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Robot-driven solids with variables: volume via unit cubes and cuboids

Robot-driven solids with variables: volume via unit cubes and cuboids
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2023-03-16 17:39
VectorSolid GeometryTransformationGeometric Construction
In collections Ⓔ Volumen zusammengesetzter Körper aus Quader und Würfel
This GeoGebra example demonstrates how a “robot” scenario uses variables to build a cuboid-like 3D shape and then motivates volume calculation through decomposition into unit cubes. The key math ideas are understanding and applying the cuboid volume formula V = length × width × height, representing volume as the count of suitable unit cubes, and investigating how changing lengths affects surface-related measures. Construction-wise, the model uses geometric primitives and controls to generate/organize objects: Vector, Point, Sequence, Shuffle, and RemoveUndefined to create and manage points/vectors (including positioned objects like Pos62/Pos61/…); Translate, Dilate, and Join to move, scale, and combine parts into coherent faces/structures; Polygon and rectangle-related elements to form the required geometric regions; Textfield to display instructions or hints; and Defined to ensure variable-driven parameters remain valid. It is well-suited for grades 5–6 for solid geometry lessons, formula comprehension, and exploratory tasks on how dimensional changes influence geometric quantities.

GeoGebra Commands & Parameters

  1. Vector(pointVec) → vec
  2. Textfield(input1) → InputBox1
  3. Textfield(input2) → InputBox2
  4. Defined((input1 * input2)) → fixed
  5. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 4, 9, 10, 10, 2, 10, 2, 1, 7, 9, 9, 2, 1, 9, 6, 0, 1, 8, 3, 8, 4, 0, 6, 8, 2, 10, 1, 6, 4, 0, 9, 5, 4, 0, 4, 0, 5, 10, 3, 6, 6, 1, 8, 9, 9, 7, 6, 3, 6, 9, 5, 9, 10, 9, 1, 9, 0, 9, 1, 8, 3, 10, 4, 10, 0, 1, 3, 10, 3, 3, 6, 4, 7, 10, 0, 5, 4, 6, 0, 4, 6, 8, 8, 0, 8, 3, 9, 3, 1, 7, 4, 7, 8, 1, 7, 0, 8, 7, 3}
  6. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  7. Translate(object01L0BG1, vec) → object01L0BG1'
  8. Sequence(Segment[Vertex[object01L0BG1(1), i], Vertex[object01L0BG1'(1), i]], i, 1, 10) → object01L1Lines
  9. RemoveUndefined(Sequence[If[i ∈ {2, 3, 4, 5, 6}, object01L1Lines(i)], i, 1, 10]) → object01L2LinesManual
  10. Translate(object02L0BG1, vec) → object02L0BG1'
  11. Sequence(Segment[Vertex[object02L0BG1(1), i], Vertex[object02L0BG1'(1), i]], i, 1, 10) → object02L1Lines
  12. RemoveUndefined(Sequence[If[i ∈ {2, 6, 7, 8}, object02L1Lines(i)], i, 1, 10]) → object02L2LinesManual
  13. Translate(object03L0BG1, vec) → object03L0BG1'
  14. Sequence(Segment[Vertex[object03L0BG1(1), i], Vertex[object03L0BG1'(1), i]], i, 1, 10) → object03L1Lines
  15. Translate(object04L0BG1, vec) → object04L0BG1'
  16. Sequence(Segment[Vertex[object04L0BG1(1), i], Vertex[object04L0BG1'(1), i]], i, 1, 10) → object04L1Lines
  17. RemoveUndefined(Sequence[If[i ∈ {1, 5, 6}, object04L1Lines(i)], i, 1, 10]) → object04L1LinesManual
  18. Translate({Segment[pointObject04P1, pointObject04P6], Segment[pointObject04P6, pointObject04P5]}, vec) → object04L4BGKontur
  19. Translate(object06L0BG1, vec) → object06L0BG1'
  20. Sequence(Segment[Vertex[object06L0BG1(1), i], Vertex[object06L0BG1'(1), i]], i, 1, 10) → object06L1Lines
  21. RemoveUndefined(Sequence[If[i ∈ {1, 3, 4, 5, 7, 8}, object06L1Lines(i)], i, 1, 10]) → object06L1LinesManual
  22. Translate({PolyLine[{pointObject06P3, pointObject06P4, pointObject06P5}], PolyLine[{pointObject06P7, pointObject06P8, pointObject06P1}]}, vec) → object06L4BGKontur
  23. Point(object06L4BGKontur) → pointObject06P9
  24. Point(object06L0BG1) → pointObject06P10
  25. Dilate(listFrame1, 0.97, Midpoint[pointFrame1, pointFrame3]) → listFrame2
  26. Dilate(listFrame1, 1.02, Midpoint[pointFrame1, pointFrame3]) → listFrame3
  27. Join({{Segment[pointObject02P7, pointObject02P4]}, {Segment[pointObject02P7 + vec, pointObject02P4 + vec]}}) → object02HintKontur
  28. Join({{Segment[pointObject02P6, pointObject02P6 + vec]}, {Segment[pointObject02P6 + vec, pointObject02P7 + vec]}, object02L2Kontur3}) → object02HintKonturDashed
  29. RemoveUndefined(Sequence[If[i ∈ {2, 3, 4, 5, 6}, object03L1Lines(i)], i, 1, 10]) → object03L1LinesManual
  30. Sequence(Rotate[Segment[CenterFBRay + (0.5, 0), CenterFBRay + (1, 0)], i°, CenterFBRay], i, 0, 360, 30) → Flashlight
  31. Polygon(pointlips1, pointlips2, pointlips3, pointlips4) → lips, f_1, g_1, h_1, i_1

AI Drawing Prompt Reference

Draw a robot-driven 3D shape controlled by variables to demonstrate volume calculation. Start by creating a base shape using a vector tool, then determine its dimensions with a sequence of randomly generated numbers. Apply translation and dilation transformations to decompose the shape into smaller unit cubes, connecting their edges with lines to form the surface of the cuboid. Finally, add a rotating light effect and draw a quadrilateral to illustrate the volume calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.