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Visual Model for Subtracting Fractions

Visual Model for Subtracting Fractions
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2020-01-22 23:14
Geometric Construction
This example demonstrates subtracting fractions visually, focusing on regrouping whole numbers into fractions (with or without common denominators). It involves core math concepts like fraction subtraction, common denominators, and integer-to-fraction conversion. Constructed using GeoGebra commands like If, Sequence, Point, etc., it's suitable for middle school math education to help students grasp fraction subtraction intuitively.

GeoGebra Commands & Parameters

  1. If(Defined[minWhole], minWhole, 0) → realMinWhole
  2. If(Defined[minNum] ∧ Defined[minDen], If[Defined[subDen] ∧ Defined[subNum] ∧ b, (minNum * LCM[minDen, subDen] / minDen), minNum], 0) → realMinNum
  3. If(Defined[subDen], If[Defined[minDen] ∧ b, LCM[minDen, subDen], subDen], 1) → realSubDen
  4. If(((¬Defined[minDen]) ∨ minDen ≟ 1) ∧ Defined[realSubDen], realSubDen, If[Defined[minDen], If[Defined[subDen] ∧ b, LCM[minDen, subDen], minDen], 1]) → realMinDen
  5. If(Defined[subWhole], subWhole, 0) → realSubWhole
  6. If(Defined[subNum] ∧ Defined[subDen], If[Defined[minDen] ∧ Defined[minNum] ∧ b, (subNum * LCM[minDen, subDen] / subDen), subNum], 0) → realSubNum
  7. Sequence(Point[{i, -1 / 2}], i, 0, floor(minuend) - floor(subtrahend)) → subPoints
  8. Point(subPoints) → SubStartingPoint
  9. Sequence(Point[{i, 1 / 2}], i, 0, floor(minuend)) → minWholesPoints
  10. Textfield(minWhole) → InputBox1
  11. Textfield(minNum) → InputBox2
  12. Textfield(minDen) → InputBox3
  13. Textfield(subWhole) → InputBox4
  14. Textfield(subNum) → InputBox5
  15. Textfield(subDen) → InputBox6
  16. Polygon((0, 0), (realMinWhole + realMinNum / realMinDen, 0), (realMinWhole + realMinNum / realMinDen, 1), (0, 1)) → minPoly, f, g, h, i
  17. Point(minWholesPoints) → MinStartingPoint
  18. Polygon(SubStartingPoint + (0, -1 / 2), SubStartingPoint + (realSubWhole + realSubNum / realSubDen, -1 / 2), SubStartingPoint + (realSubWhole + realSubNum / realSubDen, 1 / 2), SubStartingPoint + (0, 1 / 2)) → subPoly, j, k, l, m
  19. Text(x(MinStartingPoint), (x(MinStartingPoint) / 2, 1.2)) → minWholeText
  20. Text(realSubWhole, SubStartingPoint + (realSubWhole / 2, -1)) → subWholeText
  21. Sequence(Segment[SubStartingPoint + (i, -1 / 2), SubStartingPoint + (i, 1 / 2)], i, 0, ceil(subtrahend)) → subWholeLines
  22. Sequence(Segment[SubStartingPoint + (i, -1 / 2), SubStartingPoint + (i, 1 / 2)], i, realSubWhole, ceil(subtrahend), 1 / realSubDen) → subDenLines
  23. Sequence(Segment[(i, 0), (i, 1)], i, x(MinStartingPoint), ceil(minuend), 1 / realMinDen) → minDenLines
  24. Sequence(Segment[(i, 0), (i, 1)], i, 0, ceil(minuend)) → minWholeLines
  25. Segment((0, 1), (ceil(minuend), 1)) → topMin
  26. Segment((0, 0), (ceil(minuend), 0)) → bottomMin
  27. Segment(SubStartingPoint + (0, -0.5), SubStartingPoint + (ceil(subtrahend), -0.5)) → bottomSub
  28. Segment(SubStartingPoint + (0, 0.5), SubStartingPoint + (ceil(subtrahend), 0.5)) → topSub

AI Drawing Prompt Reference

Draw a figure to represent fraction subtraction, including two rectangles for the minuend and subtrahend. The minuend rectangle is divided into unit fraction parts, and the subtrahend rectangle is also divided into unit fraction parts. Draw the subtrahend rectangle below the minuend rectangle, using lines to represent unit fraction parts, and label the integer and fractional parts with text.
The prompt above was compiled from the original drawing commands and is for reference only.