own from the patterns provided or purchase 3D pentominos. Source Acknowledgment: Adapted from Cornelius M. and Parr, M. What's Your Game? Activity Description: Players alternately place a chosen pentomino on the grid (one dimension only). Play continues until one player is unable to make a move. Alternate Ideas: a) place pieces on the board to build desired shapes b) design three dimensional shapes with pentomino pieces (if 3D pentominos are available) Have students build the figures shown on the pages provided. HINTS: a) The first figure is actual size - place pieces directly on the page. b) To build the figures on the pages with grids, use the shapes as indicated on the top of each section. CELS: Numeracy, Communication Social Skills ( working together to build shapes) Critical and Creative Thinking (decision making) Adaptation/Variation/Extension: -to make it easier, shapes using fewer pieces could be designed
Resources MathsNet sketches interactive geometry activities made with Interactive geometry - Ambleside Primary School. Dynamic geometry Problems - NRICH. http://www.teachers.ash.org.au/mikemath/resources/space.html
Extractions: Get a clear and complete understanding of shapes, their patterns and properties. You will be able to change the pictures yourself using the mouse and see the effect these changes have. MathsNet sketches - interactive geometry activities made with Interactive Geometry - Ambleside Primary School Dynamic Geometry Problems - NRICH ... Absorb Mathematics Online Textbook
Extractions: Home Updates/Resources/Opportunities LMMS Articles ... Mathematical Communication Many resouces are applicable to a variety of standards. If you see a resource that would be of value in anther category, in addition to the one of which it is listed, please email karsenaultlmm@middlemaine.org. Resources for Multiple Standards iTeach Math - Used by Pam Buffington at the MLTI math content meetings, this site is a great resource for supporting teachers and students in meeting the Maine Learning Results. Many interactive links and lesson plans. K-12 Project Interactive - With a goal that has a focus on "....the creation, collection, evaluation and dissemination of interactive java-based courseware for exploration in science and mathematics," you know this resource must be rich with tools to assist students in their understanding and application of mathematics. The "How", "What", and "Why" at the top of each activity is invaluable to both student and teacher. K-12 Interactive Resources for All Subject Areas http://www.globalclassroom.org/ecell00/javamath.html