Modelling Project Guide (Leaving Cert Applied Maths): Revision Notes
Modelling Project Guide
Understanding your modelling project
The Applied Mathematics modelling project is a crucial component of your Leaving Certificate studies. You must complete a mathematical modelling project and write a comprehensive report in response to a brief issued by the State Examinations Commission (SEC) in 6th year.
Project requirements
Critical Project Requirements
Your final report must meet specific technical requirements to ensure fairness and accessibility during marking:
- Cannot exceed 900 words (excluding references, equations, diagrams, and graphs)
- Maximum of 20 images (tables, graphs, charts, diagrams, or photographs)
- Total digital file size must not exceed 100 MB (including all embedded images)
- Videos are not permitted in your submission
The most important step in beginning your project is thoroughly understanding the brief you receive. Take time to carefully analyse what the project is asking you to investigate and what the ultimate purpose of your mathematical model will be. This understanding will guide every decision you make throughout the research and writing process.
The mathematical modelling process
Mathematical modelling follows a systematic, cyclical approach that helps you tackle complex real-world problems using mathematical tools and techniques.
The mathematical modelling cycle consists of four interconnected stages that you will move through multiple times during your project:
Formulating problems: This stage involves identifying and clearly defining the real-world problem you want to investigate. You'll need to determine what questions you're trying to answer and what factors might influence the situation.
Translate to mathematics: Here, you convert the real-world problem into mathematical language. This includes identifying variables, establishing relationships between them, and selecting appropriate mathematical methods or equations to represent the situation.
Computing solutions: In this stage, you use mathematical techniques to solve the problem. This might involve calculations, using technology, creating graphs, or applying mathematical formulas to find answers.
Evaluating solutions: Finally, you assess whether your mathematical results make sense in the real-world context. You'll check if your answers are reasonable, consider limitations of your model, and determine if further refinement is needed.
Remember that this is a cyclical process - you may need to revisit earlier stages as you gain new insights or identify areas for improvement in your model.
Research and referencing skills
Finding reliable sources
When conducting research for your project, developing skills to evaluate source credibility is essential. Not all information available online is accurate or suitable for academic work, so you must learn to distinguish between reliable and unreliable sources.
Key Factors for Determining Source Credibility
Consider these factors when evaluating sources:
- Peer review status: Information that has been peer reviewed (checked by experts for accuracy) typically has high reliability because experienced professionals in the field have verified its content
- Source verification: Look for the same information across multiple reputable sources. If several independent, credible sources contain similar information, there's a stronger likelihood it's accurate
- Currency and dates: Check when information was published and last updated. False information often contains incorrect dates or altered timelines
- Bias awareness: Be conscious of how your own views might affect your judgement of information reliability
Always refer back to your problem statement and ask yourself whether the information you're finding fits into your project and supports your mathematical model.
Online research strategies
Effective online searching requires strategic thinking beyond simply using the first search result. Search engines may prioritise results for reasons other than quality, so develop systematic approaches to finding the best information.
When you discover valuable information, bookmark it immediately for easy access later. This simple step can save considerable time when you're writing your report and need to relocate sources.
Referencing requirements
Proper referencing is fundamental to academic integrity and allows readers to verify your sources. Any information gathered from secondary sources must be acknowledged, whether you're directly quoting or adapting someone else's ideas.
Referencing involves two distinct components:
- In-text citations: These appear within your report's main text and indicate when you're using someone else's work. They typically include the author's name and publication date
- Reference list: This provides complete bibliographic details for all sources cited in your text, allowing readers to locate the original materials
When creating reference list entries, you may need to include details such as author names, publication years, article or chapter titles, publication titles, issue and volume numbers, places of publication, publishers, editions, page numbers, URLs, and access dates for online materials.
Writing strategies and presentation
Organising your report structure
Before beginning to write, create an outline that organises your research and provides a clear structure to follow. This isn't simply copying and pasting information, but rather demonstrating your understanding of how the research applies to and enhances your mathematical model.
Your background research should directly relate to your specific model, with strong connections made between your research findings and the problem you're investigating.
Introduction and research section
The introduction should clearly identify the specific problems you're modelling and engage with relevant background research. Understanding your research's purpose helps you determine which information is most relevant to your particular modelling problem.
Ensure your word count is used effectively by appropriately covering:
- Background research on the brief
- Identifying specific problems to be modelled
- Researching those problems
- Identifying relevant variables
- Presenting relevant data
- Providing proper citations and references
Using effective language
Strong academic writing uses varied sentence structures and appropriate transitional phrases to create logical flow between ideas. Consider using sentence stems to help structure different sections of your report.
For introducing points, you might begin with phrases like "To begin with..." or "First of all..." For presenting your opinions, consider "I believe that..." or "In my view..." When citing other sources, use phrases like "According to..." or "As explained by..."
Conclusions and recommendations
Your conclusion should connect with other parts of your project, including background research, relevant data, assumptions, iterations, and results. The purpose is to interpret the meaning of your solutions within a real-world context, summarise your work, make statements based on findings, and reflect on your model's outcomes and the modelling process itself.
Use your conclusion to make recommendations for the particular context you're modelling and suggest areas for future research.
Interpreting and representing data
Understanding data types
When working with data, it's important to distinguish between different types. Primary data refers to information you gather yourself directly for your project. Secondary data refers to information that someone else has already collected previously.
Both qualitative (categorical) and quantitative (numerical) data can be valuable in your modelling project. Long lists of raw data can be difficult to interpret, so appropriate graphical representations help summarise information and reveal patterns or trends.
Simply presenting data isn't sufficient - you must analyse it and draw conclusions that relate directly to your problem statement and mathematical model.
Choosing appropriate data representations
Different types of data visualisation serve different purposes, so selecting the right format depends on what message you want to communicate.
This decision tree helps you determine the most suitable data representation based on your goals. If you want to show relationships between variables, consider scatter plots or bubble plots. For displaying distribution patterns, bar charts or histograms work well. When showing composition, decide whether your data is dynamic (changing) or static (fixed) to choose between stacked charts or pie charts. For comparisons, consider whether you're comparing multiple items or showing changes over time.
Types of data visualisation
Different chart types serve specific purposes:
- Line charts effectively demonstrate trends and changes over time
- Bar graphs and histograms compare data across many different items
- Pie charts express part-to-whole relationships
- Scatter plots show relationships and distribution patterns in large datasets
- Tables display precise numerical data and multiple categories
- Maps visualise data by geographical location
- Waterfall charts demonstrate static composition
- Area charts portray part-to-whole relationships over time
Data presentation guidelines
Essential Rules for Data Presentation
Follow these important guidelines when presenting data:
- Keep it simple: Excessive amounts of data and complex graphs can confuse readers and obscure key information
- Start general, then become specific: Begin with broader context before focusing on detailed findings and specific analyses
- Connect to your project: All data should relate to and help answer your modelling project's central problem statement
- Use past tense for results: Describe your findings using past tense language
- Avoid repetition: Select the best method for communicating each piece of information rather than presenting the same data in multiple formats
- Include proper references: Whether you created graphs yourself or used secondary sources, reference all visual elements to demonstrate their relevance and impact on your mathematical model
Always label images properly with figure numbers and descriptive captions, and refer to them clearly within your report text.
Remember!
Key Points to Remember:
- Understand the brief thoroughly - This is your most important first step and will guide all subsequent decisions in your project
- Follow the modelling cycle - Use the four-stage process (formulating, translating, computing, evaluating) as a systematic approach to problem-solving
- Evaluate source credibility carefully - Not all online information is reliable, so develop skills to assess the quality and accuracy of your research materials
- Reference all sources properly - Use both in-text citations and a complete reference list to maintain academic integrity and allow others to verify your sources
- Choose data representations strategically - Select charts and graphs that best communicate your specific message and support your mathematical model's conclusions