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

Inquiry Questions

How do contemporary technologies locate people and objects using trigonometric ratios?
How can we use our understanding of geometry to orientate ourselves or objects?
How might we optimise the transport and packaging of products?

Link to Australian Curriculum

Resources

Desmos

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. 

In this activity, students explore and use a strategy to find the volume of a cylinder. They build a strategy based on one they may have seen in earlier grades: multiply the area of the base shape by the height of the prism.  

Link: Activity

Khan Academy

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

Link: Learning Sequence

GeoGebra

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. 

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. 

Link: Interactives

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. 

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. 

Link: Shapes

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, although often used as a prompt for mathematical discussion and receiving evidence of reasoning, can be used as a prompt for applying calculations of volume. Many of the estimations relate to space and can be broken down into simple 3D shapes that can then be calculated by students. 

Link: Estimation of the day

reSolve

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 

Students’ understanding of trigonometric and Pythagorean relationships are reinforced through two engaging contexts at home: researching and building a thrilling (yet safe) zipline ride for a doll or toy and outlining a proposal for building glider poles in their local area. In the remote learning environment, this glider pole could have merit as a way of connecting people during isolation or lockdown. 

Link: ReSolve activities

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. 

This set of questions relates to all geometry, where you can then select “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. 

Link: Question set

The Improving Mathematics Education in Schools (TIMES) Project

The TIMES project, by the Australian Mathematical Sciences Institute, provides modules that are written for teachers. Each module contains a discussion of a component of the mathematics curriculum from early primary up to the end of Year 10.  

This module steps through applications of right-angled trigonometry, that can be adapted to suit the remote learning context. 

Link: Module