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Long Division Practice with One-Digit Divisors and Remainders

Long Division Practice with One-Digit Divisors and Remainders
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2023-07-15 10:19
Coordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the long division process of dividing multi-digit numbers by one-digit divisors, focusing on the concept of division. Using GeoGebra commands from the construction summary, it can be seen that the example employs random number generation, conditional statements, and loops. Suitable for students in grades 4-5 to practice division.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a geometric diagram of a long division vertical layout demonstrating the process of dividing a multi-digit number by a single-digit divisor with remainders. The illustration includes the basic framework of division: a main horizontal division line at the top, with three short horizontal lines below marking the positions of the first, second, and third digits of the quotient. A vertical separator line appears on the left of the dividend with a remainder area below. Multiple rectangular boxes containing numbers represent the divisor, digits of the dividend, quotient, and highlighted intermediate calculation results. Arrows indicate key steps in the calculation flow, with color blocks highlighting the two numbers currently being operated on. The entire layout is precisely positioned using coordinate points to form a standard long division format.
The prompt above was compiled from the original drawing commands and is for reference only.