Mathematics / Year 8 / Number and Algebra / Real numbers

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

Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)

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
  • calculating population growth rates in Australia and Asia and explaining their difference
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Ratios

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 ...

Interactive resource

In proportion: variables in ratios

Complete customer orders for a large hardware store by interpreting the ratios. Work in the gardening department to fill orders for liquid fertiliser (expressed as ratios). Examine the equations suggested to you by your colleagues. Choose and solve the correct equation to complete each order. This learning object is the ...

Interactive resource

In proportion: graphs of ratios, rates and scales

Complete customer orders for a large hardware store by interpreting ratios, rates and scales. Work in the manager's office and discover how ratios, rates and scales can be represented as graphs. Use the graphs to discover quantities for garden fertiliser ingredients, the cost of mulch, and for finding lengths of timber ...

Assessment resource

Vitality drinks: assessment

Assess your ability to make drinks from a menu to match customer orders. For example, calculate the volume of each juice type required when given the ratio of juices for a drink of a particular total volume. Watch an animation to determine the ratio of juices in a new recipe. Calculate the volume of each juice in the new ...

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

In proportion: variables in rates and scales

Complete customer orders for a large hardware store by interpreting rates and scales. Work in the gardening department to fill orders for mulch (expressed as rates), and help out with scale plans in the timber department. Examine the equations suggested to you by your colleagues. Choose and solve the correct equation to ...

Interactive resource

Biscuit factory: complex ratios

Examine a pair of gears that drives a conveyor belt to an oven, including cases where the belt gear is larger than the driver. Notice that the number of rotations for each gear depends on the gear size (number of teeth). Explore the relationship between the number of teeth and the number of rotations. Build a table to compare ...

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Calculating ratios using the value of the Australian dollar

The value of the Australian dollar rises and falls on a regular basis. Listen to Kirsty Bennett explain how this is good if we want to purchase goods that are produced overseas but makes Australia a more expensive place for tourists to visit. This clip provides a context to calculate ratios.

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. ...

Teacher resource

Rates and ratio

This sequence for mathematics focuses on developing the language of rates and ratios and exploring their representation of real-life events. A provocation is used as a starting point. Teachers can then choose from a number of relevant tasks depending on student needs.

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Burning Down

This resource is a web page containing a challenging problem solving task that requires an understanding of rate and proportion. It can be solved in a number of ways for example graphically, using fractions or equations and all involve reasoning. A printable resource and solution is also available to support the task. This ...

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 ...

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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.

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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 ...

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Calculating ratios and percentage: gold price

Gold is a very precious metal. Listen to reporter Natasha Thiele explain how gold became so valuable and why the price of gold fluctuates. Find out how the ratio of dollar value per unit weight is used to calculate the value of an amount of gold. This clip provides a context to calculate ratios and percentage.

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 ...

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Calculating ratios: Australian and US dollar

Have you looked at buying an item in Australia compared to buying it online? Often the online price needs to be converted to Australian dollars (AUD). Listen to Sarah Larsen describe the value of the 'Aussie' dollar compared to the US dollar (USD) and why the value keeps on changing. This clip provides a context to calculate ...

Interactive resource

The Metrix: decimals: rate 1

Measure the rate of speed required for the Metrix spacecraft to escape the Earth’s orbit. Use the metric measurement table to help you make unit conversions involving decimal numbers. This learning object is one in a series of 26 objects.

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Calculating area: locust plagues

How many locusts in a plague? Find out just how big the threat of locusts can be and how farmers try to prevent the plagues from getting out of control. This clip provides context for a combination of area, area units and rate problems.