This is a hard question to answer without knowing more about the specific requirements of your project, and the types of math used in your project.
I've done several math projects, all involving mathematical modeling--using mathematics to describe a real-life system. This generally breaks down into two different categories:
Continuous modeling: describing something that changes continuously over time. For example, we might model how a population of some animal species changes over time, especially with the introduction of predators and prey. Continuous modeling usually involves calculus, specifically differential equations.
Discrete modeling: describing things that operate in "whole" units. For example, determining the optimal route number and routes of a delivery truck, or how to most efficiently schedule classrooms to teachers, or how to maximize profit subject to some constraints. Discrete modeling can use mathematics such as linear algebra, statistics and probability, algorithms, etc.
The process of coming up with a model is roughly as follows:
1. Determine a real life situation to model, and collect real life data relating to the model.
2. Formulate a mathematical model that describes the problem
3. Use the model to predict the solution to the problem, or predict what would happen under different conditions.
4. Go back to step one, evaluate how well your model fit the problem, and continue to iterate through these steps until you have a solid model.
The experiences through all of these steps can be detailed in your project, along with the ultimately perfected model and discoveries you made.