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Geoboard
A geoboard is a mathematical manipulatives, 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 Originally made out of plywood and brass nails or pegs, geoboards are now usually made out of plastic.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: [Baidu] |
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), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
25 Peg Geoboard
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. Humans, and many other animals, have 5 digits on their limbs. Mathematics 5 is a Fermat prime, a Mersenne prime exponent, as well as a Fibonacci number. 5 is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple ( 3, 4, 5). 5 is the first safe prime and the first good prime. 11 forms the first pair of sexy primes with 5. 5 is the second Fermat prime, of a total of five known Fermat primes. 5 is also the first of three known Wilson primes (5, 13, 563). Geometry A shape with five sides is called a pentagon. The pentagon is the first regular polygon that does not tile the plane with copies of itself. It is the largest face any of the five regular three-dimensional regular Platonic solid can have. A conic is determined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' or ''corners''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a ''solid polygon''. The interior of a solid polygon is its ''body'', also known as a ''polygonal region'' or ''polygonal area''. In contexts where one is concerned only with simple and solid polygons, a ''polygon'' may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polyg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caleb Gattegno
Caleb Gattegno (1911–1988) was an educator, psychologist, and mathematician. He is considered one of the most influential and prolific mathematics educators of the twentieth century. He is best known for introducing new approaches to teaching and learning mathematics (Visible & Tangible Math), foreign languages ( The Silent Way) and reading ( Words in Color). Gattegno also developed pedagogical materials for each of these approaches, and was the author of more than 120 books and hundreds of articles largely on the topics of education and human development. Background Gattegno was Jewish and was born November 11, 1911, in Alexandria, Egypt. His parents, Menachem Gattegno, a Spanish merchant, and his wife, Bchora, had nine children. Because of poverty, Gattegno and his siblings had to work starting from a young age. The future mathematician had no formal education until he started to learn on his own at the age of 14. He took external examinations when he was 20 years old and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Lattice
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as . It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group in IUC notation as , Coxeter notation as , and orbifold notation as . Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered square lattice.. They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard. Symmetry The square lattice's symmetry category is wallpaper group . A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. An upright square lattice can be vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubber Stamp
A rubber stamp is an image or pattern that has been carved, molded, laser engraved, or vulcanized onto a sheet of rubber. Rubber stamping, also called stamping, is a craft in which some type of ink made of dye or pigment is applied to a rubber stamp, and used to make decorative images on some media, such as paper or fabric. Description A rubber stamp uses a raised-relief image molded into a sheet of rubber, often mounted onto a more stable object such as a wood, brick, or an acrylic block. For compactness, the vulcanized rubber image with an adhesive foam backing may be attached to a cling vinyl sheet which allows it to be used with an acrylic handle for support. These cling rubber stamps can be stored in a smaller amount of space, and typically cost less than the wood-mounted versions. They can also be positioned with a greater amount of accuracy due to the stamper's ability to see through the handle being used. The ink-coated rubber stamp is pressed onto any type of medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
