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Great Openings: Slots, 35 Sense, and Hole In One
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These three short activities challenge groups to fit objects through paper and index cards: "Slots" presents the challenge for one learner to figure out which objects fit through a hole cut by another

Magical Möbius
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In this tabletop activity (on pages 32-40), learners make Möbius strips -- 3D surfaces with only one side.

Paperfolding Polyhedrons
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In this activity (on pages 55-66 of PDF), learners fold paper into origami shapes and then combine several identical shapes into a three-dimensional structure.