A procedure for solving an arithmetic problem, including counting, retrieval and decomposition. Different strategies can coexist and be selected according to the problem and available knowledge.
Reexpressing a calculation through useful numerical relations, such as . Decomposition can connect practiced facts with conceptual knowledge instead of requiring direct retrieval of every whole problem.
Starting from a known quantity and counting only the added units. The strategy requires a link between the starting number and its represented quantity, rather than simply omitting words from a memorized sequence.
For addition of nonnegative natural numbers and , start at and count further units. Commutativity guarantees the same sum while minimizing the increments among the two possible choices of starting addend.
Representing the relevant collections and counting the combined items to obtain a sum. Count-all can be accurate while requiring more increments and tracking than a suitable counting-on strategy.
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