Math manipulatives are objects designed to help students learn a particular mathematical concept by manipulating it. The use of manipulatives provides a way for children to learn concepts in developmentally appropriate, hands-on ways. They are used in the first step of teaching mathematical concepts, that of concrete representation. (The second and third step are representational and abstract, respectively.)
Math manipulatives can be purchased or constructed by the teacher. Examples of commercial manipulatives include Tangrams; Cuisenaire rods; Diene's blocks; interlocking cubes; base ten blocks; pattern blocks; colored chips; links; fraction strips, circles, blocks, or stacks; and geoboards. Examples of teacher-made manipulatives used in teaching place value are beans and bean sticks or bundles of ten popsicle sticks and single popsicle sticks.