# YEAR 5 MATHS FOCUS

## NUMBERS AND ALGEBRA

Whole Numbers

Learning Experiences

Whole Numbers

## WHOLE NUMBERS

OUTCOME

A student:

MA3-4NA:

orders, reads and represents integers of any size and describes properties of whole numbers

TEACHING POINTS | In some Asian languages, such as Chinese, Japanese and Korean, the natural language structures used when expressing numbers larger than 10 000 are ‘tens of thousands’ rather than ‘thousands’, and ‘tens of millions’ rather than ‘millions’. For example, in Chinese (Mandarin), 612 000 is expressed as ’61 wàn, 2 qiān’, which translates as ’61 tens of thousands and 2 thousands’. |

The abbreviation ‘K’ is derived from the Greek word khilios, meaning ‘thousand’. It is used in many job advertisements to represent salaries (eg a salary of $70 K or $70 000). It is also used as an abbreviation for the size of computer files (eg a size of 20 K, meaning twenty thousand bytes). |

LANGUAGE | Students should be able to communicate using the following language: ascending order, descending order, zero, ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, digit, place value, expanded notation, round to, whole number, factor, highest common factor (HCF), multiple, lowest common multiple (LCM). |

## Expectations of Attainment

Recognise, represent and order numbers to at least tens of millions | apply an understanding of place value and the role of zero to read and write numbers of any size {Literacy} |

state the place value of digits in numbers of any size | |

arrange numbers of any size in ascending and descending order | |

record numbers of any size using expanded notation, eg 163 480 = 100 000 + 60 000 + 3000 + 400 + 80 | |

partition numbers of any size in non-standard forms to aid mental calculation, eg when adding 163 480 and 150 000, 163 480 could be partitioned as 150 000 + 13 480, so that 150 000 could then be doubled and added to 13 480 {Critical and creative thinking} | |

use numbers of any size in real-life situations, including in money problems | |

– interpret information from the internet, the media, the environment and other sources that use large numbers {Communicating, Reasoning, Literacy, Information and communication technology capability, Personal and social capability, Work and enterprise} | |

recognise different abbreviations of numbers used in everyday contexts, eg $350 K represents $350 000 {Literacy, Work and enterprise} | |

round numbers to a specified place value, eg round 5 461 883 to the nearest million |

Identify and describe factors and multiples of whole numbers and use them to solve problems(ACMNA098) | determine all ‘factors’ of a given whole number, eg 36 has factors 1, 2, 3, 4, 6, 9, 12, 18 and 36 {Literacy} |

determine the ‘highest common factor’ (HCF) of two whole numbers, eg the HCF of 16 and 24 is 8 {Literacy} | |

determine ‘multiples’ of a given whole number, eg multiples of 7 are 7, 14, 21, 28, … {Literacy} | |

determine the ‘lowest common multiple’ (LCM) of two whole numbers, eg the LCM of 21 and 63 is 63 {Literacy} | |

determine whether a particular number is a factor of a given number using digital technologies {Critical and creative thinking} | |

– recognise that when a given number is divided by one of its factors, the result must be a whole number {Problem Solving, Critical and creative thinking} | |

solve problems using knowledge of factors and multiples, eg ‘There are 48 people at a party. In how many ways can you set up the tables and chairs, so that each table seats the same number of people and there are no empty chairs?’ {Critical and creative thinking} |

Learning Experiences

To be added