Concrete manipulatives are objects that allow pupils to construct their own meaning of mathematical concepts. They are are an important resource when teaching mathematics (especially with younger pupils). The aim of manipulatives in to build integrated concrete ideas. Concrete materials include unifix cubes, clocks, counters, fraction blocks etc. These materials can be expensive to buy and often schools have an inadequate supply of concrete manipulatives.
Virtual manipulative are an alternative to concrete manipulatives. Virtual manipulatives are web based or app based representations of a concrete manipulative that can be used to create mathematical knowledge. Virtual manipulatives can be often be obtained free of charge unlike concrete manipulative that are expensive investment for primary school. Virtual manipulative can often be physically altered by pupils (e.g. colour of shapes). Virtual manipulatives may also be more appealing to older pupils and pupils with special educational needs than concrete manipulatives.
Here are a few virtual manipulative apps;
Virual Manipulatives! (https://itunes.apple.com/us/app/id471341079?ign-mpt=uo%3D4) See app review here
Math-U-See Manipulatives (https://itunes.apple.com/us/app/math-u-see-manipulatives/id874332429?mt=8&ign-mpt=uo%3D4)