Mental computation is dependent on a range of knowledge.
- Know that contains associations such as:
- basic number facts
- counting sequences
- the place value structure of whole numbers
- the meanings of words and symbols.
- Know how contains processes such as:
- rounding and compensating
- splitting numbers by place value and recombining them
- recording operations on an empty number line
- doubling and halving factors.
- Know why involves understanding the reasons that operations work and the connections between ideas. For example:
- collections can be regarded as units made of ones
- multiplication undoes division and vice versa
- sharing division problems can be solved by thinking "How many…?"
- Know why also involves recognising:
- the opportunity to use addition, subtraction, multiplication and division in different contexts
- the quantities that numbers refer to
- difference situations that can be solved by addition or subtraction
- that equal sharing or measuring involves division.
For further exploration of these ideas, you can read Numbers + magic = answer. Students explaining: Make the most of mental computation on the AAMT website.
