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.