Functions and Graphs

Overview

This 60-minute lesson will engage Year 11 Mathematics students in exploring linear and quadratic functions, their graphs, and real-world modelling applications, with a meaningful integration of Indigenous perspectives. The lesson aligns with the Australian Curriculum content and general capabilities, providing a culturally inclusive and rigorous mathematical experience.

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Australian Curriculum Alignment

Content Descriptors:

• Year 11 Mathematics Standard (Mathematics Standard Stage 6)
  • Solve problems involving linear and quadratic functions, including use of digital tools to graph and interpret these functions in various contexts (ACMMG289 equivalent aligned)
• Mathematical Modelling: Use algebraic and graphical techniques to solve problems involving change and practical contexts, including financial and environmental situations (building on elaborations from earlier years adapted for Year 11 depth).

General Capabilities:

• Numeracy: Developing skills to graph and interpret algebraic functions with accuracy.
• Critical and Creative Thinking: Analyzing and modelling real-world contexts with functions.
• Intercultural Understanding: Exploring Indigenous knowledge systems and applying them meaningfully in mathematical modelling.
• Ethical Understanding: Reflecting on the significance of Indigenous connections to land and natural phenomena in mathematical patterns.

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Learning Objectives

By the end of this lesson, students will:

• Understand and apply concepts of linear and quadratic functions and their graphical representations.
• Use digital graphing tools to plot functions and interpret key features (intercepts, turning points).
• Explore mathematical modelling through Indigenous hunting techniques as a contextual example to enhance relevance and cultural respect.
• Reflect critically on the connections between mathematics and Indigenous cultural practices.

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Resources Required

• Graphing calculators or digital graphing software (e.g., Desmos, GeoGebra)
• Whiteboard and markers
• Handouts with Indigenous hunting modelling problem and guided questions
• Projector/screen for demonstrations
• Calculators for computation
• Printout or visual of Indigenous artwork or story relating to quadratic-like patterns in nature (optional multimedia)

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Lesson Structure

Time	Activity	Description
0-10 min	Introduction & Engagement	- Briefly revisit definitions of linear and quadratic functions.

• Show a visual example of Indigenous hunting techniques modelled by quadratic functions (inspired by AC9M9A05_E6 elaboration).
• Discuss how Indigenous knowledge applies patterns to practical problems, fostering respect for First Nations expertise. | | 10-25 min | Exploration & Modelling Task | - Students work in pairs to model an Indigenous hunting scenario using quadratic functions.
• Problem involves interpreting data to create a quadratic model predicting catch success based on the number of hunters.
• Use tables and graphing tools to plot and analyse features: vertex (max catch), intercepts (possible outcomes).
• Teacher circulates, prompting deeper thinking and checks understanding. | | 25-35 min | Guided Graphing Demonstration | - Live demonstration of graphing linear and quadratic functions on digital tools.
• Highlight interpretations of turning points, intercepts, and real-world meaning.
• Students replicate on their devices, experimenting with function parameters. | | 35-45 min | Class Discussion & Reflection | - Facilitate a discussion on how modelling Indigenous practices reflects the connection between culture and maths.
• Invite students to consider other cultural or environmental contexts where quadratic or linear models apply.
• Connect back to the Australian Curriculum cross-curriculum priority of Aboriginal and Torres Strait Islander histories and cultures. | | 45-55 min | Individual Practice | - Students complete a worksheet involving:
  • Modelling given data using quadratic functions.
  • Graphing and interpreting key points.
  • Explaining results in context.
• Encourage inclusion of cultural perspectives or ethical considerations where relevant. | | 55-60 min | Summary and Exit Ticket | - Quick recap of main points.
• Exit ticket: Write one way Indigenous perspectives enrich mathematical understanding or one new thing learned about functions. |

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Assessment & Differentiation

• Formative Assessment: Observation during tasks and discussions; responses to exit ticket.
• Differentiation:
  • Provide scaffolds such as step-by-step guides or formula sheets to support struggling students.
  • Extension tasks for advanced students could include exploring transformations of quadratic graphs or using algebra to solve modelling problems.

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Additional Notes on Indigenous Perspectives Integration

• The example of modelling hunting techniques using quadratic functions is drawn directly from elaborations on AC9M9A05_E6, showing how Indigenous knowledge of environment and tactics is mathematically rich and relevant.
• The lesson respects Indigenous knowledge systems by presenting them as real-world mathematical models rather than abstract or token examples.
• Encourages students to appreciate the depth and applicability of First Nations’ understanding of the natural world, promoting intercultural competence.

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If further adaptation is required, this lesson can be extended to include an investigation on the use of technology supporting Indigenous land management, connecting mathematics with sustainability and ethics.

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I trust this plan will provide Australian Year 11 teachers with fresh, culturally attuned, and curriculum-aligned resources to engage students deeply and meaningfully in important mathematical concepts.

Should you require, I can prepare the accompanying student worksheet and digital tool instructions.