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New NSW Syllabuses

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

Whole Numbers 1

Outcomes

A student:

  • MA1-1WM

    describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

  • MA1-2WM

    uses objects, diagrams and technology to explore mathematical problems

  • MA1-3WM

    supports conclusions by explaining or demonstrating how answers were obtained

  • MA1-4NA

    applies place value, informally, to count, order, read and represent two- and three-digit numbers

Content

  • Students:
  • Develop confidence with number sequences to 100 by ones from any starting point (ACMNA012)
  • count forwards and backwards by ones from a given two-digit number
  • identify the number before and after a given two-digit number
  • describe the number before as 'one less than' and the number after as 'one more than' a given number (Communicating) L
  • read and use the ordinal names to at least 'thirty-first', eg when reading calendar dates L
  • count and represent large sets of objects by systematically grouping in tens
  • use and explain mental grouping to count and to assist with estimating the number of items in large groups CCT
  • use place value to partition two-digit numbers, eg 32 as 3 groups of ten and 2 ones
  • state the place value of digits in two-digit numbers, eg 'In the number 32, the "3" represents 30 or 3 tens' L
  • partition two-digit numbers in non-standard forms, eg 32 as 32 ones or 2 tens and 12 ones CCT
  • Recognise, model, read, write and order numbers to at least 100; locate these numbers on a number line (ACMNA013)
  • represent two-digit numbers using objects, pictures, words and numerals L
  • locate and place two-digit numbers on a number line
  • apply an understanding of place value and the role of zero to read, write and order two-digit numbers L
  • use number lines and number charts to assist with counting and ordering
  • give reasons for placing a set of numbers in a particular order (Communicating, Reasoning) CCT
  • round numbers to the nearest ten
  • estimate, to the nearest ten, the number of objects in a collection and check by counting, eg estimate the number of children in a room to the nearest ten
  • solve simple everyday problems with two-digit numbers LCCT
  • choose an appropriate strategy to solve problems, including trial-and-error and drawing a diagram (Communicating, Problem Solving) CCT
  • ask questions involving two-digit numbers, eg 'Why are the houses on either side of my house numbered 32 and 36?' (Communicating)
  • Recognise, describe and order Australian coins according to their value (ACMNA017)
  • identify, sort, order and count money using the appropriate language in everyday contexts, eg coins, notes, cents, dollars WE
  • recognise that total amounts can be made using different denominations, eg 20 cents can be made using a single coin or two 10-cent coins
  • recognise the symbols for dollars ($) and cents (c)

Background Information

By developing a variety of counting strategies and ways to combine quantities, students recognise that there are more efficient ways to count collections than counting by ones.

Language

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

Students should be made aware that bus, postcode and telephone numbers are said differently from cardinal numbers, ie they are not said using place value language. Ordinal names may be confused with fraction names, eg 'the third' relates to order but 'a third' is a fraction.

The word 'round' has different meanings in different contexts and some students may confuse it with the word 'around'.

Whole Numbers 2

Outcomes

A student:

  • MA1-1WM

    describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

  • MA1-2WM

    uses objects, diagrams and technology to explore mathematical problems

  • MA1-3WM

    supports conclusions by explaining or demonstrating how answers were obtained

  • MA1-4NA

    applies place value, informally, to count, order, read and represent two- and three-digit numbers

Content

  • Students:
  • Develop confidence with number sequences from 100 by ones from any starting point (ACMNA012)
  • count forwards or backwards by ones, from a given three-digit number
  • identify the numbers before and after a given three-digit number
  • describe the number before as 'one less than' and the number after as 'one more than' a given number (Communicating) L
  • Recognise, model, represent and order numbers to at least 1000 (ACMNA027)
  • represent three-digit numbers using objects, pictures, words and numerals L
  • use the terms 'more than' and 'less than' to compare numbers L
  • arrange numbers of up to three digits in ascending order
  • use number lines and number charts beyond 100 to assist with counting and ordering (Communicating, Problem Solving)
  • give reasons for placing a set of numbers in a particular order (Communicating, Reasoning) CCT
  • Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026)
  • count forwards and backwards by twos, threes and fives from any starting point
  • count forwards and backwards by tens, on and off the decade, with two- and three-digit numbers, eg 40, 30, 20, … (on the decade); 427, 437, 447, … (off the decade)
  • identify number sequences on number charts
  • Group, partition and rearrange collections of up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)
  • apply an understanding of place value and the role of zero to read, write and order three-digit numbers L
  • form the largest and smallest number from three given digits (Communicating, Reasoning) CCT
  • count and represent large sets of objects by systematically grouping in tens and hundreds
  • use models such as base 10 material, interlocking cubes and bundles of sticks to explain grouping (Communicating, Reasoning)
  • use and explain mental grouping to count and to assist with estimating the number of items in large groups CCT
  • use place value to partition three-digit numbers, eg 326 as 3 groups of one hundred, 2 groups of ten and 6 ones
  • state the place value of digits in numbers of up to three digits, eg 'In the number 583, the "5" represents 500 or 5 hundreds' L
  • partition three-digit numbers in non-standard forms, eg 326 can be 32 groups of ten and 6 ones CCT
  • round numbers to the nearest hundred
  • estimate, to the nearest hundred, the number of objects in a collection and check by counting, eg show 120 pop sticks and ask students to estimate to the nearest hundred
  • Count and order small collections of Australian coins and notes according to their value (ACMNA034)
  • use the face value of coins and notes to sort, order and count money WEL
  • compare Australian coins and notes with those from other countries, eg from students' cultural backgrounds (Communicating) IU
  • determine whether there is enough money to buy a particular item (Problem Solving, Reasoning)
  • recognise that there are 100 cents in $1, 200 cents in $2, …
  • identify equivalent values in collections of coins and in collections of notes, eg four $5 notes have the same value as one $20 note

Background Information

The learning needs of students are to be considered when determining the appropriate range of two- and three-digit numbers.

Students should be encouraged to develop different counting strategies, eg if they are counting a large number of items, they can count out groups of ten and then count the groups.

They need to learn correct rounding of numbers based on the convention of rounding up if the last digit is 5 or more and rounding down if the last digit is 4 or less.

Language

Students should be able to communicate using the following language: count forwards, count backwards, number before, number after, more than, less than, number line, number chart, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, round to.

The word 'and' is used when reading a number or writing it in words, eg five hundred and sixty-three.