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

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.

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

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 ...

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 ...

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.

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.

Moving Image

Speed, distance and time

Can you work out mathematical problems that involve speed, distance and time? Find out a simple way to remember the relationship between speed, distance and time. See how to work out problems to calculate either the speed, distance travelled or the time taken. This clip also covers average speed and it'll help you avoid ...

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. ...

Assessment resource

Biscuit factory: two gears: assessment

Test your understanding of ratios by choosing two gears of different sizes according to specific criteria. Complete a pair of gears, or choose the combination of two gears, depending on how many rotations each gear must make. For example, choose a belt gear size of 10 teeth and a driver of 40 teeth to make the belt gear ...

Interactive resource

The Metrix: decimals: rate 2

Measure the air pressure required to destroy an alien attacking the Metrix spacecraft, by converting between units of volume and time. Use the metric measurement table to help you make unit conversions involving decimals. This learning object is one in a series of 26 objects.

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.

Moving Image

Pythagorean triangles

How did the ancient Egyptians construct buildings with right-angled corners? Join Marcus du Sautoy as he describes one method that might have been used. Find out how it involves a triangle with sides that have a ratio 3:4:5.

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

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

Biscuit factory: two-gear system

Examine a pair of gears that drives a conveyor belt to an oven, including cases where the belt gear is larger than the driver gear. 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 by changing both ...

Interactive resource

The Metrix: decimals: rate 3

Match the speed of the Metrix spacecraft to an asteroid's speed by converting between units of length and rates of time. Use the metric measurement table to help you make unit conversions involving decimals. This learning object is one in a series of 26 objects.

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.