除法应用题：用可视化模型解答小学四五年级除法问题

GeoGebra 命令及参数

1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.5284661063053412, 0.979285817505015, 0.9101770025115732, 0.49307476284227525, 0.7690446926611176, 0.2102049750468799, 0.1274095304886832, 0.0745988091647357, 0.05897343710604378, 0.09787819727034701, 0.5741561825928597, 0.770520812776875, 0.272017965304488, 0.3024344873769479, 0.09518877765143312, 0.5818668467268806, 0.7957334974620108, 0.9483038841111864, 0.7344528339040909, 0.30763905869649216, 0.9188824426789309, 0.5676919437159531, 0.5055299667402583, 0.5133705810705517, 0.11072967158019593, 0.08812206028904107, 0.15215890714373567, 0.5044856755863365, 0.056532785489594985, 0.4197076453935181, 0.9894741090601267, 0.2836189888734802, 0.3339647334655052, 0.9369088962432335, 0.6462618851104389, 0.2381081834414596, 0.8315632618734742, 0.9220574698218369, 0.5291079436130708, 0.21937223936824737, 0.21259696224060998, 0.5938998720900072, 0.3208258142666294, 0.9298234098429341, 0.01596975472023307, 0.6038138903219884, 0.49800520020911115, 0.1853336277395518, 0.24995592279888706, 0.925194775001703, 0.35590940422009226, 0.21208700043007608, 0.6046649279517071, 0.8977870502997352, 0.0132758932333775, 0.6658979076876587, 0.7051802872075179, 0.8284544627920749, 0.2448385825266566, 0.9597594868381003, 0.36929923144019483, 0.01303500606911871, 0.1855913082313656, 0.5115111452125635, 0.9817197514185242, 0.09051968264596952, 0.1679505271014492, 0.3280732615119085, 0.8603792625138764, 0.8308231709434776, 0.44105158005052764, 0.6656961424545164, 0.470443297311497, 0.9508810426955128, 0.730426556265791, 0.9071053435721257, 0.41717640713994314, 0.2507125543370608, 0.036262956742374, 0.666298634782265, 0.17059587675402277, 0.6614302999877568, 0.43933080282821413, 0.22006060231530014, 0.33241734511844756, 0.9209563933084497, 0.31549237819468884, 0.7020086418880265, 0.6993459373532844, 0.2604224977343443, 0.4524721923720972, 0.1801699758488709, 0.1062488924368927, 0.4048849989472806, 0.5362659695010272, 0.47271190316577827, 0.46816575594371673, 0.5760782966438385, 0.6392064677465268, 0.1585086833661798, 0.5414694510935298, 0.2024584961723013, 0.13727917392606614, 0.20972582976440463, 0.03178678557802774, 0.28275696998877825, 0.940796067599801, 0.9225386956473667, 0.019518897820874393, 0.0736669916753413, 0.7699853098758503, 0.5494748372076133, 0.05297241725487577, 0.19012886875464532, 0.48544435754171306, 0.422680558180397, 0.23421958770152151, 0.7779580329810947, 0.672729959560286, 0.18165976388692634, 0.37385005973144886, 0.37327761261663167, 0.030621852124311746, 0.2717190306420793, 0.2877601787145037, 0.9713709597419694, 0.9437984384496373, 0.34047584838769673, 0.01204482801311484, 0.7591616465878493, 0.6828015826979325, 0.4293471871927598, 0.870914813058846, 0.9805578553403341, 0.9472431705024695, 0.7049342291170726, 0.12735728232184565, 0.19236443806692205, 0.012220563357240198, 0.44165390601726306, 0.8969896637116311, 0.680370751549935, 0.9228585944466071, 0.2318415350828311, 0.3722268369127823, 0.14056366960785371, 0.7877847977009972, 0.09285913440314886, 0.8864891386567603, 0.72919491972209, 0.4191705957402737, 0.8524920370949951, 0.07672371572905354, 0.6376484439774992, 0.2847348450049652, 0.4941018946692283, 0.9169937881220968, 0.8237076283336628, 0.22580749203292025, 0.3316275847098103, 0.1263109783752428, 0.06991459866091145, 0.6351892336340884, 0.9415854836200817, 0.01024227364585109, 0.7622423700121441, 0.8791201199585204, 0.4347193777517309, 0.6481193827584972, 0.7582678618591461, 0.7491828066780393, 0.9838847644548473, 0.11590946643811825, 0.45343819603746205, 0.9624178961832679, 0.36712676085262097, 0.7589768660402872, 0.7568640693868997, 0.8713173540209445, 0.5557199669256531, 0.2790728642087068, 0.20435357872593915, 0.6496881128735394, 0.14618752503223065, 0.9359349160508015, 0.05611674247231737, 0.5956415051882542, 0.19300210858012523, 0.485859711098386, 0.8897248453801319, 0.34916583470306545, 0.2047942335363468, 0.8975342860317926, 0.12550125324242406, 0.11887727406194355, 0.6214541799685799, 0.27926657469627747, 0.8815486263381945, 0.39062135514610935, 0.6025116976751859}
2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
3. If(countQuestion ≟ 1, 1, 1 + floor((currentRandomSeeds(1) * 6))) → questionIndex
4. If(animateControl < 2, 0, animateControl - 2) → animateImages
5. If(grouped, (animateImages - (floor(animateImages / numA) * numA)) / numA, animateImages - floor(animateImages)) → moveImg
6. If(moveImg < holdBox, 0, (moveImg - holdBox) / (1 - holdBox)) → moveCluster
7. If(grouped, (numA * floor(animateImages / numA)), Div[animateImages, 1]) → pointIndex
8. Take(Flatten[Sequence[Sequence[bottomStartPt + (((3 * inc) + spaceBetween, 0) * k) - (0, (j * (boxHeight + spaceBetween - (0.2 * inc)))), k, 0, 4], j, 0, 1]], 1, numB) → bottomStartPoints
9. Take(Join[{Flatten[Sequence[Sequence[((inc * Mod[k, 4]), (inc * Mod[j, 4])) + bottomStartPt, k, 0, 2], j, 0, 1]], Flatten[Sequence[Sequence[((inc * Mod[k, 4]), (inc * Mod[j, 4])) + bottomStartPt + (inc / 2, (2 * inc)), k, 0, 1], j, 0, 1]]}], 1, numA) → oneBucket
10. Flatten(Zip[Translate[bottomStartPoints, Vector[bottomStartPt, A]], A, oneBucket]) → bottomPoints2
11. Flatten(Zip[Translate[oneBucket, Vector[bottomStartPt, A]], A, bottomStartPoints]) → bottomPoints1
12. Element({bottomPoints2, bottomPoints1}, Mod[questionIndex, 2] + 1) → allBottomPoints
13. Take(allBottomPoints, pointIndex + 1, pointIndex + numA) → bottomCluster
14. Flatten(Sequence[Sequence[((k * inc), ((-j) * inc)) + StartPt, k, 0, numsPerRow - 1], j, 0, 9]) → allPoints
15. Take(allPoints, boxIndex, boxIndex + numA - 1) → topCluster
16. If(grouped, numA, 1) → numMoving
17. If(Mod[questionIndex, 2] ≟ 1, numA, numB) → questionNum
18. If(questionNum < 10, "\phantom{0}", "") → numSpace
19. If(fullNumber < 10, "\phantom{00}", If[fullNumber < 100, "\phantom{0}", ""]) → fullSpace
20. Flatten(Sequence[Sequence[(k, (j * 0.2)), k, 1, numA], j, 1, numB]) → MultGroups
21. Take(oneBucket, 1, (multIndex * numB)) → multPoints
22. Corner(5) → appletSize
23. If(moving, Take[allPoints, 1, fullNumber - pointIndex - numMoving], Take[allPoints, 1, fullNumber - pointIndex]) → topPoints
24. Take(allBottomPoints, 1, pointIndex) → bottomPoints
25. If(¬grouped, numB, ceil(pointIndex / numA)) → bagIndex
26. Take(Zip[makeBox[A + ((-0.2 * inc), boxHeight - (0.2 * inc)), boxWidth, boxHeight], A, bottomStartPoints], 1, bagIndex) → boxes
27. Vector(N1Start, num1End) → N1Vec
28. Vector(N2Start, num2End) → N2Vec
29. If(questionIndex ≟ 2, numA, numB) → answer
30. Element(allPoints, fullNumber - pointIndex) → imgStart
31. Element(allBottomPoints, pointIndex + 1) → imgEnd
32. Vector(imgStart, imgEnd) → imageVec
33. If(animateControl ≤ 2, animateControl, 2) → animateInitial
34. If(Mod[questionIndex, 2] ≟ 1, numB, numA) → answerNum
35. makeBox(boxLocation + (0.01, 0.05), (inc * numA), (-inc)) → currentBox
36. If(questionIndex ≟ 1 ∨ questionIndex ≟ 2, picMarble, If[questionIndex ≟ 3 ∨ questionIndex ≟ 4, picBee, picApple]) → currentPic
37. Zip(Translate[currentPic, Vector[StartPt, k]], k, Join[{topPoints, bottomPoints}]) → imagesCurrent
38. Zip(Translate[currentPic, Vector[StartPt, K]], K, topCluster) → picCluster
39. Zip(Vector[(Vector[K, J] * moveCluster)], K, topCluster, J, bottomCluster) → clusterVectors
40. Zip(Translate[A, Vector[B]], A, picCluster, Vector[B], clusterVectors) → movingClusterImages
41. If(questionIndex ≟ 1 ∨ questionIndex ≟ 2, picJar, If[questionIndex ≟ 3 ∨ questionIndex ≟ 4, picHive, picBag]) → currentContainer
42. Take(Zip[Translate[currentContainer, Vector[StartPt, k]], k, bottomStartPoints], 1, bagIndex) → imagesJar
43. Element({colorTeal, colorTeal, colorBlack, colorBlack, colorBrown, colorBrown}, questionIndex) → boxColor