Module 3 Number

Question 1

Ordinal Numbers

Answer 1

Used for ordering eg 1st, 2nd, 3rd, 4th

Question 2

Cardinal Numbers

Answer 2

Used to indicate a quantity eg 1,2,3,4,5

Question 3

Subitising

Answer 3

subitising involves the immediate recognition of the quantity of a collection of objects without having to count the objects.

Question 4

Perceptual subitising

Answer 4

The immediate recognition of numbers up to 4

Question 5

Conceptual subitising

Answer 5

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).

Question 6

Part – part – whole ideas:

Answer 6

Partitions a collection of numbers into two or more parts to add to a whole.

Question 7

Number names and symbols

Answer 7

Number names need to be connected to collections and the symbols that represent them more formally:

Question 8

Number naming sequence

Answer 8

Development of a stable ordered sequence of number names

Question 9

One – to – one correspondence

Answer 9

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.

Question 10

Counting: Can refer to:

Answer 10

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)

Question 11

Numbers as composite units

Answer 11

Units made up of other units. Eg counting by larger units 5’s or 10’s.

Question 12

Trusting the count

Answer 12

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.

Question 13

positional place value

Answer 13

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”).

Question 14

multi-unit place value

Answer 14

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.

Question 15

Children calculate mentally through three procedures (in addition to developing an increasingly sophisticated concept of 10.

Answer 15

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.

Question 16

Jump method

Answer 16

Taught before the split

incrementing by tens from the number

Question 17

Split method

Answer 17

separating and collecting tens

Question 18

Iterable units of ten

Answer 18

are formed when the units of ten are constructed during the counting process and each unit increments the total by ten

Question 19

What are the 7 aspects of the Numeracy continuum

Answer 19

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

Question 20

children must also be able to demonstrate the following skills in order to count effectively

Answer 20

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.

Question 21

demonstrate how an understanding of the number ‘seven’ could be developed using the ELPSARA framework.

Answer 21

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.

Question 22

Siemon et al. (2015, p. 15) describes the prerequisite knowledge and skills requiredby children prior to introducing place value. This includes:

Answer 22

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.