# YEAR 7 MATHS FOCUS

## NUMBER AND ALGEBRA

## PERCENTAGES

OUTCOME

A student:

MA4-5NA:

operates with fractions, decimals and percentages

TEACHING POINTS | One-cent and two-cent coins were withdrawn by the Australian Government in 1990. When an amount of money is calculated, it may have 1, 2, 3 or more decimal places, e.g. when buying petrol or making interest payments. When paying electronically, the final amount is paid correct to the nearest cent. When paying with cash, the final amount is rounded correct to the nearest five cents, eg $25.36, $25.37 round to $25.35 In questions that require calculating a fraction or percentage of a quantity, some students may benefit from first writing an expression using the word ‘of’, before replacing it with the multiplication sign (×). |

LANGUAGE | Students may need assistance with the subtleties of the English language when solving word problems. The different processes required by the words ‘to’ and ‘by’ in questions such as ‘find the percentage increase if $2 is increased to $3’ and ‘find the percentage increase if $2 is increased by $3’ should be made explicit. When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working. The word ‘cent’ is derived from the Latin word centum, meaning ‘one hundred’. ‘Percent’ means ‘out of one hundred’ or ‘hundredths’. |

PURPOSE RELEVANCE OF SUBSTRAND | There are many everyday situations where things, amounts or quantities are ‘fractions’ or parts (or ‘portions’) of whole things, whole amounts or whole quantities. Fractions are very important when taking measurements, such as when buying goods (eg three-quarters of a metre of cloth) or following a recipe (eg a third of a cup of sugar), when telling the time (eg a quarter past five), when receiving discounts while shopping (eg ‘half price’, ‘half off’), and when sharing a cake or pizza (eg ‘There are five of us, so we’ll get one-fifth of the pizza each’). ‘Decimals’ and ‘percentages’ represent different ways of expressing fractions (and whole numbers), and so are other ways of representing a part of a whole. Fractions (and decimals and percentages) are of fundamental importance in calculation, allowing us to calculate with parts of wholes and to express answers that are not whole numbers, e.g. 4÷5 = 4/5 (or 0.8 or 80%). |

## Expectations of Attainment

Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157) | classify fractions, terminating decimals, recurring decimals and percentages as ‘rational’ numbers, as they can be written in the form ab where a and b are integers and b≠0 {Literacy} |

convert fractions to decimals (terminating and recurring) and percentages | |

convert terminating decimals to fractions and percentages | |

convert percentages to fractions and decimals (terminating and recurring) | |

– evaluate the reasonableness of statements in the media that quote fractions, decimals or percentages, e.g. ‘The number of children in the average family is 2.3’ {Communicating, Problem Solving, Critical and creative thinking} | |

order fractions, decimals and percentages |

Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies (ACMNA158) | calculate percentages of quantities using mental, written and calculator methods |

choose an appropriate equivalent form for mental computation of percentages of quantities, e.g. 20% of $40 is equivalent to 1/5 × $40, which is equivalent to $40 ÷ 5 {Communicating, Critical and creative thinking} | |

express one quantity as a percentage of another, using mental, written and calculator methods, e.g. 45 minutes is 75% of an hour |

Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologies (ACMNA187) | increase and decrease a quantity by a given percentage, using mental, written and calculator methods |

– recognise equivalences when calculating percentage increases and decreases, e.g. multiplication by 1.05 will increase a number or quantity by 5%, multiplication by 0.87 will decrease a number or quantity by 13% {Reasoning} | |

interpret and calculate percentages greater than 100, e.g. an increase from $2 to $5 is an increase of 150% | |

solve a variety of real-life problems involving percentages, including percentage composition problems and problems involving money | |

– interpret calculator displays in formulating solutions to problems involving percentages by appropriately rounding decimals {Communicating, Information and communication technology capability} | |

– use the unitary method to solve problems involving percentages, e.g. find the original value, given the value after an increase of 20% {Problem Solving} | |

– interpret and use nutritional information panels on product packaging where percentages are involved {Problem Solving, Literacy} | |

– interpret and use media and sport reports involving percentages {Problem Solving, Critical and creative thinking} | |

– interpret and use statements about the environment involving percentages, e.g. energy use for different purposes, such as lighting {Problem Solving, Critical and creative thinking, Sustainability} |

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