使用视觉模型创建除法方程：分享、重复减法、矩形数组与乘法关系

GeoGebra 命令及参数

1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.00010358792919176629, 0.5763129804815318, 0.8579680495863534, 0.8669610996591123, 0.6497778491677686, 0.4542326842314304, 0.9522006290551609, 0.6450257673839399, 0.16414292714532872, 0.8148194471015536, 0.7398456708527104, 0.2796449400328511, 0.6247898425194753, 0.6238602819302576, 0.4869770206704812, 0.693386218287779, 0.5363679320873327, 0.8770906153212628, 0.2295386269824167, 0.9439621202962344, 0.12626410299574303, 0.8840171358117849, 0.5546784919266152, 0.4273108314904029, 0.3078928299267363, 0.4435870664581935, 0.782075927101162, 0.08296239272064154, 0.8847153586699644, 0.14339981489834436, 0.8363605472508391, 0.7487334910532429, 0.9549877391124951, 0.8516480515703931, 0.04319587813392271, 0.2816279655523674, 0.034806074021111126, 0.8306525998527355, 0.4027626125379253, 0.3788417916391469, 0.06927263065184737, 0.5227206836708859, 0.23522612541696217, 0.6869798065724453, 0.408550241240409, 0.45311008334676367, 0.503310253759479, 0.5789887620136758, 0.5772029307952519, 0.021121802527910356, 0.017323290378474823, 0.3968942658102572, 0.06153947580387514, 0.9487715527667578, 0.3678951559647002, 0.9242015068482912, 0.47068216976162797, 0.7071057914839506, 0.5912834074621797, 0.7847783346463393, 0.032776498243662425, 0.6130306135589041, 0.5813936536307122, 0.2251853514435457, 0.6881381617350747, 0.004511939209762918, 0.6416338793352746, 0.6847523933052072, 0.2862026809713579, 0.9491835742138655, 0.12838487254732664, 0.11222187114833826, 0.7228980986410677, 0.41076454468959717, 0.48621805666608814, 0.3894881812637013, 0.5595050150009488, 0.6492398667916558, 0.18302947334840167, 0.1318594122215752, 0.29319903555723803, 0.12449958701213262, 0.4209832721539594, 0.9603512335076417, 0.32328882874908554, 0.6390580756187615, 0.24656973970344712, 0.18479431626257684, 0.9056692609078512, 0.7335910918786538, 0.2701833097034122, 0.44699570156416035, 0.22120191617942264, 0.8093310177081983, 0.20241215617920613, 0.6408412853068504, 0.401616712125876, 0.3338505664624254, 0.47070632282702407, 0.7410599244896029, 0.6790962368189469, 0.9814431156111317, 0.3262532556652385, 0.6143916676713274, 0.552960468385221, 0.09617327624929656, 0.31673885124569057, 0.42611172351906074, 0.5488130735713935, 0.09472374966121755, 0.4462098002364153, 0.081257548440079, 0.5021409278814174, 0.07740463960452261, 0.12847728169405068, 0.7134912913604151, 0.8796773609150941, 0.7191199409614113, 0.6854140974745718, 0.8753006385807741, 0.5678449151694989, 0.9076999014816272, 0.49609739452369916, 0.32120048018923414, 0.34828744559017444, 0.5048117496553366, 0.5270355382504537, 0.8607440604890635, 0.5958815399435206, 0.5146510774975465, 0.9076930839493342, 0.9404866322421719, 0.8046861030035674, 0.9377937914654876, 0.11918919486857851, 0.5735654559933963, 0.05204472084310672, 0.04195408637941067, 0.31739503367588734, 0.6322697496891351, 0.06049851825114723, 0.6579464561943696, 0.06469235166997661, 0.29287009732735986, 0.371298394825488, 0.697889848101036, 0.4773804578800081, 0.2630610665450439, 0.7721236524475128, 0.2436202385469339, 0.14813025693599705, 0.40064221319588234, 0.42512020029514275, 0.24639259763784854, 0.23498477042077198, 0.8175217381646304, 0.16956434183505711, 0.07425643304704072, 0.6701913264696349, 0.3157731440577116, 0.9663397356663311, 0.08097891874354295, 0.9236261373554165, 0.3623099987480169, 0.8689826757561241, 0.850067846816776, 0.4067337441682235, 0.4457644723658412, 0.498307365952503, 0.40931103534411845, 0.6537536944981484, 0.673365067212106, 0.09456600833596555, 0.7553029073846289, 0.3075433137841319, 0.9570049410423151, 0.902729066843661, 0.9236675035249275, 0.10753076127764101, 0.12627652803533904, 0.02278999506272733, 0.32911651687228577, 0.517244322785442, 0.3220194018180519, 0.818004038601364, 0.8200950703646984, 0.11846341219500592, 0.18688747480692783, 0.03966444430059008, 0.6155711846236216, 0.32832403224894935, 0.809588156773561, 0.5474002325569375, 0.19651504174618722, 0.2746860248047686, 0.6167797226518557, 0.25904768894733876, 0.21179185601031603, 0.03373160218381409, 0.6111352666345558}
2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
3. Element(Remove[{3, 4, 5, 6, 7, 8, 9}, {currentQuotient}], 1 + floor((currentRandomSeeds(2) * 6))) → currentDivisor
4. Take(studentInput, 1, IndexOf[cEQUAL, studentInput] - 1) → Part1
5. Take(studentInput, IndexOf[cEQUAL, studentInput] + 1) → Part2
6. If(Defined[IndexOf[cDIVIDE, Part1]], Part1, Part2) → divPart
7. Take(divPart, IndexOf[cDIVIDE, divPart] + 1) → divisorPart
8. If(Defined[IndexOf[cDIVIDE, Part1]], Part2, Part1) → quotientPart
9. Zip(If[A ≟ cDIVIDE, "\div", If[A ≟ cEQUAL, "=", ("" * A)]], A, studentInput) → studentChars
10. listToValue(quotientPart) → studentQuotient
11. listToValue(divisorPart) → studentDivisor
12. Take(divPart, 1, IndexOf[cDIVIDE, divPart] - 1) → dividendPart
13. listToValue(dividendPart) → studentDividend
14. Div(currentDivisor, 5) → numWholeTally
15. Corner(5) → layoutAppSize
16. Sequence(A, A, 0, lineLength, jumpSize) → numberPos
17. Rotate(PolyLine[AnchorNumberLine + (-0.3, 0.5), AnchorNumberLine + (0, 0.2), AnchorNumberLine + (0.3, 0.5)], ((-2 * pi)) / 8, AnchorNumberLine + (0, 0.2)) → endArrowTemplate
18. Sequence(Translate[endArrowTemplate, (numberPos(A), 0)], A, 1, Length[numberPos] - 1) → allArrows
19. Sequence(AnchorNumberLine + ((jumpSize * (A + 0.5)), ((-cos((3 * pi / 8))) * jumpSize / 2)), A, 0, currentQuotient - 1) → arcCenter
20. Zip(Segment[AnchorNumberLine + (A, 0.2), AnchorNumberLine + (A, -0.2)], A, numberPos) → numberTicks
21. Sequence(Text[("" * (A * currentDivisor)), AnchorNumberLine + (numberPos(A + 1), 0), true, true, 0, -1], A, 0, currentQuotient) → xLbls
22. Segment(AnchorNumberLine + (-1, 0), AnchorNumberLine + (lineLength + 1, 0)) → numberLine
23. Zip(CircleArc[A, AnchorNumberLine + (B, 0), AnchorNumberLine + (C, 0)], A, arcCenter, B, Take[numberPos, 2], C, numberPos) → allArcs
24. Zip(Text[("-" * currentDivisor), A + (0, arcRadius + 0.3), true, true, 0, 0], A, arcCenter) → textSubtract
25. Sequence(Sequence[Anchor1 + (i, (-j)), i, 0, currentQuotient - 1], j, currentDivisor - 1, 0, -1) → arrayDisplay, {{(-4.43022, -0.2742500000000003), (-3.4302200000000003, -0.2742500000000003), (-2.4302200000000003, -0.2742500000000003), (-1.4302200000000003, -0.2742500000000003), (-0.43022000000000027, -0.2742500000000003)}, {(-4.43022, 0.7257499999999997), (-3.4302200000000003, 0.7257499999999997), (-2.4302200000000003, 0.7257499999999997), (-1.4302200000000003, 0.7257499999999997), (-0.43022000000000027, 0.7257499999999997)}, {(-4.43022, 1.7257499999999997), (-3.4302200000000003, 1.7257499999999997), (-2.4302200000000003, 1.7257499999999997), (-1.4302200000000003, 1.7257499999999997), (-0.43022000000000027, 1.7257499999999997)}, {(-4.43022, 2.7257499999999997), (-3.4302200000000003, 2.7257499999999997), (-2.4302200000000003, 2.7257499999999997), (-1.4302200000000003, 2.7257499999999997), (-0.43022000000000027, 2.7257499999999997)}, {(-4.43022, 3.7257499999999997), (-3.4302200000000003, 3.7257499999999997), (-2.4302200000000003, 3.7257499999999997), (-1.4302200000000003, 3.7257499999999997), (-0.43022000000000027, 3.7257499999999997)}, {(-4.43022, 4.72575), (-3.4302200000000003, 4.72575), (-2.4302200000000003, 4.72575), (-1.4302200000000003, 4.72575), (-0.43022000000000027, 4.72575)}, {(-4.43022, 5.72575), (-3.4302200000000003, 5.72575), (-2.4302200000000003, 5.72575), (-1.4302200000000003, 5.72575), (-0.43022000000000027, 5.72575)}}
26. Sequence(Sequence[If[(groupColSize * j) + i ≤ currentDivisor, (i, (-j))], i, 1, groupColSize], j, 0, groupRows - 1) → groupTemplate, {{(1, 0), (2, 0), (3, 0)}, {(1, -1), (2, -1), (3, -1)}, {(1, -2), (NaN, NaN), (NaN, NaN)}}
27. Flatten(Sequence[Sequence[If[(7 * j) + i ≤ currentQuotient, AnchorGroups + ((i * 4), ((-j) * (groupRows + 1)))], i, 1, 7], j, 0, 1]) → groupingAnchors
28. Zip(Translate[groupTemplate, A], A, groupingAnchors) → groupedModel
29. PointToPixels(Corner[1], Corner[3], Corner[5], Corner[displayResult, 1]) → BottomLeftDisplay
30. PixelsToPoint(Corner[1], Corner[3], Corner[5], (startButtonX + 160, startButtonY - 10)) → PxRightDisplay
31. PixelsToPoint(Corner[1], Corner[3], Corner[5], (startButtonX + 10, startButtonY - 48)) → PxLeftDisplay