Grade 3 / Geometry (3.9) geometry and spatial reasoning. The student recognizes congruence and symmetry . Students use five square tiles to form pentominoes and record each http://www.tenet.edu/teks/math/clarifying/cateksgrade33.html
Extractions: Clarifying Activity Each student makes a shape on a geoboard. The teacher sorts the shapes into two groups according to a secret geometric attribute, e.g. closed shapes vs. shapes that are not closed, shapes with right angles vs. shapes with no right angles, etc. Students analyze the shapes in each group, use formal geometric vocabulary to write a summarizing statement about each group, share their statements, and discuss them. Clarifying Activity Students classify geometric solids (prisms, cones, cylinders, pyramids, spheres) according to characteristics such as numbers of faces, shapes of faces, numbers of edges, numbers of vertices. Updated 11/14/97
Mathematics TEKS Toolkit 3.9A (geometry and spatial reasoning); 3.15C, D (Underlying processes and mathematical Each group should make one set of all the different pentominoes, http://www.tenet.edu/teks/math/clarifying/clgrd3ominoes.html
Extractions: Development ... support for teks and taks Oh No! My Ominoes! Lesson Overview Students use one-inch square tiles and paper ruled into one-inch squares to solve the problem of finding all the possible ways to arrange five squares into shapes called pentominoes. Mathematics Overview Students use an organized search and identify congruent and non-congruent shapes in order to determine when they have found all of the pentominoes. Grade 3 TEKS Materials Lesson Resources A Collection of Math Lessons from Grades 3-6 by Marilyn Burns Related Resources Set-up (to set the stage and motivate the students to participate) Begin the lesson by telling the students that they will be searching for different shapes that can be made from five squares, using the tiles that have been distributed. Explain that these shapes are called pentominoes.
Info On Pentomino Puzzles Here is a Pentomino Dictionary Making words from the pentominoes, 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
Welcome TEAMS Subscribers! The contents include Defining Polygons, Transformation, Tessellating Shapes,Problem Solving with pentominoes, geometry Number, Properties of Polyhedrons, http://teams.lacoe.edu/subscriber/content/geometry.html
Extractions: MATHEMATICS: GEOMETRY The Geometry series, Shapes in Space , provides lessons for first through middle school grades and gives students rich experiences with both two- and three-dimensional shapes. The content of the programs is correlated to the California Standards and NCTM standards. Students are introduced to properties and attributes of geometric shapes, angle measures, area and perimeter, transformations, and symmetry. Pre and Post Tests are available. Staff Development: Two 60-minute staff development programs These staff development programs help teachers understand geometry and the instructional strategies for effectively teaching geometry concepts. Program design, teacher guides, and online opportunities for students, teachers, and parents are explored. Strategies and resources are presented to help students learn how to use technology as a tool for processing information, visualizing and solving problems, exploring and testing conjectures, accessing data, and verifying solutions. A ssessement tools have been developed to be used in conjunction with TEAMS Mathematics modules.
LearningResources.com Problem Solving with pentominoes Book This 96-page activity book, complete with of combinations, sharpening basic geometry and problem-solving skills. http://www.learningresources.com/Category.pasp?txtCatalog=Toys&txtCategory=Pento
LearningResources.com Learning Resources absolutely loves shapes and geometry and has a great selection of pentominoes geometry, Geoboards, and geometry learning tools. http://www.learningresources.com/activities/ideas/2058ideas.asp
Extractions: The Heart of the Matter - A Valentine Special Roses are red. Violets are blue. I'm sending this poem to say "I love you!" February 14th is Valentine's Day. This is the day that everyone gets a special opportunity to show their love. How do you celebrate? Traditionally, people buy sweet token gifts to show their love. Check out the fill-in-the-word game below for some of the most traditional Valentine's Day gifts, treats, and celebrations.
Elementary Level Mathematics: Grade Five (Strand: Geometry) pentominoes can be used effectively to examine the concepts of A GeometryFair is an exciting, motivational activity to involve many classes (even http://www.sasklearning.gov.sk.ca/docs/elemath/g542note.html
Extractions: Have students share their thinking and the strategies they used as they experiment with various geometrical concepts. Students may still work with squares and triangles through matchstick or toothpick games. Concept attainment can be used to develop many geometrical concepts such as shapes, lines, and congruency. G-22(b)
Extractions: Ask students how they can tell if two shapes are congruent. They may be encouraged to talk about it with a partner before sharing with the entire class. Ask students to create a shapes mural based on a book read to the class or on a class activity. Students could use a theme from another subject area. G-19 Geoboards and elastics offer students the creative transition between the concrete (hexagon attribute block) and the pictorial (picture of a hexagon). Geoboards can be used for developing a wide range of mathematical concepts such as shape, congruency, fractions, symmetry, and measurement. Encourage students to be creative.
Cuisenarie Rods Book - Geometry & Measurement and geometry. The consistent measurement of the pentominoes allows them to fittogether to create a multitude of interesting geometric designs. Ages 7 10 http://www.educationallearninggames.com/cuisenaire-rods-book-geometry-measuremen
GO.HRW.COM Congruence is one of the most important ideas in the building of a geometry system.In this activity, you will investigate shapes formed by pentominoes and http://go.hrw.com/ndNSAPI.nd/gohrw_rls1/pKeywordResults?MG1 Pento
Kit Number Overhead pentominoes. geometry and Spatial Sense. Measurement. K7. Kit 7.Overhead pattern blocks. Patterning and Algebra. geometry and Spatial Sense http://www.trentu.ca/education/schoolofed/edukits/search_all_link.htm
Extractions: DISPLAY ALL Kit Number Name of Teaching Kit Subject Area Strand Grade Level Kit 1 Spectrum Money Pack Number Sense and Numeration Kit 2 Tangrams Geometry and Spatial Sense Measurement Number Sense and Numeration Oral and Visual Communications Visual Arts Kit 3 Transparent Relational Geosolids Geometry and Spatial Sense Measurement Kit 4 Overhead Tangrams Geometry and Spatial Sense Measurement Kit 5 Overhead Colour Tiles Geometry and Spatial Sense Measurement Number Sense and Numeration Patterning and Algebra K-6 Kit 6 Overhead Pentominoes Geometry and Spatial Sense Measurement K-7 Kit 7 Overhead pattern blocks Patterning and Algebra Geometry and Spatial Sense K-7 Kit 8 Spring scales Measurement Kit 9 B is for bully: an innovative approach to increase awareness Drama and Dance Music Oral and Visual Communication Reading Visual Arts Kit 10 Polydron frameworks Geometry and Spatial Sense K-5 Kit 11 Geometry and Spatial Sense Patterning and Algebra Kindergarten Mathematics K-2 Kit 12 Algebra tiles classroom set Patterning and Algebra Kit 13 Overhead algebra tiles Patterning and Algebra Kit 14 Measuring cups Measurement Kit 15 Time teachers manual clock Number Sense and Numeration Kit 16 Pentominoes Geometry and Spatial Sense
Geometry And Spatial Sense Tangram and pentominoes Binder and Pentomino sets. Activity sheets and assessment Excellent for developing Spatial Sense and Transformational geometry. http://www.renfrew.edu.on.ca/curriculum/geometry.htm
Extractions: Geometry and Spatial Sense Expectations covered: build three-dimensional figures and objects from nets; create and analyze designs that include translated, rotated, and reflected two-dimensional images using concrete materials and drawings, and using appropriate computer applications; construct and analyze tiling patterns with congruent tiles; sketch and build representations of three-dimensional figures Triple A Geometry Binder Includes standards, activities, and assessment / review and teacher notes. The activity book is a good way of building the scaffolds for the rest of the unit. Tangram and Pentominoes Binder and Pentomino sets. Activity sheets and assessment strategies with answers and self-evaluation sheets. Excellent for developing Spatial Sense and Transformational Geometry. Includes 18 sets of pentominoes in 3 buckets Extra Tangrams sets can be made out of paper/card (See page 4 of binder) Mira Activity Book Miras not included) Symmetry, polygons, motion geometry Polygons Pack: Properties of polygons.
Worksheets For Informal Geometry Worksheets for Informal geometry. Our worksheets can be obtained in A moregeneralized worksheet exploring triominoes, tetrominoes and pentominoes. http://euler.slu.edu/courseware/inf.geom/geometrymaster.html
Extractions: Teaching Resources Our worksheets can be obtained in Postscript (PS) or Portable Document File (PDF). One of the best introductions to GSP I know of is the one by Mike Riedy. All the labs below are just sligthly altered versions of his. You should take a look at the original an Intro to Geometer's Sketchpad PS PDF ) (A version I use in a Math. Ed. course) Another Intro to GSP PS PDF ) (This version was used in a fresmen seminar) Creating Tessellations using translations, rotations and reflections ( PS PDF An introduction to tessellations PS PDF More on tesselations PS PDF Tessellation Techniques for some special cases. ( PS PDF ) Using the "Totally Tessellated" website explore some methods for creating tessellations. Pentominos PS PDF Polynominos PS PDF ) A more generalized worksheet exploring triominoes, tetrominoes and pentominoes. Tetrominoes en Polynominoes PS PDF ) Explore tetrominoes and polynominoes. Create tessellations using some of these shapes Regular and semi-regular tessellations PDF ) Explore regular tessellations (there are 3) and semi-regular tessellations (there are 8). (Refers to pages in O'Daffer and Clemens.)
The Geometry Junkyard: All Topics This page collects in one place all the entries in the geometry junkyard. Anna Gardberg makes pentominoes out of sculpey and agate. Antipodes. http://www.math.ntnu.edu.tw/~jcchuan/all.html
Extractions: All Topics This page collects in one place all the entries in the geometry junkyard. 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. Almost research-related maths pictures . A. Kepert approximates superellipsoids by polyhedra. Angle trisection , from the geometry forum archives. Anna's pentomino page . Anna Gardberg makes pentominoes out of sculpey and agate. Antipodes . Jim Propp asks whether the two farthest apart points, as measured by surface distance, on a symmetric convex body must be opposite each other on the body. Apparently this is open even for rectangular boxes. Antiprism (Archimedean) . Some self-explanatory pictures from Eric Weisstein's treasure trove of mathematics. Aperiodic space-filling tiles: John Conway describes a way of glueing two prisms together to form a shape that tiles space only aperiodically. Ludwig Danzer speaks at NYU on various aperiodic 3d tilings including Conway's biprism.
Lowell School - Writing Book Talks Math geometry, Playing with pentominoes, Word, In this activity, students partnerto create a set of twelve pentominoes and then challenge each other to a http://wwwlow.bham.wednet.edu/schoolkit.htm
Extractions: Kid Pics Power Point Given a set of ten pictures that show one kid, two kids, three kids, and so on up to ten kids, the students will count the number of kids in each photograph then arrange them from one to ten. They will write a sentence about each picture. Teacher Tip: As an extention, take digital pics of kids to order. Students should know how to: Word In this activity, students will use their senses to identify characteristics of the country and the city and consider how those characteristics relate to the people who live in those communities. Students will write stories from the point of view of a first time visitor to the community. Teacher Tip: Good to use as whole class activity w/ projection device in K or 1st. The first part of the activity is good. The second part is not necessary. Writing involved.
Schoolzone Evaluation Of MicroSMILE Exploring Geometry Classic teaching activities such as those involving pentominoes and tessellationscan geometry, angles, quadrilaterals, triangles, pentominoes, polygon, http://www.schoolzone.co.uk/resources/evaluations/printcon.asp?p=SMIL-EXPLORINGG
Geometry Math.com geometry. Matho Flash Cards pentominoes Perimeter of Polygons Spirograph - Circles and radii. Tesselate - Create your own tesselations http://edweb.tusd.k12.az.us/ekowalcz/math/geometry.htm
Extractions: All of the sites listed on this page are interactive, unless otherwise noted. Sites that have an * next to their name are excellent sites, however, they have ad banners on the page. A All About Geometry Area of Parallelograms Area of Squares and Rectangles Area of Trapezoids ... Geometry Center Learn about shapes, patterns and symmetry Interactive Geometry Interactive Geometry - Explore the properties of regular and irregular shapes Interactive Mathematics Miscellany and Puzzles Measuring Angles Pythogaras' Haven - Interactive proof of Pythogoras' Theorem Math.com - Geometry Matho Flash Cards Pentominoes Perimeter of Polygons Spirograph - Circles and radii Tesselate - Create your own tesselations The Geometry Applet Vectors Return to Home Page
The Golden Geometry Of Solids Or Phi In 3 Dimensions Having looked at the flat geometry (two dimensional) of the number Phi, A puzzle I came across when I was 12 is a box of the 12 pentominoes, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi3DGeom.html
Extractions: Some other relationships between these shapes... More The five regular solids (where "regular" means all sides are equal and all angles are the same and all the faces are identical) are called the five Platonic solids after the Greek philosopher and mathematician, Plato. Euclid also wrote about them. For more information on these two famous Greeks, see the
