Mathematics / Year 9 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

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

  • 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)


MathXplosion, Ep 50: How to use a tetrahedron to solve the tree problem

How can you place four trees exactly the same distance apart from one other? By making a model! By using miniature trees to make a model of the problem, it becomes clear that a 2D solution is impossible. We learn how objects can help us visualise the problem situation, which in this case requires a 3D solution: a tetrahedron.


Modelling climate changes

There is a saying: 'climate is what you expect and weather is what you get'. |Understanding climate change is very difficult for most people, especially when the weather we experience is different from the information we are given by scientists about the climate changing. The difference is that weather reflects short-term ...


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 ...


The cost of cars

This lesson is designed for students to learn about car ownership in Australia and the real costs of buying and running a car. Students explore car ownership statistics in Australia, investigate the range of decisions people make about transport, calculate and compare costs of transport and make decisions on additional ...


Different ways to pay

This lesson challenges students to explore the pros and cons of various payment options, how they spend their money, different consumer products and where to go for more information about saving money and debt. During the lesson, students investigate multiple payment options to choose those that suit their circumstances, ...


reSolve: Pythagoras' Theorem - Phone finding

This lesson challenges students to apply Pythagoras' Theorem to explore a practical real-world problem. Students explore technology reliant on mathematical concepts. The lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources such as ...


reSolve: Rectilinear Polygons

In this sequence of three lessons, students use geometric reasoning to establish relationships between angles in polygons and go on to make generalisations using algebraic expressions. Students explore and enumerate right angles in a series of rectilinear polygons and generalise their findings. They then explore the number ...


reSolve: Monte Carlo Simulations

This sequence of two lessons explores how statistical techniques that rely on randomly generated data can be used to solve problems. In the first lesson, students compare different methods for calculating the area of an irregular shape, using the context of oil spill maps. They are introduced to the Monte Carlo method for ...


What are pixels?

Meet Kevin Systrom and Piper Hanson as they explain how digital images work. What are pixels, those tiny dots of light, made from? How are colours created and represented? What does Kevin say about the way mathematical functions are used to create different image filters. What is the difference between image resolution ...


Indigo Interior

This resource is a web page containing a problem solving task that requires an understanding of Pythagoras' theorem. The task involves finding the area of shaded region with a circle with a known area. To solve the problem students need to establish a right angled triangle and apply Pythagoras' theorem. A printable resource ...


Volume of a Pyramid and a Cone

This resource is a web page containing an investigative task to explore volume. Derive the formulae for the volumes of a square-based pyramid and a cone, using mathematical concepts. A printable resource is also available to support the task. This resource is an activity from the NRICH website.


In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH ...


reSolve: Gradient and Tangent

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...


reSolve: Pythagoras' Theorem - Lunch Lap

In this sequence of two lessons, students apply Pythagoras' Theorem to explore a practical problem involving optimising paths to lunch carts. In the first lesson, students investigate the length of a path that touches three sides of a rectangle, starting and finishing at the same point. They model the problem, use Pythagoras' ...


My Five Cents: Why investing can be risky

Planning to get rich quick by investing one day? Before you jump in, let Gen Fricker explain some of the risks involved with different types of investments. Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  


Surface area of prisms

This is a five-page HTML resource about solving problems concerning surface areas of prisms. It contains one video and five questions, two of which are interactive. The resource discusses and explains solving problems involving determining surface areas of prisms to reinforce students' understanding.


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 ...


Big data, better hospitals

Overcrowding in hospitals is one of the biggest challenges facing our healthcare system . In order to reduce hospital waiting times, the Patient Admission Prediction Tool (PAPT) uses historical data to predict how many patients, and with what kinds of injuries, are expected to arrive at the emergency department each day ...


My Five Cents: What is compound interest?

Compound interest will be one of the most important things you ever learn. Don't believe it? Gen Fricker will explain why. Learn how compound interest works, and why saving now can help you later. Game changer! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.


Maths inside bees and beehives

Bees are necessary for assisting many plants to produce the food we eat, including meat and milk. Colony collapse disorder, which describes the disappearance of beehives, could have catastrophic effects on food production. Australian scientists are applying their maths and science knowledge to build up a picture of a healthy ...