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Base 5 Blocks Demonstration

Base 5 Blocks Demonstration
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2020-08-23 05:47
SequenceGeometric ConstructionGraphing
① This example demonstrates counting in base‑5 using colored blocks that represent units, fives, twenty‑fives, etc. ② Core mathematical concepts: positional numeral systems, base‑5 representation, conversion of natural numbers to base‑5. ③ Construction highlights: GeoGebra commands Corner, Segment, Intersect, Sequence, First, ToBase together with objects pic1, pic2, pic3, ones, tens, huns, thos, list1, list10, list100 build a dynamic block array and labels. ④ Suitable for upper‑primary to lower‑secondary mathematics lessons, as a classroom demo or self‑study resource for base‑5 arithmetic.

GeoGebra Commands & Parameters

  1. Corner(1) → C1
  2. Corner(3) → C3
  3. Segment(((0.5 * x(C1)) + (0.5 * x(C3)), y(C3)), ((0.5 * x(C1)) + (0.5 * x(C3)), y(C1))) → h
  4. Segment((x(C1), (0.2 * y(C1)) + (0.8 * y(C3))), (x(C3), (0.2 * y(C1)) + (0.8 * y(C3)))) → f
  5. Intersect(f, h) → D
  6. Sequence(Sequence[Translate[D + (spc, 0), Vector[(((i * (1 + spc)) * dst) + (spc * floor(i / 5)), (((-j) * 6) * dst))]], i, 0, 9], j, 1, 4) → list10
  7. First(Flatten[list10], Min[tens, 40]) → list10'
  8. Segment(((0.99 * x(C1)) + (0.01 * x(C3)), y(C3)), ((0.99 * x(C1)) + (0.01 * x(C3)), y(C1))) → g
  9. Intersect(f, g) → E
  10. Sequence(Sequence[Translate[E + (spc, 0), Vector[(((i * (9 + spc)) * dst), (((-j) * (9 + spc)) * dst))]], i, 0, 2], j, 1, 4) → list100
  11. First(Flatten[list100], Min[12, huns]) → list100'
  12. Segment(((0.2 * x(C1)) + (0.8 * x(C3)), y(C3)), ((0.2 * x(C1)) + (0.8 * x(C3)), y(C1))) → i
  13. Intersect(f, i) → C
  14. Sequence(Sequence[Translate[C + (spc, ((-(2 + spc)) * dst)), Vector[(((i * (1 + spc)) * dst), (((-j) * (1 + spc)) * dst) - ((2 * spc) * floor(j / 5)))]], i, 0, 4], j, 0, 24) → list1
  15. First(Flatten[list1], Min[125, ones]) → list1'
  16. Sequence(Translate[pic2, Vector[G, Element[list10', i]]], i, 1, Min[tens, 40]) → list10b
  17. Sequence(Translate[pic3, Vector[I, Element[list100', i]]], i, 1, Min[12, huns]) → list100b
  18. Sequence(Translate[pic1, Vector[A, Element[list1', i]]], i, 1, Min[ones, 125]) → list1b
  19. ToBase((25 * Length[list100b]) + (5 * Length[list10b]) + Length[list1b], 5) → value

AI Drawing Prompt Reference

Create a base-5 block demonstration with unit blocks, five-unit blocks, twenty-five-unit blocks, and one-hundred-twenty-five-unit blocks. First, build a dynamic array of blocks, then arrange them according to the given number in base-5 representation. Finally, display the blocks and their corresponding values.
The prompt above was compiled from the original drawing commands and is for reference only.