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Fraction Bar Addition Model

Fraction Bar Addition Model
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2020-11-03 02:52
VectorFunctionGeometric Construction
This example demonstrates the geometric model of adding fractions with the same denominator. Key mathematical concepts include fraction addition. Construction highlights the use of points, rays, polygons, sequences, text fields, segments, vectors, and fraction text commands in GeoGebra. Suitable for upper elementary or middle school students learning fraction addition.

GeoGebra Commands & Parameters

  1. Point(yAxis) → C
  2. Point(Segment[C + (0, h), C + (0, (1.85 * h))]) → B
  3. If(t ≤ 0.5, 0, (2 * (t - 0.5))) → t2
  4. If(t ≤ 0.5, (2 * t), 1) → t1
  5. Point(Segment[B + (0, h), B + (0, (1.85 * h))]) → A
  6. Ray((0, 1.9), (0, 2.9)) → f
  7. Polygon({A, A + (l, 0), A + (l, h), A + (0, h)}) → poly1
  8. Polygon({B, B + (l, 0), B + (l, h), B + (0, h)}) → poly2
  9. Sequence(Segment[A + ((i * (l) / a1), 0), A + ((i * (l) / a1), h)], i, 1, a1 - 1) → list1
  10. Sequence(Segment[B + ((i * (l) / a2), 0), B + ((i * (l) / a2), h)], i, 1, a2 - 1) → list2
  11. Polygon({A, A + ((b1 * (l) / a1), 0), A + ((b1 * (l) / a1), h), A + (0, h)}) → poly3
  12. Polygon({B, B + ((b2 * (l) / a2), 0), B + ((b2 * (l) / a2), h), B + (0, h)}) → poly4
  13. Sequence(Sequence[Segment[A + ((i * (l) / a1) + (j * (l) / ((a1 * c1))), 0), A + ((i * (l) / a1) + (j * (l) / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, a1 - 1) → list3
  14. Sequence(Sequence[Segment[B + ((i * (l) / a2) + (j * (l) / ((a2 * c2))), 0), B + ((i * (l) / a2) + (j * (l) / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, a2 - 1) → list4
  15. If(a1 ≟ a2, true, false) → equald
  16. If(equald ∧ (Div[b1 + b2, a1] > 0 ∨ GCD[b1 + b2, a1] > 1), true, If[Div[(b1 * c1) + (b2 * c2), (a1 * c1)] > 0 ∨ GCD[(b1 * c1) + (b2 * c2), (a1 * c1)] > 1, true, false]) → simplify
  17. Textfield(a1) → InputBox1
  18. Textfield(b1) → InputBox2
  19. Textfield(a2) → InputBox3
  20. Textfield(b2) → InputBox4
  21. Polygon({A', A' + (l, 0), A' + (l, h), A' + (0, h)}) → poly5
  22. Polygon({B', B' + ((b2 / a2 * l), 0), B' + ((b2 / a2 * l), h), B' + (0, h)}) → poly6
  23. Polygon({A', A' + ((b1 * (l) / a1), 0), A' + ((b1 * (l) / a1), h), A' + (0, h)}) → poly7
  24. Polygon({B', B' + ((b2 * (l) / a2), 0), B' + ((b2 * (l) / a2), h), B' + (0, h)}) → poly8
  25. Sequence(Sequence[Segment[A' + ((i * (l) / a1) + (j * (l) / ((a1 * c1))), 0), A' + ((i * (l) / a1) + (j * (l) / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, b1 - 1) → list8
  26. Sequence(Sequence[Segment[B' + ((i * (l) / a2) + (j * (l) / ((a2 * c2))), 0), B' + ((i * (l) / a2) + (j * (l) / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, b2 - 1) → list9
  27. Segment(C - (0, 0.5), C - (0, 1)) → g
  28. Segment(C + ((b1 / a1 * l), -0.5), C + ((b1 / a1 * l), -1)) → i
  29. Segment(C + ((b1 / a1 * l) + (b2 / a2 * l), -0.5), C + ((b1 / a1 * l) + (b2 / a2 * l), -1)) → j
  30. Vector(Midpoint[g], Midpoint[i]) → u
  31. Vector(Midpoint[i], Midpoint[g]) → v
  32. Vector(Midpoint[i], Midpoint[j]) → w
  33. Vector(Midpoint[j], Midpoint[i]) → a
  34. Sequence(Segment[A' + ((i * (l) / a1), 0), A' + ((i * (l) / a1), h)], i, 0, b1) → list6
  35. Sequence(Segment[B' + ((i * (l) / a2), 0), B' + ((i * (l) / a2), h)], i, 0, b2) → list7
  36. Sequence(Polygon[{C + ((i * l), 0), C + ((i * l) + l, 0), C + ((i * l) + l, h), C + ((i * l), h)}], i, 1, floor(b1 / a1 + b2 / a2)) → list5
  37. Segment(B', B' + ((b2 / a2 * l), 0)) → k
  38. Segment(B' + ((b2 / a2 * l), h), B' + (0, h)) → m
  39. If(b1 / a1 + b2 / a2 ≥ 1, true, false) → improper
  40. FractionText(b1 / a1 + b2 / a2) → text19
  41. FractionText(b1 / a1 + b2 / a2 - 1) → text20
  42. Sequence(Sequence[Segment[C + ((i * (l) / ((a1 * c1))) + (j * l), 0), C + ((i * (l) / ((a1 * c1))) + (j * l), h)], i, 1, (a1 * c1) - 1], j, 0, If[b1 / a1 + b2 / a2 ≤ 1, 0, 1]) → list10

AI Drawing Prompt Reference

Draw a fraction bar addition model to demonstrate adding fractions with the same denominator. Include two long bars representing the fractions, with small units to show the fraction parts. Use different colors to highlight the parts of the fractions. Below the bars, draw a baseline with an arrow and text to display the sum of the fractions. If the sum is greater than 1, show the carry-over. Construct the bars first, then add the units, and finally the result and baseline.
The prompt above was compiled from the original drawing commands and is for reference only.