Asking questions

The most basic way to involve everyone - you can solicit answers using hands up, by shouting out, or even get people to vote by show of hands, or by sitting/standing (if you're confident this won't exclude too many people).

If you do this, make sure you give them enough time to answer - you can ask quick questions you expect them to know answers to, but you need to give them time to work on anything more complicated.

Be explicit about how an audience should respond!

For example: avoid questions like "Does anyone know about prime numbers?" - it will likely result in an awkward silence. How do they answer? Shout out? Hands up? Smug nod? Who should answer?

Instead you could try a clearer instruction: "Put your hand in the air if you already know a bit about prime numbers"; "Keep your hand in the air if you are happy to tell everyone what a prime number is" (you could then pick someone, or proceed with your own explanation, depending on the outcome).

• Even for simple questions, an effective technique is to give them time to discuss with the person next to them - 30 seconds or a minute, to share their thoughts and compare answers. This means they'll feel heard even if they don't get to put their hands up and answer. Make sure you have a good way to get everyone's attention back - putting up a timer on the screen, or having an agreed signal you specify beforehand can both work well. A microphone might become essential to give you a volume boost over the general hubbub.
• As a bonus, you may be able to circulate and overhear comments you want to pick up on later. You can even pretend you heard something that you didn't actually hear (this time), for the sake of comedy or a helpful explanation.
• Similarly - teachers sometimes use the 'think, pair, share' method which gives people a little time to think alone, then time to discuss in pairs, then a chance to give their answers to the class. This might be useful for more complex problems or puzzles, but it takes more time to do.

Other approaches

• Depending on the venue, there may be a way to use an interactive voting system to collect answers/opinions from the audience - very few venues have these built in, but for public talks many people might have a mobile phone they can use to visit a simple web-based poll or quiz site. ONLINE sessions may benefit because this is far easier to arrange.
• Getting people doing something physical is good, especially to break up a long session - this could be a hand/arm/finger trick or action you demonstrate, a standing/sitting game, interacting with someone else nearby or using their hand to point at or indicate the level of something. As always, be aware of any accessibility issues and make sure it's not essential for everyone to do the activity, or have alternatives in mind.
• It's surprising how many small group activities do translate to larger audiences - playing games against the person next to you, and discussion in small groups both scale fine. You can also do some hands-on activities depending on how much work you're prepared to put in - we've seen a speaker prepare 100 pre-perforated Möbius bands for an audience to tear in half, and have done talks that involve putting out scissors, pens and paper under each seat - just bear in mind the logistics (you may need help setting up!), and you'll need to warn the audience not to use or break things before they're needed (some inevitably will); giving things out at the right time will help, but you'll need helpers to do this. Also, make sure you build in enough time in to your session, as it can be unpredictable how long things take at scale. It is probably true that it WILL TAKE LONGER THAN YOU EXPECT.
• For big audiences, it's crucial to make sure everyone can see and hear clearly. A card trick on a small table at the front will need a webcam or visualiser so it can be seen by everyone, and props need to be big and exaggerated (or small enough to hold under a webcam!)

Working with volunteers

Grabbing one or two people from the audience to join you on stage, or to hold things up or otherwise participate, is a good way to make the audience feel involved. There are some golden rules:

• Treat them well! If you embarrass them or treat them badly, nobody will volunteer to do anything for you again (and everyone will think worse of you for it). Your volunteers are superstars - get a big round of applause for them, give them some (non-allergenic) sweets, make them look cool in front of everyone.

• Make it clear to people what you're asking them to do before you ask for volunteers, and don't change what you're doing part way through in a way that might make someone feel uncomfortable.

• Don't get volunteers you don't need! If your demo/explanation will genuinely benefit from someone else's involvement, then fine, but don't just get someone to come and hold something then send them back.

• Try to pick volunteers representative of the whole audience - often, you'll get the more confident people putting their hands up and if you only pick from them you might find it's not a representative sample. Take time to pick out the right people.

  If there's someone being disruptive, often picking them as a volunteer (provided it's sufficiently low-stakes) can give them the attention they're craving, so they'll calm down - and you'll know who they are, so you can address them directly later if they keep causing a distraction.