Catholic Education South Australia

Patterns can be used to explain relationships between variables. 

Inquiry Questions

How might we use patterns to help explain our physical world?
How might we use linear models to make sense of natural phenomena?



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: Collection of Activities

A collection of activities, each used by South Australian teachers in the past, that can be used to engage students in learning activities of between 10 and 40 minutes, in concepts related to number and algebra. 

Consider using the activity builder to assign questions that will allow you to gauge student understanding. 

Khan Academy

A video explains how exponents are related to multiplication. 

Link: Exponents Video

A selection of questions, with hints and feedback, that provide practice to questions relating to laws of exponents. 

Link: Exponents Questions


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. 

This neat interactive shows how multiplication relates to indices and may be useful in a screen cast situation to demonstrate the relationship. 

Link: GeoGebra Interactive

Estimation 180

Estimation 180 is all about estimation challenges that can be used as a prompt to start a lesson, or a way to engage with some mathematical reasoning on a regular basis. 

This resource can be used as a prompt for mathematical discussion and receiving evidence of reasoning. Using your Learning Management System, you can prompt questions such as “what is too low/high?” and ask for reasoning, so that the feedback loop can be opened, and you can check in on progress. This is a great weekly task to get a routine developed, and can be a good way to engage families, too. 

Link: Estimation of the day


Youcubed, created by Jo Boaler, is a branch of Stanford University’s school of education. The program’s main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics into accessible and practical forms. 

Link: Youcubed algebra

This resource is a four-week algebra program aimed at maintaining a positive mathematical mindset. One or more tasks can be used from the unit of work, and some minor adaptation is needed to run online. Lesson three is a particularly good selection of tasks for developing algebraic understanding for emerging learners. 

Link: Youcubed parent resources 

The Youcubed method and resources will likely be different to how many parents were educated in mathematics. To keep abreast of the research that informs it, and to find out more about mathematical mindsets, parents can access the Youcubed parent resources.

Open Middle

While “Open Middle” is an unusual name for a website of mathematics problems, it is a great way of getting students to practice and work within a higher depth of knowledge and conceptual understanding and encourage critical and creative thinking to approach a problem.  

Link 1: Equivalent Exponents

Link 2: Expressions

The problems in this section can be set for practice in a lesson, reducing the number of problems that need to be set. The strategy for the teacher is to “talk-through” the different methods and supporting students to move beyond “guess and check” methods and consider linking their prior knowledge to solve the problems. 


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. 

As an inquiry protocol, these mathematics resources do need some structure and group norms to be formed around them, but when used effectively, they can be powerful. In a remote environment, some lessons will be very useful for getting students to actively collect data or information from the world around them. The "Working with Algebra” activity, in particular, can be adapted for remote learning and using your Learning Management System to have students collaborate and share their responses. 

Link: ReSolve Teaching Resources

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 Question set

This set of questions relates to the Algebra of straight-line graphs. 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.