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Walk the Line - Adding/Subtracting Integers

Walk the Line - Adding/Subtracting Integers
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2017-07-12 05:24
VectorFunctionCoordinate Geometry
This example visually demonstrates the concept of adding and subtracting integers. It involves key mathematical concepts such as integers, vectors, and geometric construction. Using GeoGebra commands like Point, Vector, Segment, etc., users can intuitively understand the geometric meaning of integer addition and subtraction. Suitable for students from upper elementary to middle school.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Vector(C, A) → u
  5. Vector(C, B) → v
  6. If(a ≟ 0, (Starting - Walk, 0), (Starting + Walk, 0)) → F
  7. If(directionA ≟ 0, 1, 0) → Direction
  8. Point(xAxis) → O
  9. Point(xAxis) → Q
  10. Point(xAxis) → R
  11. Vector(Q, R) → z
  12. Point(xAxis) → D_3
  13. Point(xAxis) → M_4
  14. Point(xAxis) → N_4
  15. Vector(M_4, N_4) → a_1
  16. Segment(U_4, U_4 + (0, 0.7)) → d_1
  17. Segment(U_4, U_4 + (0, 0.7)) → e_1
  18. If(a ≟ 0, (Starting - Walk, 0.8), (Starting + Walk, 0.8)) → WalkStop
  19. Vector(WalkStart, WalkStop) → f_1
  20. Vector((0, 0.4), WalkStart + (0, -0.4)) → h_1
  21. Polygon(ResetPolyPt, ResetPolyPt + (2, 0), ResetPolyPt + (2, 1), ResetPolyPt + (0, 1)) → resetPoly, resetPolySegB, resetPolySegR, resetPolySegT, resetPolySegL
  22. Sequence(Segment[(i, 0.14), (i, -0.14)], i, -15, 20, 1) → hashTops
  23. Point(xAxis) → W_4
  24. OrthogonalLine(W_4, xAxis) → f
  25. Point(f) → Z_4
  26. OrthogonalLine(Z_4, f) → g
  27. Point(f) → A_5
  28. OrthogonalLine(A_5, f) → h
  29. Point(h) → B_5
  30. OrthogonalLine(B_5, h) → i
  31. Point(h) → C_5
  32. OrthogonalLine(C_5, h) → j
  33. Intersect(g, i) → D_5
  34. Intersect(g, j) → E_5
  35. Point(h) → F_5
  36. OrthogonalLine(F_5, g) → k
  37. Intersect(g, k) → G_5
  38. Polygon(A_5, B_5, D_5, Z_4) → poly1, a_5, b_5, d_5, z_4
  39. Polygon(B_5, C_5, E_5, D_5) → poly2, b_1, c_5, e_5, d_2
  40. Polygon(C_5, F_5, G_5, E_5) → poly3, c_1, f_5, g_5, e_2

AI Drawing Prompt Reference

Draw a graph to demonstrate the concept of adding and subtracting integers using vectors and geometric constructions. Start by plotting points A, B, C on the x-axis and creating vectors u and v. Then, mark point F on the x-axis based on the integer a and determine the direction. Plot points O, Q, R and vector z. Next, mark points D_3, M_4, N_4 on the x-axis, create vector a_1, and draw line segments d_1 and e_1. Based on the value of a, mark point WalkStop and create vectors f_1 and h_1. Finally, draw several squares and triangles to illustrate the geometric process of integer addition and subtraction.
The prompt above was compiled from the original drawing commands and is for reference only.