 Mathematical manipulatives can be purchased or constructed by the teacher.Examples of commercial manipulatives include unifix cubes; tangrams; Cuisenaire rods; numicon patterns; color tiles; base ten blocks (also known as Dienes or multibase blocks); interlocking cubes; pattern blocks; colored chips; links; fraction strips, blocks, or stacks; Shape Math; Polydron; Zometool; rekenreks 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.