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Conceptual Structures for Multiplication and Division. 2. 2. 2. Multiplication: Repeated Addition. This is the first multiplication structure to which children should be introduced as it builds on established understanding that children have about addition. 2 multiplied 3 times (2 x 3).
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2 2 2 Multiplication: Repeated Addition This is the first multiplication structure to which children should be introduced as it builds on established understanding that children have about addition. 2 multiplied 3 times (2 x 3)
Multiplication: Rectangular Array This is likely to be the second multiplication structure to which children are introduced formally. It provides a visual representation of the commutative law (a x b = b x a). 5 x 2 4 x 3 2 x 5 3 x 4 8 x 3 3 x 8
Multiplication: Scaling This is probably the hardest multiplication structure since it cannot be understood by counting though it is frequently used in everyday life in the context of comparing quantities or measurements and in calculations of the cost of multiple purchases. Apples 25 p. I need to buy 5 apples, one for each day of the week. So it will cost me 5 x 25 pence which equals 125 pence which is £1.25!
Division: Equal Sharing Here we are sharing objects between a given number of groups (for example people). This structure is often used to explain division but the limitation is that the divisor must always be a whole number since to share 8 sweets by half a person would be a nonsense. Look Miss. I’ve shared out the stars for our group!
Division: Equal grouping This involves repeatedly subtracting the divisor until there is either nothing left or there is a remainder. I’ve given everyone 2 sweets and there is one left over!
Division: Ratio This is a comparison of the scale of two quantities or measurements in which the quotient is regarded as the scale factor. Children often find this structure difficult to understand and frequently confuse it with comparison by (subtractive) difference. A B A is 2 times larger than B since 8 divided by 4 equals 2.
While it is important that you, as a teacher, recognise these structures and identify them in use within classroom activities, you should not expect children to name them! Children will, however, need to recognise the operation involved (multiplication or division) in practical contexts where the underlying structure will be one of those described.
