混合数乘法建模：面积模型与交互式解法

GeoGebra 命令及参数

1. Shuffle({{1 / 2, 3 / 4}, {3 / 4, 1 / 2}, {1 / 2, 2 / 3}, {2 / 3, 1 / 2}, {1 / 3, 1 / 2}, {1 / 2, 1 / 3}, {1 / 4, 3 / 5}, {3 / 5, 1 / 4}, {2 / 5, 1 / 3}, {1 / 3, 2 / 5}, {2 / 3, 3 / 4}, {3 / 4, 2 / 3}, {1 / 2, 3 / 5}, {3 / 5, 1 / 2}, {2 / 5, 1 / 4}, {1 / 4, 2 / 5}}) → fracPairs, {{0.6, 0.25}, {0.6666666666666666, 0.5}, {0.6, 0.5}, {0.5, 0.75}, {0.25, 0.6}, {0.75, 0.5}, {0.6666666666666666, 0.75}, {0.4, 0.25}, {0.5, 0.6666666666666666}, {0.25, 0.4}, {0.4, 0.3333333333333333}, {0.3333333333333333, 0.5}, {0.75, 0.6666666666666666}, {0.3333333333333333, 0.4}, {0.5, 0.6}, {0.5, 0.3333333333333333}}
2. Shuffle({{1, 2}, {2, 1}, {1, 1}, {1, 2}, {3, 1}, {2, 3}, {1, 3}, {1, 1}, {2, 1}, {2, 2}, {1, 2}, {2, 1}, {1, 3}, {3, 1}, {2, 1}, {2, 2}}) → wholePairs, {{1, 2}, {3, 1}, {2, 2}, {1, 1}, {1, 2}, {1, 3}, {1, 3}, {1, 2}, {2, 1}, {3, 1}, {1, 1}, {2, 3}, {2, 1}, {2, 1}, {2, 1}, {2, 2}}
3. Polygon({PAnchor + (1, -1), PAnchor + (5, -1), PAnchor + (5, -5), PAnchor + (1, -5)}) → moveArea
4. PointIn(moveArea) → PMove
5. Denominator(fracB) → denomB
6. Denominator(fracA) → denomA
7. If(showsolution, (numA, (-numB)), PMove) → PReference
8. Numerator(fracA) → numerA
9. Numerator(fracB) → numerB
10. RemoveUndefined(Flatten[Sequence[Sequence[If[i ≥ (wholeA * denomA) ∨ j ≥ (wholeB * denomB), (i / denomA, ((-j)) / denomB) + PAnchor], i, 0, numCols - 1], j, 0, numRows - 1]]) → startPositions
11. Flatten(Sequence[Sequence[(i / denomA, ((-j)) / denomB) + PAnchor2 + (((wholeA * wholeB) * (1 + spacer)), 0), i, 0, denomA - 1], j, 0, denomB - 1]) → endPositionTemplate
12. Sequence(If[A ≤ numCompositeWholes, (denomA * denomB), ((fracAB * denomA) * denomB)], A, 1, numCompositeWholes + 1) → numBlocks
13. Flatten(Sequence[Zip[Translate[A, ((K * (spacer + 1)), 0)], A, endPositionTemplate], K, 0, Length[numBlocks] - 1]) → endPositionsWithExtras
14. Sequence(endPositionsWithExtras(A), A, 1, Sum[numBlocks]) → allEndPositions
15. Polygon({PAnchor, (x(PAnchor), y(PReference)), PReference, (x(PReference), y(PAnchor))}) → studentArea
16. Polygon({(0, 0), (1 / denomA, 0), (1 / denomA, -1 / denomB), (0, -1 / denomB)}) → smallBoxTemplate
17. Zip(Translate[smallBoxTemplate, A], A, startPositions) → allSmallBoxes
18. Flatten(Sequence[Sequence[(i, (-j)), i, 0, wholeA - 1], j, 0, wholeB - 1]) → startUnitPositions
19. Polygon({(0, 0), (1, 0), (1, -1), (0, -1)}) → unitBoxTemplate
20. Sequence(PAnchor2 + ((i * (1 + spacer)), 0), i, 0, (wholeA * wholeB) - 1) → unitEndPositions
21. Zip(Translate[unitBoxTemplate, Vector[PAnchor, A]], A, startUnitPositions) → allUnitBoxes
22. Sequence(Segment[(x(PAnchor) + A, y(PAnchor)), (x(PAnchor) + A, y(PCorner))], A, 0, x(PCorner), 1) → gridWholeVertical
23. Sequence(Segment[(x(PCorner) - 1 + A, y(PCorner)), (x(PCorner) + A - 1, y(PAnchor) + If[x(PMove) < 1, -1, 0])], A, 0, 1, 1 / Denominator[fracA]) → gridPartsVertical
24. Sequence(Segment[(x(PAnchor) + If[y(PMove) < -1, 0, 1], y(PCorner)) + (0, A), (x(PCorner), y(PCorner)) + (0, A)], A, 0, 1, 1 / Denominator[fracB]) → gridPartsHorizontal
25. Zip(Translate[A, Vector[(sliderSoln * Vector[B, C])]], A, allSmallBoxes, B, startPositions, C, allEndPositions) → smallBoxes
26. Zip(Translate[A, Vector[(sliderSoln * Vector[B, C])]], A, allUnitBoxes, B, startUnitPositions, C, unitEndPositions) → unitBoxes
27. Sequence(Segment[(x(PAnchor), y(PCorner) + A), (x(PCorner), y(PCorner) + A)], A, y(PAnchor) - y(PCorner), 0, -1) → gridWholeHorizontal
28. Midpoint(PAnchor, (x(PAnchor), y(PReference)) + (-1, 0)) → AnchorNum2
29. Circle(SolnPoint, 0.2) → solnOutline
30. circlePixels(PMove, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingPoint