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加减数列探索

加减数列探索
几何画板及绘图内容加载中，请稍等……
2023-06-24 18:38
数列解析几何滑块动画
本范例展示了数列中的加法或减法模式，帮助学生发现数列中的规律并推断出数列的延续方式。通过使用GeoGebra命令如Sequence、Min、Element等，学生可以直观地理解数列的概念。适合4-5年级学生学习数列识别与生成，以及纠正数列中的错误或解释数列特征。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.5772282716165421, 0.7782178867143921, 0.1860809768849399, 0.8727684193678532, 0.32078461393601765, 0.6966950978452615, 0.5997337230698409, 0.06077452879160551, 0.20490292781736558, 0.8913982321541603, 0.6887637574705286, 0.678860719657529, 0.16433646917662523, 0.591572907540836, 0.32035571797491835, 0.11565662033151111, 0.946441649719177, 0.27053417686828185, 0.7487017163803429, 0.4384749182620633, 0.40019279063434615, 0.9188097475414247, 0.45509283546101575, 0.27472473020260835, 0.2658020374566143, 0.1285956284664711, 0.20514661010666127, 0.3419636204364093, 0.1266179090202311, 0.9420651191465486, 0.4454661047355585, 0.4317419981120512, 0.5673898647754426, 0.6943439411327604, 0.9355300417944526, 0.41550838642649285, 0.45508474348314665, 0.03742323696956816, 0.8288086442911913, 0.5361472515562876, 0.14022842236186306, 0.653928317927499, 0.7399794069403377, 0.13621089342121942, 0.40822078411636475, 0.26949587491518634, 0.9226860246333086, 0.24358519233915532, 0.3412338534010827, 0.9095324102515462, 0.2445393364079097, 0.32719325277881794, 0.3421529248311042, 0.13033738925710822, 0.4730027155809593, 0.4693952003230946, 0.5125572649472089, 0.5159695736975112, 0.5674345835371339, 0.9479809057940038, 0.8469619910317061, 0.590819804550891, 0.4588803012241707, 0.08908175171163885, 0.8854544171267202, 0.6236250809272714, 0.43020998126629095, 0.5229415397126279, 0.17645798724095446, 0.31161679594262404, 0.47489350336036273, 0.08729019045686079, 0.31064420894599043, 0.8236439647067858, 0.653083998754092, 0.2280535726535636, 0.43598696074274884, 0.6684448297882823, 0.2587499103990693, 0.9743111377568535, 0.6526166520839958, 0.25876262208772033, 0.461351235753515, 0.0637774057340328, 0.334480307236624, 0.9037099789731815, 0.3099993419165156, 0.32663709383505346, 0.2328513965431105, 0.27068281598652555, 0.967170126062371, 0.5293030574427937, 0.07445776124683352, 0.5942087707353476, 0.7528589450032857, 0.5255944948382602, 0.53440772819744, 0.6523865665781479, 0.7485717415077584, 0.690947710480758, 0.6411946981264767, 0.14203163501475213, 0.813739620663265, 0.3855748749341333, 0.1378469619661762, 0.6312901630709012, 0.3750255768574534, 0.6149762034035522, 0.7897647764932151, 0.1433171414825095, 0.5415601198175608, 0.05088841857324402, 0.5959481285231992, 0.11663594317725316, 0.30639830300436405, 0.5426184914826011, 0.22616892411687287, 0.7370058366824519, 0.7064344588041077, 0.27776330958599565, 0.6921779594072323, 0.9520200782231236, 0.5996412876802728, 0.3225569542216779, 0.8962616739672442, 0.3032417145416085, 0.02981864725114584, 0.23551459726790133, 0.3253761938370465, 0.24145497433007862, 0.2150431439597653, 0.8836573747914785, 0.5236854035018359, 0.05857008004948221, 0.03670285766014083, 0.18840555093512132, 0.8606167769076101, 0.7348646530062893, 0.8913828476479506, 0.8682168302468313, 0.5055239633467334, 0.5525800680209683, 0.34793462389222096, 0.8172254370099187, 0.913706392907939, 0.14641152242661692, 0.016819646932496417, 0.6035019416092835, 0.031886300082842635, 0.07814031858019009, 0.14825933803911828, 0.09710677125475492, 0.644280881308323, 0.726553028130966, 0.7298555783083527, 0.09685109885949159, 0.023130902820034573, 0.30487616716906907, 0.033163787770262985, 0.7756056630434714, 0.15996067673861555, 0.46622658704519426, 0.4122065244887696, 0.7571138960159866, 0.13594237899855477, 0.9330369318547271, 0.665108819235147, 0.162568680468092, 0.6515261229243265, 0.8190613304340925, 0.16291782746500363, 0.0027012069428718477, 0.05697080469835493, 0.062401648363462854, 0.8572368012279309, 0.5208096835199705, 0.2965735732438918, 0.7350148162802549, 0.8705603260436433, 0.8340194984906901, 0.7102448967330856, 0.3883716217092312, 0.9201401748474342, 0.3841199582548486, 0.9766134155407714, 0.5063335981260207, 0.25784274988712663, 0.28556277473264335, 0.2620698804677332, 0.7948983439983888, 0.5247768012398515, 0.6366351803173702, 0.5200705429217891, 0.5642356854790325, 0.5704765385404011, 0.12043550548993245, 0.8446211522691587, 0.6813952579197537, 0.38211807448612267, 0.035082651375737094}
  2. PixelsToPoint((xMin, yMin), (xMax, yMax), (PXwidth, PXheight), (31, 350)) → lineStart
  3. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  4. If(typeMultiplication, 1 + floor((currentRandomSeeds(1) * 5)), If[typeAddition, 1, 100] + floor((currentRandomSeeds(1) * If[typeAddition, 100, 200]))) → numStart
  5. If(typeAddition ∨ typeMultiplication, 1, -1) → numSign
  6. If(typeMultiplication, Sequence[(numStart * numInc^(k)), k, 0, 7], Sequence[numStart + ((numSign * numInc) * k), k, 0, 7]) → numSequence
  7. Sequence(numSequence(k), k, 1, numShown + 1) → numsUsed, {215, 212, 209, 206, 203, 200}
  8. If(typeMultiplication, 0, Max[Min[numsUsed] - numInc, 0]) → minNum
  9. If(typeAddition ∨ typeSubtraction, Max[numsUsed] + numInc, (ceil(Max[numsUsed] / 50) * 50)) → maxNum
  10. If(smallHops, -0.04, 0) → shiftLabels
  11. Sequence(lineStart + ((k * unitLength), 0), k, 0, maxNum - minNum) → linePoints
  12. Sequence(Sum[hopLengths, k] + x(hopStart), k, 0, Length[hopLengths]) → listFunStart, {665.2857142857143, 559.5714285714287, 453.8571428571429, 348.14285714285717, 242.42857142857144, 136.71428571428567}
  13. Sequence(hopStart + (((k * numSign) * hopLength), 0), k, 0, numShown) → hopPoints
  14. Min({animateSolutionIndex, numShown}) → solutionLabelIndex
  15. Element({textNumbers3, textNumbers4, textNumbers5}, numShown - 2) → textNumbers
  16. Textfield(input1) → InputBox1
  17. Textfield(input2) → InputBox2
  18. Corner(5) → layoutAppSize
  19. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  20. If(typeAddition, "\text{ \plus }", "\text{ \minus }") → textSign
  21. Take(numsUsed, 1, numShown) → labelNums
  22. Take(hopPoints, 1, numShown) → labelLocationsAddSub
  23. If(¬typeMultiplication, hopPoints(Length[hopPoints] - 1), (listFunStart(numShown), 0)) → finalPoint
  24. If(typeAddition, x(hopStart), x(hopStart) - (hopLength * (numShown - 1))) → funcStart
  25. If(typeAddition, x(hopStart + (hopLength * (numShown - 1))), x(hopStart)) → funcEnd
  26. Sequence(startTopPoint + (numSign * ((hopLength * k), 0)), k, 0, numShown - 1) → topPoints
  27. If(typeMultiplication, hopStart + (Sum[hopLengths, numShown], 0), hopPoints(numShown + 1)) → SolutionPoint
  28. Zip(Text[(("" * topLabel) * ""), B, true, true, 0, 1], B, Take[topPoints, 1, animateHopIndex]) → topLabels
  29. Zip(Segment[A + (0, (tickHeight * 1.5)), A - (0, (tickHeight * 1.5))], A, labelLocationsAddSub) → labelTicks
  30. Point(linePoints) → studentPoint
  31. Min({x(studentPoint), x(finalPoint)}) → studentStart
  32. Max({x(studentPoint), x(finalPoint)}) → studentEnd
  33. Sequence(Segment[lineStart + ((k * unitLength), tickHeight), lineStart + ((k * unitLength), (-tickHeight))], k, 0, maxNum - minNum) → ticksAddSub
  34. Take(listFunStart, 2, Length[listFunStart]) → listFunEnd
  35. Sequence(hopStart + (Sum[hopLengths, k], 0), k, 0, numShown - 1) → labelLocationsMultiplication
  36. Sequence(numsUsed(k + 1) - numsUsed(k), k, 1, numShown) → hopLengthNum, {-3, -3, -3, -3, -3}
  37. Zip(startTopPoint + If[smallHops, (-0.04, 0), (0, 0)] + (((-hopLength1)) / 2 + Sum[hopLengths, k - 1] + hopLengths(k) / 2, shiftLabels), k, Sequence[numShown]) → topPointsMult
  38. Zip(hopStart + (Sum[hopLengths, k - 1], 0), k, Sequence[numShown]) → hopPointsMult
  39. Zip(Text[(("" * A) * ""), B, true, true, 0, -1], A, Take[numsUsed, 1, solutionLabelIndex], B, Zip[k - (0, hintLabelShift), k, Take[labelLocationsMultiplication, 1, solutionLabelIndex]]) → solutionLabelsMultiplication
  40. Text((("" * numCorrect) * ""), SolutionPoint - (0, hintLabelShift), true, true, 0, -1) → solutionLabel
  41. Take(hopPointsMult, 1, Min[animateSolutionIndex, numShown]) → hopPointsMultSolution
  42. Segment(studentPoint - (0, (2 * hintLabelShift)), studentPoint - (0, (4 * hintLabelShift))) → studentArrow
  43. Text((("" * studentPointValue) * ""), studentPoint - (0, (If[lowerLabel, 4, 1] * hintLabelShift)), true, true, 0, -1) → studentPointLabel
  44. Sequence(Segment[lineStart + ((before10 * unitLength) + ((k * 10) * unitLength), (2 * tickHeight)), lineStart + ((before10 * unitLength) + ((k * 10) * unitLength), (-2 * tickHeight))], k, 0, floor((maxNum - minNum) / 10) - 1) → ticksLargeAddSub
  45. Take(hopPoints, 1, numShown) → hopPointsAddSub
  46. Take(hopPointsAddSub, 1, Min[animateSolutionIndex, numShown]) → hopPointsAddSubSolution
  47. expandCircle(studentPoint, 8 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingCircle
  48. If(smallHops, "\footnotesize", "") → textSize
  49. Zip(Text[(((("" * textSize) * "\text{") * topLabelMult) * "}"), B, true, true, 0, 1], K, hopLengthNum, B, Take[topPointsMult, 1, animateHopIndex]) → topLabelsMult
  50. Sequence(linePoints(A + 1), A, labelNums(2), Length[linePoints], labelNums(2)) → tickMultiplyLocations
  51. Zip(Segment[A + (0, (-tickHeight)), A + (0, tickHeight)], A, tickMultiplyLocations) → ticksMultiplication
  52. Sequence(Segment[tickMultiplyLocations(A) + (0, (-2 * tickHeight)), tickMultiplyLocations(A) + (0, (tickHeight * 2))], A, numInc, 200, numInc) → ticksMultiplicationLarge
  53. Zip(If[k < x < j, (jumpHeight * abs(sin((pi / L * (x - k))))) + y(lineStart)], k, listFunStart, j, listFunEnd, L, Take[hopLengths, 1, numShown - 1]) → hopCurveMult
  54. Take(Zip[If[k < x < j, (jumpHeight * abs(sin((pi / L * (x - k))))) + y(lineStart)], k, listFunStart, j, listFunEnd, L, Take[hopLengths, 1, numShown]], 1, animateSolutionIndex - 1) → hopCurveMultSolution
  55. Zip(Text[(("" * A) * ""), B, true, true, 0, -1], A, labelNums, B, Zip[k - (0, hintLabelShift), k, If[typeMultiplication, labelLocationsMultiplication, labelLocationsAddSub]]) → labels
  56. Zip(Text[(("" * A) * ""), B, true, true, 0, -1], A, Take[numsUsed, 1, solutionLabelIndex], B, Zip[k - (0, hintLabelShift), k, Take[hopPoints, 1, solutionLabelIndex]]) → solutionLabelsAddSub
  57. Zip(Text[K, J, true, true, 0, 1], K, {minNum, maxNum}, J, {lineStart, lineEnd} + (0, hintLabelShift)) → endLabels
  58. Zip(Segment[A, A + (0, (3 * tickHeight))], A, {lineStart, lineEnd}) → endTicks
  59. Segment(lineStart - ((15 * windowWidth / PXwidth), 0), lineEnd + ((15 * windowWidth / PXwidth), 0)) → numberLine

AI 绘图提示语参考

这是一个带有数字标记的线段图形。线段上分布着若干数字点，数字序列可能是加法或乘法模式。线段两端有标记点，输入框用于输入起始数字。图形布局包含标题和输入框，整体呈现为数学序列可视化工具。
以上提示语为根据原始绘图命令整理而来，仅供参考。