41. Math Online - Materials & Technology pentominoes, measurement area, perimeter geometry transformations, tesselations,symmetry, 1 set per 2 students. playing cards, general, 1 per student http://jeffcoweb.jeffco.k12.co.us/isu/math/mathsd/materials/uses.htm

Manipulatives Diagram Electronic Technology Types of Manipulatives Types of Manipulatives Pre-K - 2 Grades 3-5 Grades 6-8 Printable Documents Pre-K-2 Grades 3-5 Grades 6-8 Microsoft Word Format Microsoft Word Format Microsoft Word Format PDF Format ... PDF Format Pre-K - 2 Bold represents basic manipulatives for each classroom in these grades. Manipulative Standard: Concept Classroom Quantities attribute shapes algebra: sorting, classifying, attribute 1 set per 2 students balance (non-calibrated) measurement 1 per 2 students base ten blocks number sense: place value 10-15 sets 1 set includes 100 ones, 10 tens, and 10 hundreds, 1 thousand (cube) calculators (T1-108) number sense: place value algebra: number patterns computation: combining and separating 1 per student circular counters general 50 counters per student clocks number sense measurement 1 per student color cubes general 50 per student Cuisinaire Rods number sense: fractions, whole number computation 1 set per 2 students dice (number cubes) data analysis: probability number sense: part/part/whole computation: all operations 1 per student Dominoes number sense: part/part/whole computation: addition and subtraction 1 set per 3 students fraction strips/circles (2nd grade) number sense 1 set per student geoboards/geobands number sense: fractions geometry: polygons measurement: area, perimeter

42. Mathematics Interactive geometry problems and puzzles. pentominoes Jigsaw puzzle involvingtwelve rectilinear pieces. These pieces constitute all the ways in which five http://www.primaryschool.com.au/mathematics-lessonsresults.php?strand=Space and

43. Activity 7 There are twelve pentominoes. Use cutout squares or cubes to make all twelve ofthe different pentominoes and sketch the shapes on the grid paper below. http://homepage.mac.com/efithian/Geometry/Activity-07.html

Activity 7 Polyominoes and Polyiamonds Polyominoes and polyiamonds are connected arrangements of squares and triangles, respectively. They can be used to explore both reflectional and rotational symmetry, they can be arranged to form other shapes, and they can be extended into three-dimensional shapes to form solid objects. Polyominoes A polyomino is a connected arrangement of squares that satisfies the following conditions: If two squares touch, they must have a side in common, or both must share a side with another square. All squares must be in the same plane. Two polyominoes are the same if one can be flipped, turned, or moved so as to coincide with the other. Dominoes There is only one domino. Trominoes There are two trominoes. Tetrominoes There are five tetrominoes. Use cut-out squares or cubes to make all five of the different tetrominoes and sketch the shapes on the grid paper below. Label the shapes a, b, c, d, e and find the number of lines of reflectional symmetry and the order of rotational symmetry for each tetromino. Shape Reflectional Rotational a b c d e Pentominoes There are twelve pentominoes. Use cut-out squares or cubes to make all twelve of the different pentominoes and sketch the shapes on the grid paper below. Label the shapes with a letter that looks like the shape and find the number of lines of reflectional symmetry and the order of rotational symmetry for each pentomino.

44. EDCI5234 Internet Lesson Plans: Geometry And Measurement I chose an activity on symmetry, the beginnings of geometry. The object isto put together as many different pentominoes as possible. http://www.math.vt.edu/people/lloyd/class_home/old/5234geometryplans.html

Activities We Like ... Related to GEOMETRY Amanda Bailey abailey@vt.edu I chose an activity on symmetry Amy Bishop abishop@vt.edu The lesson plan I chose, , is a math activity on tangrams Angie R. Thomasson angie.thomasson@vt.edu I chose a measurement lesson plan called Integrating Math into a Spring Thematic Unit . This lesson plan not only includes measurement, it provides practice using addition, subtraction, > is more important to the concept of measurement than the addition is. I think these parts were just added to take up more time. Although, maybe I'm wrong. Jason Brennan jabrenna@vt.edu Jeff Meehan jmeehan@vt.edu I chose a lesson plan which deals with measurement of volume . I thought it was pretty interesting, and it sounds like it could be fun. The lesson plan actually doesn't have much of a procedure to follow, it is left up to the children to decide what to do. The teacher merely divides the children into groups, gives them the materials (scissors and tape and paper), and tells them to make a square centimeter, inch and meter and then a cubic centimeter, inch and meter. The lack of a exact procedure allows for problem solving and cooperation between the children. When the students are done building the boxes, they elect one member of the group to explain what they had done. I liked this lesson plan because it involves teamwork and allows room for creativity. It is actually quite a simple lesson plan, but is adequate nonetheless. Jennifer Sykes jsykes@vt.edu

45. Exploring Geometry V1.0 : Mathematics : Shape, Space And Measure R-E-M The Educa Exploring geometry V1.0. The disk contains fifteen short programs introducing and Building pentominoes • Enlarging pentominoes • Polygon Names http://www.r-e-m.co.uk/cgi-bin/xrem/S_12/U_20/M_1/T_26170/G_8/SN_

Early Learning Primary Secondary FE/Adult Learning ... Contact Us if( "20" == 5) document.write(' '); else document.write(''); if( "20" == 5) document.write(''); else document.write(''); General if( "20" == 25) document.write(' '); else document.write(''); if( "20" == 25) document.write(''); else document.write(''); Algebra if( "20" == 22) document.write(' '); else document.write(''); if( "20" == 22) document.write(''); else document.write(''); Handling Data if( "20" == 15) document.write(' '); else document.write(''); if( "20" == 15) document.write(''); else document.write(''); Number if( "20" == 35) document.write(' '); else document.write(''); if( "20" == 35) document.write(''); else document.write(''); Revision Aids if( "20" == 20) document.write(' '); else document.write(''); if( "20" == 20) document.write(''); else document.write(''); Shape, Space and Measure

46. Boreal Laboratories - Geometry geometry leading provider of educational materials for K-12 schools. Our productsencompass all pentominoes, 6 Rainbow Colors, Set/72 1703505 $17.95 http://boreal.com/category.asp?start=36&c=563865

47. National Curriculum Network Conference | CFGE to develop spatial reasoning in two and three dimensions, including Soma cubes,pentominoes, fractals, projective geometry, and spatial puzzles. http://cfge.wm.edu/ncn.php

• CFGE home • Graduate Programs Graduate Programs Master's Program ... • Site Index QuickSearch Find People Navigate the WM Web Contact the College Prospective Students Parents Current Students Campus Visitors Academics   Undergraduate   Graduate Administration Admission Athletics Campus Construction Campus Life Economic Development Events/Calendars Financial Aid Human Resources Libraries Office of the President Public Service Research Restructuring Technology myWM National Curriculum Network Conference National Curriculum Network Conference NCNC 2006 dates March 6-8 About NCNC NCNC 2006 Forms coming in October (thes e require Acrobat Reader available for free from www.adobe.com NCNC 2006 Brochure coming in October NCNC 2006 Registration Form coming in October Preconference Descriptions coming in October Keynote Speakers for last year (for information on any of the speakers, click here Tuesday, March 8th Richard Paul , Foundation for Critical Thinking Rena Subotnik, American Psychological Association Wednesday, March 9th

48. Web Citations - Dissections: Plane & Fancy resources for geometry.(Find under Spatial Sense and Geometric Concepts ) pentominoes Click on pentominoes and select Dissections . http://www.cs.purdue.edu/homes/gnf/book/webref.html

Pages with web citations related to Links to my page: Links to my page: Links to my page: Hinged dissection of squares Links to my page: David Singmaster's Hinged Model ... References to my page: Geometric Dissections on the Web Links to my page: Math Forum Internet Mathematics Library Triangles/Polygons. Symmetry/Tesselltns. Books. Joseph Malkevitch's Tidbit: Geometric Packing Geometry in Utopia II (See 13. Equidecomposability (Dissection Problems).) Popular Books About Mathematics High School Student Mathematics Research (See Appendix VIII Miscellaneous Resources.) David Eppstein's Geometry Junkyard All Topics Dissection Dissection Tiling Ed Pegg's Math Games column The Sam Loyd Cyclopedia of Puzzles January 3, 2005 Greg Blonder's Genuine Ideas Related Links Ed Pegg's mathpuzzle.com Books Previous Puzzles of the Week Other Puzzles dissect Julian Davies' Tymless links Centre for Innovation in Mathematics Teaching: A Guide to Sources of Information about Recreational Mathematics Puzzle Info Source puzzle 5 pieces form a square Dick Klingens Henry Perigal things magazine (London, UK)

49. Glencoe Math 2001 - Geometry - Problem Of The Week Chapter 11, Planar pentominoes Pythagoras in 3D Truncated Polyhedra Answer Answer Answer. Chapter 12, The Intersecting Circles http://www.glencoe.com/sec/math/geometry/geo/geo_01/problem.htm

Enhance your classroom with critical-thinking problems correlated to the content of our textbooks. Nine of the thirty-six problems available are included here. Select a problem below and print it to use in class. Chapter 1 The Supernova The Moving Dominoes The Shortest Distance Answer ... Answer Chapter 2 Miquel's Theorem The Curious Cube Aristotle's Wheel Answer ... Answer Chapter 3 A Domino Knot The Extra Square One Into Three Answer ... Answer Chapter 4 The Amazing Triangle The Cuboctahedron Answer Answer Chapter 5 The Nine Puzzle Are All Triangles Isosceles? A Möbius Trisection Answer ... Answer Chapter 6 Square Assembly T-Squares Checks Into Stripes Answer ... Answer Chapter 7 The Divisible V The Work Problem A Logarithmic Spiral Answer ... Answer Chapter 8 Squaring a Greek Cross Pythagoras Without Squares A Square Proof Answer ... Answer Chapter 9

50. Titles Subjects Grades Call Read-to-Learn The Crayola Counting Middle Grades Math Overhead kit geometry, geometry, Tangrams, pentominoes,6 9, 396. Multicultural Math Lab, geometry, Tangrams, Dice, 4 6, 408 http://library.uncwil.edu/kathrynb/cmcwebpage/CMC Kits/MathKits.htm

Titles Subjects Grades Call # Read-to-Learn: The Crayola Counting Book Counting Pre K - 2 Big 1 Part A Read-to-Learn Math Packet: Crayola Counting Book Counting Pre K - 2 Big 1 Part B Read-to-Learn: Ten Monsters in a Bed Counting, Number Operations Pre K - 2 Big 2 Part A Read-to-Learn Math Packet: Ten Monsters in a Bed Counting, Number Operations Pre K - 2 Big 2 Part B Read-to-Learn: Little Number Stories Counting Pre K - 2 Big 3 Part A Read-to-Learn Math Packet: Little Number Stories Counting Pre K - 2 Big 3 Part B Read-to-Learn: Let's Measure It Measuring Pre K - 2 Big 4 Part A Read-to-Learn Math Packet: Let's Measure It Measuring Pre K - 2 Big 4 Part B Read-to-Learn: Lunch with Cat and Dog Pre K - 2 Big 5 Part A Read-to-Learn Math Packet: Lunch with Cat and Dog Pre K - 2 Big 5 Part B Timing It Right Game Telling Time - digital and analog ages 7+ Counting Eggs Counting Pre K - 2 Combo Money Kit Play money: bills and coins K - 8 Problem Solving: Set B Problem Solving Purchase Financial decisions, Strategy, Money Math Chase Middle School Game Money, Measurement, Numeration

51. Math - Interactive Sites Tangrams, pentominoes, graphs, scatterplot, medians, tiling the plane, 3D pentominoes Unfolding Polyhedra Polyhedra Tessellations geometry http://www.globalclassroom.org/ecell00/javamath.html

Read about our Palm handheld activities! Using Interactive Math What's New at Delmar Delmar El. Resources KidSpace ... Mrs. Weeg's computer lab skills Teacher Resources (by content standards) Grade Level Skills Help Pages Language Arts, Math, Science, Social Studies Treasure Chest of technology resources Math Multiplication Hidden Picture ArithmAttack basic operations: +, -, x, / Create a Graph Make your dream house! www.smallblueprinter.com Math Playground - a math learning site for students in K-6. Find the area and perimeter of rectangles Count Us In - Games to help younger students understand basic math concepts. From Australia. Temperature Quiz - from the BBC Flips, slides and turns Decimal number line HomeSchool Math - links to many activities on all school levels! Oswego City School District (NY) Educational Math Games Math Zone McGraw-Hill Mathematics - Click your book cover! Visualize Multiplication Interactive Examples of NCTM Standards - excellent for all grades! Illuminations from NCTM Interactive Math - (Geoboard, Tangrams, Pentominoes, graphs, scatterplot, medians, tiling the plane, and more) Utah State University Function Machine - excellent!

52. Growing A Thematic Interdisciplinary Unit After a number of years happily conducting my architecture and geometry unit, using pattern blocks, geoboards, pentominoes and solid geometric shapes http://www.ncrel.org/mands/docs/5-7.htm

GROWING A THEMATIC INTERDISCIPLINARY UNIT: From Prairie Ecosystem to Prairie Architecture by Chris Davis/Davis Educational Media Oak Park, Illinois For twenty years, as a third- and fourth-grade teacher in Oak Park, Illinois, I incorporated the study of Frank Lloyd Wright's architecture with the Geometry unit found in the back of our math textbook. Since Frank Lloyd Wright had done much of his early work here in Oak Park and his Prairie Style architecture identified and reflected geometric shapes, it seemed logical to tie these two units together. In most middle-grade math classes, geometry is overlooked because we teachers concentrate on reviewing the basic facts, teaching the regrouping process of addition and subtraction, and introducing two-place multiplication and long division. Geometry is reserved as an enrichment unit to be taught, if we have time, at the end of the year. I decided to reverse this timetable and begin each year with the combined architecture and geometry units. Not only did this schedule ensure that we actually got to geometry - the fall weather was also very pleasant for our walks to the Frank Lloyd Wright Home and Studio, the Unity Temple, and the Historic District in Oak Park. It was fun to stroll in the vicinity of our school and observe geometric shapes, building materials, and the various roof and window styles of the structures in the neighborhood. After a number of years happily conducting my architecture and geometry unit, I took a math methods class that showed me I needed to make further changes. The professor read the following quote from

53. Solution For /geometry/pentomino Solution to the /geometry/pentomino problem. I ve seen several different namingschemes used for pentominoes. This is the system I m using (I think only F http://rec-puzzles.org/sol.pl/geometry/pentomino

Solution to the /geometry/pentomino problem 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 E-mail to the index to Arlet's home page Linux ... Apache ... ``follow me,'' the wise man said, but he walked behind...

54. Pentomino I ve seen several different naming schemes used for pentominoes. This is thesystem I m using (I think only F N require a bit of imagination) FF I L N PP http://rec-puzzles.org/new/sol.pl/geometry/pentomino

Pentomino Arrange pentominos in 3x20, 4x15, 5x12, 6x10, 2x3x10, 2x5x6 and 3x4x5 forms. Solution: E-mail Puzzle index Arlet's home page Linux ... Apache

55. Exemplars: State Correlations - Colorado geometry and Measurement (Content Standards 4 5) Using three pentominoes,students make as many shapes possible with 12 sides or less. k2, geometry http://www.exemplars.com/resources/alignments/state_co.html

@import "../../css/global.css"; Click on a state below to access its standards: Colorado Delaware Illinois Maine Massachussetts ... Washington The Essential Academic Learning Requirements in Mathematics Colorado State Standards Covered by Exemplars Tasks - Grade Level - Exemplars Description All of Exemplars tasks meet the standards for problem solving, language and communication. Grade Knowledge and Skills Number Task Title Exemplars Description Exemplars k-2 Tasks Number Sense (Content Standard 1) k-2 Number Sense Pieces of Pizza Pizzas are cut in three ways: in 4 slices, 6 slices, and in 8 slices. Students determine how to share the pizzas with six of their friends. k-2 Number Sense Octopus Students determine the number of tentacles on four octopuses. k-2 Number Sense Ski Slope Given a number of tracks, students determine the number of skiers and snow boarders that went down the trail. k-2 Number Sense Marshmallow Peeps All in All Students determine the length of a train of 2-inch marshmallow peeps, where each peep is separated by 1/2 inch. k-2 Number Sense Average Number of Letters Students determine the average number of letters in five names.

56. Exemplars: State Correlations - Illinois geometry and Measurement (Illinois State Goals 7 9) K2, geometry andMeasurement, A067, Pentomino Problem, Using 3 pentominoes, students make as many http://www.exemplars.com/resources/alignments/state_il.html

@import "../../css/global.css"; Click on a state below to access its standards: Colorado Delaware Illinois Maine Massachussetts New York Pennsylvania ... Washington The Essential Academic Learning Requirements in Mathematics Illinois State Standards Covered by Exemplars Tasks - Grade Level - Exemplars Description All of Exemplars tasks meet the standards for problem solving, language and communication. Grade Knowledge and Skills Number Task Title Exemplars Description Exemplars K-2 Tasks Statistics and Probability (Illinois State Goal 10) K-2 Statistics and Probability Chip Chance Students determine the number of color child in a bag based on sampling of data. K-2 Statistics and Probability K-2 Statistics and Probability Number Cube Game Students determine which sum is most likely when rolling two number cubes. K-2 Statistics and Probability Snow Play Given a number of sleds that carry different numbers of children, students determine the number of sleds needed for the class. Numeration and Operations (Illinois State Goal 6) K-2 Numeration and Operations Pieces of Pizza Pizzas are cut in three ways: in 4 slices, 6 slices, and in 8 slices. Students determine how to share the pizzas with 6 of their friends.

57. Geometry - Science Kit And Boreal Laboratories geometry a leading provider of educational materials for K-12 schools pentominoes, 6 Rainbow Colors, Set/72 pentominoes, 6 Rainbow Colors, Set/72 http://sciencekit.com/category.asp?start=36&c=564911

58. Problem Solving With Pentominoes translations; reflections; rotations; geometry (Spatial Sense, Conceptualization, The students use a set of pentominoes to analyze the problem. http://www.tcet.unt.edu/START/instruct/lp0005.htm

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 Goals and objectives: The student will be able to use the Logo programming language to create defined shapes and reorient those shapes. The student will develop spatial visualization skills necessary to solve the five puzzle problems. Math TEKS Problem solving; translations; reflections; rotations; Geometry (Spatial Sense, Conceptualization, Connections, Reasoning, Problem solving) Technology Application TEKS 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.

59. ENC Online: Curriculum Resources: Problem Solving With Pentominoes (ENC-101824, Problem solving with pentominoes. Grades 3 4 5 6 7 8 URL http//teams.lacoe.edu/documentation/classrooms/amy/geometry/34/activities/pentominos/pentominos http://www.enc.org/resources/records/0,1240,101824,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Resource of the Day 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. Problem solving with pentominoes Grades: URL: http://teams.lacoe.edu/documentation/classrooms/amy/geometry/3-4/activities/pentominos/pentominos.html ENC#: ENC-101824 Publisher: Los Angeles County Office of Education (LACOE) Date: Similar Records Subjects: Mathematics Geometry. Process skills. Shapes. Visualization. Resource Type: Media Type: Internet resource. Abstract: Using this puzzle applet, the student selects four boxes on an eight-by-eight grid to remain blank and is challenged to completely cover the remainder of the grid with the 12 non-overlapping pentomino pieces. The 12 pentomino pieces represent all the possible distinct shapes that can be formed by connecting five congruent squares.

60. Perplexing Problems and famous geometric puzzles such as tangrams and pentominoes. geometry andart are explored through compass designs, tessellations and three http://www.sachem.edu/gate/Gate Web Page/perplexi.html

Perplexing Problems An exploration of problem solving, arithmetic sequences, and famous geometric puzzles such as tangrams and pentominoes. Geometry and art are explored through compass designs, tessellations and three dimensional construction of polyhedrons. CLICK HERE TO VIEW DESIGNS CREATED BY STUDENTS IN 2000-2001 Return to Thematic Units Return to Sachem's Home Page

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