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Comparing Rational Numbers - Klecksaufgaben

Comparing Rational Numbers - Klecksaufgaben
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2025-06-04 17:41
In collections Ordnen und Vergleichen von rationalen Zahlen
This example demonstrates how to compare rational numbers. Students can adjust the numbers to compare the size of rational numbers. The core math concepts involved are the comparison of rational numbers and the representation of rational numbers on the coordinate plane. The construction points include using GeoGebra's Join, Zip, Transpose commands, and using Sequence and If commands to control the

GeoGebra Commands & Parameters

  1. Join(Sequence[Shuffle[{1, 2}], m, 1, 60]) → listExType
  2. Zip(If[m ≟ 1, 0, RandomElement[{1, 1, 0}]], m, listExType) → listExType2Minus
  3. Join(Sequence[Shuffle[{-1, -1, 1}], m, 1, 40]) → listVZX
  4. Join(Sequence[Shuffle[{-1, -1, 1}], m, 1, 40]) → listVZY
  5. Join(Sequence[Shuffle[{1, 2, 3, 4, 4}], m, 1, 30]) → listNumTypeY
  6. Join(Sequence[Shuffle[{1, 2, 3, 4, 4}], m, 1, 30]) → listNumTypeX
  7. Transpose({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}, {A14, B14}, {A15, B15}, {A16, B16}, {A17, B17}, {A18, B18}, {A19, B19}, {A20, B20}, {A21, B21}, {A22, B22}, {A23, B23}, {A24, B24}, {A25, B25}, {A26, B26}, {A27, B27}, {A28, B28}, {A29, B29}, {A30, B30}, {A31, B31}, {A32, B32}, {A33, B33}, {A34, B34}, {A35, B35}, {A36, B36}, {A37, B37}, {A38, B38}, {A39, B39}, {A40, B40}, {A41, B41}, {A42, B42}, {A43, B43}, {A44, B44}, {A45, B45}, {A46, B46}, {A47, B47}, {A48, B48}, {A49, B49}, {A50, B50}, {A51, B51}, {A52, B52}, {A53, B53}, {A54, B54}, {A55, B55}, {A56, B56}, {A57, B57}, {A58, B58}, {A59, B59}, {A60, B60}, {A61, B61}, {A62, B62}, {A63, B63}, {A64, B64}, {A65, B65}, {A66, B66}, {A67, B67}, {A68, B68}, {A69, B69}, {A70, B70}}) → listFractionsAll
  8. Sequence(Random[2, Length[listFractionsAll(1)]], m, 1, 120) → randomNosForXBruch, {33, 30, 38, 41, 69, 27, 47, 24, 7, 67, 58, 46, 19, 46, 44, 57, 45, 62, 29, 60, 48, 57, 56, 50, 68, 24, 43, 68, 55, 15, 23, 33, 16, 20, 40, 57, 19, 66, 41, 30, 20, 39, 20, 37, 40, 48, 19, 65, 42, 12, 17, 68, 15, 37, 69, 64, 31, 11, 23, 36, 40, 44, 31, 24, 32, 16, 16, 43, 58, 41, 48, 55, 44, 55, 66, 21, 10, 25, 33, 26, 60, 54, 36, 27, 70, 49, 62, 45, 33, 51, 33, 60, 56, 37, 50, 64, 18, 52, 10, 49, 55, 58, 48, 3, 10, 41, 33, 34, 15, 49, 62, 68, 47, 24, 59, 42, 6, 16, 49, 34}
  9. Zip(Random[1, m - 1], m, randomNosForXBruch) → randomNosForYBruch
  10. Sequence(Random[2, Length[listDecimalNums1]], m, 1, 120) → randomNosForXDezimal, {603, 146, 369, 696, 44, 30, 326, 694, 194, 696, 145, 810, 288, 416, 776, 406, 674, 775, 397, 723, 333, 657, 383, 737, 664, 255, 176, 675, 518, 322, 16, 356, 715, 665, 590, 213, 781, 303, 165, 306, 677, 782, 104, 567, 702, 367, 810, 608, 540, 712, 161, 262, 691, 621, 22, 138, 723, 598, 102, 657, 81, 346, 278, 326, 364, 756, 614, 211, 148, 551, 514, 254, 171, 626, 482, 711, 807, 319, 138, 731, 76, 609, 504, 61, 8, 709, 382, 389, 217, 126, 537, 309, 168, 323, 694, 654, 80, 26, 519, 519, 15, 138, 433, 336, 449, 623, 654, 778, 790, 243, 399, 280, 413, 676, 183, 637, 560, 424, 670, 761}
  11. Zip(Random[1, m - 1], m, randomNosForXDezimal) → randomNosForYDezimal
  12. Sequence(Random[1, 2], m, 1, 120) → listPosX, {1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2}
  13. If(numX3 ≟ numY3first, numY3second, numY3first) → numY3
  14. If(numY3 ≟ 0, RandomElement[{1, 2, 4}], listNumTypeY(Mod[questionCount, 100] + 1)) → numtypeY
  15. If(exType ≟ 2 ∧ exType2Minus, -1, listVZX(Mod[questionCount, 100] + 1)) → vzX
  16. If(numX2 ≟ numY2first, numY2second, numY2first) → numY2
  17. If(isSame, numYSameDezimal, (vzY * Element[{numY1, numY2, numY3, numY4}, numtypeY])) → numY
  18. If(exType ≟ 2 ∧ exType2Minus, If[numX > numY, 1, 2], listPosX(Mod[questionCount, 100] + 1)) → posX
  19. Element({numX, numY}, posX) → num1
  20. Element({2, 1}, posX) → posY
  21. Element({numX, numY}, posY) → num2
  22. Element({vzX, vzY}, posY) → vz2
  23. If(IsInteger[(100000 * num2)], num2, (vz2 * floor((100 * abs(num2))) / 100)) → num2Dezi
  24. If(exType ≟ 2 ∧ exType2Minus, 2, If[num1 > num2, 2, If[num1 < num2, 3, If[num1 ≟ num2, 4]]]) → sol1
  25. Element({"", ">", "<", "<"}, sol1) → TextZeichen2
  26. Element({TextNumX, TextNumY}, posX) → TextNum1
  27. Element({vzX, vzY}, posX) → vz1
  28. If(IsInteger[(100000 * num1)], num1, (vz1 * floor((100 * abs(num1))) / 100)) → num1Dezi
  29. Element({"", ">", "<", "="}, sol1) → TextZeichen1
  30. SelectedIndex(DropDown1) → input1
  31. SelectedIndex(DropDown2a) → input2a
  32. Textfield(input2c) → Eingabefeld2c
  33. Textfield(input2b) → Eingabefeld2b
  34. Element({numtypeX, numtypeY}, posY) → numtype2
  35. If(numtype2 ≟ 4, 2, 1) → exType2answer
  36. If(exType2answer ≟ 1, input3, (Element[{1, 1, -1}, input2a] * input2b / input2c)) → input2
  37. Transpose({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}, {A14, B14}, {A15, B15}, {A16, B16}, {A17, B17}, {A18, B18}, {A19, B19}, {A20, B20}, {A21, B21}, {A22, B22}, {A23, B23}, {A24, B24}, {A25, B25}, {A26, B26}, {A27, B27}, {A28, B28}, {A29, B29}, {A30, B30}, {A31, B31}, {A32, B32}, {A33, B33}, {A34, B34}, {A35, B35}}) → listFractionsEcht
  38. Element({correct1, correct2}, exType) → correct
  39. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → AltrandomNosForX, {7, 1, 3, 4, 7, 10, 7, 6, 4, 5, 8, 7, 3, 8, 8, 1, 6, 7, 5, 3, 5, 4, 0, 2, 0, 9, 3, 10, 5, 6, 7, 3, 1, 9, 9, 9, 5, 7, 8, 6, 4, 7, 8, 2, 6, 8, 0, 8, 9, 2, 10, 10, 7, 0, 1, 3, 10, 9, 9, 4, 4, 7, 8, 9, 3, 10, 10, 0, 4, 6, 4, 2, 3, 1, 3, 7, 2, 10, 7, 8, 1, 2, 0, 8, 7, 9, 0, 9, 10, 9, 8, 2, 5, 3, 7, 8, 7, 6, 5, 2}
  40. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → AltrandomNosForY, {1, 6, 7, 7, 10, 3, 4, 1, 8, 9, 4, 4, 1, 4, 0, 7, 2, 0, 6, 3, 5, 7, 5, 8, 3, 7, 10, 6, 9, 0, 10, 0, 0, 0, 1, 2, 1, 2, 5, 1, 5, 9, 8, 10, 8, 2, 0, 8, 9, 3, 7, 6, 3, 7, 5, 8, 9, 10, 6, 7, 1, 0, 10, 5, 2, 5, 8, 2, 7, 4, 4, 7, 1, 6, 4, 7, 7, 1, 3, 0, 10, 2, 4, 9, 2, 6, 6, 7, 6, 10, 9, 3, 3, 2, 10, 4, 0, 3, 6, 8}
  41. Append(true, Sequence[If[AltrandomNosForX(i) ≟ AltrandomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  42. Append(true, Sequence[If[AltrandomNosForY(i) ≟ AltrandomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  43. Remove(Sequence[If[stayX(i), AltrandomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  44. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen
  45. Textfield(input3) → Eingabefeld3
  46. Zip(a / b, a, listFractionsAll(1), b, listFractionsAll(2)) → listFractionsValues
  47. Sequence(0, 10) → listWholeNums
  48. If(num1 ≟ num2, num1 + 1, num2) → solYDezimal
  49. Element({numX4b, numY4b}, posX) → num1b
  50. If(num1a > 0 ∧ sol1 ≟ 2, (-num1a), If[num1a > 0 ∧ sol1 ∈ {3, 4}, num1a + 1, If[num1a < 0 ∧ sol1 ≟ 2, num1a - 1, (-num1a)]]) → sol1BruchA
  51. Element({numtypeX, numtypeY}, posX) → numtype1
  52. Element({TextNumX, TextNumY}, posY) → TextNum2
  53. If(vz1 ≠ vz2, 1, If[¬(4 ∈ {numtype1, numtype2}), 2, If[numtype1 ≟ 4 ≟ numtype2, 3, If[numtype1 ≟ 4, 4, 5]]]) → solutionNum
  54. Point(Line[PKlecks1, xAxis]) → PKlecks2
  55. Point(Line[PKlecks3, xAxis]) → PKlecks4
  56. Point(Line[PKlecks5, xAxis]) → PKlecks6