NSW Syllabuses

# Mathematics K–10 - Stage 2 - Number and Algebra Whole Numbers

## Whole Numbers 1

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM

selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-4NA

applies place value to order, read and represent numbers of up to five digits

### Content

• Students:
• Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)
• represent numbers of up to four digits using objects, words, numerals and digital displays
• make the largest and smallest number from four given digits (Communicating)
• identify the number before and after a given two-, three- or four-digit number
• describe the number before as 'one less than' and the number after as 'one more than' a given number (Communicating)
• count forwards and backwards by tens and hundreds on and off the decade, eg 1220, 1230, 1240, … (on the decade); 423, 323, 223, … (off the decade)
• arrange numbers of up to four digits in ascending and descending order
• use place value to compare and explain the relative size of four-digit numbers (Communicating, Reasoning)
• use the terms and symbols for 'is less than' $$\left( < \right)$$ and 'is greater than' $$\left( > \right)$$ to show the relationship between two numbers
• Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)
• apply an understanding of place value and the role of zero to read, write and order numbers of up to four digits
• interpret four-digit numbers used in everyday contexts (Problem Solving)
• use place value to partition numbers of up to four digits, eg 3265 as 3 groups of one thousand, 2 groups of one hundred, 6 groups of ten and 5 ones
• state the 'place value' of digits in numbers of up to four digits, eg 'In the number 3426, the place value of the "4" is 400 or 4 hundreds'
• record numbers of up to four digits using place value, eg 5429 = 5000 + 400 + 20 + 9
• partition numbers of up to four digits in non-standard forms, eg 3265 as 32 hundreds and 65 ones
• round numbers to the nearest ten, hundred or thousand

### Background Information

The place value of digits in various numerals should be investigated. Students should understand, for example, that the '5' in 35 represents 5 ones, but the '5' in 53 represents 50 or 5 tens.

### Language

Students should be able to communicate using the following language: number before, number after, more than, greater than, less than, largest number, smallest number, ascending order, descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to.

The word 'and' is used between the hundreds and the tens when reading and writing a number in words, but not in other places, eg 3568 is read as 'three thousand, five hundred and sixty-eight'.

The word 'round' has different meanings in different contexts, eg 'The plate is round', 'Round 23 to the nearest ten'.

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

When working towards the outcome MA2‑4NA the sub-elements (and levels) of Quantifying numbers (QuN8-QuN10) 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.

## Whole Numbers 2

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-4NA

applies place value to order, read and represent numbers of up to five digits

### Content

• Students:
• Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
• apply an understanding of place value to read and write numbers of up to five digits
• arrange numbers of up to five digits in ascending and descending order
• state the place value of digits in numbers of up to five digits
• pose and answer questions that extend understanding of numbers, eg 'What happens if I rearrange the digits in the number 12 345?', 'How can I rearrange the digits to make the largest number?' (Communicating, Reasoning)
• use place value to partition numbers of up to five digits and recognise this as 'expanded notation', eg 67 012 is 60 000 + 7000 + 10 + 2
• partition numbers of up to five digits in non-standard forms, eg 67 000 as 50 000 + 17 000
• round numbers to the nearest ten, hundred, thousand or ten thousand

### Background Information

The convention for writing numbers of more than four digits requires that numerals have a space (and not a comma) to the left of each group of three digits when counting from the units column, eg 16 234. No space is used in a four-digit number, eg 6234.

### Language

Students should be able to communicate using the following language: largest number, smallest number, ascending order, descending order, digit, ones, tens, hundreds, thousands, tens of thousands, place value, expanded notation, round to.

Refer also to language in Whole Numbers 1.

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

When working towards the outcome MA2‑4NA the sub-elements (and levels) of Quantifying numbers (QuN10) 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.