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GeoGebra Exploration of Divisibility by 3 and 9 with Interactive Checks

GeoGebra Exploration of Divisibility by 3 and 9 with Interactive Checks
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2024-05-16 13:29
PolygonSequenceGeometric ConstructionGraphing
In collections Teilbarkeitsregeln
This GeoGebra example uses interactive text and generated data to illustrate how numbers behave with respect to divisibility by 3 and by 9. It supports classroom practice focused on whether a claim about divisibility is true, and encourages reasoning using verifiable conditions. The key math concepts are factors and multiples, divisibility rules, and justification (or refutation) of statements about divisibility. Construction-wise, the lesson organizes visual/text components and dynamic behavior: it uses Polygon for structured on-screen geometry/layout, RandomList3 and RandomList9 to generate test numbers, Midpoint to compute geometric reference points, Textfield to collect or display inputs, and Element/Append/Remove to manage dynamic objects. Conditional logic is implemented with If and IsInRegion to decide which statements to show, while Join helps combine text/parts of results; multiple colored text objects convey prompts and outcomes. Suitable for grades 5–6 and for teaching/learning number sense, factors, and multiples through interactive exploration.

GeoGebra Commands & Parameters

  1. Polygon(Q1E1, Q1E2, 4) → Q1, q1_1, q1_2, q1_3, q1_4, Q1E3, Q1E4
  2. Polygon(Q2E1, Q2E2, 4) → Q2, q2_1, q2_2, q2_3, q2_4, Q2E3, Q2E4
  3. Polygon(Q3E1, Q3E2, 4) → Q3, q3_4, q3_1, q3_2, q3_3, Q3E3, Q3E4
  4. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 3), k, 1, 333]], i], i, 1, 5]) → RandomList3, {117, 591, 651, 807, 303}
  5. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 9), k, 1, 111]], i], i, 1, 5]) → RandomList9, {189, 423, 270, 909, 180}
  6. Shuffle(Sequence[Element[Shuffle[Sequence[k, k, 100, 1000] \ Sequence[(k * 3), k, 1, 333]], i], i, 1, 5]) → RandomListNot39, {371, 625, 583, 232, 316}
  7. Shuffle(Unique[Join[{RandomList3, RandomList9, RandomListNot39}]]) → RandomListNum, {232, 651, 180, 909, 316, 591, 270, 303, 117, 371, 625, 807, 583, 189, 423}
  8. Midpoint(Corner[NumText7, 1], Corner[NumText7, 3]) → Pos7
  9. Midpoint(Corner[NumText10, 1], Corner[NumText10, 3]) → Pos10
  10. Midpoint(Corner[T1830, 1], Corner[T1830, 3]) → Pos1830
  11. Midpoint(Corner[NumText6, 1], Corner[NumText6, 3]) → Pos6
  12. Midpoint(Corner[NumText3, 1], Corner[NumText3, 3]) → Pos3
  13. Midpoint(Corner[T1826, 1], Corner[T1826, 3]) → Pos1826
  14. Midpoint(Corner[NumText5, 1], Corner[NumText5, 3]) → Pos5
  15. Midpoint(Corner[NumText9, 1], Corner[NumText9, 3]) → Pos9
  16. Midpoint(Corner[T2628, 1], Corner[T2628, 3]) → Pos2628
  17. Midpoint(Corner[NumText8, 1], Corner[NumText8, 3]) → Pos8
  18. Midpoint(Corner[NumText4, 1], Corner[NumText4, 3]) → Pos4
  19. Midpoint(Corner[NumText2, 1], Corner[NumText2, 3]) → Pos2
  20. Midpoint(Corner[NumText1, 1], Corner[NumText1, 3]) → Pos1
  21. Textfield(aInput) → InputBox1
  22. Textfield(bInput) → InputBox2
  23. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  24. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 10, 3, 6, 10, 10, 6, 1, 5, 9, 3, 6, 5, 10, 4, 10, 1, 3, 9, 2, 1, 1, 0, 2, 1, 4, 2, 8, 7, 9, 9, 5, 8, 9, 1, 5, 8, 6, 1, 7, 2, 10, 1, 2, 4, 1, 3, 2, 3, 1, 7, 8, 2, 2, 7, 2, 6, 9, 4, 7, 10, 8, 6, 4, 2, 9, 10, 8, 0, 5, 10, 5, 7, 3, 5, 0, 7, 9, 8, 9, 7, 2, 3, 9, 3, 5, 2, 0, 7, 3, 2, 2, 0, 1, 8, 9, 1, 4, 5, 10}
  25. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  26. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {5, 5, 1, 6, 1, 7, 1, 10, 10, 0, 8, 6, 8, 4, 1, 5, 1, 3, 5, 4, 3, 5, 8, 8, 1, 3, 2, 9, 7, 4, 2, 2, 2, 9, 10, 7, 6, 3, 1, 4, 3, 5, 7, 8, 5, 0, 2, 10, 6, 2, 6, 9, 4, 7, 9, 7, 9, 8, 10, 10, 10, 6, 4, 10, 0, 2, 9, 6, 9, 1, 0, 5, 5, 5, 7, 5, 1, 10, 10, 8, 3, 9, 3, 9, 2, 1, 7, 0, 3, 3, 8, 6, 2, 0, 5, 7, 4, 5, 4, 6}
  27. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  28. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  29. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  30. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  31. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  32. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  33. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  34. If(Mod[num1, 9] ≟ 0, 2, Mod[num1, 3] ≠ 0, 3, 1) → num1meta
  35. If(Mod[num2, 9] ≟ 0, 2, Mod[num2, 3] ≠ 0, 3, 1) → num2meta
  36. If(Mod[num3, 9] ≟ 0, 2, Mod[num3, 3] ≠ 0, 3, 1) → num3meta
  37. If(Mod[num4, 9] ≟ 0, 2, Mod[num4, 3] ≠ 0, 3, 1) → num4meta
  38. If(Mod[num5, 9] ≟ 0, 2, Mod[num5, 3] ≠ 0, 3, 1) → num5meta
  39. If(Mod[num6, 9] ≟ 0, 2, Mod[num6, 3] ≠ 0, 3, 1) → num6meta
  40. If(Mod[num7, 9] ≟ 0, 2, Mod[num7, 3] ≠ 0, 3, 1) → num7meta
  41. If(Mod[num8, 9] ≟ 0, 2, Mod[num8, 3] ≠ 0, 3, 1) → num8meta
  42. If(Mod[num9, 9] ≟ 0, 2, Mod[num9, 3] ≠ 0, 3, 1) → num9meta
  43. If(Mod[num10, 9] ≟ 0, 2, Mod[num10, 3] ≠ 0, 3, 1) → num10meta
  44. IsInRegion(Pos1, If[num1meta ≟ 1, Q1, num1meta ≟ 2, Q2, Q3]) → correct1
  45. IsInRegion(Pos2, If[num2meta ≟ 1, Q1, num2meta ≟ 2, Q2, Q3]) → correct2
  46. IsInRegion(Pos3, If[num3meta ≟ 1, Q1, num3meta ≟ 2, Q2, Q3]) → correct3
  47. IsInRegion(Pos4, If[num4meta ≟ 1, Q1, num4meta ≟ 2, Q2, Q3]) → correct4
  48. IsInRegion(Pos5, If[num5meta ≟ 1, Q1, num5meta ≟ 2, Q2, Q3]) → correct5
  49. IsInRegion(Pos6, If[num6meta ≟ 1, Q1, num6meta ≟ 2, Q2, Q3]) → correct6
  50. IsInRegion(Pos7, If[num7meta ≟ 1, Q1, num7meta ≟ 2, Q2, Q3]) → correct7
  51. IsInRegion(Pos8, If[num8meta ≟ 1, Q1, num8meta ≟ 2, Q2, Q3]) → correct8
  52. IsInRegion(Pos9, If[num9meta ≟ 1, Q1, num9meta ≟ 2, Q2, Q3]) → correct9
  53. IsInRegion(Pos10, If[num10meta ≟ 1, Q1, num10meta ≟ 2, Q2, Q3]) → correct10
  54. Join(Sequence[Element[Sequence[Sequence[Q1E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge1
  55. Join(Sequence[Element[Sequence[Sequence[Q2E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge2
  56. Join(Sequence[Element[Sequence[Sequence[Q3E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge3
  57. Text(CorrHelper, A, false, true, 0, 0) → Text11

AI Drawing Prompt Reference

This is an interactive math exploration graphic featuring multiple quadrilaterals (Q1, Q2, Q3) representing number regions, along with midpoint markers (Pos1 to Pos10) for positioning. Input boxes (InputBox1, InputBox2) and text areas (NumText1 to NumText10) are included for displaying and entering numbers. Randomly generated number lists (RandomList3, RandomList9, etc.) are mapped to quadrilaterals, with If and IsInRegion logic determining whether each number falls within its corresponding region, displaying correct or incorrect prompts. The overall layout uses Polygon and Midpoint tools to construct geometry, illustrating the visual relationship between numbers and regions, suitable for teaching divisibility concepts.
The prompt above was compiled from the original drawing commands and is for reference only.