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输入输出表中的模式识别：乘法与除法

输入输出表中的模式识别：乘法与除法
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2023-07-18 21:02
函数数列变换滑块动画函数图像
该范例通过交互式函数机器演示输入输出表中乘法与除法模式的识别与代数表达。核心数学概念包括函数关系、变量对应、乘法与除法运算规律以及代数式表示。作图要点：使用GeoGebra命令如RandomUniform生成随机数，Take和Element提取数据，Zip构造列表，If实现条件逻辑，Textfield用于用户输入，TableText生成表格，以及滑块动画（anim）控制机器运动，结合Translate和Text显示文本。适合小学4-5年级学生，用于练习根据给定关系构建或完成数值表，并通过动画直观理解函数机器如何将输入映射到输出，进而将模式抽象为代数表达式。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.7972723403473906, 0.9820586243711863, 0.6021710932189611, 0.8339214018249029, 0.254039653059072, 0.0633790700598275, 0.2931016295885725, 0.22692504590426074, 0.39991264883172345, 0.43632487320182345, 0.10853037604146284, 0.15579343756163833, 0.6397728938378975, 0.17356875554715073, 0.14188398032092914, 0.3471774071407089, 0.07656869081471043, 0.7192616000773597, 0.7133908137461569, 0.7121857553097987, 0.03773977249710319, 0.32404883993568395, 0.9171230802791757, 0.546579923636661, 0.04241331882180641, 0.435660831223492, 0.4922084426537765, 0.10297193305730777, 0.9368296292071585, 0.5011556250586994, 0.8082036886099893, 0.5746929321835718, 0.4523204635502315, 0.8127429647920392, 0.573831717391819, 0.8329436313105556, 0.7392167862916296, 0.6346545561172462, 0.4146796165874032, 0.6254683439685866, 0.9513017189424305, 0.5637511134899453, 0.39903982211957467, 0.7763128648904509, 0.8788533977483853, 0.8414683220923921, 0.8618476753885671, 0.6222325240168857, 0.9039365567651256, 0.4493033817965361, 0.4846272439966251, 0.7920094969996913, 0.6494053201624638, 0.7343313066990635, 0.7845049149174326, 0.7303200069005299, 0.35306939480642563, 0.045214416400721956, 0.6776828560575061, 0.42786004432840974, 0.17065380315474374, 0.7228308009717755, 0.5822870043750411, 0.3941938442819968, 0.02554717430382557, 0.1629969083311442, 0.9422125127028967, 0.4192336201147013, 0.5398871583963614, 0.5617966314411368, 0.8174867006221926, 0.3733885310701217, 0.930270648587337, 0.8567541862569382, 0.08775288126871926, 0.24524089002101865, 0.35230527171768755, 0.549499386333102, 0.6837504246828943, 0.6191116229278514, 0.38133309018310624, 0.047674616312487, 0.9671253727380894, 0.04307221441845739, 0.891960682153394, 0.13561876835658848, 0.741551722784647, 0.9408397189947558, 0.33651966999428257, 0.024839029060659833, 0.22797872855395496, 0.5885606380337506, 0.8622596604101832, 0.8264427359562867, 0.5038397576772372, 0.7697450774612764, 0.6289408986332797, 0.6185517340503368, 0.3502681898358615, 0.24855584891846808, 0.38254644264094984, 0.7222582903734782, 0.5127615844978732, 0.5132883682079379, 0.40707383346275433, 0.6599064974802891, 0.7693201673863495, 0.9281949963535605, 0.5647945757132605, 0.9393952268623467, 0.975856231531058, 0.31281402930051766, 0.655984139000378, 0.877798080305586, 0.37163072972238587, 0.6336562904947237, 0.08192837495834845, 0.8568832427118829, 0.1676195687893555, 0.1834835766568343, 0.9200027558772497, 0.6420903361187857, 0.3380460972859277, 0.018481265995648, 0.2867978678786004, 0.9551838605662916, 0.009837770857277247, 0.8133833705565189, 0.4246304061504482, 0.019152078356288908, 0.5164739690181848, 0.03905183156864793, 0.9883313238348775, 0.5819577293437198, 0.7515884380612665, 0.5861423579591524, 0.1829434172448009, 0.0434711187000521, 0.5737738325713018, 0.7623078328221671, 0.9188878211822987, 0.007328473579299082, 0.5773072782969788, 0.4788959476266181, 0.9392744094955866, 0.29655810666130583, 0.5939747966751127, 0.7262911249413804, 0.34433421003844444, 0.5386038969027886, 0.37881914066206923, 0.024931824681968823, 0.9604411304132311, 0.06185037306245286, 0.987469340343154, 0.46160221447475513, 0.5458693573410232, 0.6719155113227921, 0.31473175316624824, 0.4478538394724332, 0.9022969290091851, 0.6618273557712686, 0.8333315985724137, 0.1693552528866244, 0.10011922838680709, 0.3657373824297058, 0.7680904024612076, 0.6315996519755896, 0.45687645572311286, 0.8910481128226467, 0.9544082768019345, 0.6087174190104095, 0.011526377483832671, 0.028745122043949273, 0.7606923873070373, 0.5481482297359582, 0.4429096756064679, 0.4763220955978963, 0.45233096868232087, 0.6546185099429193, 0.29855706998530923, 0.8619761290627578, 0.9899592845637166, 0.28225315348580715, 0.4899781269780977, 0.012723901103003362, 0.427098094814539, 0.08371682914688451, 0.5827497189783513, 0.5727518141431167, 0.09176568977458155, 0.860037540770505, 0.5340862550443364, 0.9216633161612863, 0.1433750968646358, 0.5542073019432809, 0.6471278662720539, 0.505322842589442, 0.7001228178058662, 0.4657866818776382}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element({"+", "-", "\times", "\div"}, randomNum1) → chosenOperation
  4. Zip(kk + randomNum2, kk, ins) → out1
  5. Zip(kk - randomNum2, kk, ins) → out2
  6. Zip((kk * randomNum2), kk, ins) → out3
  7. Zip(kk / randomNum2, kk, ins) → out4
  8. Element({out1, out2, out3, out4}, randomNum1) → outs
  9. If(currentRandomSeeds(9) ≥ 0.5, 0, 1) → showInOut2
  10. If(currentRandomSeeds(8) ≥ 0.5, 0, 1) → showInOut1
  11. Textfield(input1) → InputBox1
  12. Textfield(input2) → InputBox2
  13. Corner(5) → layoutAppSize
  14. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  15. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  16. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  17. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  18. Translate(vGL, Vector[(Vector[Corner[1], Corner[2]] / 800 * 16)]) → vGL'
  19. Text(text1, H, true, true, 0, 1) → text2
  20. If(anim ≤ 2.5, (5, 5.45), (5 + (2 * (anim - 2.5)), 5.45 - ((anim - 2.5)^(0.2) * (5.45 - 4.8)))) → AnimPoint3
  21. Element({AnimPoint1, AnimPoint2, AnimPoint3, AnimPoint3}, floor(anim) + 1) → AnimPoint
  22. Text(text3, AnimPoint, true, true, 0, 0) → text4
  23. Text((chosenOperation * randomNum2), AnimPointDrop, true, true, 0, 0) → text5
  24. Zip(((If[kk, "\bold{", "{"] * nn) * "}"), kk, boldIns, nn, ins) → insText
  25. Zip(((If[kk, "\bold{", "{"] * nn) * "}"), kk, boldOuts, nn, outs) → outsText
  26. TableText(Append["\textsf{Input}", Zip[Text[kk], kk, ({inp1, inp2, inp3, inp4, inp5} * If[randomNum1 ≟ 4, randomNum2, 1])]], Append["\textsf{Output}", Zip[Text[kk], kk, outs]], "c_|v", 100, 46) → table
  27. TableText(Take[insText, 1, Min[animCount, 5]], Sequence[chosenOperation, ii, 1, Min[animCount, 5]], Sequence[randomNum2, ii, 1, Min[animCount, 5]], Sequence["=", ii, 1, Min[animCount, 5]], Take[outsText, 1, Min[animCount, 5] - If[anim ≤ 2.5, 1, 0]], "v,c", 10, 46) → tableSol
  28. Translate(hGL, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGL'

AI 绘图提示语参考

绘制一个互动的数学函数机器演示，包含以下元素：一个可拖动的滑块控制动画进程，画面中央是一个抽象的函数机器图形，上方显示当前运算符号（加、减、乘或除）；在机器左侧有输入框区域，右侧有输出区域；画面下方展现一张清晰的输入输出对照表格，表格左侧列出输入值（1、2、3、4、5），右侧列出对应的计算结果；表格下方用公式形式展示运算关系，如"输入值 × 数字 = 输出值"，数字会随动画更新；当拖动滑块时，机器产生脉动效果，输入输出表格逐行显示计算过程，整个演示用于帮助学生理解乘除法函数关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。