When running online workshops and talks, you should aim to use a variety of types of interaction. Obviously, there are limitations to this - mostly interaction will still involve looking at a screen, and depending on people's tech setup they may not always be able to access it - but here are some suggestions.
Data collection (lottery, statistics, probability - coin/dice) - and have a plan for what happens if the data doesn’t reflect what you’re trying to demonstrate, like a backup data set or a good explanation
Interactive gadget - could be anything from a cryptography interactive, visual applet, calculation tool, etc. Use existing ones, or build your own - plenty of suggestions on the Interactive Maths Software handout.
Quiz questions - could use something like Kahoot or Desmos for an interactive quiz, where you can see answers in real-time.
Hands-on activity at home (paper folding, drawing - instructions for construction, build something, etc) - producing an artistic item, craft, etc or just playing. Warn people with advance notice what they’ll need (size/type of paper, table space etc), and make sure instructions are clear and easy to follow. People could submit what they've made using a phone camera and an online submission point - depending on the context, this could be a Google form, a website like Padlet, or via social media using a hashtag
Away-from-screen time - if it's possible, it's fun to get participants to do something that involves leaving their computer, even if it's only briefly: challenges to find a household object with a given property, or collect a number of something, or take a photo of part of the house/building that has given symmetry. This could be during a scheduled break (to make sure people do actually take a break!) or as an activity during the session that everyone does together.
Whiteboard/drawing activity - Desmos, whiteboard.fi, or on webcam; all together, or separately (although if you’re all working on the same sheet, watch out for fights breaking out, and have a way to lock editing - Desmos has this, and you can revoke editing permissions on Google Sheets/Docs)
Games - played online (through specialist sites, or using a drawing app/spreadsheet) or on webcam - discuss strategy, predict outcomes
Demonstrations - magic trick, physical principle, etc; could be on-screen (you doing some live coding/spreadsheeting) or pre-recorded if it's difficult to get it working on demand, but live is more engaging
Puzzles - something easy/quick to solve, or with a rich extension; Use a multiple choice poll? Pick someone to share their answer on screen? Get people to type answers (and all press enter at the same time)?
Does it scale? Some interactive activities may work fine for 10 people, but not 100 people - be clear with the organisers how many people you’re expecting, and have a fallback plan in case that changes.
Think about extension activities. Some people may finish quickly; have a way for them to explore further, but don’t make others feel like they haven’t finished - use private messages to chat to people who finish early, or keep things open-ended. This is harder if you’re not in the room talking to people - usually, you can spot people working at different rates but it’s more difficult if you can’t see what they’re doing.
Ways to make use of the chat/built-in resources in e.g. Zoom:
Get everyone to press enter together - a.k.a. a 'chatblast' (good for collecting thoughts/opinions, but not necessarily for answers you might get wrong as it can make it obvious); something anonymous like Itempool might be better for anonymous answering
Use the 'hands up' feature - this is sometimes more useful when employed as ‘everyone put your hands up’ (especially as a starter to get people used to the software) ‘and put your hands down if…’