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Countdown to Learn Multiplication Tables: Sequences and Frequency Visualization

Countdown to Learn Multiplication Tables: Sequences and Frequency Visualization
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2020-08-25 00:07
PolygonSequenceLimitProbability & StatisticsGeometric Construction
This example demonstrates a countdown-style, sequence-driven way to practice multiplication tables, where randomly generated steps and modulo-controlled cycles translate numerical outcomes into dynamic geometric constructions (points, segments, and polygons). It highlights key ideas such as sequence generation (Sequence) and periodic behavior via modular arithmetic (Mod), conditional mapping of results to different visual elements (If), distance-based evaluation or placement (Distance), and randomized selection for repeated training steps (RandomElement). The construction is built using GeoGebra commands Mod, If, Distance, RandomElement, Point, Polygon, Segment, and Sequence, and a collection of generated geometric objects (many named points and lists/parameters like liste1, as well as sequences of points such as BB–II, AA, TT, SS, RR, LL, QQ, KK, OO, NN, PP, MM). The activity is suitable for middle and high school learners and for introductory statistics/data-visualization lessons, supporting multiplication practice while also motivating concepts related to frequency distributions and median-style thinking through visualization.

GeoGebra Commands & Parameters

  1. Mod(Random[0, 100], 10) → aa
  2. If(aa ≟ 0, BB, If[aa ≟ 1, CC, If[aa ≟ 2, DD, If[aa ≟ 3, EE, If[aa ≟ 4, FF, If[aa ≟ 5, GG, If[aa ≟ 6, HH, If[aa ≟ 7, II, If[aa ≟ 8, JJ, AA]]]]]]]]) → TT
  3. If(aa ≟ 0, CC, If[aa ≟ 1, DD, If[aa ≟ 2, EE, If[aa ≟ 3, FF, If[aa ≟ 4, GG, If[aa ≟ 5, HH, If[aa ≟ 6, II, If[aa ≟ 7, JJ, If[aa ≟ 8, AA, BB]]]]]]]]) → SS
  4. If(aa ≟ 0, DD, If[aa ≟ 1, EE, If[aa ≟ 2, FF, If[aa ≟ 3, GG, If[aa ≟ 4, HH, If[aa ≟ 5, II, If[aa ≟ 6, JJ, If[aa ≟ 7, AA, If[aa ≟ 8, BB, CC]]]]]]]]) → RR
  5. If(aa ≟ 0, EE, If[aa ≟ 1, FF, If[aa ≟ 2, GG, If[aa ≟ 3, HH, If[aa ≟ 4, II, If[aa ≟ 5, JJ, If[aa ≟ 6, AA, If[aa ≟ 7, BB, If[aa ≟ 8, CC, DD]]]]]]]]) → LL
  6. If(aa ≟ 0, FF, If[aa ≟ 1, GG, If[aa ≟ 2, HH, If[aa ≟ 3, II, If[aa ≟ 4, JJ, If[aa ≟ 5, AA, If[aa ≟ 6, BB, If[aa ≟ 7, CC, If[aa ≟ 8, DD, EE]]]]]]]]) → QQ
  7. If(aa ≟ 0, GG, If[aa ≟ 1, HH, If[aa ≟ 2, II, If[aa ≟ 3, JJ, If[aa ≟ 4, AA, If[aa ≟ 5, BB, If[aa ≟ 6, CC, If[aa ≟ 7, DD, If[aa ≟ 8, EE, FF]]]]]]]]) → KK
  8. If(aa ≟ 0, HH, If[aa ≟ 1, II, If[aa ≟ 2, JJ, If[aa ≟ 3, AA, If[aa ≟ 4, BB, If[aa ≟ 5, CC, If[aa ≟ 6, DD, If[aa ≟ 7, EE, If[aa ≟ 8, FF, GG]]]]]]]]) → OO
  9. If(aa ≟ 0, II, If[aa ≟ 1, JJ, If[aa ≟ 2, AA, If[aa ≟ 3, BB, If[aa ≟ 4, CC, If[aa ≟ 5, DD, If[aa ≟ 6, EE, If[aa ≟ 7, FF, If[aa ≟ 8, GG, HH]]]]]]]]) → NN
  10. If(aa ≟ 0, JJ, If[aa ≟ 1, AA, If[aa ≟ 2, BB, If[aa ≟ 3, CC, If[aa ≟ 4, DD, If[aa ≟ 5, EE, If[aa ≟ 6, FF, If[aa ≟ 7, GG, If[aa ≟ 8, HH, II]]]]]]]]) → PP
  11. If(aa ≟ 0, AA, If[aa ≟ 1, BB, If[aa ≟ 2, CC, If[aa ≟ 3, DD, If[aa ≟ 4, EE, If[aa ≟ 5, FF, If[aa ≟ 6, GG, If[aa ≟ 7, HH, If[aa ≟ 8, II, JJ]]]]]]]]) → MM
  12. Distance(M, MM) → mm
  13. Distance(N, NN) → nn
  14. Distance(L, LL) → ll
  15. Distance(O, OO) → oo
  16. Distance(P, PP) → pp
  17. Distance(Q, QQ) → qq
  18. Distance(R, RR) → rr
  19. Distance(S, SS) → ss
  20. Distance(K, KK) → kk
  21. Distance(T, TT) → tt
  22. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, 9) → res
  23. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, 8]) → resfin
  24. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, 6]]]) → f
  25. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 6, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 5, 4]]]]]) → g
  26. If(kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt < 0.1, 10, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss < 0.1 ∧ tt > 0.1, 9, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr < 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 8, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq < 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 7, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp < 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 6, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo < 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 5, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn < 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 4, If[kk < 0.1 ∧ ll < 0.1 ∧ mm < 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 3, If[kk < 0.1 ∧ ll < 0.1 ∧ mm > 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 2, If[kk < 0.1 ∧ ll > 0.1 ∧ mm > 0.1 ∧ nn > 0.1 ∧ oo > 0.1 ∧ pp > 0.1 ∧ qq > 0.1 ∧ rr > 0.1 ∧ ss > 0.1 ∧ tt > 0.1, 1, 0]]]]]]]]]) → gg
  27. RandomElement(liste1) → b
  28. Point(xAxis) → A
  29. If(kk < 0.1, 1, 0) → s1
  30. If(ll < 0.1, 1, 0) → s2
  31. If(mm < 0.1, 1, 0) → s3
  32. If(nn < 0.1, 1, 0) → s4
  33. If(oo < 0.1, 1, 0) → s5
  34. If(pp < 0.1, 1, 0) → s6
  35. If(qq < 0.1, 1, 0) → s7
  36. If(rr < 0.1, 1, 0) → s8
  37. If(ss < 0.1, 1, 0) → s9
  38. If(tt < 0.1, 1, 0) → s10
  39. If(score ≟ 10, true, false) → dem
  40. Polygon(H, I, E, D) → poly1, h, i, e, d_1
  41. Polygon(J, Z, G, F) → poly2, j, z, g_1, f_1
  42. RandomElement(liste1) → k
  43. Segment(A_1, B_1) → l
  44. Sequence(Text[pas1 + (" x " * i), (11.5, i - 0.2)], i, 0, 10) → l1