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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.