Hands-on activities – at a stall or part of a science fair/open day – need to be planned differently to a long-form workshop or talk. There can still be a narrative arc through what visitors see, or it can be a collection of separate activities they can engage with as they wish.

You still need to (if anything, more so than for a larger audience talk or workshop) think about your audience. You might have groups of different ages coming to the stall, and you may need to plan several different versions of the activity, or different activities, to accommodate them. You should aim to have multiple people there and not run something like this on your own, if at all possible.

Whoever is working on your stall will need to know all the different activities/versions of the activity, (or who is responsible for each), as part of pre-event training - ideally, everyone should be able to deliver the activity to any audience. You’ll develop better explanations the more times you present things to different people, and this experience can and should be passed on to the rest of the team when possible.

Examples of stall activities could include:

Visual puzzles: things to draw on with dry-erase markers, or pieces to arrange, which could be 'draw a shape/diagram', 'put the numbers in the right places', 'colour this using N colours' etc. The Fun Maths Roadshow has lots of good examples, and you can buy a download of printable PDFs from them.

Physical puzzles: assembly puzzles like the Soma cube, or twisty puzzles like the Rubik's cube - but these should be accompanied by some deeper maths content so people don't just associate maths with toys.

Games - simple games to play, against you or each other, can encourage thinking about strategy, and inspire insights about the maths behind games like Nim or tic-tac-toe.

General manipulatives - coins, tokens, multilink cubes, cuisenaire rods, assembly toys like Geomag, Zometool, Polydron and K'nex and even common household objects like cups and saucers can be incorporated into abstract puzzles and games to give them a more physical element.

Demonstrations - curiosities like Euler's disc, rattlebacks and tippee tops can demonstrate physical principles and raise mathematical questions. You may also be able to design or create demonstrations to illustrate specific mathematical principles, like laminar flow demos, parabolic reflectors or braid theory.

This type of one-to-one/one-to-small-group engagement can be much more tiring and intensive than talking to a large audience at once - you’re less in control of the interaction and have to adapt to the situation quickly. Make sure your team get plenty of breaks and chances to rest/decompress away from the public - arrange shifts and make sure there’s somewhere they can go to take breaks and get refreshments. If your activity is part of a bigger science festival or event this should be provided, but you may need to find out where it is.

Using tactile hands-on items to make things more engaging is good – but make sure your objects are robust (up to repeated handling) and replaceable, in case anyone wanders off with them. Simple, familiar items like counters, dice and cards, used to communicate maths concepts, can be really effective, and allow people to replicate the activity at home with others. Handouts, to facilitate this (and include promotional branding!) can be useful.

If your activity involves someone solving a puzzle, is there a way for visitors to do that without input from you? Is there any structure you can provide, with a planned series of prompts, to guide them toward a solution? Some people prefer time to think about things alone – is there a way they can take the puzzle away to work on it elsewhere, and come back later?

Avoid setting people puzzles that are impossible! It might sound obvious, but someone who comes to try an activity may give up before completing it – and you can’t necessarily keep an eye on everyone to step in and explain at the right moment. If they go away having confirmed their suspicion that maths is hard and not for them, you’re shooting yourself in the foot. Things can be interesting because they’re impossible – but reframing it as “can you convince me it’s not possible” or “can you change it so it is possible” makes it still a viable challenge.

Think about accessibility – can people reach everything you need them to, to participate in your activity? Do you have a way for a person with visual or hearing access needs to participate in your activity?