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Two-digit place value: Understanding digit composition and position

Two-digit place value: Understanding digit composition and position
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2025-12-12 10:12
This example demonstrates how to visualize two-digit place value through geometric figures. Key mathematical concepts include place value, digit decomposition, and coordinate geometry. Construction involves GeoGebra commands like Polygon, Translate, and Sequence to represent digits graphically. Suitable for middle school students or math teaching assistance.

GeoGebra Commands & Parameters

  1. If(t > 2 / 3 ∧ t < 1, (3 * (t - 2 / 3)), If[t ≤ 2 / 3, 0, 1]) → t5
  2. If(t > 0 ∧ t < 1 / 3, (3 * (t - 0)), If[t ≤ 0, 0, 1]) → t3
  3. If(t > 1 / 3 ∧ t < 2 / 3, (3 * (t - 1 / 3)), If[t ≤ 1 / 3, 0, 1]) → t4
  4. Textfield(digit1) → InputBox1
  5. Polygon((0, 0), (7, 0), (7, 12), (0, 12)) → poly1, f, g, h, i
  6. Polygon(A, A + (-7.5, 12), A + (-15, 12), A + (-15, 0)) → q1, j, k, l, m
  7. Textfield(digit3) → InputBox3
  8. Textfield(digit2) → InputBox2
  9. Polygon(C, C + (-7.5, 12), C + (-30, 12), C + (-30, 0)) → q4, c, b, e, f_1
  10. Translate(If[digit3 ≟ "0", pic0, If[digit3 ≟ "1", pic1, If[digit3 ≟ "2", pic2, If[digit3 ≟ "3", pic3, If[digit3 ≟ "4", pic4, If[digit3 ≟ "5", pic5, If[digit3 ≟ "6", pic6, If[digit3 ≟ "7", pic7, If[digit3 ≟ "8", pic8, If[digit3 ≟ "9", pic9]]]]]]]]]], Vector[C - (30, 0)]) → picC
  11. Translate(pic0, Vector[C - (22.5, 0)]) → picC_0
  12. Translate(pic0, Vector[C - (15, 0)]) → picC_{00}
  13. Sequence(Segment[C + ((-7.5 * i), 0), C + ((-7.5 * i), 12)], i, 1, 3) → l5
  14. Polygon(B, B + (-7.5, 12), B + (-22.5, 12), B + (-22.5, 0)) → q5, b_1, g_1, h_1, i_1
  15. Sequence(Segment[B + ((-7.5 * i), 0), B + ((-7.5 * i), 12)], i, 1, 2) → l6
  16. Translate(If[digit2 ≟ "0", pic0, If[digit2 ≟ "1", pic1, If[digit2 ≟ "2", pic2, If[digit2 ≟ "3", pic3, If[digit2 ≟ "4", pic4, If[digit2 ≟ "5", pic5, If[digit2 ≟ "6", pic6, If[digit2 ≟ "7", pic7, If[digit2 ≟ "8", pic8, If[digit2 ≟ "9", pic9]]]]]]]]]], Vector[B - (22.5, 0)]) → picB
  17. Translate(pic0, Vector[B - (15, 0)]) → picB_0
  18. Sequence(Segment[A + ((-7.5 * i), 0), A + ((-7.5 * i), 12)], i, 1, 1) → l7
  19. Translate(If[digit1 ≟ "0", pic0, If[digit1 ≟ "1", pic1, If[digit1 ≟ "2", pic2, If[digit1 ≟ "3", pic3, If[digit1 ≟ "4", pic4, If[digit1 ≟ "5", pic5, If[digit1 ≟ "6", pic6, If[digit1 ≟ "7", pic7, If[digit1 ≟ "8", pic8, If[digit1 ≟ "9", pic9]]]]]]]]]], Vector[A - (15, 0)]) → picA
  20. If(digit1 ≠ "", true, false) → input1
  21. If(digit2 ≠ "", true, false) → input2
  22. If(digit3 ≠ "", true, false) → input3
  23. If(digit4 ≠ "", true, false) → input4
  24. Element(TextToUnicode[digit1] - 48, 1) → placevalue1