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一位数除法带余数的长除法练习

一位数除法带余数的长除法练习
几何画板及绘图内容加载中，请稍等……
2023-07-15 10:19
解析几何几何作图滑块动画
该范例演示了多位数除以一位数的长除法过程，涉及的核心数学概念是除法运算。通过构造摘要中的GeoGebra命令，可以了解到该范例使用了随机数生成、条件语句、循环等方法。适合小学四年级至五年级学生进行除法运算练习。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.31798107992601704, 0.01823666635479007, 0.003297525784614034, 0.19501208324926259, 0.286711927202044, 0.8940835797941982, 0.9187245148649484, 0.6472984023525928, 0.21310525768661584, 0.1528210545366587, 0.419614680252715, 0.2549521716084285, 0.7066347723125765, 0.7635834995110738, 0.9856587962382447, 0.14187299598299075, 0.18900304972908163, 0.6290989628905366, 0.27121387690781534, 0.6856133872433351, 0.6412536359562706, 0.7026490828420404, 0.1518048978697028, 0.41682430988674635, 0.013925039607192454, 0.22150630320480613, 0.5221442014260113, 0.18481004040555912, 0.4191109574330287, 0.4705830635187884, 0.6595682191601104, 0.8790165917602669, 0.5751564675153742, 0.0008778841711892537, 0.5909983319196779, 0.643220819319425, 0.5187724900944977, 0.6378401309874648, 0.07293060067924134, 0.4708183827225166, 0.6155914876748486, 0.48499954122831107, 0.842541738638861, 0.4759270902505447, 0.6186141651483945, 0.7081194163245064, 0.013771660974018437, 0.1160278426050449, 0.9246135990208195, 0.16473110990466322, 0.055200446301114044, 0.24755914435485074, 0.03136428461554595, 0.8531954999977384, 0.24668531174939118, 0.5462613409748057, 0.19355544379885836, 0.6844108584373291, 0.5990561372898615, 0.43913605226294483, 0.19242431365256893, 0.287949149179108, 0.37569042328397034, 0.7246410504493481, 0.6535114379053831, 0.4427525597125558, 0.6464968613241696, 0.1621852188549575, 0.2184918706884497, 0.4105583911653171, 0.9737337452536741, 0.35111800540733895, 0.2807769955381504, 0.20794607646715355, 0.505171856925237, 0.9232275278390569, 0.5605092519726241, 0.2903112707581429, 0.17338360488486856, 0.2812658242005413, 0.08268719977744479, 0.03817229312129063, 0.9103986691456666, 0.9792141317084324, 0.32246097834169263, 0.05300078751959393, 0.8046128932943694, 0.8778818308849728, 0.7741289840829536, 0.7062434525835353, 0.07167165159673682, 0.7220004742708219, 0.7950436344176999, 0.2413633976340599, 0.843069721792367, 0.5422308704663426, 0.03249977221598485, 0.3045798567919849, 0.47541938076907797, 0.17744402176167143, 0.2807318789770784, 0.3255215099079306, 0.5697341188602203, 0.8792680447283276, 0.7763863686572445, 0.714233657408967, 0.06366025508384274, 0.642211075828829, 0.18426344676262119, 0.7758914712799659, 0.69035936348535, 0.4486763633658963, 0.5707372314317058, 0.2591710421086674, 0.07570413859314057, 0.9488790927673358, 0.020067086862256535, 0.48851747874896456, 0.560596229676206, 0.881055058047375, 0.8188017497610642, 0.5945232699604037, 0.7075488718262642, 0.8774200961983878, 0.8156566931154048, 0.41029277294659416, 0.9601986862070154, 0.8760946205121399, 0.3986100493872731, 0.68501804574877, 0.5411197383587952, 0.718651275647662, 0.007514915200030595, 0.6990286018944536, 0.2672094960650044, 0.37707445247305094, 0.029266498047095794, 0.4773016941094433, 0.10300070222504236, 0.10273871964474761, 0.7734900000581844, 0.7808325093272486, 0.8505239719828853, 0.833519166302286, 0.33983051507798673, 0.4873632176377656, 0.25980551212697556, 0.44334014714055897, 0.5832289679112744, 0.03475605994133877, 0.17673060544407068, 0.5813492841242712, 0.6210581600543075, 0.6017715038410453, 0.26483734741468773, 0.7454726817534391, 0.22567095365968737, 0.05217381411315355, 0.7746269066802244, 0.45736245543118764, 0.5377778315194223, 0.6489360201081354, 0.5181853156977145, 0.5326914662561598, 0.5701236335161286, 0.7558538488486053, 0.18830856083440775, 0.3623809924772728, 0.3971735728409021, 0.594102357456207, 0.49990623365177866, 0.13666509542985605, 0.10494669306057092, 0.7311810547980887, 0.5072310713058804, 0.4049017919348765, 0.7657493973912048, 0.4392935744424817, 0.40344031805150327, 0.7197339818683113, 0.6053654557202042, 0.48949405930380363, 0.08914147174850365, 0.7045845084531611, 0.4952480636963895, 0.15690800127373597, 0.39390888667029567, 0.7085373599438688, 0.8094381484174105, 0.7009967471513737, 0.6292792113541332, 0.12241384944838463, 0.38529779389205143, 0.23318468415966226, 0.5734428067190688, 0.414294843364366, 0.7987004765947686, 0.5522053396336191, 0.6067443185942593, 0.3718720411685297}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(numDigitsDividend < 3, 0, 1 + floor((currentRandomSeeds(5) * If[numDigitsDividend ≟ 3, divisorDigit - 1, 9]))) → numHundreds
  4. If(numDigitsDividend < 4, 0, 1 + floor((currentRandomSeeds(3) * (divisorDigit - 1)))) → numThousands
  5. Element({{numTens, numUnits}, {numHundreds, numTens, numUnits}, {numThousands, numHundreds, numTens, numUnits}}, numDigitsDividend - 1) → dividendDigits
  6. If(ansQuotient < 10, {quotientUnits}, If[quotientHundreds ≟ 0, {quotientTens, quotientUnits}, {quotientHundreds, quotientTens, quotientUnits}]) → quotientDigits
  7. If(numDigitsDividend > 2, (((dividendDigits(1) * 10) + dividendDigits(2) - row1) * 10) + If[numDigitsDividend > 2, dividendDigits(3), 0], (dividendDigits(1) * 10) + dividendDigits(2) - row1) → row2
  8. Length(quotientDigits) → numDigitsQuotient
  9. Zip(AnchorDiv + (0.15, -0.1) + A, A, {(0, 0), (1, 0), (1, -1), (2, -1), (1, -2), (2, -2), (2, -3), (3, -3), (2, -4), (3, -4), (3, -5), (0, 2), (1, 2), (2, 2), (3, 2), (-1, 1), (0, 1), (1, 1), (2, 1), (3, 1)}) → allAnchors
  10. Shuffle({{1, 2}, {1, 4}, {2, 4}, {3, 4}, {1, 5}, {2, 5}, {3, 5}, {4, 5}, {3, 6}, {1, 8}, {2, 8}, {3, 8}, {4, 8}, {5, 8}, {6, 8}, {7, 8}}) → randomPairs, {{2, 4}, {3, 8}, {1, 2}, {3, 4}, {3, 6}, {4, 8}, {6, 8}, {3, 5}, {4, 5}, {1, 8}, {2, 8}, {1, 4}, {1, 5}, {2, 5}, {7, 8}, {5, 8}}
  11. Element(randomPairs, randIndex, 1) → numer
  12. Element(randomPairs, randIndex, 2) → denom
  13. If(ansThousandths ≠ 0, 3, If[ansHundredths ≠ 0, 2, 1]) → numDP
  14. Shuffle(Join[Sequence[{A, A, A, A, A, A, A, A, A, A}, A, 1, 9]]) → randomDigits, {8, 3, 9, 5, 9, 6, 5, 1, 4, 7, 9, 8, 2, 2, 6, 9, 1, 9, 2, 4, 8, 1, 4, 4, 1, 8, 1, 7, 4, 8, 2, 3, 3, 5, 4, 3, 3, 3, 9, 2, 1, 4, 6, 8, 9, 2, 4, 9, 5, 6, 5, 1, 8, 6, 3, 8, 6, 3, 7, 3, 5, 7, 9, 6, 5, 5, 6, 7, 3, 5, 2, 1, 7, 6, 6, 2, 8, 4, 4, 1, 1, 2, 5, 7, 2, 9, 8, 7, 7, 7}
  15. If(numerPlaced ∧ denomPlaced, 2 + zeroIndex, NaN) → zeroPlace
  16. Segment(AnchorDiv + (0, -1), AnchorDiv + (2, -1)) → divLine1
  17. Segment(AnchorDiv + (1, -3), AnchorDiv + (3, -3)) → divLine2
  18. Segment(AnchorDiv + (2, -5), AnchorDiv + (4, -5)) → divLine5
  19. Zip((("SetCaption(" * A) * ",emptyLabel)"), A, allBoxNames) → cmdEmptyLabels
  20. Element({numDP ≟ 1, numDP ≟ 2, numDP ≟ 3}, step - 3) → allDone
  21. Segment(AnchorDiv + (2.5, 0), AnchorDiv + (2.5, -1)) → arrow1
  22. Segment(AnchorDiv + (3.5, 0), AnchorDiv + (3.5, -3)) → arrow2
  23. Segment(AnchorDiv + (0, -5.55), AnchorDiv + (3, -5.55)) → vRemainder3
  24. Segment(AnchorDiv + (0, -3.55), AnchorDiv + (2, -3.55)) → vRemainder2
  25. Segment(AnchorDiv + (0, -1.55), AnchorDiv + (1, -1.55)) → vRemainder1
  26. Translate(Polygon[{(-1, 1), (-1, 0), (1, 0), (1, 1)}], allAnchors(If[step ≟ 1, 3, If[step ≟ 4, 7, If[step ≟ 7, 11]]])) → highlightTwoDigits
  27. Translate(Polygon[{(0, 1), (1, 1), (1, 0), (0, 0)}], allAnchors(16) + (-0.15, -1)) → highlightDivisor
  28. Zip(allAnchors(A) + (-1, 0), A, {1, 5, 9}) → minusAnchors

AI 绘图提示语参考

绘制一个长除法竖式的几何示意图，用于演示一位数除数除多位数且有余数的运算过程。画面中包含除法竖式的基本框架：顶部有一条横向的主除线，其下方在对应位置有三条短横线分别标记商的第一位、第二位和第三位。在被除数左侧有一个垂直分隔线，下方对应有余数区域。画面中有多个带矩形边框的数字框，代表除数、被除数的各位数字以及商和高亮显示的中间计算结果。使用箭头指示计算流程中的关键步骤，并在某些数字上用色块高亮标注当前参与运算的两个数字。整个布局通过坐标点精确控制，形成规范的长除法竖式排列。
以上提示语为根据原始绘图命令整理而来，仅供参考。