Multiplication structures
Repeated addition/aggregation: an extension of the aggregation/combining structure of addition.
· 52 + 52 + 52 + 52 + 52 becomes 52 × 5
5 ‘lots/sets of’ 52
· A bag of crisps costs 74p.(Unit cost)
How much will 8 bags cost?
· Bill earns £5.80 per hour. How much will he earn if he works for 25 hours?
Scaling structure: Making something bigger (or smaller) by multiplying by a scale factor.
Multiplication as the inverse of division
Using division to answer a multiplication question.
Ensure pupils meet the different structures within a range of different contexts.
1
Number lines : Repeated addition – regular increments
Visualising and demonstrating the commutative law: Number lines
1
Visualising and demonstrating the distributive law: Arrays
Progression from arrays to area to the grid method.
The grid method:
Written partitioning method:
1
Similar principles to those above can be applied to money and decimals.
For example:
Expanded vertical column multiplication:
Compact vertical column multiplication:
1
Appendix
Known facts: Mental recall and known facts tables
The recall of multiplication and division facts is extremely important and underpins mental and written calculations. Of equal importance is a pupil’s ability to find new facts from their existing bank (or box) of known facts.
For example; if a pupil knows that 5 ‘lots of’ 6 equals 30 (6 × 5 = 30) then they can use this known fact as a starting point to find a wide range of new multiplication facts depending on their level and other skills.
· 4 ‘lots of’ 6 equals 24 [by subtracting one 6]
· 6 ‘lots of’ 6 equals 36 [by adding one 6]
· 10 ‘lots of’ 6 equals 60 [by doubling]
· 50 ‘lots of’ 6 equals 300 [by multiplying by ten]
In this way pupils can quickly build up a ‘known facts table’ that can be used to support mental and informal written approaches and that can lead to other new facts being found and written into the table/picture. Supporting pupils to learn the processes behind developing a bank of known facts [as illustrated above] in this way can lessen their anxiety that you must ‘learn’ a large number of multiplication facts when in fact processes such as subtracting, adding, doubling, multiplying by ten can ‘start you off’ and be applied to any multiplication – including beyond the ten ‘times table’. These processes can be modelled on a counting stick.
It should be restated that the quick recall of multiplication facts is extremely important and creative use of a counting stick, sing-a-long activities, practical equipment, manipulatives, models and images and ‘times tables’ will support the learning of these facts.
1