Learning Sequence Design

This learning sequence forms part of an overarching unit that covers the development of formulas for volumes of rectangular and triangular prisms and prisms in general. The students will ultimately use those formulas to solve problems involving volume (Australian Curriculum, ACMMG198).

Prior knowledge of learners include a basic knowledge of measuring and constructing angles, triangles, computing areas of various basic and composite shapes, and units of measurements and converting units of measurement.

Lesson objectives shall include selecting appropriate units of measurement for the calculation of areas and volumes and the conversion of units. Students will find perimeters and areas for rectangles and triangles and investigate the relationship between the features of rectangles and triangles such as perimeter, area and volume. Students will develop, review, share and use formulas to solve problems involving volumes of rectangular and triangular prisms and prisms in general.

The main aim of this unit is to encourage a growth mindset among students and to apply creativity in their reasoning and work, to develop deep knowledge through higher-order critical thinking, facilitate collaborative learning through conversation and knowledge and resources sharing, and to engage in problem-based, self-managed learning in realistic contexts. Students will not simply use already existing formulas and resources, instead they will be required to create their own solutions by engaging with relevant digital technologies and producing and using coded web calculators to develop volume-based solutions, specifically volumes for rectangular and triangular prisms in this instance.

It is expected that the students will consider the Australian curriculum general capabilities of literacy, numeracy, information and communication technology (ICT) capability, critical and creative thinking, personal and social capability, ethical understanding and intercultural understanding throughout their planning, reasoning, research, workings and information and knowledge sharing.

Phase 1 – Project Brief and Preparation

Students will be provided with a work brief that will outline the main task definitions, expectations, requirements, relevant possible resources and expected task outcomes.

One complete mathematics lesson will be devoted to discussing and explaining web calculators, the code required and the process involved in writing an effective mathematical application as a web calculator in the combination of html, CSS and JavaScript. The set of rules of the open web will be clarified to allow students to run their software and share it on the worldwide web.

In addition, a very brief revision of shapes, areas and volumes will be conducted prior to commencement of the task.

Safety, privacy and ethical digital protocols will be thoughtfully considered and discussed with the students, including considerations such as copyright, cyber safety, ethical considerations and privacy protocols. The students will be referred to the Creative Commons and Queensland Government Cybersafety web sites for consultation.

It is recognised that a significant benefit of on-line interactive web spaces such as wikis and blogs is the enabling of powerful two-way global dialogue, collaboration and information exchange. As such, students will be encouraged to establish and utilise such digital technologies for the specific purpose of their assignment to optimally exploit the sharing potential of ideas, knowledge and information, and collaboration, discussion and problem-solving potential among the students in an unrestrained, student-led global on-line environment without physical or time constraints.

Phase 2 – Planning and Concept Design

Applying the applicable literacy definitions from the Australian Curriculum, students will describe their reasoning and thinking, problem definition and expected outcomes. They will work collaboratively and individually to formulate a basis for the design of their web calculators.

During this phase, the students will need to demonstrate their deep understanding of geometry and how they will apply those mathematical principles and knowledge to arrive at a realistic solution while applying creativity and higher-order critical thinking through collaboration and resources sharing.

During this phase, concept designs will be created for evaluation, collaborative discussion and modification or re-design.

Phase 3 – Implementation, Testing and Reporting

During this final phase of this learning sequence the students will develop their own mathematical web calculators where the code for the web calculator needs to run in a variety of browsers. The students will understand and appreciate the global benefit of web browsers that enable world-changing digital technologies. The building of such a truly universal computation machine consists of a set of code that adheres to the basic standards for what most browsers can read, and as such the students will develop their own scientific applications as web calculators in the combination of html (describing the structure and words of the document), CSS (describing the format) and JavaScript (enabling execution).

Upon completion, the web calculators will be able to run on most devices, from Apple Watches to regular Windows desktop personal computers, and on a large number of browsers. Adhering to the set of rules of the open web, everyone will be able to run the created software after it is shared it on the web, allowing the rest of the mathematics class and beyond to perform computations the instant the web calculator is published.

Prior to launching their web calculators, the students will carry out extensive testing on the prototype digital models and the results will be discussed, errors fixed and the design of web calculators finalised for implementation.

Following the launch of the students’ web calculators, the final stage of phase three will consist of the students each submitting a professional written report outlining their design, testing and implementation strategies and processes, and findings and recommendations.