Close message Scootle has stopped supporting resources that use the Adobe Flash plug-in from 18 Dec 2020. Learning paths that include these resources will have alerts to notify teachers and students that one or more of the resources will be unavailable. Click here for more info.

Mathematics / Year 9 / Measurement and Geometry / Geometric reasoning

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

Solve problems using ratio and scale factors in similar figures (ACMMG221)

Elaborations
  • establishing the relationship between areas of similar figures and the ratio of corresponding sides (scale factor)
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Ratios,  Scale (Proportions),  Similarity (Geometry)

Online

reSolve: Tree Biomass

In this sequence of two lessons, students investigate how many trees would be required to supply paper for their school for a year. Students use similar triangles, Pythagoras' Theorem and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree. They measure trees, calculate their ...

Video

Comparing fuel consumption

Is it more fuel efficient to drive or fly between two places? Watch this clip and learn how to calculate the answer. What are the various factors that need to be taken into account? This video was made using the American measurement of gallons per hour, American firgures for the average number of passengers in a car and ...

Video

Measure a tree without using a ladder

What do you do when you need to measure a length, height or distance but don't have a ruler or some other measuring instrument? You can compute linear measurements with surprising accuracy using indirect measurements, proportions and estimations. Learn a nifty trick to measure a tree from a distance.

Video

How many heads tall are you?

What are non-standard measurement units? Did you know we can reliably use objects in the real world, including our own body parts, to measure things? This concept of anthropometry, the ratios of body measurements, was first proposed by Leonardo da Vinci.

Video

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.

Video

Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Video

Nautical Robots

How might you find out how much and where the Earth's oceans are warming? Watch the report by Ruben Meerman and discover how more than 3000 'nautical robots', known as argo floats, have been placed in the oceans to collect data on variations in temperature, pressure and salinity.

Video

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.

Text

Mixing Paints

This resource is a web page containing an investigative task to explore ratios. The context of mixing paints to particular ratios of colours provides a useful task to model practical situations involving ratios. A 'Getting started' and 'Solutions' page is also available to support the task. This resource is an activity ...

Image

Bookmaker's indicator board, 1947

This is a bookmaker's indicator board, an apparatus for the display of betting odds, comprising four die-cast metal pieces joined to form an indicator board that is rectangular in shape and painted green. It was manufactured by Diecasters Australia in 1947. There is provision for a total of 12 names, each having a corresponding ...

Online

reSolve: Fibonacci Miles

This lesson introduces students to a trick for quick conversion between miles and kilometres using the Fibonacci sequence. Students are challenged to explain why the trick works. They investigate using their knowledge of ratio and discover that the miles/kilometres conversion rate is close to the golden ratio. The lesson ...

Online

reSolve: Mechanical Linkages: Similar Triangles

This sequence of lessons explores the geometry of similar triangles using two real world objects: ironing boards and pantographs. In the first lesson, students investigate different ironing board leg lengths and pivot positions using similar and congruent triangles. In the second lesson, they use their knowledge of parallelogram ...

Online

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 ...

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 ...

Text

Six Notes All Nice Ratios

This resource is a web page containing a short task to explore ratio and fractions. The task is based on the Pythagoreans discovery that simple ratios of string length made nice sounds together. A 'Getting started' page, printable resource and solution is also available to support the task.This resource is an activity ...

Text

Round and Round and Round

This resource is a web page containing an interactive that can be used to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements. The task provides an opportunity to apply their understanding of division and recurring decimals. A 'Getting started' page, printable ...

Online

reSolve: Mechanical Linkages: Geometry Proofs

This series of six lessons explores geometry proofs using real world contexts focused on the dynamics of linkages and moving joints. Students use physical models and computer simulations, the lessons move from a view of geometry as a study to static diagrams to encompass movement. Each lesson is outlined in detail including ...

Text

Mixing More Paints

This resource is a web page containing an investigative task to explore ratios and is a follow up to the task Mixing Paints. The context of mixing paints to particular ratios of colours provides a useful task to model practical situations involving ratios. A 'Getting started' and 'Solutions' page is also available to support ...

Video

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.

Video

Drawing a floor plan

How do we know what a house will look like before it is built? Discover how house plans work by looking at the design of a house that Hugo's family is going to build. See how a floor plan shows the room layout. See drawings of what the house will look like from different views.