Extractions: TEAMS Distance Learning - MATHEMATICS PROGRAMS TEAMS mathematics programs complement classroom curriculum for first through eighth grades. They model effective teaching strategies and are starting points to a rich and rigorous mathematics program. Students explore, investigate and use problem solving skills as they develop mathematical thinking skills related to algebra, number and geometry concepts. Through the TEAMS Distance Learning Home Page , teachers and students can access resources that extend and support the mathematics program. The algebra series provides students with activities that build a foundation for understanding algebraic concepts. Algebra: Staff Development Teaching Algebraic Concepts (Two 60-minute programs) These staff development programs help teachers understand what algebraic thinking is and the importance of teaching algebraic concepts throughout the grades. Strategies for helping students develop algebraic thinking are modeled. Program design, teacher guides, and online opportunities for students, teachers, and parents are explored. (Six 30-minute programs) This module develops an understanding of how naturally occurring situations can be represented algebraically. Through active investigation, students model, represent, and interpret number relationships. They use algebraic symbols to create and solve problems using addition and subtraction. Equations are introduced as a way to generalize patterns and describe number relationships.
Home - Search Geometry geometry. pi geometry. pentominoes geometry. pascals triangle geometry. origami paper folding geometry. geometry. euclidean geometry. analytic http://www.algebraic.net/cgi-bin/988.cgi?q=geometry&show_page=1
The Geometry Junkyard: Polyominoes Pentomino projectof-the-month from the geometry Forum. List the pentominoes; fold them to form a cube; play a pentomino game. See http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html
Extractions: Polyominoes and Other Animals Connected subsets of the square lattice tiling of the plane are called polyominoes . These are often classified by their number of squares, so e.g. a tetromino has four squares and a pentomino has five; this nomenclature is by analogy to the word "domino" (a shape formed by two connected squares, but unrelated in etymology to the roots for "two" or "square"). If a polyomino or a higher-dimensional collection of cubes forms a shape topologically equivalent to a ball, it is called an animal . A famous open problem asks whether any animal in three dimensions can be transformed into a single cube by adding and removing cubes, at each step remaining an animal (it is known that removal alone does not always work). Other related figures include polyiamonds (collections of equilateral triangles), polyabolos (collections of half-squares), and polyhexes (collections of regular hexagons). Anna's pentomino page . Anna Gardberg makes pentominoes out of sculpey and agate. Arranging six squares . This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube. NebulaSearch: Polyomino Blocking polyominos . R. M. Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a "blocked" configuration in which no piece can be slid free of the others, but in which any subconfiguration is not blocked.
PENTOMINOES pentominoes. By Rashmi Bhat Audrey Fletcher. November 20, 1995. pentominoes are said to have been "invented" by Solomon W. Golomb in 1953 at a talk he gave to the Harvard Mathematics Club. geometry that is ingrained in pentomino discovery is an excellent nonthreatening activity with which to provide students. pentominoes 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.
Geometry geometry. Home More About This Category. Main Math. geometry. geometry. Check Latest Price. Formulas; geometric symbols; area and volume; transversals; angles; triangles; equivalent figures; more. Teacher's Key geometry e-math-geome - school supplies teaching geometry, Grades 5 to 6. Check Latest Price. Students will begin their explorations of plane figures with pentominoes as http://www.teachersparadise.com/store/e-math-geome.html
Extractions: Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Activiti ... Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Activiti ... Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Activiti ...
The Geometry Junkyard: All Topics 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. Anna Gardberg makes pentominoes out of sculpey and agate http://www.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 Algebraic surface advent calendar 2002 Algebraic surface models . Oliver Labs makes models of algebraic geometry examples using a 3d printer. Algorithmic mathematical art , Xah Lee.
The Geometry Junkyard: Unfolded Polyhedra Paper models of polyhedra. Pentomino projectof-the-month from the geometry Forum. List the pentominoes; fold them to form a cube; play a pentomino game. http://www.ics.uci.edu/~eppstein/junkyard/unfold.html
Extractions: Unfolded Polyhedra A common way of making models of polyhedra is to unfold the faces into a planar pattern, cut the pattern out of paper, and fold it back up. Is this always possible? Arranging six squares . This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube. Build your own polyhedra , Paul Bourke. Dodecahedron calendar , generated by a postscript program. The 85 foldings of the Latin cross , E. Demaine et al. Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes , Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke, cs.CG/0007019. Find all polytopes . Koichi Hirata's web software for finding all ways of gluing the edges of a polygon so that it can fold into a convex polytope. Flexagons . Folded paper polyiamonds which can be "flexed" to show different sets of faces. See also Harold McIntosh's flexagon papers , including copies of the original 1962 Conrad-Hartline papers, also mirrored on Erik Demaine's website HyperGami program for unfolding polyhedra, also described in
Pentomino Example teams.lacoe.edu/documentation/classrooms/jeannie/geometry/68/activities/pentominos/pentominos.html InterMath Investigations geometry Click to go to 3-D Objects geometry Investigations. Click to go to Number Concepts Investigations. How many pentominoes are possible? http://teams.lacoe.edu/documentation/classrooms/amy/geometry/3-4/activities/pent
Extractions: Pentominoes are the names of shapes created by 5 congruent squares connected together. The object of the puzzle is to place all 12 pentominoes inside the square with 4 boxes of your choice remaining empty. (This puzzle requires a Java-enabled browser.) Read the instructions before clicking "Start." To begin solving the puzzle, click the " begin " button. Choose 4 squares, anywhere on the grid, to remain empty. Click on them, and they will turn black. Drag over the pentominoes, one at a time, and place them on the puzzle board. Rotate and flip the pieces if needed Fill all the remaining squares. If you change your mind, drag the pieces out of the puzzle area. If you can fill all the spaces and use all the pentominoes, you are a Champion Pentominoes Puzzle Solver To rotate a pentomino: PC - Right click and hold your mouse on it. Mac - Click the mouse, while holding down the command key. To reflect - double click.
Internet Geometry Content A+dvanced Learning System®. INTERNET geometry. GRADE LEVELS 912 LESSON TITLE. LESSON CONTENT. 1. pentominoes. Students will study the use of pentominoes in board games. http://www.coloradocourseware.com/manuals/curr/ig.htm
Extractions: GRADE LEVELS 9-12 LESSON TITLE LESSON CONTENT Pentominoes Students will study the use of pentominoes in board games. They will then write an essay about the use of pentominoes in board games. Pentominoes Again After reviewing the use of pentominoes, students will compose a song about pentominoes and their "alphabet" names. Roller Coasters Students will investigate the physics and mathematics used in roller coasters. They will prepare a report discussing the physics of roller coasters. Pendulum Students will explore the patterns of the pendulum. They will write a report about amusement park rides that are based on the pendulum. Geometry Terms Students will learn basic geometric terms. They will identify common examples of points, lines and planes. Postulates Students will study postulates and their applications in geometry. The Pythagorean Theorem Students will investigate practical applications of the Pythagorean Theorem. They will use the theorem to calculate lengths of connecting pipes. Right Triangles Students will study right triangles and their properties. They will then create a right triangle using a paper folding.
InterMath | Investigations | Geometry Us. Sitemap nav. Search the Site. Investigations geometry Polygons Additional Investigations Perplexing pentominoes A pentominoe http://www.intermath-uga.gatech.edu/topics/geometry/polygons/a10.htm
Extractions: Search the Site Investigations Geometry Polygons ... Additional Investigations A pentominoe is a shape that can be made using five different squares, with each square touching an entire side of another square. How many pentominoes are possible? Do all pentominoes have the same area? Do all pentominoes have the same perimeter? Examples of pentominoes are:
Math Tools Browse in Tessellations; Teacher Information Pattern Blocks; Teacher Information pentominoes; Teacher Information Polyominoes; Tessellations geometry and Symmetry; http://mathforum.org/mathtools/cell.html?co=g&tp=10.13
Math Tools Browse Geoboard Circular; Tangrams; Triominoes; Turtle geometry. Support Materials Parallelograms pentominoes. Lesson Plans Paper Folding Activity; Teacher Information http://mathforum.org/mathtools/cell.html?co=m6&tp=8.11
Math Forum - Geometry.pre-college Harold Stanley) 11/02/96. geometry of Eggs ( John A Benson) 10/18/96 Reflection of Tetrominoes and pentominoes ( Don E. Ryoti) 10/14/96. geometry Problem ( John Puskar) 10 http://mathforum.com/~sarah/HTMLthreads/geopre.html
Extractions: [Switch to the Annotated Version] ... Probability Problem: Broken Sticks (Archie Benton) 11/29/96 Software and Hardware Advice (Carol Hattan) 11/07/96 Equation of an Ellipse (Harold Stanley) 11/02/96 Geometry of Eggs (John A Benson) 10/18/96 Lenart Sphere (Dennis Wallace) 10/16/96 Tetris: Reflection of Tetrominoes and Pentominoes (Don E. Ryoti) 10/14/96 Geometry Problem (John Puskar) 10/08/96 Sharing Geometer's Sketchpad Labs (D. Miller) 10/07/96 Proof by Picture? (Tracy L. Rusch) 10/01/96 Geoboards (Don Campbell) 09/29/96 Quadrilaterals Lesson Plan (Don E. Ryoti) 09/25/96 A Construction Problem (Dennis Wallace) 09/24/96 Archive? (Doron M.) 09/23/96 Question about Elliptical Arcs (Dani Macho Ortiz) 09/19/96 Dissecting a Square (Don Campbell) 09/15/96 Practical Math Workshop (Johnny Hamilton) 09/12/96 Vocabulary Question: Curvilinear Polygon (Susan Cronin) 09/09/96 Source of open-ended problems? (Heidi Warrington) 08/29/96 Geometry Courseware (Charles Weaver) 08/11/96 A paradox?
Extractions: Students will begin their explorations of plane figures with pentominoes as they construct rectangles, then measure perimeter and area. They will explore relationships between length, height, and volume as they build rectangular prisms with linkingcubes, then investigate surface area by cutting out nets for them. Geoboards and GeoMirrors will have your students exploring symmetry, turns, flips, slides, and the properties of triangles and quadrilaterals. They will develop spatial sense as theybuild a variety of space figures with cubes, then draw them from different perspectives. These hands-on explorations actively engage students in doing mathematics, which is emphasized by the National Council of Teachers of Mathematics (NCTM). 64 pp
Plane Geometry 1969. Hill, Jane M. (ed.). geometry for Grades K to 6 Readings from the Arithmetic Teacher. Problem Solving with pentominoes, 1992, Learning Resources, Inc. http://mathcentral.uregina.ca/RR/database/RR.09.96/lockhart1.html
Extractions: Topic: Plane The students should: Demonstrate confidence, desire and an ability to solve a variety of mathematically related problems. Demonstrate knowledge and understanding of why, when and how to collect, organize and interpret numerical data: Demonstrate and understanding of numbers, patterns, counting, operations, and estimation: Demonstrate a sense of spatial awareness and familiarity with two dimensional shapes and recognize relationships between geometry and the environment. Note: Some activities may be extended if time is available. Manipulatives could be available for free time exploration. The stations would take a varied number of hours depending on such variables as number of students and their abilities, as well as the number of stations each student is expected to complete. 1. Free Exploring
Redirect | EMINTS Tangram Puzzle (SB or G.). Day 10Geometry Everywhere pentominoes Polyominoes is the general name given to plane shapes made by joining squares together. http://emintsteachers.more.net/mccutchm/mathwebbits/geometry.html
Exploring Geometry polygons. Tessellating pentominoes explores regular and irregular tessellation. 2D Quiz reviews two dimensional geometry. Shape http://smilemathematics.co.uk/explgeom.html
Extractions: These programs can be used flexibly in the classroom, either as lesson starters, main activities, plenary sessions or consolidation. They are particularly suited for use with data projectors and interactive whiteboards. Angle Fit consolidates the angle sum of triangles, quadrilaterals, angles on a straight line and about a point. Square Jigsaw is a challenge in spatial reasoning. Building Pentominoes is a challenge, to find all the pentominoes. Symmetry Match is an introduction to line symmetry. Enlarging Pentominoes explores enlargement. Symmetry Review consolidates line and rotational symmetry. Polygon Names consolidates properties of polygons.