Mathematical Manipulatives
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Mathematical Manipulatives
In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience. The use of manipulatives in mathematics classrooms throughout the world grew considerably in popularity throughout the second half of the 20th century. Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher. Examples of common manipulatives include number lines, Cuisenaire rods; fraction strips, blocks, or stacks; base ten blocks (also known as Dienes or multibase blocks); interlocking linking cubes (such as Unifix); construction sets (such as Polydron and Zo ...
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Cuisenaire Staircase
Cuisenaire rods are mathematics learning aids for students that provide an interactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. In the early 1950s, Caleb Gattegno popularised this set of coloured number rods created by Georges Cuisenaire (1891–1975), a Belgan primary school teacher, who called the rods ''réglettes''. According to Gattegno, "Georges Cuisenaire showed in the early 1950s that students who had been taught traditionally, and were rated 'weak', took huge strides when they shifted to using the material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods." History The educationalists Maria Montessori and Friedrich Fröbel had used rods to represent numbers, but it was Georges Cuisenaire who introduced the rods that were to be used across the world from the 1950s onwards. In 1952 he published ''Les nomb ...
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Geoboard
A geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons. It consists of a physical board with a certain number of nails half driven in, around which are wrapped geo bands that are made of rubber. Normal rubber bands can also be used. Geoboards were invented and popularized in the 1950s by Egyptian mathematician Caleb Gattegno (1911-1988). Structure and use Geoboard is a board. A variety of boards are used. Originally made out of plywood and brass nails or pegs, geoboards are now usually made out of plastic. They may have an upright square lattice of 9, 16 or 25 nails or more, or a circle of nails around a central nail. Students are asked to place rubber bands around the nails to explore geometric concepts or to solve mathematical puzzles. Geoboards may be used to learn about: * plane shapes; * translation; * rotation; * reflection; * similarity; * co-ordination ...
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Mathematical Manipulatives
In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience. The use of manipulatives in mathematics classrooms throughout the world grew considerably in popularity throughout the second half of the 20th century. Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher. Examples of common manipulatives include number lines, Cuisenaire rods; fraction strips, blocks, or stacks; base ten blocks (also known as Dienes or multibase blocks); interlocking linking cubes (such as Unifix); construction sets (such as Polydron and Zo ...
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Primary Mathematics:Negative Numbers
Primary or primaries may refer to: Arts, entertainment, and media Music Groups and labels * Primary (band), from Australia * Primary (musician), hip hop musician and record producer from South Korea * Primary Music, Israeli record label Works * ''Primary'' (album) by Rubicon (2002) * "Primary" (song) by The Cure * "Primary", song by Spoon from the album ''Telephono'' Other uses in arts, entertainment, and media * Primaries or primary beams, in E. E. Smith's science-fiction series ''Lensman'' * ''Primary'' (film), American political documentary (1960) Computing * PRIMARY, an X Window selection * Primary data storage, computer technology used to retain digital data * Primary server, main server on the server farm Education * Primary education, the first stage of compulsory education * Primary FRCA, academic examination for anaesthetists in the U.K. * Primary school, school providing primary education Mathematics * ''p''-group of prime power order * Primary decompositi ...
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Tile-based Game
A tile-based game is a game that uses tiles as one of the fundamental elements of play. Traditional tile-based games use small tiles as playing pieces for gambling or entertainment games. Some board games use tiles to create their board, giving multiple possibilities for board layout, or allowing changes in the board geometry during play. Each tile has a back (undifferentiated) side and a face side. Domino tiles are usually rectangular, twice as long as they are wide and at least twice as wide as they are thick, though games exist with square tiles, triangular tiles and even hexagonal tiles. Traditional games * Anagrams * Chinese dominoes * Dominoes * Mahjong Commercial games * '' Okey'' * '' Quad-Ominos'' * '' Qwirkle'' * ''Rummikub'' * ''Scrabble'' Games using non-rectangular tiles * '' Bendomino'' * '' Blokus'' * '' Gheos'' * ''Heroscape'' * ''Hive'' * '' Tantrix'' * '' Triominos'' Board games * ''Alhambra'' * ''Azul (board game)'' * ''Betrayal at House on the Hill'' * ...
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Guesstimation
''Guesstimate'' is an informal English portmanteau of '' guess'' and ''estimate'', first used by American statisticians in 1934 or 1935.''guesstimate''
Dictionary.com Unabridged (v 1.1)
It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture.''guesstimate''
American Heritage Dictionary
Like the words estimate and guess, guesstimate may be used as a verb or a noun (with the same change in

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Pattern
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict r ...
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Pattern Blocks
Pattern Blocks are a set of mathematical manipulatives developed in the 1960s. The six shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things, they allow children to see how shapes can be composed and decomposed into other shapes, and introduce children to ideas of tilings. Pattern blocks sets are multiple copies of just six shapes: *Equilateral triangle (Green) *60° rhombus (2 triangles) (Blue) that can be matched with two of the green triangles *30° Narrow rhombus (Beige) with the same side-length as the green triangle *Trapezoid (half hexagon or 3 triangles) (Red) that can be matched with three of the green triangles *Regular Hexagon (6 triangles) (Yellow) that can be matched with six of the green triangles *Square (Orange) with the same side-length as the green triangle All the angles are multiples of 30° (1/12 of a circle): 30° (1×), 60 ...
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Wooden Pattern Blocks Dodecagon
Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin that resists compression. Wood is sometimes defined as only the secondary xylem in the stems of trees, or it is defined more broadly to include the same type of tissue elsewhere such as in the roots of trees or shrubs. In a living tree it performs a support function, enabling woody plants to grow large or to stand up by themselves. It also conveys water and nutrients between the leaves, other growing tissues, and the roots. Wood may also refer to other plant materials with comparable properties, and to material engineered from wood, or woodchips or fiber. Wood has been used for thousands of years for fuel, as a construction material, for making tools and weapons, furniture and paper. More recently it emerged as a feedstock for the produ ...
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NCTM
Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds annual national and regional conferences for teachers and publishes five journals. Journals NCTM publishes five official journals. All are available in print and online versions. ''Teaching Children Mathematics'' supports improvement of pre-K–6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics idea, activities, and pedagogical strategies, and or sharing and interpreting research. ''Mathematics Teaching in the Middle School'' supports the improvement of grade 5–9 mathematics education by serving as a resource for practicing and prospective teachers, as well as supervisors and teacher educators. It is a forum for the e ...
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Ubersketch
The Ubersketch is a moniker for a collection of sketches created in The Geometer's Sketchpad by thPRISM-NEO projectwhich mimic ( virtual) manipulatives, such as the ones found aThe National Library of Virtual Manipulatives. The editor of the collection is Greg Clarke of the Simcoe-Muskoka Catholic District School Board. There is a related set of Adobe Flash objects called thUberFlashcollection which are being implemented as part of the Ontario Ontario ( ; ) is one of the thirteen provinces and territories of Canada.Ontario is located in the geographic eastern half of Canada, but it has historically and politically been considered to be part of Central Canada. Located in Central C ... Ministry of Education'CLIPS project Thhas been affectionately called the uberCalc since it is another useful collection of tools compiled by Greg Clarke. External linksUberSketch Download
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