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Mathematics / Year 6 / Number

Curriculum content descriptions

solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate (AC9M6N07)

Elaborations
  • explaining how \(\frac13\) of a quantity can be achieved by dividing by \(3\), and how knowledge of \(\frac13\) of a quantity can be used to find \(\frac23\) or \(\frac43\) of the same quantity using situations involving money, length, duration, mass or capacity
  • investigating percentage discounts of \(15\)%, \(30\)% and \(45\)% in an online toy sale, using their equivalent decimal representations of \(0.15, 0.3\) and \(0.45\) to calculate the amount of discount on sale items, with and without digital tools
  • linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding \(30\)% discount by using its equivalence to \(0.3\), dividing by \(10\) and multiplying the result by \(3\) to give \(30\)%
  • explaining the equivalence between percentages and fractions; for example, \(33\frac13\)% and \(\frac13\); keeping to percentages that are equivalent to fractions with small denominators such as \(66\frac23\)% and \(12.5\)%
  • representing a situation with a mathematical expression; for example, numbers and symbols such as \(\frac14\times24\), that involve finding a familiar fraction or percentage of a quantity; using mental strategies or a calculator and explaining the result in terms of the situation in question
General capabilities
  • Numeracy Numeracy
ScOT terms

Simple fractions,  Calculators,  Decimals,  Percentages,  Discounts (Price)

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Fractions

This is a website designed for both teachers and students that addresses components of the arithmetic of fractions. It is particularly relevant for comparison and addition and subtraction of fractions with related denominators. It also contains material on finding a fraction of a quantity where the result is a whole number. ...

Interactive

Sites2See – number for primary

Selected links to a range of interactive online resources for the study of number in Foundation to Year 6 Mathematics.

Online

Fractions, decimals and percentages: Year 6 – planning tool

This planning resource for Year 6 is for the topic of Fractions, decimals and percentages. Students use their knowledge of percentage and decimal equivalents to calculate percentage discounts.

Downloadable

Smart shopping

Students compare and evaluate different shopping options.

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Work sample Year 6 Mathematics: Fundraiser

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 6 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

Online

TIMES Module 14: Number and Algebra: fractions - teacher guide

This is a 16-page guide for teachers that provides an introduction to fractions. It covers ordering, the four basic arithmetic operations, cancelling, writing in simplest form, the use of the area model for multiplication and the use of the number line for ordering, adding and subtracting. A history of the development of ...

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Imperial pie

This activity involves making a cake using a recipe in which the quantities of the ingredients required are measured using a variety of imperial units. To complete the recipe, students need to convert the imperial units to metric units in order to be able to use their metric measuring instruments. The activity serves to ...

Online

TIMES Module 9: Number and Algebra: multiplication of whole numbers - teacher guide

This is a 23-page guide for teachers. This module contains a description of suitable models for multiplication, a discussion of the types of problems that require multiplication for their solution, and mental and written strategies for multiplication. The use of the commutative, associative and distributive laws is described. ...

Video

Decimals and fractions

This is a video demonstration of converting decimal fractions to simplified fractions. In the commentary, the presenter highlights the relevance of understanding and applying place value concepts, including the efficiency in initially interpreting the fractional part of the decimal fraction as a single fraction. Practice ...

Video

Subtracting decimals

This is a video demonstration, with audio commentary, of the procedure for pen-and-paper subtraction of decimal fractions. In the commentary, the presenter emphasises the links with the underpinning concepts of place value. Practice questions, limited to subtraction of decimal fractions involving tenths and hundredths, ...

Video

Adding decimals

This is a video demonstration, with audio commentary, of the procedure of adding decimal fractions. In the commentary, the presenter emphasises the links with the underpinning concepts of place value. Practice questions, limited to addition of decimal fractions involving tenths and hundredths, are presented with answers, ...

Interactive

Wishball: hundredths

Test your understanding of decimal place value with numbers that include hundredths. Receive a starting number, such as 46.87, and work towards turning it into a target number, such as 85.32. Spin a random digit, choose its decimal place value and decide whether to add or subtract the random digit from your starting number. ...

Interactive

Playground percentages

Help a town planner to design two site plans for a school. Assign regions on a 10x10 grid for different uses such as a playground, canteen, car park or lawn. Calculate the percentage of the total site used for each region. Use a number line to display fractions and equivalent fractions.

Interactive

The foul food maker: go figure

This tutorial is suitable for use with a screen reader. It explains how the use of simple words can describe the likelihood of everyday events. How likely is an event: certain, likely, equal chance, unlikely or certainly not? Answer some questions using these words and then build your own examples. Learn how to describe ...

Interactive

MoneySmart: helping out

This is an activity about making choices to raise money for imaginary animals called gumbutangs. Their habitat is being eradicated and something must be done to save them. The user's first choice is between two websites, one a trusted one, the other a scam site. Then they are given choices about how to raise money for the ...

Interactive

Summing Decimals

An interactive resource in which students learn how to add and subtract numbers that have up to two decimal places.

Online

Literacy and numeracy improvement: a whole-school approach

This teacher resource describes how 74 public schools in metropolitan, regional and rural Western Australia used three major components of the school improvement cycle to achieve significant improvement in the literacy and numeracy learning outcomes of their students. The resource is organised in nine sections: Summary, ...

Online

TIMES Module 18: Number and Algebra: decimals and percentages - teacher guide

This is a 21-page guide for teachers containing an introduction to decimals and percentages. It shows how place value is extended to describe positive numbers less than one. It also explores how to represent decimals on the number line, compare decimals, undertake the four basic arithmetic operations with decimals and change ...

Interactive

Arithmetic four

This is an interactive game for two students in which they solve arithmetic problems, similar to 'Connect four'. The players can choose to work with whole number and integer addition, subtraction, multiplication and division. The length of time each player will have and the level of difficulty of the problems can also be ...

Interactive

Ordering Decimals

An animated tutorial about ordering numbers with up to 3 decimal places. An interactive quiz is included.