See-Saw Game: Finding the Mean

See-Saw Game: Finding the Mean
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2020-06-08 19:45
① This interactive see-saw game demonstrates the concept of arithmetic mean through a physical balance metaphor, where students adjust data values to achieve equilibrium on a lever, linking statistics to physics. ② Core mathematical concepts include arithmetic mean (average), data distribution, and the lever principle (moment balance), with connections to histograms, rotation, and reflection. ③ Construction uses GeoGebra commands: Random, Unique, Length, Polygon, Textfield, Sequence, Rotate; objects include valueend, valuestart, nend, nstart, n, entry, ans, e, F, size, nfinal, B, pic1, v1, v2, v3, C, D, E, poly3, e_1, c_1, d_1, inputBox1, button1, button2, polygonlist, button3, polyfinal, a, b, c, d, angle, and their variants, enabling dynamic data generation, interactive input, and visual feedback. ④ Suitable for middle school to high school students learning statistics and averages, as well as for interdisciplinary STEM lessons combining mathematics and physics, promoting kinesthetic and inquiry-based learning.

GeoGebra Commands & Parameters

  1. Random(nend, nstart) → n
  2. Unique(Sequence[Random[valuestart, valueend], k, 1, n]) → entry
  3. Length(entry) → nfinal
  4. Polygon(C, D, E) → poly3, e_1, c_1, d_1
  5. Textfield(entry) → inputBox1
  6. Sequence(Polygon[((-Element[entry, k]) - size, (2 * size)), ((-Element[entry, k]) + size, (2 * size)), ((-Element[entry, k]) + size, 0), ((-Element[entry, k]) - size, 0)], k, 1, n) → polygonlist
  7. Polygon((x(F) - size, 0), (x(F) + size, 0), (x(F) + size, ((2 * nfinal) * size)), (x(F) - size, ((2 * nfinal) * size))) → polyfinal, a, b, c, d
  8. Rotate(polygonlist, angle) → polygonlist'
  9. Rotate(pic1, angle, (0, 0)) → pic1'
  10. Rotate(polyfinal, angle, (0, 0)) → polyfinal'