# Big ideas

Big ideas

The big ideas underpinning mental computation include key number knowledge, being able to generalise patterns and relationships, developing fluency and flexibility, and thinking strategically.

Mental computation is the ability to work out the answer to a calculation mentally. It requires the recall of number facts and the use of a range of thinking strategies.

There are four big ideas that underpin mental computation.

• Knowledge influences the range of possible strategies. It enables students to choose appropriate strategies. The range of key knowledge is broader than the essential basic facts for addition, subtraction, multiplication and division. Key knowledge includes:
• place value
• number sequences
• understanding the meaning of symbols
• number properties.
• Searching for patterns and relationships helps students to make connections between mathematical ideas and within different contexts. Exploring patterns and relationships leads to generalisation of the properties of the four operations (e.g. using arrays to generalise the commutative property of multiplication).
• Fluency with mental computation is the ease with which a student carries out a calculation.
Flexibility is recognising the demands of a problem and choosing the best strategy for the numbers.
• Strategic thinking in mental computation is deciding which operation to use and then the best way to carry out that operation.

For further exploration of these ideas, you can read the articles Strategies For Going Mental and Is Your Classroom Mental? on the AAMT website.

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Name Class Section
Key knowledge Folder 17
Generalising patterns and relationships Folder 17
Fluency and flexibility Folder 17
Strategic choice Folder 17