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Pentominoes Geometry:     more detail
1. Pentominoes by Carson-Dellosa Publishing, 1999-01-26
2. Pentominos/ Pentaminoes: Acertijos de formas para hacerte pensar/ Puzzle Pieces to Make You Think (Jugando Aprendo/ Learning Through Play) (Spanish Edition) by Jon Millington, 2007-02-28
3. Math discoveries with pentominoes by Ann Roper, 1995

lists with details

1. Monroe County School District
230 300 Adventures in Art. 200 - 245 TEAMS geometry In My World Program4 Problem Solving with pentominoes 245 - 300 Introduction to Sculpture.
http://www.monroe.k12.fl.us/itv/feb10.htm

2. ENC: Curriculum Resources: Problem Solving With Pentominoes (ENC-016461, Full Re
Congruence and similarity Teacher's notes Congruent shapes Making congruent shapesSimilar shapes Doubling pentominoes Tripling pentominoes Share at geometry.
http://www.enc.org/resources/records/full/0,1240,016461,00.shtm

Extractions: Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. ENC#: ENC-016461

3. ENC: Curriculum Resources: Problem Solving With Pentominoes (ENC-016461, Brief R
In the activities, students cover shapes with different numbers of pentominoes andconsider turning and flipping pieces to cover other given shapes. geometry.
http://www.enc.org/resources/records/0,1240,016461,00.shtm

Extractions: Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. ENC#: ENC-016461 Terms governing use and reproduction: Each blackline master is intended for reproduction in quantities sufficient for classroom use. Permission is granted to the purchaser to produce each blackline master in quantities suitable for noncommercial classroom use. All information in this catalog record was verified and accurate when it was first made available to the public. ENC updates catalog records when resources are featured in special projects or when we learn that the information in the record is out of date.

4. Solution For /geometry/pentomino
Solution to the /geometry/pentomino problem. I've seen several differentnaming schemes used for pentominoes. This is the system
http://rec-puzzles.org/sol.pl/geometry/pentomino

Extractions: FF I L N PP TTT U U V V W W W X X Y ZZ FF I L NN PP T UUU V V W W X YY Z F I L N P T V X X Y ZZ I LL N Y A 3x20 solution (the other solution is easily obtained by a rotation of the section from the Z to the L inclusive): UUXPPPZYYYYWTFNNNVVV UXXXPPZZZYWWTFFFNNLV UUXIIIIIZWWTTTFLLLLV A 4x15 solution: IIIIINNLLLLTVVV UUXNNNFZZWLTTTV UXXXYFFFZWWTPPV UUXYYYYFZZWWPPP NFVVV YYYYI NFFFV LLYZI NNFXV LZZZI PNXXX LZWTI PPUXU LWWTI PPUUU WWTTT The 2x3x10 and 3x4x5 solutions are tricky to show - I hope these diagrams make sense: A 2x3x10 solution (shown as 2 layers; Y and L are shared between the 2 layers): VVVZIIIIIF UUXTTTWWPP VZZZNNNFFF UXXXTWWPPP VZYYYYNNFL UUXYTWLLLL

5. PENTOMINOES
The informal geometry that is ingrained in pentomino discovery is an excellent nonthreateningactivity with which to provide students. pentominoes can also be
http://www.andrews.edu/~calkins/math/pentos.htm

Extractions: November 20, 1995 Shapes that use five square blocks joined together with at least one common side are called pentominoes. There are twelve shapes in the set of unique pentominoes, named T, U, V, W, X, Y, Z, F, I, L, P, and N respectively. As a mnemonic device, one only has to remember the end of the alphabet (TUVWXYZ) and the word FILiPiNo. In order to make a set of unique pentominoes, there are only two rules which must be followed. First, if one shape can be rotated to look like another, the two shapes are not considered to be different. Second, if one shape can be flipped to look like another, the two shapes are not considered to be different. Since there are twelve distinct pentomino shapes with each covering five squares, their total area is sixty squares. There are several ways to place all twelve different pentominoes on an 8 x 8 board, with four squares always left over. By artistically specifying the positions of the four extra squares, many interesting patterns can be created. Another evident possibility is to require that the four extra squares form a 2 x 2 area (a square tetromino) in a specified position on the board. This placement leads to a remarkable theorem, which can be proved by using only three constructions: Wherever on the checkerboard a square tetromino is placed, the rest of the board can be covered with the twelve pentominoes. Another problem is to determine the least number of pentominoes which will span the checkerboard. In other words, some of the pentominoes are placed on the board in such a way that none of the rest can be added. Although there are several different configurations for solving this puzzle, the minimum number is five pentominoes. Other patterns include forming the configurations of 6 x 10, 5 x 12, 4 x 15, and 3 x 20 rectangles using all twelve pentominoes. The 3 x 20 is the most difficult to derive, and there is only one unique solution, except for the possibility of rotating the shaded central portion by 180 degrees.

6. H&H - GEOMETRY- MATH
Math Discoveries about geometry Handson workbooks investigate angles, areas, perimeter tiles)Gr.5 - 6 (geomirror, 10x10 geoboards, pentominoes, linking cubes
http://www.home-hearth.com/mathgeom.htm

Extractions: Ideal for students experiencing difficulty in key math requirements - presents skills and concepts in short, carefully sequenced and very focused lessons, assuming little background knowledge. Would also be good for unschoolers that need to catch up on high school requirements. Designed for independent study so includes answers for every other question plus all the review questions. The teacher guide is thus optional, giving all the answers, plus extra tests and practice, extra activities, and ideas for teaching the concepts.

3D Drawing and geometry http//forum.swarthmore.edu/workshops/sum98/participants/sanders JavaPuzzles pentominoes http//enchantedmind.com/newjava.htm Pent.

Extractions: (Courtesy Dr. R Freese) Contents: Experiment with Volume (simle worksheet, estimating volume) http://math.rice.edu/~lanius/Geom/cyls.html Volume Functions: (Worksheet)Calculating volumes http://math.rice.edu/~lanius/Geom/cyls2.html Geoboard Area : a worksheet exploring area. (Based on the geoboard) Designs with Circles: construction of circles (rotation and reflection symmetry) http://forum.swarthmore.edu/alejandre/circles.html Percentage Circle http://forum.swarthmore.edu/~sarah/shapiro/gsp.percent.circle.gif Nets of crystals: paper construction of crystals, polyhedrahttp://forum.swarthmore.edu/alejandre/workshops/crystalnet.html Systems of Crystals (type of crystals, and physical examples) http://forum.swarthmore.edu/alejandre/workshops/chart.html Real World - Viewing Crystals (applications of Tesselations in the real world) http://forum.swarthmore.edu/alejandre/workshops/crystal.html Isometric Drawing http://forum.swarthmore.edu/workshops/sum98/participants/sanders/Isom.html

8. 20,000 Problems Under The Sea
geometry Recreational Mathematics arrays polygonal arrays Solid geometry polyhedra pentahedra Solid geometry pentominoes Recreational Mathematics
http://problems.math.umr.edu/keywords/p/pe.html

Extractions: Home Search Tips Power Search Subject Index ... House of Math Keywords beginning with: pe Keywords are listed alphabetically. Following each keyword is a list of all classifications containing that keyword. To perform a search, select one or more checkboxes then click the "Find Problems" button. Select the maximum number of problems to be displayed per screen: peculiar years pedal curves pedal lines pedal points pedal triangles

9. 20,000 Problems Under The Sea
solid geometry cones Probability solid geometry spheres Recreational Mathematics polyominoes pentominoes Solid geometry cylinders Solid geometry
http://problems.math.umr.edu/keywords/h/ho.html

Extractions: Home Search Tips Power Search Subject Index ... House of Math Keywords beginning with: ho Keywords are listed alphabetically. Following each keyword is a list of all classifications containing that keyword. To perform a search, select one or more checkboxes then click the "Find Problems" button. Select the maximum number of problems to be displayed per screen: hockey hodographs hogs holes

10. Problem Solving With Pentominoes
After creating the 12 pentominoes letters, students use their letters Math TEKS Problemsolving; translations; reflections; rotations; geometry (Spatial Sense
http://www.tcet.unt.edu/START/instruct/lp0005.htm

Extractions: Problem Solving with Pentominoes Overview: Students create the 12 different pentomino shapes (letters) on the computer using the Logo programming language. Students build each letter based on a 30 by 30 square. Students use super procedures to create each letter. After creating the 12 pentominoes letters, students use their letters to create new "flip" letters. Students then combine letters to create five different puzzles: two different rectangles, two different sets of stairs, and a hat shape. Grade level Time frame Subject Areas TEKS 10 days of 5 minute warm ups, then 5 days in the lab Mathematics Technology Applications Use of foundation and enrichment curricula in the creation of products; Use of GroupWare, collaborative software, and productivity tools to create products; Resolve information conflicts and validate information through research and comparison of data.

11. The Geometry Junkyard: All Topics
Interlocking Puzzles LLC are makers of hand crafted hardwood puzzlesincluding burrs, pentominoes, and polyhedra. Inversive geometry.
http://www1.ics.uci.edu/~eppstein/junkyard/all.html

Extractions: All Topics This page collects in one place all the entries in the geometry junkyard. Jan Abas' Islamic Patterns Page Acme Klein Bottle . A topologist's delight, handcrafted in glass. Acute square triangulation . Can one partition the square into triangles with all angles acute? How many triangles are needed, and what is the best angle bound possible? Adventitious geometry . Quadrilaterals in which the sides and diagonals form more rational angles with each other than one might expect. Dave Rusin's known math pages include another article on the same problem. Adventures among the toroids . Reference to a book on polyhedral tori by B. M. Stewart. The Aesthetics of Symmetry , essay and design tips by Jeff Chapman. 1st and 2nd Ajima-Malfatti points . How to pack three circles in a triangle so they each touch the other two and two triangle sides. This problem has a curious history, described in Wells' Penguin Dictionary of Curious and Interesting Geometry : Malfatti's original (1803) question was to carve three columns out of a prism-shaped block of marble with as little wasted stone as possible, but it wasn't until 1967 that it was shown that these three mutually tangent circles are never the right answer. See also this Cabri geometry page and the MathWorld Malfatti circles page The Albion College Menger Sponge Algorithms for coloring quadtrees Are all triangles isosceles?

12. Combinatorial Geometry Puzzles
Soma Cubes and pentominoes are examples of tiling problems. These areall the subject of combinatorial geometry. Some Technicalities.
http://www.massey.ac.nz/~bimills/comb/

Extractions: Most recent noted update on Friday 21st June 2002. Combinatorial geometry deals with the manner in which a typically finite collection of geometric shapes can be arranged. A large variety of problems come under a small number of headings. Packing Problems: Given a collection of pieces can we fit them into a region without any overlap? This is the sort of problem that you attempt to solve when you pack to go on a holiday. Questions such as ... how many oranges can you pack in a crate (formalized as how many sphere can you pack into a rectangular prism) are by and large still open questions in mathematics. The efficiency of the packing is the percentage of space that has been filled by the pieces. Covering Problems: A class of problems that are more intuitive in two dimensions, but nonetheless apply to multidimensional space. Given a collection of cloths can we cover a table completely so that nothing is showing. The efficiency of a covering is measured by the total amount of overlap of the cloths. Tiling Problems: Suppose that we can pack a set of shapes into a given area in such a way that NO space is left over. Then the packing is also a covering. These dual situations are called tiling problems.

13. Science And Math - Geometry
collective body of Russian geometers that rejected the methods of differential geometry.Logical Art and the Art of Logic learn about pentominoes and what
http://www.information-entertainment.com/ScienceMath/Geometry.html

Extractions: Please show your support for this site and visit the sponsors Science And Math - Geometry Geometry is more than about measuring angles and circles or anything to do with shapes. Although that is a big part of this subject, there is a key to how they relate to real life use. The key is logic. You might think that you only need this logic when building things, but you can use this skill of deductive reasoning in everyday life. Geometry has a basic set of postulates and theories. You must have them memorized and understand those principles before you can move too far into this subject. Once you get a grip on them, you must be able to reason how you get from point A to point Z using those principles. This is where your skills of logic come in. It is not merely a matter to accept the final result, but to understand the process of coming from the beginning to the end. Engineers and scientists will need Geometry in their professional fields. All students who plan to enter college need this skill to graduate. For them, it is mandatory to learn this subject. For everyone else, the ability to think in a logical manner will save you from making a lot of wrong choices. Geometry will help you get there.

14. TE 490: Applications Of Geometry To The K-8 Classroom
Michigan Framework Standards and Benchmarks, geometry overview. 4. September 24. 10.November 5. Congruence, pentominoes, Tangrams, Project DUE, Presentations. 11.
http://www.svsu.edu/mathsci-center/te490geometry.htm

Extractions: TE 490: Applications of Geometry to the K-8 Classroom Fall 2001 Class meets Mondays from 7:00 - 8:50 p.m. Instructors: Mike Dobrinski and Karen Wuerfel Office: (College of Education Bldg ) Office Hours : Mondays from 4:30 - 5:00 p.m. Telephone office (989) 964-4114 Mike Dobrinski (989) 893-8159 Karen Wuerfel (989) 799-8286 Course Prerequisites Students must have successfully completed MATH 104: Geometry or have instructor permission. Course Description This course is designed to explore the teaching of K-8 mathematics in a manner consistent with the Principals and Standards of School Mathematics published by the National Council of Teachers of Mathematics (2000) and the Michigan Curriculum Framework standards and benchmarks for mathematics. The focus is on methods and materials that are most effective in teaching geometry to elementary and middle school students and this course is taught as an extension of MATH 104: Geometry. Teacher as Decision Maker Model The following model of the teacher as decision maker has been adopted by the Department of Teacher Education at SVSU and provides a foundation upon which the activities and ideas in this course are based.

15. Pentomino Puzzle Game Lets You Create Geometric Puzzles.
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, download Category Science Math Recreations Polyominoes Arranging pentominoes in various shapes and designs teaches geometry students aboutthe basic geometric transformations slides, rotations, and reflections.
http://www.virtu-software.com/products/PentoMania.asp

16. Ma3 Shape, Space And Measures
geometry a large collection of lesson ideas to help KS2 children analyze Logical ArtLearn about pentominoes and the patterns they create and what pentominoes
http://www.schoolzone.co.uk/teachers/szresources/curriculumguides/primaryMa3.htm

17. Geometry
and geometry (Tasks graded from easiest to hardest) The Cat on the Mat PerfectMatch. Matching Matches. The Sphinx Squares Squares. Hex a Hexagon. pentominoes.
http://www.dlk.com.au/beingmathematical/geometry.htm

Extractions: The Cat on the Mat The Sphinx Squares Squares Hex a Hexagon Pentominoes Other Ominoes Shapely Borders Fitting Bits Vanishing Line Five Hats and a Dome Geo Gems Midgets, Mutts, Guys and Geese Triangles Triangles Make More Squares Patterns in the Pie Patterns in the Pie - Beware Pentagonal Man Optical Illusions Optical Illusions - the Challenge Set Triangles One The Four Colour Map Problem An Odd Thing About Vertices Tiling Without Flaws Reptiles Repetition Tiles Points, Lines and Spaces Between The Mobius Strip Horrible Triangles Derived Polygons Apollonius' Problem The Cantor Set The Golden Rectangle The Golden Ratio Fibonacci and the Golden Ratio The Golden Ratio and Architecture The Golden Ratio and Art Proof: All Triangles are Isosceles The Koch Curve Basic Trigonometry and the Unit Circle Iterating sin, cos and tan

18. Web Citations - Dissections: Plane & Fancy
pentominoes Click on pentominoes and select Dissections . Andrew Crompton'sgrotesque geometry. Magic 4 U's tricks. Godfried Toussaint's Links to the World
http://www.cs.purdue.edu/homes/gnf/book/webref.html

19. Pentom.htm
geometry 34. Math Smart 2, geometry, Grades 3,4. These are pentominoes (the whiteones). The red one is not! Each of these figures have five connected squares.
http://www.orondo.wednet.edu/mathsmart2/Orondo/pentom.htm

Extractions: Geometry 3-4 Math Smart 2, Geometry, Grades 3,4 1. How many times must you fold a square in half to get five squares? Explain your answer. (OCTME, Oct. #16) 2. Here is a riddle for you to chew on: I am a geometric figure A solid answer you can claim. I have a different face For each letter in my name. Who am I? (OCTME, Oct. #21 ) 3. How many triangles can you find in this drawing? Can you find any other geometric figures? Name at least two. Explain your reasoning. (OCTME, Oct. #34 ) DRAWING OF EQUILATERAL TRIANGLE, WITH EACH SIDE DIVIDED INTO FOUR EQUAL SEGMENTS, AND THOSE CONNECTED, TO FORM 16 SMALL TRIANGLES. 4. Name common items that match these three shapes exactly. Label them. DRAWINGS OF RECTANGLES THAT HAVE DIMENSIONS WITH RATIO OF 2:1, AND 5:1, AND CIRCLE. (OCTME, P. 34, #18, Dec. # 18) 5. In a square made up of 25 smaller squares, shade five of the 25 squares. No shaded square can be on the same vertical, horizontal or diagonal line as another square. OCTME, p. 41, #11, Jan. # 11) 6. From a picture of a snowflake: a. How many lines of symmetry are there in the snowflake?

20. Turning Manipulatives And Turtle Geometry Inside Out
be used including pattern blocks, Cuisenaire Rods, Infix Cubes, tangrams and pentominoes. students)use their bodies, common sense and turtle geometry to solve
http://www.stager.org/articles/manipulatives.html

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