In mathematics, 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 students to learn concepts in a developmentally appropriate, hands-on and an experiencing way. They can be useful for introducing a concept and helping to make it more concrete but should not be over relied on. Students must eventually transition from concrete (hands-on) or visual representations to internalised abstract representations.

Most manipulatives are geared to very young students, but some are used to instruct more advanced students. Advanced LEGO kits, for example, are used at the college level for computer programming, robotics, and more.

Many professionals use manipulatives to help visualize the end results or think through problems. Police and archeologists use reconstructions. Architects draw plans to scale and produce scale models to communicate their ideas and ensure they are feasible. Engineers use 3-D modeling software, building toys, and prototypes to think through problems.

Virtual manipulatives for mathematics are computer models of these objects.

Useful manipulatives can be found at the national library of virtual manipulatives site at http://nlvm.usu.edu/en/nav/grade_g_4.html,

Also at http://www.ct4me.net/math_manipulatives_2.htm

And at http://www.mathplayground.com/math_manipulatives.html.

One virtual application containing several manipulatives through a common interface (illustrated above) can be found at http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html

The toolbar along the bottom has hand, text, pen, straight line, ruler, timer, stop watch, count-down timer and protractor tools. You can had various back grounds. The collection of manipulatives include: attribute blocks and buttons, base ten blocks, bucket balance, calendar, centimeter cubes, clock, colour tiles, connecting cubes, currency, fraction circles/tiles, geoboard, hundred chart, number lines, spinner, tangrams, thermometer and two-colour counters. It is very easy to use and a single student can use it on their computer or it can be shown to a whole class if using an electronic whiteboard.

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