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Divisibility by 2 and 5

Divisibility by 2 and 5
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2024-01-23 15:06
Inequality
In collections Teilbarkeitsregeln
This example demonstrates how to use GeoGebra to explore the divisibility rules for 2 and 5. The underlying math concepts include divisibility, factors, and multiples. The construction involves using GeoGebra commands such as Polygon, Shuffle, Midpoint, etc. to create the graph. It is suitable for middle school math education, particularly for learning divisibility and factors.

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 * 5), k, 1, 20]], i], i, 1, 6]) → RandomList5, {20, 25, 15, 50, 65, 75}
  5. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 2), k, 1, 50]], i], i, 1, 6]) → RandomList2, {22, 20, 98, 4, 44, 32}
  6. Shuffle(Sequence[Element[Shuffle[Sequence[(k * 10), k, 1, 10]], i], i, 1, 6]) → RandomList10, {80, 90, 30, 30, 50, 50}
  7. Shuffle(Unique[Join[{RandomList2, RandomList5, RandomList10}]]) → RandomListNum, {22, 25, 15, 80, 75, 50, 32, 65, 4, 98, 90, 44, 20, 30}
  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, {8, 10, 10, 2, 5, 1, 1, 3, 0, 9, 4, 0, 2, 2, 2, 1, 0, 7, 0, 5, 1, 8, 8, 3, 7, 1, 9, 2, 2, 1, 6, 6, 0, 4, 4, 8, 4, 10, 2, 2, 8, 7, 10, 7, 7, 7, 9, 0, 10, 8, 5, 1, 0, 2, 2, 8, 6, 1, 6, 0, 5, 8, 10, 0, 6, 4, 7, 7, 0, 8, 10, 7, 2, 0, 5, 9, 0, 2, 5, 10, 3, 2, 10, 9, 7, 7, 1, 3, 5, 6, 4, 8, 6, 8, 1, 6, 2, 10, 7, 1}
  25. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  26. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {10, 7, 9, 9, 1, 5, 8, 1, 6, 1, 10, 2, 3, 5, 7, 7, 2, 8, 2, 9, 9, 5, 3, 1, 6, 5, 8, 1, 8, 4, 5, 3, 7, 6, 8, 10, 0, 6, 7, 10, 5, 9, 8, 5, 4, 4, 5, 0, 9, 1, 8, 0, 7, 7, 10, 2, 5, 3, 4, 1, 0, 5, 6, 0, 9, 4, 5, 7, 6, 6, 7, 1, 2, 3, 6, 8, 6, 4, 1, 10, 2, 3, 0, 10, 8, 5, 3, 8, 10, 8, 0, 5, 4, 6, 1, 7, 0, 1, 9, 8}
  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, 10] ≟ 0, 1, Mod[num1, 5] ≟ 0, 3, 2) → num1meta
  35. If(Mod[num2, 10] ≟ 0, 1, Mod[num2, 5] ≟ 0, 3, 2) → num2meta
  36. If(Mod[num3, 10] ≟ 0, 1, Mod[num3, 5] ≟ 0, 3, 2) → num3meta
  37. If(Mod[num4, 10] ≟ 0, 1, Mod[num4, 5] ≟ 0, 3, 2) → num4meta
  38. If(Mod[num5, 10] ≟ 0, 1, Mod[num5, 5] ≟ 0, 3, 2) → num5meta
  39. If(Mod[num6, 10] ≟ 0, 1, Mod[num6, 5] ≟ 0, 3, 2) → num6meta
  40. If(Mod[num7, 10] ≟ 0, 1, Mod[num7, 5] ≟ 0, 3, 2) → num7meta
  41. If(Mod[num8, 10] ≟ 0, 1, Mod[num8, 5] ≟ 0, 3, 2) → num8meta
  42. If(Mod[num9, 10] ≟ 0, 1, Mod[num9, 5] ≟ 0, 3, 2) → num9meta
  43. If(Mod[num10, 10] ≟ 0, 1, Mod[num10, 5] ≟ 0, 3, 2) → 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[Q2E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge2
  55. Join(Sequence[Element[Sequence[Sequence[Q1E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge1
  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
  58. Length(RandomListNum) → a

AI Drawing Prompt Reference

Create a graphic to explore the divisibility rules for 2 and 5. Start by drawing three polygons Q1, Q2, and Q3 to represent multiples of 2 and 5. Then, randomly generate some numbers and distribute them among these polygons. Next, based on whether the numbers are divisible by 2 or 5, place them in the corresponding polygons. Finally, drag points Pos1 to Pos10 to check if they are in the correct polygons to verify the divisibility rules.
The prompt above was compiled from the original drawing commands and is for reference only.