NSW Syllabuses

# Mathematics K–10 - Early Stage 1 - Number and Algebra Whole Numbers

## Outcomes

#### A student:

• MAe-1WM

describes mathematical situations using everyday language, actions, materials and informal recordings

• MAe-2WM

uses objects, actions, technology and/or trial and error to explore mathematical problems

• MAe-3WM

uses concrete materials and/or pictorial representations to support conclusions

• MAe-4NA

counts to 30, and orders, reads and represents numbers in the range 0 to 20

## Content

• Students:
• Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)
• count forwards to 30 from a given number
• count backwards from a given number in the range 0 to 20
• identify the number before and after a given number
• describe the number before as 'one less than' and the number after as 'one more than' a given number (Communicating)
• read and use the ordinal names to at least 'tenth'
• Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)
• read numbers to at least 20, including zero, and represent these using objects (such as fingers), pictures, words and numerals
• recognise numbers in a variety of contexts, eg classroom charts, cash register, computer keyboard, telephone (Communicating)
• communicate the use of numbers through everyday language, actions, materials and informal recordings (Communicating)
• estimate the number of objects in a group of up to 20 objects, and count to check
• use 5 as a reference in forming numbers from 6 to 10, eg 'Six is one more than five'
• use 10 as a reference in forming numbers from 11 to 20, eg 'Thirteen is 1 group of ten and 3 ones'
• Subitise small collections of objects (ACMNA003)
• recognise the number of objects or dots in a pattern of objects or dots instantly, eg
• recognise dice and domino dot patterns, eg
(Communicating)
• instantly recognise (subitise) different arrangements for the same number, eg different representations of five
• recognise that the way objects are arranged affects how easy it is to subitise (Reasoning)
• Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)
• recognise that the last number name represents the total number in the collection when counting (Communicating)
• make correspondences between collections, eg 'I have four counters, you have seven counters. So you have more counters than me'
• compare and order numbers and groups of objects
• apply counting strategies to solve simple everyday problems and justify answers (Problem Solving, Reasoning)
• use the term 'is the same as' to express equality of groups
• determine whether two groups have the same number of objects and describe the equality, eg 'The number of objects here is the same as the number there' (Communicating, Reasoning)
• Use the language of money
• use the language of money in everyday contexts, eg coins, notes, cents, dollars
• recognise that there are different coins and notes in our monetary system
• exchange money for goods in a play situation (Problem Solving)

### Background Information

In Early Stage 1, students are expected to be able to count to 30. Many classes have between 20 and 30 students, and counting the number of students is a common activity. Students will also encounter numbers up to 31 in calendars.

Counting is an important component of number and the early learning of operations. There is a distinction between counting by rote and counting with understanding. Regularly counting forwards and backwards from a given number will familiarise students with the sequence. Counting with understanding involves counting with one-to-one correspondence, recognising that the last number name represents the total number in the collection, and developing a sense of the size of numbers, their order and their relationships. Representing numbers in a variety of ways is essential for developing number sense.

Subitising involves immediately recognising the number of objects in a small collection without having to count the objects. The word 'subitise' is derived from Latin and means 'to arrive suddenly'.

In Early Stage 1, forming groups of objects that have the same number of elements helps to develop the concept of equality.

### Language

Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, zero, ones, groups of ten, tens, is the same as, coins, notes, cents, dollars.

The teen numbers are often the most difficult for students. The oral language pattern of teen numbers is the reverse of the usual pattern of 'tens first and then ones'.

Students may use incorrect terms since these are frequently heard in everyday language, eg 'How much did you get?' rather than 'How many did you get?' when referring to a score in a game.

To represent the equality of groups, the terms 'is the same as' and 'is equal to' should be used. In Early Stage 1, the term 'is the same as' is emphasised as it is more appropriate for students' level of conceptual understanding.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MAe‑4NA the sub-elements (and levels) of Quantifying numbers (QuN1-QuN6), Understanding money (UnM1- UnM3) and Number patterns and algebraic thinking (NPA1-NPA2) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.