Module 3 Number Flashcards
Ordinal Numbers
Used for ordering eg 1st, 2nd, 3rd, 4th
Cardinal Numbers
Used to indicate a quantity eg 1,2,3,4,5
Subitising
subitising involves the immediate recognition of the quantity of a collection of objects without having to count the objects.
Perceptual subitising
The immediate recognition of numbers up to 4
Conceptual subitising
with practice recognition of numbers can extend past 5 up to 10 where these numbers can be recognised in terms of there subitised parts (eg. 8 is seen as 1 more than 7, as 5 and 3 more as double 4, or as 2 more than 6).
Part – part – whole ideas:
Partitions a collection of numbers into two or more parts to add to a whole.
Number names and symbols
Number names need to be connected to collections and the symbols that represent them more formally:
Number naming sequence
Development of a stable ordered sequence of number names
One – to – one correspondence
Before learning to count a child needs to understand ‘one to one correspondence’. This means being able to match one object to one other object or person. You can practise ‘one to one correspondence’ in all sorts of different contexts. Laying the table is a good idea. The total count is important to understanding on-to-one correspondence.
Counting: Can refer to:
reciting the numbers names without reference to a collection,
To the physical act of enumerating a collection
To recognising that the last number says how many.
Match number words to objects in a one-to-one correspondence
Recognise invariance of cardinality (eg that three means three no matter what it looks like)
Numbers as composite units
Units made up of other units. Eg counting by larger units 5’s or 10’s.
Trusting the count
When they believe that counting the same collection will produce an invariant (never changing) result but also when they have access to a mental object for that number that renders counting unnecessary in most dealings with that number.
positional place value
Positional notation is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the “ones place”, “tens place”, “hundreds place”).
multi-unit place value
Understanding 34 as three tens and four, or 340 as 34 tens, is essential in using the multi-unit place value structure of numbers in carrying out the four operations.
Children calculate mentally through three procedures (in addition to developing an increasingly sophisticated concept of 10.
a mental replay of the written algorithm
2. Jump Method: a counting-based approach to building on (or decreasing) from one number in tens and ones
Split method: a collection-based approach, allowing separation and recombining of tens and ones.
Jump method
Taught before the split
incrementing by tens from the number
Split method
separating and collecting tens
Iterable units of ten
are formed when the units of ten are constructed during the counting process and each unit increments the total by ten
What are the 7 aspects of the Numeracy continuum
Aspect 1: Counting sequences and numerals
Aspect 2: Counting as a problem solving process - Early arithmetical strategies
Aspect 3: Pattern and number structure
Aspect 4: Multi-unit place value
Aspect 5: Multiplication and division
Aspect 6: Fraction units
Aspect 7: Measurement
children must also be able to demonstrate the following skills in order to count effectively
know the correct order for counting numbers
count using one - to - one correspondence
recognise that a number means the same no matter what form it is in. This means they must be familiar with both cardinal and ordinal numbers as well as being able to recognise and use numerals and the names of numbers
comprehend that when they have finished counting a group of objects, whatever number they finished on is how many objects there are in the collection.
demonstrate how an understanding of the number ‘seven’ could be developed using the ELPSARA framework.
E - Experiences
Establish where the children have seen the numeral 7 before. Point out is location on an analog clock and in the calendar. Is it located anywhere within the school? It maybe on a classroom door, or in the playground or on a building. Have the children heard the number seven before? Where?
L - Language
What does the number seven sound like? Counting aloud, saying nursery rhymes and singing songs can assist in the development of language skills. Reading books that include the name and numeral for seven can also be very helpful.
P - Pictorial representation
A variety of materials including stars, books, pencils, blocks, and counters can be used to represent a quantity of seven objects.
Subitising could be included at this stage as well. Remember that subitising involves the immediate recognition of the quantity of a collection of objects without having to count the objects. Dominoes are an effective classroom resource for this.
S - Symbolic representation
Playing a card game such as SNAP where students need to correctly match the numeral 7 with the name seven or a collection of seven would be a suitable activity for this step of the framework. Students need to be able to recognise and use the numeral and the name when referring to seven.
A - Application
An application would be the part - part - whole concept where 7 is equal to 0 and 7, 6 and 1, 5 and 2, 4 and 3 or even 1 + 2 + 4 or 2 + 5 + 0.
R - Reflection
Did the students learn anything new? What did they enjoy? Why?
A - Assessment
Provide students with an A4 sheet of blank paper and ask them to make a poster which tells their parents everything they know about the number seven.
Siemon et al. (2015, p. 15) describes the prerequisite knowledge and skills requiredby children prior to introducing place value. This includes:
Correctly recognising and counting collections of 20 and more
Recognising and representing the numbers to ten using names, symbols, collections of objects and pictures
Subitising collections of up to 10
Trusting the count for numbers to 10
Recognising that a number greater than 10 is made up of a group of 10 and some ones.
Counting larger collections of objects by grouping objects together into groups of two, five or ten.
