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Addition and Subtractions structures - Coggle Diagram
Addition and Subtractions structures
WHAT ARE THE DIFFERENT KINDS OF SITUATION THAT PRIMARY CHILDREN MIGHT ENCOUNTER TO WHICH THE OPERATION OF ADDITION CAN BE CONNECTED?
two basic categories of real-life problems that are modelled by the mathematical operation we call addition.
the aggregation structure;
the augmentation structure.
WHAT IS THE AGGREGATION STRUCTURE OF ADDITION?
aggregation
o refer to a situation in which two (or more) quantities are combined into a single quantity and the operation of addition is used to determine the total.
discrete sets
two sets that do not overlap
two sets are combined into one set, they form what is called the union of sets.
key language
how many altogether? How much altogether? The total.
CONTEXTS IN WHICH CHILDREN WILL MEET ADDITION IN THE AGGREGATION STRUCTURE?
they are putting together two sets of objects into a single set, to find the total number
context of money.
finding the total cost of two or more purchases, or the total bill for a number of services
measurements
Ensure that children experience the aggregation structure in a range of relevant contexts
WHAT IS THE AUGMENTATION STRUCTURE OF ADDITION?
where a quantity is increased by some amount and the operation of addition is required in order to find the augmented or increased value.
key vocab
start at and count on, increase by, go up by.
CONTEXTS IN WHICH CHILDREN WILL MEET ADDITION IN THE AUGMENTATION STRUCTURE?
money
increases in prices and wages
temperature the increase in temperature
their age increasing
length
CONTEXTS IN WHICH CHILDREN WILL MEET ADDITION IN THE AUGMENTATION STRUCTURE?
Which set is on the left and which on the right makes no difference to the total number of marbles. The fact that these two additions come to the same result is an example of what is called the commutative law of addition.
WHAT ARE THE DIFFERENT KINDS OF SITUATION THAT PRIMARY CHILDREN MIGHT ENCOUNTER TO WHICH THE OPERATION OF SUBTRACTION CAN BE CONNECTED?
4 different kinds of situations
the partitioning structure;
The partitioning structure refers to a situation in which a quantity is partitioned off in some way or other and subtraction is required to calculate how many or how much remains.
how many left? How many are not? How many do not?
CONTEXTS
any practical situation where we ask how many are left, or how much is left.
significant occurrences in the context of money and shopping.
the reduction structure;
It is simply the reverse process of the augmentation structure of addition. It refers to a situation in which a quantity is reduced by some amount and the operation of subtraction is required to find the reduced value.
CONTEXTS
money
reducing prices and costs, or cutting wages and salaries.
the comparison structure;
where subtraction is required to make a comparison between two quantities
CONTEXTS
Wherever two numbers occur, we will often find ourselves wanting to compare them.
measurement
the inverse-of-addition structure.
situations where we have to determine what must be added to a given quantity in order to reach some target.
whenever one operation or transformation undoes the effect of another one
example of an everyday situation with this structure would be: the entrance fee is 80p, but I have only 52p, so how much more do I need?
CONTEXTS
where we have a number of objects or a number of individuals and we require some more in order to reach a target.
measurement, such as: how much further do you have to drive to complete a journey of 345 miles if you have so far driven 196 miles?