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Australian Curriculum v9 - Mathematics Year 8

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F-10 Curriculum | V9 Australian Curriculum

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ACARA acknowledges the Traditional Owners and Custodians of Country and Place throughout Australia and their continuing connection to land, waters, sky and community.

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SAMR Framework with real life examples

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Good technology integration isn't about using the fanciest tool, it's about being aware of the range of options and picking the right strategy-or strategies-for the lesson at hand.

The biggest obstacle to teaching online probably isn't the technology. Teachers seek out educational technology, in fact, because it "can have considerable positive impacts on student performance," according to a 2016 study -improving test scores and allowing teachers to assess student achievement more efficiently. The big problem is how to integrate it: Beyond the sheer number of tech tools available, the same researchers identified "inadequate professional development and training" as the primary obstacle to using technology productively in classrooms.

Understandably, the emergence of the coronavirus has dramatically accelerated the process of integrating edtech, as educators around the country race to get online as fast as they can. But as many of our teachers have noted, the current state of K-12 online learning is more like triage-a form of crisis management-and not at all like skillfully managed distance education.

What's missing from the conversation right now, which makes sense given the immediacy of the need, is a focus on the bigger question of what the highest quality technology integration actually looks like. That's an important conversation to have, because in a post-coronavirus world there's likely to be a greater emphasis on digital learning, even as we return to physical schools and take advantage of face-to-face opportunities.

A Hierarchy of Tech Uses

A powerful conceptual tool to think about technology integration-and edtech's best uses-is the SAMR model, developed in 2010 by education researcher Ruben Puentedura, who was the 1991 recipient of a Phi Beta Kappa teaching award.

The SAMR model lays out four tiers of online learning, presented roughly in order of their sophistication and transformative power: substitution, augmentation, modification, and r edefinition. When switching to an online format, teachers often focus on the first two levels, which involve replacing traditional materials with digital ones: converting lessons and worksheets into PDFs and posting them online, or recording lectures on video and making them available for asynchronous learning, for example.
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Those are important steps, especially when teaching online for the first time, but in classrooms where tech integration has moved to the mastery level, the last two levels of the SAMR model-modification and redefinition-should also be in the mix. Students in classes where this kind of mastery is embedded find more novel and immersive uses for technology. They are creators and publishers of their own work across multiple forms of media, for example, or they are inviting professionals to provide feedback on their work products, or participating in digital forums with other peers around the world.

It's tempting to think of SAMR as a mountain to be summited. But good technology integration isn't about living at the top of the SAMR model; it's about being aware of the range of options and picking the right strategy-or strategies-for the lesson at hand.

Here's a closer look at good classroom practices at each level in the model:

Substitution

"Substitution" means replacing traditional activities and materials-like in-class lectures or paper worksheets-with digital versions. There is no substantial change to the content, just the way that it is delivered.

The goal here is to keep things simple: there's no need to reinvent the wheel. Scan your lessons and worksheets, convert them into PDFs, and post them online using Microsoft OneDrive, Google Drive, or a similar file-sharing service. Think about the information you have on your walls, such as the classroom norms, the daily schedule, or vocabulary lists, and convert them into digital formats that students can easily reference.

It may also help to provide synchronous as well as asynchronous versions of your lectures. If you're holding class meetings over a videoconferencing service like Zoom or Skype, provide a recording for students who can't attend. You can also create your own instructional videos for students to view at their own pace.

Augmentation

This level involves incorporating interactive digital enhancements and elements like comments, hyperlinks, or multimedia. The content remains unchanged, but students can now take advantage of digital features to enhance the lesson.

For example, students can create digital portfolios to create multimedia presentations, giving them more options to demonstrate their understanding of a topic. And instead of handing out paper quizzes, you can gamify your quizzes with tools like Socrative and Kahoot.

Teachers can also create virtual bulletin boards-using an app like Padlet -where students can post questions, links, and pictures.

Modification

At this level, teachers can think about using a learning management system like Google Classroom, Moodle, Schoology, or Canvas to handle the logistical aspects of running a classroom, like tracking grades, messaging students, creating a calendar, and posting assignments.

Teaching online opens up new channels of communication, many of which can help students who have traditionally been marginalized. Research shows that girls may be less likely to speak up in class, for example, so they may benefit from backchannels -alternative conversations that can run alongside instruction-that encourage participation.

Zoom's text chat feature, meanwhile, gives students an opportunity to write their questions out, which can feel less intrusive if there are dozens of students participating in the call. Also, students who prefer to collect their thoughts may benefit from slower-paced, asynchronous discussions in an online forum or email threads.

Redefinition

Learning is fundamentally transformed at the "redefinition" level, enabling activities that were previously impossible in the classroom.

For example, virtual pen pals can connect students to other parts of the world, whether it's with other students or experts in a field. Virtual field trips enable students to visit locations like the Amazon rainforest, the Louvre, or the Egyptian pyramids. After reading a book in class, you can invite the author to chat about their work and answer questions.

Technology also provides an opportunity to bring authentic audiences into your virtual classroom, and can make publishers out of your students. Kids can write their own wikis or blogs for public consumption and feedback-and platforms like Quadblogging can connect distant classrooms together so students both write and respond. Students can tackle local problems-like investigating the water quality of a nearby river-and invite members of the community to assess their digital proposals.

Going Beyond SAMR

Finally, consider how technology can be used not just as a way to deliver content, but also to strengthen relationships with your students. For elementary school teacher John Thomas, Seesaw and Flipgrid allow him to share a daily greeting, which his students then respond to-or to each other-with a typed or voiced comment. It's a good way to provide some stability while they're isolated.

How can my lesson be improved using technology?

How can I engage and empower students through technology?

How can online learning more closely resemble authentic, real-world learning?

Remember, again, that SAMR is sometimes thought of as a mountain to summit, but it's really more like a toolbox. The goal isn't to use the most sophisticated tool, but to find the right one for the job. More importantly, however, it's a way to reflect on your technology integration by thinking about a few key questions:

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A Powerful Model for Understanding Good Tech Integration

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Good technology integration isn't about using the fanciest tool, it's about being aware of the range of options and picking the right strategy-or strategies-for the lesson at hand.

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For teachers just starting out with educational technology, the task at hand can sometimes seem daunting. Even though tools such as the SAMR model can help, the plethora of choices available can prove paralyzing, frequently resulting in ongoing substitutive uses of the technology that block, rather than enable, more ambitious transformative goals.

The approach below is designed to help overcome this barrier, and is inspired in its form by Alexander's notion of Design Patterns -- a clearly structured solution to a recurring design problem -- which has been applied to education scenarios by Bergin et al. While it is not laid out exactly as a design pattern would be, it nonetheless provides a framework that a teacher could use in similar fashion.

The goal for the teacher is to construct a simple SAMR ladder that is coupled to Bloom's Revised Taxonomy -- i.e., as the task moves from lower to upper levels of the taxonomy, it also moves from lower to upper levels of SAMR. The two Enhancement levels of SAMR (Substitution, Augmentation) are associated with the three lower levels of Bloom (Remember, Understand, Apply), while the two Transformation levels of SAMR (Modification, Redefinition) are associated with the upper levels of Bloom (Analyze, Evaluate, Create). In turn, within each grouping a similar ordering occurs -- e.g., Remember-type tasks are primarily associated with S-level uses of the technology, Understand-type tasks are associated with either S- or A-level uses of the technology, and so on. The following diagram illustrates this association.

This coupling of the SAMR model and Bloom's Taxonomy has several desirable outcomes:

The already-familiar drive to reach the upper levels of Bloom's Taxonomy now also acts as a drive to reach the upper levels of SAMR;

The approach outlines a clear set of steps that help guide the introduction of technology in the classroom;

Finally, the approach helps avoid pitfalls of self deception -- i.e., assuming that a particular task is at a higher level in either the Bloom or SAMR sense than it actually is.

Avoid epic fails and get the most out of technology.

It is important to realize that this association between SAMR and Bloom's Taxonomy is not a necessary -- or even habitual -- coupling. Thus, it is possible to use extremely powerful redefinition-level approaches to make certain types of memorization tasks possible; conversely, it is also possible to undertake novel create-type tasks that only make basic substitution/augmentation use of the technology. Additionally, far more complex couplings between SAMR and Bloom are possible, involving convergent/divergent branchings, oscillations between levels, skipping of some SAMR levels, etc. Nonetheless, the simple structure described above is well suited to beginning practitioners' needs, and even retains usefulness for more experienced faculty.

In addition to the integration of SAMR and Bloom described above, two more ingredients are necessary for the best results:

a clear motivation for the change -- the best results are obtained when a teacher has a strong reason for changing existing practice that is independent of the introduction of technology.

a clean app flow, designed to move through the tasks, that is as simple as possible, avoiding needless complexity -- e.g., in transferring work products from one app to the next.

Finally, let's look at an example of this approach in practice. In this example, we will set up a general pattern for math activities, where the motivating factor is to take math instruction from a mode where -- to use Richard Skemp's words -- instrumental understanding dominates (how) to a mode where relational understanding is primary (how and why). This shift in math instruction can be seen in changes in curricula worldwide, and is crucial to students' capacity to use -- and enjoy -- the math they have learned in the world outside the classroom. In the interest of making the example more tangible, the context will be a course in introductory statistics, although the general pattern is readily applicable to other math courses.

1. Substitution/Remember: Students use ebooks and other Open Education Resources to acquire basic knowledge about statistical tools and procedures.

2. Substitution/Understand: At the same time, they begin a process of gathering information online describing applications of these statistical tools to an area of interest to them, using simple bookmark aggregation services (e.g., Diigo, Delicious) to collect and tag these resources, relating them to the knowledge gained in 1.

3. Augmentation/Apply: Using a simple yet powerful tool for visualization like GeoGebra, students explore the concepts covered in the resources described in 1., and solve related standard problems. The scope and number of the problems is not governed by what is available in the "back of the book," but rather driven by the evolution of student understanding, as measured by suitable formative assessment processes.

4. Modification/Analyze: The students also apply similar problem-solving approaches to questions raised in the materials they found in 2. In doing so, they will reconstruct the reasoning of the original authors, and verify -- or disprove -- their conclusions.

5. Modification/Evaluate: Students now select a subset of the materials studied in 4. for further critique and/or development, using GeoGebra as their primary analysis tool. Via a blog, they explain this work to fellow students, and invite their feedback to refine both the clarity of their explanations and the focus of their work.

6. Redefinition/Create: Students refine their blog post into a short digital video project, with the goal that it will be used as part of instructional materials in subsequent years.

Photo " sky puzzle" by Jared Tarbell. Used under a CC BY 2.0 license.

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SAMR and Bloom's Taxonomy: Assembling the Puzzle | Common Sense Education

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Find out how you can use technology to engage students in rich learning experiences.

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The Department for Education Unit of Work for Year 8 Mathematics provides great examples of activities and resources (digital and physical) for student learning.

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Statista is a website that enables users to access a huge range global of statistics and data.

Students can access real-life data in an area of interest and familiarity, such as Apple, Google and Netflix, or trending statistics, to analyse and interpret in a classroom setting to apply their knowledge and understanding of data collection.

The website can be accessed using and device (laptop, iPad etc.).

The data available for free on the site is limited however, could be worthwhile subscribing at a whole-school level given the wide variety of data available and cross-curriculum and year level connections.

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Apr 15, 2024 | Mobile Devices

Quarterly smartphone market share worldwide by vendor 2009-2024

Samsung held the largest slice of the global smartphone market by shipments during the first quarter of 2024, followed by Apple. Xiaomi has taken a tight grip on the third position, accounting for a market share of 14 in the first quarter of 2024.

Samsung and Apple smartphone sales Smartphone vendors have been suffering from the events of the past couple of years, including the pandemic and the economic downturn. However, they all appear to be recovering, as shown by the recent increase in shipments. For instance, mostly based on the main line of Galaxy Series, Samsung's smartphone shipments totaled nearly 226.5 million units globally in 2023.

Next to Samsung, Apple is a major manufacturer of smartphones worldwide, with the company shipping more than 232 million iPhones worldwide in 2023 - a number that made Apple leading smartphone vendor for the first time ever. Apple's sales tend to be very cyclical, peaking in the fourth quarter each year, much like in the fourth quarter of 2023, when they took the first spot in terms of units shipped globally with around 80.5 units.

Huawei falls outside the leading five vendors While Apple and Samsung are typically the two major companies challenging for the top spot, Huawei had provided a strong challenge in recent years. Particularly, the Chinese company managed to climb the smartphone market ladder between 2011 and 2020, recording shipments of over 32 million smartphones in the fourth quarter of 2020. However, strong performances from rivals like Xiaomi and the effects of the U.S. trade ban have since seen Huawei fall outside the list of top five vendors by smartphone shipments.

Read more

Apr 16, 2024 | Business Enterprise

Most affluent women worldwide 2023, by net worth

The granddaughter of the L'Oréal founder, Francoise Bettencourt Meyers was the wealthiest woman in the world as of April 2024. She and her family's net worth was estimated at 99.5 billion U.S. dollars. Alice Walton was ranked second with over 70 billion U.S. dollars in net worth. By comparison, the richest man in the world had a fortune of over 258 billion dollars as of December 2023.

Read more

Apr 16, 2024 | Population

Total population of China 1980-2029

According to data published by the National Bureau of Statistics of China in January 2024, the Chinese population decreased by 2.08 million people to around 1,41 billion in 2023. This was a stronger decrease than expected by the IMF, which underestimated China's population decrease already in 2022. China arrived at the turning point of its population growth earlier than expected by many observers, and current IMF estimates for the total population until 2029 very likely need to be adjusted downwards.

Population development in China China had for a long time been the country with the largest population worldwide, but according to UN estimates, it has been overtaken by India in 2023. As the population in India is still growing, the country is very likely to remain being home of the largest population on earth in the near future. Due to several mechanisms put into place by the Chinese government as well as changing circumstances in the working and social environment of the Chinese people, population growth has subsided over the past decades, displaying an annual population growth rate of -0.15 percent in 2023. Nevertheless, compared to the world population in total, China held a share of about 18 percent of the overall global population in 2022.

China's aging population In terms of demographic developments, the birth control efforts of the Chinese government had considerable effects on the demographic pyramid in China. Upon closer examination of the age distribution, a clear trend of an aging population becomes visible. In order to curb the negative effects of an aging population, the Chinese government abolished the one-child policy in 2015, which had been in effect since 1979, and introduced a three-child policy in May 2021. However, many Chinese parents nowadays are reluctant to have a second or third child, as is the case in most of the developed countries in the world. The number of births in China varied in the years following the abolishment of the one-child policy, but did not increase considerably. Among the reasons most prominent for parents not having more children are the rising living costs and costs for child care, growing work pressure, a growing trend towards self-realization and individualism, and changing social behaviors.

Read more

Apr 17, 2024 | Online Retail

Visitors to most popular online retailers in Japan 2024

As of March 2024, Amazon Japan's e-commerce website was the leading e-commerce site accessed in Japan, with almost 587 million visits. The subsidiary of the American technology company competes in the Japanese e-commerce market against the major business-to-consumer (B2C) retailers Rakuten and Yahoo Japan.

Read more

Apr 15, 2024 | Soccer

Most German soccer titles 1903-2024, by club

In 2024 Bayer Leverkusen won the Bundesliga for the first time, with the team going unbeaten in all competitions for over 40 matches. Previously, Bayern Munich had won the league every year since 2013.

Read more

Apr 16, 2024 | Vehicle Manufacturing

Latin America: number of motor vehicles produced 2013-2023, by country

In the last years, Mexico has positioned itself as the largest producer of vehicles in Latin America. In 2023, the North American country produced just over four million motor vehicles, followed by Brazil, where around 2.3 million units were produced. In addition, most of the motor vehicles produced in Mexico were light commercial vehicles.

Read more

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Find statistics, consumer survey results and industry studies from over 22,500 sources on over 60,000 topics on the internet's leading statistics database

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Desmos (Desmos, 2024) is a fun online activity platform, providing students with an interactive and meaningful alternative to explore and apply their learning about mathematical concepts.

Activities are available in collections relevant to year levels and curriculum content and are designed to be completed in stages relevant to the level of classroom learning.

As activities are assigned by the teacher, they can view how many attempts students have at each stage of an activity and their responses providing a great tool to check for learning. The activities do not allow students to progress to completion without completing each step.

Students can access activities assigned by the teacher using an iPad or laptop and can complete the tasks collaboratively or individually depending on the nature of the task. Desmos could be integrated into learning for a variety of purposes such as brain break, check for learning or introductory activity.

Desmos also reflects the transformative level of the SAMR model as it allows for significant task redesign and the creation of new tasks that would otherwise be impossible without the use of this digital tool and technology (Terada, 2020). This is evident through the ability for students to explore mathematical concepts using an interactive medium where students can apply their thinking to real-life scenarios and problem solve in real time. The staged progression of each task also allows students to become familiar with the technology before the final task within that unit where they have the freedom to use the least-structured version of the tool. The unique features makes Desmos an effective partner in the classroom, while offering students the opportunity to grow in their understanding of digital tools in the process.

Given the versatility of the tool, progression of activities in stages and ability to make real-life connections to activities to enhance student understanding, Desmos would be an effective learning tool to incorporate into teaching and learning at all levels of a unit topic.

Terada, Y. (2024). A Powerful Model for Understanding Good Tech Integration. edutopia. https://www.edutopia.org/article/powerful-model-understanding-good-tech-integration

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Transum Mathematics is a website that provides a variety of fun maths games for students up to Year 8.

Teachers can select activities from a variety of mathematical topics relevant to the unit of focus in the classroom.

Some activities are interactive and require data input for responses whereas other activities are not and could be used for whole class discussions as a check for learning or share the link with students to complete in their digital learning portfolio individually (e.g. blog, Daymap etc.).

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Free online interactive resources for Mathematics teachers, pupils and parents.

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The Mathematical Association of South Australia Inc

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The Mathematical Association of South Australia Inc

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Membership to MASA provides support to South Australian Mathematics teachers.

Teaching resources or tickets to networking/professional learning events are also available for purchase on their website.

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Become A Member

Join the Mathematical Association of South Australia

Pre-Service Colleague

Only available for current registered Pre- service Teachers

Personal discounted rates for professional learning workshops and conference

Discount on many items in The MASA Shop

Curriculum Support

Registration each year, with proof of study

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The Mathematical Association of South Australia - Supporting the mathematics teachers of South Australia

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Become A Member Only available for current registered Pre- service Teachers Personal discounted rates for professional learning workshops and conference Discount on many items in The MASA Shop Curriculum Support Registration each year, with proof of study

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AAMT represent mathematics education in Australian schools. Membership provides access to professional learning for teachers, events and resources (physical and digital e.g. Maths300).

Maths300 is a library of inquiry-based maths lessons maintained by AAMT, available to teachers via subscription.

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Australian Association of Mathematics Teachers

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Banqer High is an experiential learning platform that helps educators teach financial literacy through engaging and educational activities. Our platform offers comprehensive curriculum-aligned lesson plans, allowing you to seamlessly integrate financial literacy into your teaching - and save precious time.

We've made learning about money both engaging and enjoyable, so your students can develop crucial financial skills while having fun. Students will navigate through real-life scenarios in a safe, controlled environment, learning key financial and mathematical concepts along the way. With Banqer High, your students won't just learn about money- they'll experience it.

Banqer High features

Easily deliver curriculum-aligned, deeply engaging financial education that reinforces mathematical learning

Save time with teaching resources that ensure curriculum alignment

Help your students develop financial literacy skills

Engaging and immersive simulated economy that brings mathematical concepts to life

Discover the ease of teaching financial literacy with Banqer High. Equip your students with the financial skills they need, all while enhancing their mathematical abilities.

Interested in bringing the Banqer approach to your classroom? Reach out to our team to get started, or book a 10-minute exploration chat.

Read about Teaching Financial Literacy

Read about Teaching Digital Currency

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The Australian Association of Mathematics Teachers

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The Australian Association of Mathematics Teachers is the leading organisation representing mathematics education in schools throughout Australia.

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The NRICH Project website offers engaging mathematical experiences for learners linked closely to the Australian curriculum.

A unique feature of NRICH is the 'Live Problems' section, inviting students to collaborate with NRICH and other online learners across the globe on providing solutions to selected problems.

NRICH provides a range of free-to-use resources in both printable and interactive (both general and specific activity) form. The Department for Education 'Units of Work' show links between units of learning and where some of NRICH's activities may be useful to enhance learning experiences in the classroom (see link in Padlet to DfE Units of Work).

The versatility and ability to access NRICH from anywhere at any time, provides a unique resource to integrate into teaching and learning activities.

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Gizmos is an online simulation STEM based program, providing hundreds of short interactive mathematics activities.

Each activity enables students to explore concepts, analyse data and dive deeper into inquiry-based activities to allow students to apply their learning of curriculum content.

The vast library ensures there is an activity for all areas of curriculum for the appropriate year level.

Gizmos is free for the first 45 days and a paid subscription is required after this however, the free-trial period would allow sufficient time for a class to explore its tools for learning for a specific unit if well planned by the teacher.

This resource was originally shared by Kira Lloyd-Jones (2024) via their Padlet in a science context however, being a STEM tool it can also be applied in a Maths context.

Lloyd-Jones, K. (2024). EDSE1202 AT2 Resources. Padlet.

https://padlet.com/kiralloydjones/edse1202-at2-resources-exa4uxzz1z9xnhxk

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Interactive STEM Simulations & Virtual Labs | Gizmos

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Unlock STEM potential with our 550+ virtual labs and interactive math and science simulations. Discover engaging activities and STEM lessons with Gizmos!

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Mathematics Hub is an Australian Government funded online teaching and learning resources for maths for Foundation to Year 10.

Resources are available by unit topic for each year level and state the relevant links to the Australian curriculum.

Mathematics Hub offers a unique 'Planning Tool' to guide teachers with the expected level of development for each year level including teaching and learning focus, learning goals, learning from home activities and support for addressing areas of confusion in learning. Teachers also have access to suggested teaching strategies, additional resources and assessment ideas.

The 'Learning from Home' section provides students with a step-by-step learning progression task with access to interactive activities at each stage.

Mathematics Hub would be a useful tool to integrate into teaching and learning, especially as a beginning teacher, as it provides a broad guide for implementing and teaching a unit at the appropriate year level in-line with the Australian Curriculum, and indicators for student learning success. Teachers can use the Planning Tool but still have the freedom to enhance learning opportunities by incorporating other digital tools and activities into teaching and learning outside of Mathematics Hub.

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The Maths Hub supports mathematics and numeracy education for primary and secondary schools; providing resources for teachers, students and their families, including the Number Check for teachers.