Real-World Problem: The Start of Mathematical Modelling
Hypothetical Situation:
The Environmental Protection Department (EPD) planned to clear school playgrounds for tree planting to offset carbon emissions for environmental conservation. However, the King's College Student Union wanted to preserve the playground for student activities.
The Environmental Protection Department (EPD) planned to clear school playgrounds for tree planting to offset carbon emissions for environmental conservation. However, the King's College Student Union wanted to preserve the playground for student activities.
1
EPD's Proposal
Clear school playground to plant trees for carbon dioxide absorption and environmental conservation
2
Student Union's Counter-offer
Keep playground intact and offer alternative empty land of equal area for tree planting
3
Mathematical Investigation
Design floor plan and calculate carbon dioxide absorption for an alternative site
Learning Tasks and Its Key Considerations
Learning Tasks for Secondary 2 Students
- Draft a proposed floor plan showing tree arrangement
- Calculate estimated carbon dioxide absorption per year
EPD Condition
- The area of the piece of alternative empty land must equal to that of the school playground
Mathematical Considerations
Students needed to identify the key mathematical parameters and assumptions during area calculations, spatial arrangements and environmental factors consideration in their designs.
Key Mathematical Parameters
- Playground area: 1,050 m² (rounded to 1,000 m²)
- Tree species: Chinese Banyan (細葉榕)
- Tree area: 60 m² per tree
- Carbon dioxide absorption: 28.5 kg/year per tree
Data Collection
When developing the mathematical model, students proposed and analysed essential information needed for their floor plan design and carbon dioxide absorption calculations.
Area Calculations
Playground area and new land area, individual tree areas, and spatial arrangement considerations
Tree Specifications
Types of trees, shapes, carbon dioxide absorption amounts, and growth requirements including sunlight and water needs
Environmental Factors
Sunlight levels, irrigation requirements, and aesthetic considerations
Student Design Process
- Students worked collaboratively in small groups in a dynamic 10-minute design sprint to create detailed floor plans for tree-planting arrangements.
- This design process required various mathematical concepts and manipulations, including area and perimeter calculations, spatial geometry for optimal tree placement, and scaling to determine the number and size of trees.
- Their design approach involved initial brainstorming and sketching draft layouts, followed by iterative refinement, all while strictly adhering to a 1 cm : 1 m scale to illustrate the conversion from floor plans to real-world dimension.
- Throughout the process, students made rapid design decisions, prioritised key mathematical considerations, and communicated effectively under pressure.
- Upon completion, finalised designs and supporting calculations were submitted digitally via collaborative online platforms, enabling seamless sharing and feedback among the students.
Student Performance
Students developed problem-solving and collaborative skills after experiencing this mathematical modelling lesson and project. They took on different roles within groups to design suitable trees arrangements while demonstrating creativity in the process of formulating project proposals.
Key Skills Developed
- Collaborative problem-solving
- Creative design thinking
- Mathematical concept application
- Peer assessment and critique
Students applied mathematical concepts including using carbon dioxide absorption rates to estimate the effectiveness of environmental conservation; and using ratios, scales, and proportions to present their proposals proficiently while gaining solid understanding of mathematical modelling processes. Peer assessment sessions sparked meaningful intellectual conversations, encouraging deeper thinking and continuous improvement.
Professional Growth and Future Development
The mathematical modelling experience proved highly beneficial for curriculum leaders, teachers, and students, fostering pedagogical reflection and professional development.
Teachers gained insights into lessons that scaffold mathematical modelling activities in authentic contexts, utilising mathematical tools to solve real-world problems, while strengthening collaborative practices such as co-teaching models and collective reflection.
Key Outcomes
- Mastered mathematical modeling transforming real-world problems into mathematical problems
- Developed collaborative and creative problem-solving skills
- Transformed abstract mathematics into practical environmental solutions
- Bridged disciplines such as mathematics, science and technology education through integrated, project-based learning
"There is no single correct answer in mathematical modelling" - This principle encouraged students to explore multiple solutions and think critically about real-world problems.
Future Development
Scale this transformative approach by engaging more colleagues in mathematical modelling pedagogy and extending its implementation across the curriculum, multiplying its impact and embedding real-world problem-solving as a cornerstone of mathematics education in King's College.