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An example would be where one is given one positive x 2 tile, three positive x tiles, and two positive unit tiles. The student forms the rectangle by having the x 2 tile in the upper right corner, then one has two x tiles on the right side of the x 2 tile, one x tile underneath the x 2 tile, and two unit tiles are in the bottom right corner.
For example, there are manipulatives specifically designed to help students learn fractions, geometry and algebra. [3] Here we will look at pattern blocks, interlocking cubes, and tiles and the various concepts taught through using them.
Virtual math manipulatives are sometimes included in the general academic curriculum as assistive technology for students with physical or mental disabilities. [4] Students with disabilities are often able to still participate in activities using virtual manipulatives even if they are unable to engage in physical activity.
The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
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Discrete algebras include: Boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages.