Course Content
Mathematical Modelling Project
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Applied Maths Project
##### UPDATE!

We’ve added new and improved sample projects for all members right here!

As we typically get many students signing up around this time, we’ve temporarily discounted our full memberships to just €59 for the year!

## Project Information & Guide

#### OVERVIEW

In the new syllabus of Applied Maths, 20% (100 marks) of the overall marks (500 marks) for the subject are awarded to a project that each student completes in the latter half of 6th year.

On this page, we will detail what the project is, how to approach writing the project and how the project is assessed.

Members also gain access to examples of completed projects as well as tips and tricks that are specific to this year’s project.

##### What do I write about?

Towards the end of the first term of 6th year (~ November), the States Examination Committee (SEC), the body that creates the Leaving Cert exam papers, announces the title of the project.

This title will be associated with a concept, or multiple concepts, within Applied Maths (or, at least, concepts within Applied Maths can be used to investigate the topic). This title is the same for every student in Ireland in that particular 6th year, both at Higher and Ordinary Level.

##### What are some examples of what the project title might be?

“Investigate how high a tennis ball would bounce if dropped from the top of the Spire.”

“When someone does a push-up, what percentage of their weight are they lifting?”

“How much faster could someone run across O’Connell Bridge on a windy day compared to a calm day?”

“Describe what would happen to a bowling ball that is dropped from a height of 80 km.”

“If climate change is causing sea levels to rise, why are the prices of homes near the coast not plummeting?”

“Conduct research into explaining why airplanes fly so high.”

“Investigate how much energy is required to keep a human heart beating in a typical lifetime.”

“Is it possible to use a yo-yo in space?”

“Do I receive the same amount of energy from bread if I toast it?”

“Person A states that all marathons must be run on flat ground if the times for different marathons can be compared. Person B instead states that all that matters is that the start and finish are at the same height. Who is correct?”

Investigate what happens when a tennis ball impacts the surface of the eight planets.”

“If a flashlight is turned on in space, does the emitted light propel the flashlight backwards?”

“If a person skydives in the rain, does that rain hit their back, their stomach, or both?”

“Investigate why the definition of a metre has changed over time.”

“If Earth was shaped like a donut, how would the moon behave if placed in the centre?”

“A stationary football can hypothetically be kicked into space if kicked hard enough. Investigate what impact needs to be imparted to that ball in order for it end up orbiting the Earth 300 km from the Earth’s surface.”

“Investigate why an elevator into space has never been built.”

“More boys study Applied Maths than girls.” Conduct research into whether this statement is true or not and why.

“Investigate the road network of your hometown and whether you believe it is optimised for its residents in regard to the location of the largest supermarket.”

“Conduct an analysis on the history of the 100 metre world record.”

Describe the triple jump track and field event in terms of energy and power.”

##### How do I go about writing the project?

There are two important documents for students in relation to the project:

Student Modelling Journal

This file is provided by the Professional Development Service for Teachers (PDST). Although using this file is completely optional, we believe that it provides a good way for students to keep track of their progress during the project. Even if you decide not to use it, we recommend at least reading the first few pages of this document as it provides a nice insight into what to expect with the project.

Project Reporting Booklet

This document is what you will actually write your project report in.

The second document above also gives a lot of details as to the structure of the project. Here are the highlights:

“Your report must not exceed 900 words (excluding references, equations, diagrams, graphs, etc.).”

“Your report must not include more than 20 images.”

“Videos must not be included in your report.”

“When referring in the body of the report to any specific image, the image must be properly labelled (Figure 1, Figure 2, etc.).”

“You must reference any information used in your report.”

“The mathematical modelling project and report must be your own individual work – authenticated by yourself, by your teacher and by your school management authority.”

“While you may carry out background research relevant to the brief on your own and/or at home, all other parts of your project and your report must be completed under the supervision of your teacher.”

##### What if I don’t have an Applied Maths teacher?

As we are unaffiliated with the SEC, or indeed any examinations body, we are not the most suitable point of contact for answering this question. Instead, we recommend directly contacting the SEC at 090 644 2745 if any student, parent, tutor, teacher or principal is in need of clarification to the answer of this question.

Note, however, that the answer that you receive to this question is highly dependent on who you speak to at the SEC. (We cannot stress the word highly enough.)

##### How are the 100 marks for the project distributed?

There are three different sections in the Project Reporting Booklet that students must complete.

1) Introduction and Research (20 marks)

2) The Modelling Process (50 marks)

3) Interpretation of Results (15 marks)

The remaining 15 marks are then given for the quality of your project as a whole under the heading of Communication and Innovation.

These marks are then further broken down according to the below table.

Section Indicative Content Marks

Introduction and Research

• Background research on brief
• Identify specific problem(s) to be modelled
• Research specific problem(s)
• Identify relevant variables
• Present relevant data
• Provide citations and references

20

The Modelling Process

• Explain and justify model and assumptions
• Compute solutions
• Present solutions using appropriate mathematical and graphical representations
• Analysis of solution(s) – sensitivity to changes in assumptions; comparison with other solutions or real-world data
• Iterative Process

50

Interpretation of Results

• Interpretation of solution(s) in real-world context
• Conclusions and reflections

15

Communication and Innovation

• Innovative and creative approaches
• Overall coherence

15

##### So, as long as I cover each of those bullet points, I will get full marks?

Well, not quite!

The amount of marks you get depends on how well you cover each of those bullet points.

This is further described by the official project assessment criteria shown below.

High Quality Medium Quality Low Quality

states the problem statement concisely, early in the written report. References sources from background research.

identifies several variables affecting the model and notes and justifies the need for the main factor that influences the phenomena being modelled.

clearly identifies and justifies the assumptions used to develop the model and, where appropriate, states the limitations of the simplification of the problem due to the assumptions made.

indicates exactly what the output of the model will be and, if appropriate, identifies the audience and/or perspective of the modeller.

identifies a problem statement which is not precise or consistent with other statements in the report.

lists important parameters and variables properly, but without sufficient explanation.

notes primary assumptions, but without justification.

presents a problem statement that is difficult to understand or is buried in the text.

identifies assumptions and justifies them, but they are difficult to identify in the text.

barely mentions variables/ parameters or, if mentioned, they are difficult for the reader to identify in the text.

provides clear insight with logical mathematical reasoning into the mathematical method(s) used to describe the relationship between the variables,
and to solve the problem. Presents a plausible approach and outcome.

states a mathematical approach, however with aspects of the method(s) which are inconsistent, difficult to understand or
incomplete

states a model which contains fixable mathematical errors.

clearly presents an accurately-computed solution and analysis of the relationship between variables, supported where appropriate with visual aids and graphic representation that is consistent with the original problem statement.

states an answer, however with aspects of the solution(s) which are inconsistent, difficult to understand or incomplete (e.g. fails to identify units of measure).

states an answer but without contextual background (i.e. appropriate graphics, appropriate units, etc.).

addresses the viability and reliability of the mathematical modelling solution.

considers how sensitive the model is to changes in parameter values or altered assumptions; how it compares to other solutions or historical data. The model is refined and the process iterated.

addresses the viability and reliability of the mathematical modelling solution, however with analysis which lacks proper dimensionality, e.g. obvious consequences of the stated outcome are ignored or well-known comparisons are disregarded

provides some analysis but without any sense of perspective.

uses incorrect mathematics in the analysis.

presents a paper that is well-formatted and enjoyable to read, with easy to interpret visual aids (if appropriate).

presents a paper with multiple spelling, formatting or grammatical errors, visual aids which are missing key readability features or which do not clearly connect to the solution.

presents a paper with significant disregard for common spelling, grammatical and mathematical rules.

If the project meets the majority of the criteria listed in the “High Quality” column, that project is considered to be of high quality and will therefore receive high marks, and so on.

While writing the project, it is a good idea to occasionally glance at the above two tables to ensure that you are both 1) covering all of the necessary bullet points of the first table and 2) covering those bullet points well according to the second table

As already mentioned, members gain access to three completed projects, all of which are for the same sample investigation. The first project will be of high quality, the next of medium quality and the final of low quality. This will allow you to easily visualise what are often small differences between submitting a great project and submitting an average project.

##### One of the criteria for a high quality project is, “The model is refined and the process iterated.” What does that mean?

In science and many other fields, the best approach to tackling a complicated problem is often to first simplify that problem down as much as possible.

For example, if we are are asked to investigate the motion of an object on a rough surface, it seems logical to first investigate the motion of that object on a smooth surface.

Then, we refine the problem, gradually getting closer to the original problem with each iteration.

Likewise, we may also perform an additional iteration if we instead found a better, more accurate way of determining a solution.

This criterion suggests that this is what should also be done for the project. Therefore, a simplified investigation should first be performed with the process repeated several times until the original problem has been tackled as accurately as possible.

This will become more clear when reading the completed project reports found on this website.

##### Another of the criteria is, “References sources from background research.” What does that mean?

In order to compute the solution to a problem, it is often the case that various quantities need to be either determined or looked up first.

For example, let us consider the following project title.

“Investigate how high a tennis ball would bounce if dropped from the top of the Spire.”

To perform this investigation, one quantity we need to know is the coefficient of restitution between a typical tennis ball and a surface similar to the base of the Spire.

We could of course attempt to find this value (by using the internet for example) but it would reflect better in our project if we instead determined it ourselves by performing an experiment. We could release a tennis ball from a particular height, e.g. shoulder height, and then measure (using our eyes, a laser etc.) the maximum height after the first bounce on such a surface. These values could then be used to determine the coefficient of restitution. (To increase accuracy, we should repeat this experiment multiple times and take the average value.)

However, not all quantities can be determined by experiment. For example, another quantity that we would need to know is the height of the Spire, and there is no real way to determine that (well, not safely at least!).

Instead, we would have to look up that value using a source, the three main types of which are websites, books and articles.

Anytime such a value is then stated in our report, we need to reference what source we got that value from. This is done using what is known as a bibliography, i.e. a list of the sources that we have used in our investigation.

Within each iteration of our investigation, we reference a source in this bibliography by placing a number in square brackets next to the quantity we have stated, e.g. [3], where that number indicates that this is the third source we have used thus far in our report. This is what is known as citing a reference.

For example, within a report, we may write the following.

“The height of the Spire is 120 metres [3].”

The third entry of the bibliography that we include as an attachment would then look as below.

[3] Spire of Dublin URL:https://en.wikipedia.org/wiki/Spire_of_Dublin (Accessed on September 1st, 2022).

Note that the form of this entry is as shown below.

[3] Website page name, website URL, date the webpage was accessed.

The order you put these elements in, as well as the style used, is not important – all that matters is that you use that same order/style for all entries that are from websites.

The formatting is slightly different if the other types of sources are used, namely books or articles. In that case, we would instead write this entry as shown below.

[3] Kenny, C. Monuments of Dublin. Newton Publications, 2022.

The formatting in this case is instead as below.

[3] Author(s), title, publisher, year of publication.

Again, ordering and styling doesn’t matter, as long as you are consistent!

Note that this is just one of many different ways of referencing sources. If you already have your own method of referencing, feel free to use it! If, on the other hand, you are unfamiliar with referencing, we suggest using the approach above.

In summary, when stating any value that isn’t immediately obvious, you should:

1) Consider if you can derive that value yourself by experiment and explain how you did so in your project.

2) If not, add an entry to that source in your bibliography.

Again, this will become more clear when looking at the examples of bibliographies in the sample projects.

##### Do I have to use a program to create my graphs, charts etc.?

Not at all! You are not being assessed on your ability to use fancy programs to create graphs etc. as such programs are not in the official Applied Maths syllabus. You are free to draw your graphs using pens, pencils, rulers etc. and scan or take photos of them if you prefer. You will not receive less marks for using that approach.

What’s more important is that you labels those graphs correctly!

Once complete, your Project Reporting Booklet will be submitted through the Schools Portal by your school as described here and here.

##### Can I work on the project with other students at my school?

Well, yes and no!

One of the the primary objectives of the project is to demonstrate that students are capable of working independently. As such, projects that are submitted from the same school which are similar in content and style will have their grades lowered (or worse), regardless of their quality.

Therefore, we suggest only working together in the sense of brainstorming, i.e. helping each other come up with ideas as to how to approach certain aspects of the project.

##### Am I allowed to use artificial intelligence?

Surprisingly, yes!

However, you are only allowed to use it as a source of information, not as a means to write the project itself.

In other words, you can use it to find specific details as you would with a webpage, book etc.

Also, as it’s considered a source, you must include “any material generated using artificial intelligence (AI) software or applications” as a reference in your bibliography.

##### Do you have any sample projects?

Yes! There are three sample projects included in this section of the website.

These projects are for members only!

##### Do you have any tips for this year’s project?

Yes! Tips & tricks specific to this year’s project are shown on the last page of this section.

These tips are for members only!