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As you say College-level: Simulate field biologists' jobs, for any statistics class (or for data input for mathematical modelling). Basically any physically spaced situation you can recreate, and choose a mathematical level appropriate for your group (how science-heavy is your course?; US college = university; UK college = 16--18y olds; etc). From my ...

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Teaching the addition and subtraction of negative numbers by walking along a number line. The idea of the exercise is that you draw out a number line on the floor, and have your students stand next to it on the zero position, facing the positive direction. You then have them calculate additions and subtractions by walking along the line; whenever they ...

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Graph traversals Many students do a lot of graph doodling in discrete mathematics courses, at least at first before they master the theoretical techniques. Instead of having your students draw the graphs on paper, have them lay them out on the floor or ground. Having access to a gym or an outdoor area helps, but isn't truly necessary if you move desks and ...

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w.r.t. "Hungarian Quicksort Dance" - mentioned by @Schwern in his answer - Stephenson's book Anathem has a section where a group of physicists do the following at a sort of community "open house": Three fraas and two suurs sang a five-part motet while twelve others milled around in front of them. Actually they weren't milling; it just looked that way from ...

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My favourite is addition and multiplication by walking. This is my go-to activity when I talk at schools. $+2$ is two steps forward. Then we get to negative numbers, and $-3$ is three steps back. Multiplication scales and rotates- so multiplication by $-1$ turns you backwards (or rotates your "true north"), and $\times 2$ does something twice. Now we can do ...

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Take a look at Computer Science Unplugged. They have a well curated list of activities ready to use with students, quite a few of which include physical activity. You might need to adjust them a bit for older audience, but they are definitely worth the attention.

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To build intuition for the Cartesian plane, assign axes to the room (or to students, depending on how many you have and how they're arranged in the room). Then you can do things like: Stand up if your $x$-coordinate is 0, 1, 2 etc. Stand up if your $y$-coordinate is less than five. Stand up if your $y$-coordinate is less than or equal to five. Stand up if ...

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For example when explaining the properties of a perpendicular bisector of a segment, you can take the students to a hall, place 2 sheets on the ground (that will be our segment) and then give students a measuring tape and ask them to find a spot that is equidistant from both extremities of the segment (the 2 sheets) and another student find another spot and ...

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I took a small math class over the summer (about 11 people) where instead of lecturing the whole time (as is customary for many college math classes), the professor gave us some problems once in a while that we would do in groups. The act of forming groups, talking, and then explaining the solutions to the professor (at the group) I think allowed for a lot ...

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How about drawing an ellipse, a parabola, and a hyperbola, using string and a straightedge:                                         Snapshots from MathLapse: "pin-and-string conics."

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The Hungarian Quicksort Dance demonstrates a computer science algorithm with dance. It's pretty advanced, but the idea is to have your students physically act out algorithms. Perhaps something similar can be done with a number line. Line your students up and have one walk down the line to demonstrate addition and subtraction, or take big steps for ...

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A technique I use a lot is to use software to put students in random groups, then have them do active learning activities in those groups. These activities are sometimes the "conceptest" technique created by Mazur, or think-pair-share. My set of conceptest activities for freshman calc are here (click through to "active learning resources"). The conceptest ...

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One activity I've seen done at the high school level is a scavenger hunt. You come up with a group of questions with numeric answers, and then you print out a bunch of papers to hang around the room (or hallway or wherever). One paper has the answer to #$1$ and the question to #$2$, one has the answer to #$2$ and the question to #$3$, all the way around to ...

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To start things off, some moments my students move around during class: I have given students tape measures and had them determine how much they would spend at the paint store if they wanted to paint the walls and ceiling of the lecture room (while projecting two images on the overhead: one of a paint can label, showing the number of square feet per gallon; ...

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