WIn 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.
WBase ten blocks, also known as multibase arithmetic blocks (MAB) or Dienes blocks, are a mathematical manipulative used by students to learn basic mathematical concepts including addition, subtraction, number sense, place value and counting. The student can manipulate the blocks in different ways to express numbers and patterns. Generally, the three-dimensional blocks are made of a solid material such as plastic or wood and come in four sizes to indicate their individual place value: Units, Longs, Flats and Blocks. There are also computer programs available that simulate base ten blocks.
WCuisenaire 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 the Belgian primary school teacher Georges Cuisenaire (1891–1975), who called the rods réglettes.
WThe Froebel gifts are educational play materials for young children, originally designed by Friedrich Fröbel for the first kindergarten at Bad Blankenburg. Playing with Froebel gifts, singing, dancing, and growing plants were each important aspects of this child-centered approach to education. The series was later extended from the original six to at least ten sets of Gifts.
WA 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.
WMontessori sensorial materials are materials used in the Montessori classroom to help a child develop and refine their five senses. Use of these materials constitutes the next level of difficulty after those of practical life.
WPattern 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 (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 (Red) that can be matched with three of the green triangles Regular Hexagon (Yellow) that can be matched with six of the green triangles Square (Orange) with the same side-length as the green triangle
WThe tangram is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern generally found in a puzzle book using all seven pieces without overlap. Alternatively the tans can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline. It is reputed to have been invented in China sometime around the late 18th century CE and then carried over to America and Europe by trading ships shortly after. It became very popular in Europe for a time, and then again during World War I. It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education.