Subtraction Structures
From “Mathematics explained for Primary Teachers” Derek Haylock,
Partitioning
This is when one amount is partitioned off from a given quantity.
e.g. I have 10 cars are 5 are removed. How many are left?
Language
take away, remove, how many are left? how many do not? how many are not taken?
Calculator entry
10 – 5 =
Contexts
taking away or removing objects, and in the context of measures
Examples
56 children are in Yr6. 38 go on a school journey, how many are left?
If I have £160 and spend £45 how much money will I have left?
Models
NOTES
Subtraction Structures
From “Mathematics explained for Primary Teachers” Derek Haylock,
Reduction
This is similar to take away but uses different language. A given quantity is reduced by a given amount – find the reduced amount. It is this structure that lies behind the idea of counting back
e.g. a £100 bicycle is reduced by £10, what is the new price of the bicycle?
Language
Start at, reduce by, count back, go down by
Calculator entry
100 – 10 =
Contexts
Often used in the context of money and measures.
If my monthly utility bill was £99 and it has been reduced by £28 what is the new monthly bill?
Models
NOTES
Subtraction Structures
From “Mathematics explained for Primary Teachers” Derek Haylock,
Comparison
This is when two sets are compared. How many fewer girls are there than boys? How many more green cubes are there than yellow ones? This is a very important structure because there are so many practical applications
Language
What is the difference? How many more? How many less/fewer? How much greater/smaller?
Calculator
Contexts
This structure is used in almost any context. It can be used to find out how much more expensive one item is rather than another and also used in the context of length, mass, capacity, temperature, speed and time
Models
NOTES
Subtraction Structures
From “Mathematics explained for Primary Teachers” Derek Haylock,
Inverse of Addition
This asks what must be added to a given value in order to reach a target value.
e.g I want to buy a DSi which costs £149. I have £109. How much more do I need to be able to afford to buy it?
We know that 24 + 16 = 40
Subtraction ‘undoes’ the adding so if I wanted to know what has to be added to 24 to make 40 then 24 must be subtracted from 40.
24 + ? = 40
40 – 24 = ?
Language
How much more do I need? What must be added to? How many/much more are needed?
Calculator
40 – 24 =
Contexts
The entrance fee is 80p I have 52p. How much more do I need?
From “Mathematics explained for Primary Teachers” Derek Haylock, 2006, London, third edition