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有理数比较 - Klecksaufgaben

有理数比较 - Klecksaufgaben
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2025-06-04 17:41
所属专题 Ordnen und Vergleichen von rationalen Zahlen
本范例演示了如何比较有理数。学生可以通过调整数字来比较有理数的大小。这个范例涉及的核心数学概念是有理数的比较和有理数在坐标系中的表示。作图要点包括使用 GeoGebra 的 Join、Zip、Transpose 等命令，以及使用 Sequence 和 If 等命令来控制图形的显示。这个范例适合 7-8 年级学生使用。

GeoGebra 命令及参数

  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