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Mental calculation
Mental computation is a window to students' understanding of important mathematical ideas, particularly in number and algebra.
The following are the key ideas that underpin fluent and flexible calculation strategies.

Counting
Meaningful counting requires understanding of important principles, including cardinality.

Place value
The understanding of place value progresses from a way to abbreviate counting initially, to a multiplicative system based on powers of ten.

Reliance on counting then adding and subtracting
Increased sophistication with number operations means moving from counting to additive thinking to multiplicative thinking.

Division as sharing and measuring
Students need to understand that division can be viewed as two actions – sharing and measuring – and that the numbers in the same division equation can involve different types of units.
Place value
Students' understanding of place value reflects their understanding of counting, as well as their thinking about the operations of addition, subtraction, multiplication and division.
Reliance on counting
Progress in mental calculation involves a transition from counting to additive thinking to multiplicative thinking.
Division as sharing and measuring
Division can refer to two different actions, sharing or measuring.