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Integer Comparison and Sorting - Basic Math Application

Integer Comparison and Sorting - Basic Math Application
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2024-05-23 18:24
Geometric Construction
In collections Ganze Zahlen & Arbeiten mit der Zahlengerade
This example demonstrates how to compare and sort integers to understand their magnitude. Key mathematical concepts include integer comparison, sorting, and representation on the number line. Construction involves GeoGebra commands like Join, Sequence, Random, and others to create integer sequences and comparison tools. Suitable for elementary students in grades 5-6 to reinforce integer operations and number sense.

GeoGebra Commands & Parameters

  1. Join({{2}, Sequence[RandomElement[{2, 3, 4, 5}], k, 1, 99]}) → StepCList1
  2. Sequence(RandomElement[{2, 3, 4, 5}], k, 1, 100) → StepCList2, {3, 2, 2, 2, 4, 3, 2, 2, 5, 5, 3, 3, 2, 3, 3, 3, 5, 4, 4, 2, 2, 5, 4, 2, 4, 2, 3, 3, 4, 5, 4, 3, 2, 4, 5, 2, 3, 5, 2, 2, 5, 4, 5, 2, 3, 4, 2, 3, 3, 4, 2, 2, 5, 4, 3, 4, 4, 4, 4, 2, 2, 5, 3, 4, 4, 3, 2, 2, 4, 5, 2, 4, 2, 4, 3, 3, 5, 3, 5, 5, 2, 4, 4, 4, 4, 3, 4, 3, 3, 3, 3, 4, 3, 5, 5, 2, 4, 5, 4, 3}
  3. Random(-20, -10, 100) → StartList2, {-18, -16, -12, -15, -18, -13, -11, -12, -18, -15, -14, -16, -16, -17, -12, -16, -12, -11, -12, -17, -20, -16, -20, -18, -18, -10, -20, -17, -15, -10, -17, -18, -13, -14, -12, -13, -20, -10, -17, -10, -16, -12, -17, -12, -20, -12, -18, -13, -19, -12, -12, -10, -11, -18, -10, -16, -11, -19, -13, -10, -20, -14, -13, -17, -10, -17, -18, -19, -13, -13, -15, -12, -18, -19, -12, -10, -11, -15, -14, -13, -11, -17, -20, -12, -11, -11, -15, -18, -11, -12, -19, -12, -13, -18, -17, -18, -16, -13, -14, -10}
  4. Sequence(RandomElement[Remove[(StartList2(k))…(StartList2(k) + 20), Sequence[(m * StepCList2(k)), m, -25, 25]]], k, 1, 100) → NumberList2, {-10, -15, -7, -13, -11, -4, 5, -7, -4, 1, -10, -13, -1, -7, -1, -7, -8, 3, 6, -3, -9, -7, -15, -5, -9, -3, -17, -14, -13, -7, -7, -7, -11, -2, 2, -1, -16, -1, -5, -1, -2, -3, -9, 7, -10, -1, 1, 4, -1, 7, 7, 5, -8, 1, -7, -14, 3, 1, -2, 3, -11, 6, -10, -7, -2, 2, -3, -15, 6, -1, -9, -5, -7, -15, 2, -5, 3, -10, -14, 1, -11, -5, -10, -2, 5, 4, -3, -14, -8, 4, -8, 2, -13, -2, -13, -5, -2, -3, 6, 5}
  5. Sequence(RandomElement[{2, 3, 4, 5}], k, 1, 100) → StepCList3, {3, 5, 3, 3, 2, 5, 5, 5, 5, 3, 3, 2, 4, 3, 3, 5, 4, 5, 3, 4, 5, 3, 2, 2, 4, 4, 4, 4, 2, 3, 2, 2, 2, 2, 3, 3, 4, 3, 3, 5, 4, 5, 5, 3, 5, 4, 4, 5, 5, 5, 3, 4, 3, 5, 2, 3, 3, 5, 4, 4, 4, 3, 2, 3, 4, 2, 2, 2, 5, 3, 4, 5, 5, 2, 3, 5, 3, 5, 3, 5, 4, 2, 3, 4, 5, 5, 3, 4, 3, 4, 5, 3, 5, 4, 4, 4, 2, 3, 5, 2}
  6. Element(If[level ≟ 1, StepCList1, level ≟ 2, StepCList2, StepCList3], counter) → stepC
  7. If(level ≟ 1, 21, level ≟ 2, 21, 21) → anzahl
  8. Sequence(-10, k, 1, 100) → StartList1
  9. Random(-50, 30, 100) → StartList3, {28, 13, -11, 25, -48, 18, -49, 28, 4, -45, 25, -9, -5, 29, 28, -27, -3, 29, 27, 28, -47, 20, -49, -9, -47, -45, 21, 28, 0, -16, 11, 19, 11, -5, -28, -23, -16, -48, 17, -16, -36, 22, -46, -46, 13, 29, 2, 16, -14, -47, -44, 17, 7, -14, -46, 19, 15, 9, 3, -24, 19, -16, 1, -49, -19, -21, 19, -40, 9, -37, -4, 23, 30, 8, -46, 23, 23, -23, -36, -14, -45, -37, 22, -1, -6, -6, 19, -5, -32, -25, 2, 4, -15, -8, -29, 11, -7, -29, -23, 1}
  10. If(level ≟ 1, StartList1(counter), level ≟ 2, StartList2(counter), StartList3(counter)) → startNumber
  11. If(show0, Mod[(-startNumber), stepC], 0) → diff
  12. Sequence(RandomElement[Join[{Remove[-10…10, Sequence[(m * StepCList1(k)), m, -100, 100]], Remove[-10…-1, Sequence[(m * StepCList1(k)), m, -100, 100]]}]], k, 1, 100) → NumberList1, {-9, -7, 7, -7, -9, -1, -5, -3, -7, -9, 10, -9, -9, 7, 5, -9, 5, 5, 1, -7, -10, 7, 3, -8, -9, -4, -2, 1, 7, -2, -10, -3, 5, -7, -1, -4, -8, -7, -4, -6, 9, -5, -1, -1, -1, 3, -7, 9, -9, -3, -2, -1, 1, -1, 7, -1, 9, 2, -1, 3, -9, -3, -7, -1, -1, -1, -7, -3, -5, -8, -7, -5, -1, -9, 1, 4, -5, -6, -2, 2, 7, -5, 4, -1, 1, 9, -3, -2, -10, -9, 4, -5, -5, 9, -7, -9, -6, -7, -3, -9}
  13. Sequence(RandomElement[Remove[(StartList3(k))…(StartList3(k) + 20), Sequence[(m * StepCList3(k)), m, -25, 25]]], k, 1, 100) → NumberList3, {29, 14, 7, 40, -41, 38, -31, 33, 7, -37, 28, 11, 6, 38, 31, -26, 1, 29, 46, 41, -31, 35, -43, 7, -42, -45, 25, 33, 5, 2, 21, 27, 17, -3, -28, -22, -5, -34, 17, 1, -29, 31, -27, -31, 23, 39, 10, 22, -14, -46, -29, 18, 19, 6, -35, 32, 16, 13, 14, -22, 27, -10, 5, -37, -17, -19, 31, -33, 13, -22, 15, 34, 36, 13, -28, 33, 23, -22, -25, -3, -35, -35, 25, 18, -2, -3, 32, 9, -17, -19, 18, 20, -1, -5, -21, 25, 1, -10, -18, 3}
  14. Element(If[level ≟ 1, NumberList1, level ≟ 2, NumberList2, NumberList3], counter) → number
  15. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 10, 6, 10, 6, 1, 7, 2, 9, 9}
  16. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  17. Textfield(input) → inputBox
  18. Defined(input) → clickableBtnValidate
  19. Segment(Origin + ((-lengthAxis) - 0.5, 0), Origin + (lengthAxis + 0.5, 0)) → segAxis
  20. Sequence(Origin + ((-lengthAxis), 0) + (((k * 2) * lengthAxis / (anzahl - 1)), 0), k, 0, anzahl - 1) → PointsList
  21. Sequence(Origin + ((-lengthAxis), 0) + (((k * 2) * lengthAxis / (anzahl - 1)), 0), k, 0, anzahl - 1, stepM) → SelectablePoints
  22. Sequence(Segment[PointsList(k) + (0, If[Mod[NumbersOnAxis(k), stepC] ≟ 0, (-segLength2), (-segLength1)]), PointsList(k) + (0, If[Mod[NumbersOnAxis(k), stepC] ≟ 0, segLength2, segLength1])], k, 1, 21, stepM) → SegAxisList
  23. Sequence((If[startNumber < 0, ceil(startNumber / stepC), startNumber > 0, floor(startNumber / stepC), 0] * stepC) + (k * stepC), k, 0, floor(anzahl / stepC)) → NumbersCap, {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}
  24. Sequence(Text[(((((("\textsf{" * If[k < 0, "\(", ""]) * "") * k) * "") * If[k < 0, "\)", ""]) * "\vphantom{2}}"), PointsList(k - startNumber + 1) + (If[k < 0, -0.166, 0], (-segLength2)), false, true, 0, -1], k, startNumber + diff, startNumber + anzahl - 1 + diff, stepC) → CapList
  25. Sequence(Text[(((((("\textcolor{" * If[NumbersOnAxis(k) ∈ NumbersCap, "#000000", NumbersOnAxis(k) ≟ number, "#006758", "616161"]) * "}{\textsf{") * If[NumbersOnAxis(k) ∈ NumbersCap, "\small{\(", NumbersOnAxis(k) ≟ number, "\small{\(", "\scriptsize{\("]) * "") * NumbersOnAxis(k)) * "\)}}}"), SelectablePoints(k) + (If[NumbersOnAxis(k) < 0, -0.166, 0], (-segLength2)) + If[NumbersOnAxis(k) ≥ 0 ∧ (NumbersOnAxis(k) ∈ NumbersCap ∨ NumbersOnAxis(k) ≟ number), (0, 0), NumbersOnAxis(k) ≥ 0, (-0.02, 0), (0.05, 0)], false, true, 0, -1], k, 1, Length[NumbersOnAxis], 1) → CapListSol
  26. Translate(imgChilliRot1, Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)]) → imgChilliRot2
  27. Translate(imgChilliRot1, Vector[(2 * Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)])]) → imgChilliRot3
  28. Translate(imgChilliGrau1, Vector[PosImgChilliRot1, PosImgChilliRot1 + ((0.8 * dimChilli), 0)]) → imgChilliGrau2

AI Drawing Prompt Reference

Draw a coordinate plane with a horizontal number line. Place a row of equally spaced, clickable tick points along the axis and label the corresponding integers at those positions, including negative values, zero, and positive values. Below or along the axis, generate a discrete set of integers using a chosen start number and step size, and use these values as inputs for a basic compare/sort task. Construct small segment-like highlights on the axis that follow the step-based alignment rules so that selected integer locations are visually emphasized and aligned to the tick grid. Finally, add a comparison indicator that, depending on a selected mode (different levels), determines which integer sequence is used for the labeled target number.
The prompt above was compiled from the original drawing commands and is for reference only.