Manipulative (mathematics education)

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.

Examples of common manipulatives include number lines, Cuisenaire rods, fraction strips,[1] base ten blocks (also known as Dienes or multibase blocks), interlocking linking cubes (such as Unifix), construction sets (such as Polydron and Zometool), colored tiles or tangrams, pattern blocks, colored counting chips,[2] numicon tiles, chainable links, abaci such as "rekenreks", and geoboards.

For example, there are manipulatives specifically designed to help students learn fractions, geometry and algebra.

Students are able to physically represent place value in the operations of addition, subtraction, multiplication, and division.

Pattern blocks consist of various wooden shapes (green triangles, red trapezoids, yellow hexagons, orange squares, tan (long) rhombi, and blue (wide) rhombi) that are sized in such a way that students will be able to see relationships among shapes.

These include cars, trains, boats, rockets, flowers, animals, insects, birds, people, household objects, etc.

Also, one can learn addition, subtraction, multiplication and division, guesstimation, measuring, and graphing, perimeter, area, and volume.

[4] Tiles are one inch-by-one inch colored squares (red, green, yellow, blue).

Seeing the same concept represented in multiple ways as well as using a variety of concrete models will expand students’ understandings.