Mathematics / Year 7 / Number and Algebra / Real numbers

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Recognise and solve problems involving simple ratios (ACMNA173)

Elaborations
  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Ratios

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Year level 7-8
Resource type
Learning area Mathematics
Interactive resource

Exploring ratios and proportions

Explore ratios by comparing the dimensions of two rectangles. Choose a scale to enlarge the smaller shape and identify whether its sides are proportional to those of the larger rectangle. For example, a rectangle with sides in the ratio 4:5 has an equivalent ratio to a rectangle with sides in the ratio 12:15. Watch a video ...

Interactive Resource

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Interactive resource

Squirt: three containers: level 1

Examine the relationships between capacities of containers of the same shape, but different size. Squirt liquids between three containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. Express relationships using mathematical notation such as 2a=6b=3c. ...

Moving Image

Phi challenge

The golden ratio, Phi: fact or fallacy? What about the Fibonacci sequence? We are told this ratio and its cousin Fibonacci occur everywhere in nature. Let's see which of these claims stacks up when put to the test.

Interactive resource

Squirt: three containers: level 2

Examine the relationships between capacities of containers of different shapes and sizes. Squirt liquids between three containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. Express relationships using mathematical notation such as 2a=6b=3c. This learning ...

Assessment resource

Biscuit factory: three gears: assessment

Test your understanding of ratios by interpreting three-wheel gear systems where the wheels have different numbers of teeth. For example, how many rotations does a 10-tooth gear wheel make when driven by two driver wheels having 20 and 10 teeth? Also, choose a combination of three gear wheels to achieve a required number ...

Moving Image

Introduction to ratios

This is a video resource, with audio commentary, that discusses what a ratio is, the different ways a ratio can be expressed and typical examples of questions about ratios. The resource poses various problems and, through handwritten solutions to these problems, demonstrates how ratios can be calculated from raw data and ...

Text

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 ...

Moving Image

Simplifying rates and ratios

This is a short video presentation, with audio commentary, of an example of simplifying the relationship between two different quantities expressed as a rate. In simplifying the rate, the presenter discusses the prime factorisation of numbers and presents a factor tree diagram as a method for finding the greatest common ...

Interactive resource

Squirt: three containers

Examine the relationships between capacities of various containers. Look at three containers that may have different diameters, heights and shapes. Fill a container and squirt liquids between the containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. ...

Interactive Resource

Syllabus Bites: Revisiting proportion

This is the first in a series of Syllabus Bites related to direct and indirect proportion. Students revise the concept of ratio. They create short visual explanations showing how problems can be solved.

Text

Mixing Lemonade

This resource is a web page containing an interactive task to explore ratios and proportions. Compare different mixtures of lemonade and develop a strategy for deciding which is stronger each time. The task requires students to apply their understanding of ratio and proportions. A 'Getting started' page, 'Solution' and ...

Teacher resource

TIMES Module 17: Number and Algebra: the unitary method - teacher guide

This is an 18-page guide for teachers. This module introduces the idea of ratios and rates.

Moving Image

Are plants mathematicians?

Ever noticed that plants are examples of Fibonacci numbers? Watch Vi Hart draw examples of flower petals and leaf growth that follow this pattern. See how plants seem to use Phi (.), the golden ratio. Find out how to make your own 'angle-a-tron' to create interesting petal designs. This is the second in a series of two.

Dataset

Australia's population: countries of birth - dataset

The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is in MS Excel format.

Interactive Resource

ConCensus

Bring Australian statistics to life with ConCensus – a data visualisation game which allows you to interact with real data from the Australian Bureau of Statistics 2011 Census. ConCensus presents population data as numbers, as a percentage and as representations such as data visualisations, graphs and tables. Use data from ...

Teacher resource

Using ConCensus for mathematical enquiry

This teaching resource demonstrates ways in which real Australian Census data (in this case data from the 2011 Census placed into the ConCensus interactive) can be interpreted and analysed. Population data is presented both in numbers and as a percentage. The representations include data visualisations, graphs and tables. ...

Teacher resource

Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

Teacher resource

Top drawer teachers: reasoning

This is a web page that comprehensively covers the teaching of the ‘Reasoning’ proficiency and its integration into the mathematics curriculum through links to five sections. The first section covers the ‘Big ideas’ behind reasoning and shows how reasoning can be developed in even very young students. The second section ...

Teacher resource

Measuring Millennium Development Goals progress

This is a unit of work about progress towards achieving the United Nation's Millennium Development Goals (MDG). Written from a global education perspective, the resource consists of four single- or multi-lesson activities, titled: What do the Millennium Development Goals measure?; Tracking the world's progress; Comparing ...