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Algebra Tiles for Algebraic Factorization

Algebra Tiles for Algebraic Factorization
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2018-01-14 12:12
VectorGeometric Construction
This example uses algebra tiles to demonstrate the process of algebraic factorization. Key mathematical concepts include algebra, rectangles, and squares. Using GeoGebra commands like Vector, Segment, and Point, users can visually understand the geometric meaning of algebraic factorization. Suitable for middle school and above students learning algebra.

GeoGebra Commands & Parameters

  1. Vector((0, 0), (0, (-n) - q)) → v_1
  2. Segment((x(L) + q, y(L)), (x(L) + (b_3 * m) + ((b_3 - 1) * q), y(L))) → l
  3. Point(l) → M
  4. KeepIf(x < x(M), Sequence[x(L) + ((t - 1) * m) + ((t - 1) * q), t, 1, b_3]) → Re1
  5. Length(Re1) → r_1
  6. Segment((x(K), y(K) - q), (x(K), y(K) - (b_1 * n) - ((b_1 - 1) * q))) → k
  7. Point(k) → I
  8. KeepIf(x > y(I), Sequence[y(K) - ((t - 1) * n) - ((t - 1) * q), t, 1, b_1]) → Bq2
  9. Length(Bq2) → a_1
  10. Vector((0, 0), (n + q, 0)) → v
  11. Segment((x(H) + q, y(H)), (x(H) + (b_1 * n) + ((b_1 - 1) * q), y(H))) → j
  12. Point(j) → J
  13. KeepIf(x < x(J), Sequence[x(H) + ((t - 1) * n) + ((t - 1) * q), t, 1, b_1]) → Bq1
  14. Length(Bq1) → a_2
  15. Segment((x(R), y(R) - q), (x(R), y(R) - (b_3 * m) - ((b_3 - 1) * q))) → s
  16. Point(s) → S
  17. KeepIf(x > y(S), Sequence[y(R) - ((t - 1) * m) - ((t - 1) * q), t, 1, b_3]) → Re2
  18. Length(Re2) → r_2
  19. Segment((x(T) + q, y(T)), (x(T) + (b_2 * m) + ((b_2 - 1) * q), y(T))) → t
  20. Point(t) → U
  21. Segment((x(V), y(V) - q), (x(V), y(V) - (b_2 * m) - ((b_2 - 1) * q))) → a
  22. Point(a) → W
  23. KeepIf(x > y(W), Sequence[y(V) - ((t - 1) * m) - ((t - 1) * q), t, 1, b_2]) → Sq2
  24. KeepIf(x < x(U), Sequence[x(T) + ((t - 1) * m) + ((t - 1) * q), t, 1, b_2]) → Sq1
  25. Length(Sq1) → e_2
  26. Length(Sq2) → e_1
  27. Vector((0, 0), (m + q, 0)) → u
  28. Sequence(Translate[Sequence[Polygon[(x(B) + (0.5 * n), y(B) + (0.5 * m) - (p * (m + q))), (x(B) - (0.5 * n), y(B) + (0.5 * m) - (p * (m + q))), (x(B) - (0.5 * n), y(B) - (0.5 * m) - (p * (m + q))), (x(B) + (0.5 * n), y(B) - (0.5 * m) - (p * (m + q)))], p, 0, r_2 - 1], Vector[(r * v)]], r, 0, a_2 - 1) → Rh2
  29. Vector((0, 0), (0, -2)) → w
  30. Ray(E, w) → f
  31. Point(f) → F
  32. Circle(F, E) → g
  33. OrthogonalLine(F, f) → h
  34. Intersect(g, h, 1) → G
  35. Ray(G, F) → i
  36. SelectedIndex(Bahasa) → nn
  37. Sequence(Translate[Sequence[Polygon[(x(C) + (0.5 * m), y(C) + (0.5 * m) - (p * (m + q))), (x(C) - (0.5 * m), y(C) + (0.5 * m) - (p * (m + q))), (x(C) - (0.5 * m), y(C) - (0.5 * m) - (p * (m + q))), (x(C) + (0.5 * m), y(C) - (0.5 * m) - (p * (m + q)))], p, 0, e_1 - 1], Vector[(r * u)]], r, 0, e_2 - 1) → Sqs
  38. Sequence(Translate[Sequence[Polygon[(x(D) + (0.5 * n), y(D) + (0.5 * n) - (p * (n + q))), (x(D) - (0.5 * n), y(D) + (0.5 * n) - (p * (n + q))), (x(D) - (0.5 * n), y(D) - (0.5 * n) - (p * (n + q))), (x(D) + (0.5 * n), y(D) - (0.5 * n) - (p * (n + q)))], p, 0, a_1 - 1], Vector[(r * v)]], r, 0, a_2 - 1) → Sqb
  39. Sequence((x(Rp) + ((r + 0.5) * n) + (0.5 * m) + ((r + 1) * q), y(Rp)), r, 0, b_1 - 1) → Lp2
  40. Sequence((x(Rp), y(Rp) - ((r + 0.5) * n) - (0.5 * m) - ((r + 1) * q)), r, 0, b_1 - 1) → Lp3
  41. Sequence(Translate[Sequence[Polygon[(x(A) + (0.5 * m) + (p * (m + q)), y(A) + (0.5 * n)), (x(A) - (0.5 * m) + (p * (m + q)), y(A) + (0.5 * n)), (x(A) - (0.5 * m) + (p * (m + q)), y(A) - (0.5 * n)), (x(A) + (0.5 * m) + (p * (m + q)), y(A) - (0.5 * n))], p, 0, r_1 - 1], Vector[(r * v_1)]], r, 0, a_1 - 1) → Rh1
  42. Sequence((x(Rp) + ((r + 0.5) * n) + (0.5 * m) + ((r + 1) * q), y(Rp) - (0.5 * n) - q - (0.5 * m)), r, 0, b_1 - 1) → Lp1
  43. Sequence((x(A), y(Rp) - ((r + 0.5) * n) - (0.5 * m) - ((r + 1) * q)), r, 0, b_1 - 1) → Lp1a