积极 AI Logo 积极 AI

解一步方程：通过数轴与条形图探索变量求解

解一步方程：通过数轴与条形图探索变量求解
几何画板及绘图内容加载中，请稍等……
2023-07-18 05:00
函数数列不等式滑块动画函数图像
该GeoGebra范例演示了如何通过数轴（strip diagram）和方程逐步求解一步方程，帮助学生直观理解变量在等式中的意义。核心数学概念包括一元一次方程、等式的性质、加减乘除运算的逆运算，以及用图形表示数量关系。作图要点：利用RandomUniform生成随机数，通过Textfield和InputBox1接收用户输入，使用Text、Take、If、Element、Sequence等命令构建动态方程与条形图，并借助PointToPixels、centerBox、Corner、Translate、Segment、Min等对象实现图形布局与动画控制（如animateControl、animateAddition）。适合小学4-5年级学生练习，也可用于初中代数入门教学，支持西班牙语版本，是经过验证的优质教学资源。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.24309416209828497, 0.23575968388160132, 0.05637143677548921, 0.7663634909605562, 0.6843540034428994, 0.03173646648991745, 0.7480307932851396, 0.447237517991689, 0.4039964793829785, 0.7713820619874071, 0.45809155280153324, 0.8596886144955532, 0.46276755961442617, 0.21898020772482568, 0.32328197297151007, 0.9727205620943419, 0.7831270658301578, 0.38826426125976976, 0.6768351615810564, 0.24192065960284068, 0.8676927803882839, 0.04941569465163856, 0.43798648025720877, 0.603222984606823, 0.7765947799953208, 0.07095313286882719, 0.9442698619976504, 0.2057673284306999, 0.4344054398573109, 0.2019313047207908, 0.8798916288804389, 0.37106510724567854, 0.07558366364362334, 0.5933755219371996, 0.7465753644655122, 0.23778368781117376, 0.3728291967915565, 0.7660703120795281, 0.19857435452880412, 0.23324739855256496, 0.39539077758759, 0.9647021086063126, 0.20103858780017866, 0.6742282055295554, 0.9542049433021985, 0.4559239861591829, 0.520600228401039, 0.08076091023819311, 0.5077642107147805, 0.8601662946344996, 0.6189078136306079, 0.8775678490229782, 0.8168221591118795, 0.6539606033420841, 0.2838911230382109, 0.2382144948696543, 0.1574396919259567, 0.6211748199120799, 0.8397796019099308, 0.6873426926347507, 0.5404603636965887, 0.5678763793384387, 0.8053246752440516, 0.9162396954362756, 0.9712743269052319, 0.5765454545210382, 0.030291540427799083, 0.2766013536159407, 0.2066896031247761, 0.7210541270614637, 0.3730888126193086, 0.32663439279513673, 0.6358756312801304, 0.6942080892968363, 0.06739459826632864, 0.7226179611634703, 0.7096779532177, 0.5647156255028781, 0.2928152187611787, 0.3277059171295252, 0.6271247730250025, 0.8302049319476487, 0.8739783700087319, 0.9181017500279075, 0.019654717694082134, 0.007353674046759228, 0.04401468648149956, 0.004774702045388483, 0.5024918637423577, 0.1093259177823831, 0.14212257495852462, 0.5566100936213371, 0.5986777676157804, 0.05452979559564425, 0.5308381972143849, 0.40829954886672454, 0.5245422485559347, 0.15921510848745055, 0.21674847435821581, 0.3633759132609266, 0.8558531918483919, 0.9696233932971632, 0.008686978386047888, 0.3595849970450599, 0.9715320104298864, 0.3372841068668233, 0.4099434012156451, 0.8902606694105346, 0.2066562433069596, 0.5736184496383566, 0.18569482371188953, 0.11153236244096866, 0.5984910264336895, 0.06726857815656265, 0.7837319403336064, 0.45104328884606765, 0.028501300760129206, 0.4995135653198859, 0.6456066289206982, 0.19939475499091155, 0.9196922712120189, 0.8797633378705944, 0.12656728507428538, 0.940756801564691, 0.8722099563562037, 0.7444414783098166, 0.5760758304089827, 0.8839975416283762, 0.4609055355294768, 0.008572576233774849, 0.7963160207872346, 0.8302826946880881, 0.496525118294161, 0.7300837203437597, 0.303904942735752, 0.9073847356223177, 0.007334306781938987, 0.3122106127743558, 0.6800100458342836, 0.4149147055473462, 0.510320039649063, 0.5794665733992769, 0.33625205211048326, 0.468352726569357, 0.5206338982075878, 0.15738947821711893, 0.2881386072253394, 0.09310251114022591, 0.9446503619289418, 0.5257241825653521, 0.8043270856047782, 0.7028317953223625, 0.395909492552568, 0.4088291671898534, 0.7787545379782896, 0.41908646819063744, 0.9342977672013733, 0.575914818185117, 0.49360103041166475, 0.12157668794645299, 0.9570924893434051, 0.5772261729094923, 0.6341674445586456, 0.05063429618948855, 0.17595357077729445, 0.8204761068122595, 0.8320517237290249, 0.5851271281734549, 0.6265936371192506, 0.9747169218484317, 0.9404978503753142, 0.8305905699798128, 0.037690958931394854, 0.056405172226775664, 0.6554695129843771, 0.003499107257445866, 0.0326312586392705, 0.25467143188043395, 0.757865390363651, 0.7784499806500158, 0.4718738274668245, 0.5397499117346121, 0.4863463848492693, 0.6755679708478345, 0.9651330577943193, 0.7301532882053272, 0.9464845389308749, 0.5656655484693643, 0.021151316535512856, 0.2004968843041442, 0.6603717963758396, 0.06060414915868328, 0.15861013340942773, 0.45288210880050395, 0.41144154900490315, 0.7859022229282462, 0.5146857098549239, 0.43044214640516076, 0.652058873088471, 0.32192270494829744}
  2. Textfield(input1) → InputBox1
  3. Text(InputBox1) → inputText
  4. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  5. If(isAddition ∨ isSubtraction, num1 + 2, 2) → num2Start
  6. Element({num2 - num1, num1 + num2, num2Mult / num1Mult, (num1Div * num2Div)}, indexQuestion) → answer
  7. If(isAddition, animateControl, 0) → animateAddition
  8. Sequence(equationStart + ((0, (-spaceBetweenEquationLines)) * k), k, 0, 2) → equationPoints
  9. Element({"x", "y"}, indexVariable) → variable
  10. Sequence(startHome + (k * (spaceHome, 0)), k, 0, 10) → allHomeAnchors
  11. PointToPixels(onboardingPoint, Corner[1], Corner[3], Corner[5]) → onboardingPointPixels
  12. Sequence(startEnd + (K * (spaceEnd, 0)), K, 0, 10) → boxAnchors
  13. centerBox(boxWidth, boxHeight, boxAnchors(8)) → frame8
  14. centerBox(boxWidth, boxHeight, boxAnchors(7)) → frame7
  15. centerBox(boxWidth, boxHeight, boxAnchors(6)) → frame6
  16. centerBox(boxWidth, boxHeight, boxAnchors(5)) → frame5
  17. centerBox(boxWidth, boxHeight, boxAnchors(4)) → frame4
  18. centerBox(boxWidth, boxHeight, boxAnchors(3)) → frame3
  19. centerBox(boxWidth, boxHeight, boxAnchors(2)) → frame2
  20. centerBox(boxWidth, boxHeight, boxAnchors(1)) → frame1
  21. Textfield(input2) → InputBox2
  22. Corner(5) → layoutAppSize
  23. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  24. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  25. Sequence(k, k, 1, 10) → homeIndices
  26. Zip(allHomeAnchors(J), J, homeIndices) → homeLocations
  27. Take({P1, P2, P3, P4, P5, P6, P7, P8}, 1, numDragBoxes) → movingPoints
  28. centerBox(boxWidth, boxHeight, P1) → box1
  29. centerBox(boxWidth, boxHeight, P2) → box2
  30. centerBox(boxWidth, boxHeight, P3) → box3
  31. centerBox(boxWidth, boxHeight, P4) → box4
  32. centerBox(boxWidth, boxHeight, P5) → box5
  33. centerBox(boxWidth, boxHeight, P6) → box6
  34. Element(movingPoints, movingIndex) → PMove
  35. centerBox(boxWidth, boxHeight, PMove) → highlightBox
  36. Text(("" * boxText(movingIndex)), If[Defined[PMove], PMove, (300, 300)], false, true, 0, 0) → textHightlight
  37. Sequence(HOME, k, 1, numDragBoxes) → allHome
  38. centerBox(boxWidth, boxHeight, P7) → box7
  39. centerBox(boxWidth, boxHeight, P8) → box8
  40. Sequence((((("SetValue(P" * K) * ",homeLocations(") * K) * "))"), K, 1, numDragBoxes) → cmdSendHome
  41. Zip(Text[("" * K), J, true, true, 0, 0], K, Take[boxText, 1, numDragBoxes], J, Take[movingPoints, 1, numDragBoxes]) → boxTextDisplay
  42. expandQuad(Vertex[box1, 1], Vertex[box1, 2], Vertex[box1, 3], Vertex[box1, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox1
  43. expandQuad(Vertex[box2, 1], Vertex[box2, 2], Vertex[box2, 3], Vertex[box2, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox2
  44. expandQuad(Vertex[box3, 1], Vertex[box3, 2], Vertex[box3, 3], Vertex[box3, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox3
  45. expandQuad(Vertex[box4, 1], Vertex[box4, 2], Vertex[box4, 3], Vertex[box4, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox4
  46. expandQuad(Vertex[box5, 1], Vertex[box5, 2], Vertex[box5, 3], Vertex[box5, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox5
  47. expandQuad(Vertex[box6, 1], Vertex[box6, 2], Vertex[box6, 3], Vertex[box6, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox6
  48. expandQuad(Vertex[box7, 1], Vertex[box7, 2], Vertex[box7, 3], Vertex[box7, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox7
  49. expandQuad(Vertex[box8, 1], Vertex[box8, 2], Vertex[box8, 3], Vertex[box8, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingBox8
  50. makeBox(pointStrip1, lengthStrip, heightStrip) → strip1
  51. Element({questionAddition, questionSubtraction, questionMultiplication, questionDivision}, indexQuestion) → question
  52. makeBox(pointStrip2, lengthStrip, heightStrip) → strip2
  53. makeBox(pointStrip1, (unitLengthAddition * (num2 - num1)), heightStrip) → addS1XBox
  54. makeBox(additionS1P1, (num1 * unitLengthAddition), heightStrip) → addS1NumBox
  55. Translate(addS1XBox, Vector[pointStrip1, pointStrip2]) → addS2XBox
  56. Translate(addS1NumBox, Vector[additionS1P1, additionS2P1]) → addS2NumBox
  57. makeBox(pointStrip2, lengthStrip, heightStrip) → addS2WholeBox
  58. Text((("" * variable) * ""), additionS1XLabel, true, true, 0, 0) → additionS1X
  59. Text((("" * num1) * ""), additionS1NumLabel, true, true, 0, 0) → additionS1Num1
  60. Text((("" * answer) * ""), additionS2AnswerLabel, true, true, 0, 0) → additionS2Answer
  61. Text((("" * num2) * ""), additionS2Num2Label, true, true, 0, 0) → additionS2Num2
  62. Segment(lineStart, lineStart + (2, 0)) → equationLine
  63. makeBox(pointStrip1, lengthStrip, heightStrip) → subS1XBox
  64. makeBox(pointStrip2, (unitLengthSubtraction * num2), heightStrip) → subS2Num1Box
  65. makeBox(subS2P1, (unitLengthSubtraction * num1), heightStrip) → subS2NumBox
  66. If(isSubtraction, animateControl, 0) → animateSubtraction
  67. Text(variable, subS1XLabelPos, true, true, 0, 0) → subS1XLabel
  68. Text((("\minus" * num1) * ""), subS1NumLabelPos, true, true, 0, 0) → subS1NumLabelNeg
  69. Text((("" * num2) * ""), subS2Num1LabelPos, true, true, 0, 0) → subS2Num1Label
  70. Text(answer, subS2AnswerLabelPos, true, true, 0, 0) → subS2AnswerLabel
  71. Text(num1, subS2Num2LabelPos, true, true, 0, 0) → subS2Num2Label
  72. Text((("" * num1) * ""), subS1NumLabelPos, true, true, 0, 0) → subS1NumLabel
  73. makeBox(pointStrip2, lengthStrip, heightStrip) → subS2SolBox
  74. If(animateAddition ≤ 0.5, greyNum, ((animateAddition - 0.5) * 2)) → animateAdditionFade
  75. makeBox(pointStrip1, lengthStrip, heightStrip) → multS1FullBox
  76. makeBox(pointStrip2, lengthStrip, heightStrip) → multS2FullBox
  77. If(isMultiplication, animateControl, 0) → animateMultiplication
  78. Sequence(pointStrip2 + (((unitLengthMult * answer), 0) * k), k, 1, num1Mult - 1) → multS2TopPoints
  79. Sequence(pointStrip1 + (((unitLengthMult * answer), 0) * k), k, 1, num1Mult - 1) → multS1TopPoints
  80. Sequence(pointStrip1 + (((unitLengthMult * answer) * k), 0) + ((unitLengthMult * answer / 2), ((-heightStrip)) / 2), k, 0, num1Mult - 1) → multS1LabelPoints
  81. Sequence(pointStrip2 + (((unitLengthMult * answer) * k), 0) + ((unitLengthMult * answer / 2), ((-heightStrip)) / 2), k, 0, num1Mult - 1) → multS2LabelPoints
  82. Zip(Segment[A, A + ((0, (-heightStrip)) * animateMultiplication)], A, multS2TopPoints) → multS2Segs
  83. Zip(Text[variable, A, true, true, 0, 0], A, multS1LabelPoints) → multS1Labels
  84. Zip(Text[(("" * answer) * ""), A, true, true, 0, 0], A, multS2LabelPoints) → multS2LabelsAnswer
  85. Text((("" * num2Mult) * ""), multS2LabelPoint, true, true, 0, 0) → multS2Label
  86. makeBox(pointStrip1, lengthStrip / num1Div, heightStrip) → divStrip1Initial
  87. makeBox(pointStrip2, lengthStrip / num1Div, heightStrip) → divStrip2Initial
  88. If(isDivision, animateControl, 0) → animateDivision
  89. Sequence(pointStrip1 + (k * ((num2Div * unitLengthDiv), 0)), k, 1, num1Div - 1) → divS1TopPoints
  90. Sequence(pointStrip2 + (k * ((num2Div * unitLengthDiv), 0)), k, 1, num1Div - 1) → divS2TopPoints
  91. Min(1, (animateDivision * 2)) → animateDivisionBoxes
  92. Sequence(divS1LabelStart + (k * (lengthStrip / num1Div, 0)), k, 1, num1Div - 1) → divS1LabelPoints
  93. Sequence(divS2LabelStart + (k * (lengthStrip / num1Div, 0)), k, 1, num1Div - 1) → divS2LabelPoints
  94. Text((("" * num2Div) * ""), divS2LabelStart, true, true, 0, 0) → divS2Label
  95. If(animateDivision ≤ 0.5, greyNum, ((animateDivision - 0.5) * 2)) → animateDivisionFade
  96. If(animateDivision ≤ 0.5, 1, Max[((1 - animateDivision) * 2), greyNum]) → animateDivisionIncrease
  97. makeBox(pointStrip1, lengthStrip, heightStrip) → divStrip1Outline
  98. makeBox(pointStrip2, lengthStrip, heightStrip) → divStrip2Outline
  99. Text((("" * variable) * ""), divS1LabelCenter, true, true, 0, 0) → divS1FinalLabel
  100. Text((("" * answer) * ""), divS2LabelCenter, true, true, 0, 0) → divS2FinalLabel
  101. If(animateSubtraction < greyNum, greyNum, animateSubtraction) → animateSubtractionFade
  102. If(1 - animateSubtraction > greyNum, 1 - animateSubtraction, greyNum) → animateSubtractionIncrease
  103. Text((((("" * num1) * "") * variable) * ""), multS1LabelPoint, true, true, 0, 0) → multS1Label
  104. Text("=", pointStrip2 - (spaceBetween / 2, heightStrip / 2), true, true, 0, 0) → textEquals
  105. Zip(Segment[A, A + (0, (-heightStrip))], A, multS1TopPoints) → multS1Segs
  106. Translate(divStrip1Initial, Vector[pointStrip1, animateStartPointS1]) → divStripInitialAnimateS1
  107. Translate(divStrip2Initial, Vector[pointStrip2, animateStartPointS2]) → divStripInitialAnimateS2
  108. Zip(Translate[divStripInitialAnimateS2, Vector[animateStartPointS2, K]], K, Take[divS2TopPoints, 1, animateDivisionBoxesIndex]) → divS2Boxes
  109. Translate(divStripInitialAnimateS1, Vector[(animateDivisionBoxesMove * Vector[animateStartPointS1, divS1TopPoints(animateDivisionBoxesIndex + 1)])]) → divMovingBox1
  110. Translate(divStripInitialAnimateS2, Vector[(animateDivisionBoxesMove * Vector[animateStartPointS2, divS2TopPoints(animateDivisionBoxesIndex + 1)])]) → divMovingBox2
  111. Zip(Text[(("" * num2Div) * ""), divS2LabelStart + K - divS2LabelStart, true, true, 0, 0], K, Take[divS2LabelPoints, 1, animateDivisionBoxesIndex]) → divS2Labels
  112. Take(question, 1, IndexOf["=", question] - 2) → questionS1
  113. Take(question, IndexOf["=", question] + 1) → questionS2
  114. Sequence(equationStart + ((spaceBetweenEquation * k), 0), k, -1, 1) → equationL1
  115. Sequence(equationStart + (0, (-spaceBetweenEquationLines)) + ((spaceBetweenEquation * k), 0), k, -1, 1) → equationL2
  116. Sequence(equationStart + (0, (-2 * spaceBetweenEquationLines)) + ((spaceBetweenEquation * k), 0), k, -1, 1) → equationL3
  117. Text("=", equationL1(2), true, true, 0, 0) → questionL1equals
  118. Text("=", equationL3(2), true, true, 0, 0) → questionL3equals
  119. Text(questionS1, equationL1(1), true, true, -1, 0) → questionL1S1
  120. Text(questionS2, equationL1(3), true, true, 1, 0) → questionL1S2
  121. Element({(("\minus" * num1) * ""), (("+" * num1) * ""), (("\div" * num1Mult) * ""), (("\times" * num1Div) * "")}, indexQuestion) → questionOp
  122. Text(questionOp, equationL2(1), true, true, -1, 0) → questionL2S1
  123. Text(questionOp, equationL2(3), true, true, 1, 0) → questionL2S2
  124. Text((("" * variable) * ""), equationL3(1), true, true, -1, 0) → questionL3S1
  125. Text((("" * answer) * ""), equationL3(3), true, true, 1, 0) → questionL3S2
  126. Text((((("" * variable) * "\div") * num1Div) * ""), divS1LabelStart, true, true, 0, 0) → divS1Label
  127. Zip(Translate[divStripInitialAnimateS2, Vector[animateStartPointS2, K]], K, Take[divS2TopPoints, animateDivisionBoxesIndex + 1, num1Div - 1]) → divS2DashedBoxes
  128. Min((animateAddition * 2), 1) → animateAdditionDivide
  129. Segment(additionS2P1, additionS2P1 + (0, ((-heightStrip) * animateAdditionDivide))) → additionSegS2
  130. Text((("" * num1) * ""), additionS2Num1Label, true, true, 0, 0) → additionS2Num1Neg
  131. Text((("" * num1) * ""), additionS1NumLabel, true, true, 0, 0) → additionS1Num1Neg

AI 绘图提示语参考

一个用于解决一步方程的交互式练习界面。界面包含一个输入框用于输入数字，一个显示方程的框，其中包含变量x或y，以及一些可以拖动调整的框。用户可以输入数字，然后查看方程和答案。图形包括随机生成的数字、方程和变量。
以上提示语为根据原始绘图命令整理而来，仅供参考。