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Slope and Slope Triangle

Slope and Slope Triangle
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2025-10-04 18:53
In collections Homogen lineare Funktionen
This example uses multiple-choice questions to help students understand the concept of slope and slope triangle. Key mathematical concepts include the slope of a line, slope triangle, and linear functions. GeoGebra commands such as Sequence, Element, Textfield, Join are used in construction. Suitable for 7-8 grade students to learn the properties of linear functions.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {3, 5, 9, 3, 7, 2, 9, 8, 1, 6}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  7. Corner(txt012Vali1, 1) → Vali1LU
  8. Corner(txt012Vali1, 2) → Vali1RU
  9. Corner(txt012Vali1, 3) → Vali1RO
  10. Corner(txt012Vali1, 4) → Vali1LO
  11. Segment(Vali1HO, Vali1LO) → vali1Border_{4}
  12. Segment(Vali1LO, Vali1RO) → vali1Border_{3}
  13. Segment(Vali1RO, Vali1RU) → vali1Border_{2}
  14. Segment(Vali1RU, Vali1LU) → vali1Border_{1}
  15. Segment(Vali1LU, Vali1HU) → vali1Border
  16. Segment(Vali1HU, Vali1HV) → vali1Border_{6}
  17. Segment(Vali1HV, Vali1HO) → vali1Border_{5}
  18. Corner(txt031Sprech, 1) → Vali3LU
  19. Corner(txt031Sprech, 2) → Vali3RU
  20. Corner(txt031Sprech, 3) → Vali3RO
  21. Corner(txt031Sprech, 4) → Vali3LO
  22. Segment(Vali3HV, Vali3HU) → valli3Border
  23. Segment(Vali3LU, Vali3HU) → valli3Border_{1}
  24. Segment(Vali3LU, Vali3RU) → valli3Border_{2}
  25. Segment(Vali3RU, Vali3RO) → valli3Border_{3}
  26. Segment(Vali3RO, Vali3LO) → valli3Border_{4}
  27. Segment(Vali3LO, Vali3HO) → valli3Border_{5}
  28. Segment(Vali3HO, Vali3HV) → valli3Border_{6}
  29. Textfield(input3O) → inputBox3O
  30. Polygon(PCorrect3LO, PCorrect3RO, PCorrect3RU, PCorrect3LU) → v1, a, b, c, d
  31. Segment(DiagramYU, DiagramYO) → d1Y
  32. Segment(DiagramXL, DiagramXR) → d1X
  33. Polygon(whiteSquare_{16}, whiteSquare_{17}, whiteSquare_{18}, whiteSquare_{19}) → q4_{4}, c_{6}, d_{6}, e_{5}, f_{6}
  34. Line(C, D) → p
  35. Line(p07SDLU, p07SDRO) → g
  36. Line(p07SDLU_{1}, p07SDRO_{1}) → g_{2}
  37. Intersect(p, g_{2}) → pGeradeU
  38. Line(E, F) → q
  39. Intersect(q, g_{2}) → pGeradeOH
  40. Segment(pGeradeU, pGeradeO) → f
  41. Line(pHelp05_{1}, pHelp05_{2}) → r
  42. Line(pHelp05_{3}, pHelp05) → s
  43. Intersect(f, r) → p05HilfsU
  44. Intersect(s, f) → p05HilfsO
  45. Segment(p05HilfsU, p05HilfsO) → fRange
  46. Point(listPosSteigung) → pSteigungOBewege
  47. If(step ≠ 5 ∧ step ≠ 6, (x(DiagramXL) + 0.4 + (6 * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0.4)) / 8), y(DiagramYU) + 0.4 + (5 * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0.4)) / 6)), pSteigungOBewege) → pSteigungO
  48. Segment(pSteigungL, pSteigungR) → s04X
  49. Segment(pSteigungR, pSteigungO) → s04Y
  50. Polygon(pSteigungL, pSteigungO, pSteigungR) → t1, psteigungr, psteigungl, psteigungo
  51. Corner(txt071, 1) → Valli7LU
  52. Corner(txt071, 2) → Valli7RU
  53. Corner(txt071, 3) → Valli7RO
  54. Corner(txt071, 4) → Valli7LO
  55. Segment(Valli7LU, Valli7RU) → valli7Border_{2}
  56. Segment(Valli7RU, Valli7RO) → valli7Border_{3}
  57. Segment(Valli7RO, Valli7LO) → valli7Border_{4}
  58. Segment(Valli7LO, Valli7HO) → valli7Border_{5}
  59. Segment(Valli7HO, Valli7HV) → valli7Border_{6}
  60. Segment(Valli7HV, Valli7HU) → valli7Border
  61. Segment(Valli7HU, Valli7LU) → valli7Border_{1}
  62. Polygon(p07SDLU, p07SDRU, p07SDRO) → t2, p07sdro, p07sdlu, p07sdru
  63. Polygon(pKlemmbrett_{1}, pKlemmbrett, pKlemmbrett_{2}, pKlemmbrett_{3}) → q1, c_1, d_1, e, f_1
  64. Polygon(pKlemmbrett_{4}, pKlemmbrett_{5}, pKlemmbrett_{6}, pKlemmbrett_{7}) → q2, g_1, h, i, j
  65. Polygon(p11LO, p11RO, p11RU, p11LU) → q3, s11O, s11R, s11U, s11L
  66. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((1 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow1
  67. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((2 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow2
  68. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((3 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow3
  69. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((4 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow4
  70. Polygon(whiteSquare_{1}, whiteSquare_{2}, whiteSquare_{3}, whiteSquare) → q4, c_2, d_2, e_1, f_2
  71. Polygon(whiteSquare_{4}, whiteSquare_{5}, whiteSquare_{6}, whiteSquare_{7}) → q4_{1}, c_{3}, d_{3}, e_{2}, f_{3}
  72. Polygon(whiteSquare_{8}, whiteSquare_{9}, whiteSquare_{10}, whiteSquare_{11}) → q4_{2}, c_{4}, d_{4}, e_{3}, f_{4}
  73. Polygon(whiteSquare_{12}, whiteSquare_{13}, whiteSquare_{14}, whiteSquare_{15}) → q4_{3}, c_{5}, d_{5}, e_{4}, f_{5}
  74. Corner(txt08Vali, 1) → p08Eck1
  75. Corner(txt08Vali, 2) → p08Eck2
  76. Corner(txt08Vali, 3) → p08Eck3
  77. Corner(txt08Vali, 4) → p08Eck4
  78. Segment(p08EckO, p08Eck4) → s08Vali_{3}
  79. Segment(p08Eck4, p08Eck3) → s08Vali_{4}
  80. Segment(p08Eck3, p08Eck2) → s08Vali_{6}
  81. Segment(p08Eck2, p08Eck1) → s08Vali_{5}
  82. Segment(p08Eck1, p08EckU) → s08Vali
  83. Segment(p08EckU, p08EckV) → s08Vali_{1}
  84. Segment(p08EckV, p08EckO) → s08Vali_{2}
  85. Segment(DiagramYU_{1}, DiagramYO_{1}) → diagramY_{1}
  86. Segment(DiagramXL_{1}, DiagramXR_{1}) → diagramX_{1}
  87. Segment(DiagramYU_{2}, DiagramYO_{2}) → d2Y
  88. Segment(DiagramXL_{2}, DiagramXR_{2}) → d2X
  89. Segment(DiagramYU_{4}, DiagramYO_{4}) → d2Y_{1}
  90. Segment(DiagramXL_{4}, DiagramXR_{4}) → d2X_{1}
  91. Segment(G_{1}, H_{1}) → t_{1}
  92. Segment(DiagramYU_{5}, DiagramYO_{5}) → d2Y_{2}
  93. Segment(DiagramXL_{5}, DiagramXR_{5}) → d2X_{2}
  94. Polygon(p11WhiteLO, p11WhiteRO, p11WhiteRU, p11WhiteLU) → q5, i_1, j_1, k_1, l_1
  95. Polygon(p11WhiteLO_{1}, p11WhiteRO_{1}, p11WhiteRU_{1}, p11WhiteLU_{1}) → q5_{1}, i_{2}, j_{2}, k_{2}, l_{2}
  96. Polygon(p11WhiteLO_{2}, p11WhiteRO_{2}, p11WhiteRU_{2}, p11WhiteLU_{2}) → q5_{2}, i_{3}, j_{3}, k_{3}, l_{3}
  97. Segment(G_{3}, H_{3}) → t_{2}
  98. Segment(G_{4}, H_{4}) → t_{3}
  99. Segment(DiagramYU_{6}, DiagramYO_{6}) → d1Y_{1}
  100. Segment(DiagramXL_{6}, DiagramXR_{6}) → d1X_{1}
  101. Line(C_{1}, D_{1}) → p_{1}
  102. Line(p07SDLU_{6}, p07SDRO_{2}) → g_{3}
  103. Intersect(p_{1}, g_{3}) → pGeradeU_{1}
  104. Line(E_{1}, F_{1}) → q_{1}
  105. Intersect(q_{1}, g_{3}) → pGeradeOH_{1}
  106. Segment(pGeradeU_{1}, pGeradeO_{1}) → f_{7}
  107. Line(pHelp05_{5}, pHelp05_{4}) → r_{1}
  108. Line(pHelp05_{6}, pHelp05_{7}) → s_{1}
  109. Intersect(f_{7}, r_{1}) → p05HilfsU_{1}
  110. Intersect(s_{1}, f_{7}) → p05HilfsO_{1}
  111. Segment(p05HilfsU_{1}, p05HilfsO_{1}) → fRange_{1}
  112. Point(fRange_{1}) → pSteigungOBewege_{1}
  113. If(step ≠ 5, (x(DiagramXL_{6}) + 0.4 + (5 * (x(DiagramXR_{6}) - 0.4 - (x(DiagramXL_{6}) + 0.4)) / 8), y(DiagramYU_{6}) + 0.4 + (4 * (y(DiagramYO_{6}) - 0.4 - (y(DiagramYU_{6}) + 0.4)) / 6)), pSteigungOBewege_{1}) → pSteigungO_{1}
  114. Segment(pSteigungR_{1}, pSteigungO_{1}) → s04Y_{1}
  115. Segment(DiagramYU_{7}, DiagramYO_{7}) → diagramY_{2}
  116. Segment(DiagramXL_{7}, DiagramXR_{7}) → diagramX_{2}
  117. Sequence(If[i ≥ 0, Segment[DiagramXL + (0.4, y(DiagramYO) - y(DiagramXL)) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0.4)) / 8), 0), DiagramXL + (0.4, y(DiagramYU) - y(DiagramXL)) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0.4)) / 8), 0)]], i, 0, 8) → d1kleineStricheY
  118. Sequence(If[i ≥ 0, Segment[DiagramYU + (x(DiagramXR) - x(DiagramYU), 0.4) + (0, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0.4)) / 6)), DiagramYU + (x(DiagramXL) - x(DiagramYO), 0.4) + (0, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0.4)) / 6))]], i, 0, 6) → d1kleineStricheX
  119. Segment(DiagramYU_{8}, DiagramYO_{8}) → d1Y_{2}
  120. Segment(DiagramXL_{8}, DiagramXR_{8}) → d1X_{2}
  121. Segment(pSteigungR, pSteigungO) → s04Y_{2}
  122. Line(I, J) → t
  123. Sequence(If[i ≠ 2, Segment[DiagramYU + (0, 0.4) + (0.12, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0.4)) / 6)), DiagramYU + (0, 0.4) + (-0.12, (i * (y(DiagramYO) - 0.4 - (y(DiagramYU) + 0.4)) / 6))]], i, 0, 6) → d1StricheY
  124. Sequence(If[i ≠ 2, Segment[DiagramXL + (0.4, 0) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0.4)) / 8), 0.12), DiagramXL + (0.4, 0) + ((i * (x(DiagramXR) - 0.4 - (x(DiagramXL) + 0.4)) / 8), -0.12)]], i, 0, 8) → d1StricheX