Presenting a math topic to passing crowds/judges is more about explaining what the project is, why it came to be, and where you want to go with it.
No matter what science event you go to, everyone there is going to have a varying degrees of knowledge/experience in certain fields. You’re going to have people who have never heard of a topic before, and people people who do it everyday as a passion. The goal here (in order to impress people) is to dynamically gauge this when you present your topic, and try to explain it in a way that relates to the audience. Of course, you don’t have to give them a life story, and all the background information, of the project, but just enough that they understand and can sort-of see why the project came about, and how it can be impactful/useful/interesting
If your topic of choice is something that can have images attributed to it, or even objects, make those and bring it with you! Things that people look at when walking by can catch their attention have them come to you curious about the importance of graphics and physical items (and you may have an easier time explaining ideas and topics with accessory objects).
Some other considerations:
- A poster with graphics is nearly a must-have for presentations of science. If you’re at a college, they often provide free research poster templates, but if you’re not, then you should Google around and find some templates you like. Here are some I found that are freely online
- Small handouts/pamphlets of the topic are common with math presentations
- Include QR codes that when scanned links back to a digital copy of your poster
Nonetheless, remember when you present your first few times at the fair it won’t be great (it happens to everyone, I stuttered for an hour the first time I presented research at a conference), but you’ll get your groove and get better as the event goes on. The most important thing to remember is to ensure that you level with your audience and just try to have fun!