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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 and diversified 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, base ten blocks (also known as Dienes or multibase blocks), interlocking linking cubes (such as Unifix), construction sets (such as Polydron and Zometool), ...
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Cuisenaire Staircase
Cuisenaire rods are mathematics learning aids for pupils 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 Belgium, Belgian primary school teacher, who called the rods ''réglettes''. According to Gattegno, "Georges Cuisenaire showed in the early 1950s that pupils 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 ...
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Bean
A bean is the seed of some plants in the legume family (Fabaceae) used as a vegetable for human consumption or animal feed. The seeds are often preserved through drying (a ''pulse''), but fresh beans are also sold. Dried beans are traditionally soaked and boiled, and used in many traditional dishes throughout the world. They can be cooked in many different ways, however, including frying and baking. The unripe seedpods of some varieties are also eaten whole as green beans or '' edamame'' (immature soybean), but many fully ripened beans contain toxins like phytohemagglutinin and require cooking. Terminology The word "bean" and its Germanic cognates (e.g. German '' Bohne'') have existed in common use in West Germanic languages since before the 12th century, referring to broad beans, chickpeas, and other pod-borne seeds. This was long before the New World genus '' Phaseolus'' was known in Europe. With the Columbian exchange of domestic plants between Europe and the A ...
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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 decom ...
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Attribute Blocks
Attribute blocks, also called logic blocks, are mathematical manipulatives used to teach logic. Each block Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 ... in a set has a unique combination of four attributes, namely size, color, shape, and thickness. References Mathematical manipulatives {{math-stub ...
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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. Modern games may use unconventional non-tileable shapes such as the curved-shaped Bendominoes, or use many different shapes that together tile a surface such as the polyominoes in Blokus. Traditional * Anagrams * Chinese dominoes * Dominoes * Khorol * Mahjong Commercial * '' Okey'' * '' Quad-Ominos'' * '' Qwirkle'' * '' Rummikub'' * ''Scrabble ''Scrabble'' is a word game ...
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Graphics Processing Unit
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs were later found to be useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. History 1970s Arcade system boards have used specialized graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scann ...
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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 work or .''guesstimate''
American Heritage Dictionary
Like the words estimate and guess, guesstimate may be used as a verb or ...
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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 pred ...
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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×), 6 ...
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Wooden Pattern Blocks Dodecagon
Wood is a structural tissue/material found as xylem in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulosic 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 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 mechanical-support function, enabling woody plants to grow large or to stand up by themselves. It also conveys water and nutrients among 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, woodchips, or fibers. 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 production of ...
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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 three official journals. All are available in print and online versions. ''Mathematics Teacher: Learning and Teaching PK-12''. According to the NCTM, this journal "reflects the current practices of mathematics education, as well as maintaining a knowledge base of practice and policy in looking at the future of the field. Content is aimed at preschool to 12th grade with peer-reviewed and invited articles." Until 2018, this was three journals: ''Teaching Children Mathematics'' (called ''The Arithmetic Teacher'' until 1994), which focused on teaching math in elementary school, ''Mathematics Teaching in the Middle School'', and ''Mathema ...
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