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Catholic Education South Australia

Concepts of measurement and geometry can be used to solve novel problems.

Inquiry Questions

How does an athlete’s perception of the goals change, based on where they are on a field?
How can we use our understanding of geometry to orientate ourselves or objects?



Desmos is an interactive graphing calculator that allows teachers to set engaging instruction, exploration and practice tasks. With many existing resources, and capacity to create your own, there are applications for all year levels and topics. 

Link: Activity Collection

This collection, that contains three commonly used geometry tasks in South Australian classrooms, Exploring Length with Geoboards, Polygraphs: Triangles, and Taco Truck, provides a platform for students to explore a simple concept of right triangles, through to applying concepts alongside distance and velocity. 

Khan Academy

A sequence of learning that includes videos and practice questions relating to trigonometric ratios, solving for sides, and solving for angles. 

Link: Trigonometry Sequence of Learning


Which One Doesn’t Belong?

Which One Doesn't Belong? Is a website that provides thought-provoking puzzles for mathematics teachers, students and families. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. 

Link: Which one doesn't belong - shapes

The shapes problems can be used as a prompt for a lesson that can be streamed, or alternatively, engaging students in providing their own reasoning through effective communication. In the online environment, posting one of these problems on your Learning Management System, and asking students to vote for their correct answer (but keep this hidden from the students) and write a short response that summarises their reasoning. A follow up can be to review the votes of the poll, and then ask students to write why they think someone would have chosen the other answers. The final step in the sequence is to then reveal a model answer and explain what makes more effective mathematical communication. This can be done once a week to continue to build on the quality of responses over time. 



GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. 

Link: Set of interactives

A set of interactive activities that allows students to clarify their knowledge of trigonometric ratios. It can also be used to screen cast within Office 365 teams to demonstrate with a class. Followed with some example questions, this can be a good resource to support the development of this important skill. 


Diagnostic Questions

Diagnostic questions are designed to help identify, and crucially understand students' mistakes and misconceptions in an efficient and accurate manner. In a remote learning environment, these questions are vital for checking on progress. At crucial moments in a lesson, set a diagnostic question or two to quickly ascertain the progress of the class, and importantly, understand misconceptions quickly, which can be hard to achieve in a remote environment. You will need to sign in (for free) to access. 

Link: Diagnostic Questions Set

This set of questions relates to all geometry, where you can then select “Pythagoras” and “basic trigonometry”. After a period of content delivery or inquiry, set one or two diagnostic questions, to each member of the class via the Learning Management System, collect the results and identify any student or group of students that have misconceptions that you can then address. 


The reSolve teaching resources provide exemplary materials from Years F to 10. They put into practice the elements of the reSolve Protocol and promote fluency, deep understanding, strategic problem solving, and mathematical reasoning. A number of the resources have been made by South Australian teachers, and all are aligned with the Australian Curriculum

Link: Resolve Activity - Mobile Phone Finding

This activity could be started using a prompt of trying to locate or trace the location of people, using mobile phones, or objects using a tracking device. Students apply Pythagoras’ Theorem to locate a lost mobile phone, using information about mobile phone towers in their local region. This task develops understandings of the functionality of Pythagoras’ Theorem in three dimensions. Students also see the importance of precision when working in real world contexts.