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Adding Fractions with Fraction Squares

Adding Fractions with Fraction Squares
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2024-06-12 21:17
PolygonSequenceGeometric ConstructionSlider AnimationGraphing
In collections Erstes Rechnen mit Brüchen - Addieren
This GeoGebra example uses visual fraction squares (Bruchquadraten) to help students understand the addition of fractions with like denominators. It demonstrates how to add two fractions and represent the sum graphically. The core mathematical concept is fraction addition, specifically adding fractions with the same denominator. The construction uses commands such as Textfield, Polygon, Midpoint, Length, Sequence, and Join to create the fraction squares and interactive elements. Multiple buttons (btnCont, btnAgain, btnBack) and input boxes (InputBox1-4) allow students to enter fractions and check their answers. The example is designed for grades 5-6, offering open-ended questions and multiple-choice items to practice fraction addition and visual representation. It is suitable for classroom use or self-study, promoting both computational skills and geometric understanding.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Textfield(input3) → InputBox3
  4. Textfield(input4) → InputBox4
  5. Polygon(A, C, B, D) → VL, a, c, b, d
  6. Midpoint(Corner[BText41, 1], Corner[BText41, 3]) → BPos41
  7. Midpoint(Corner[BText42, 1], Corner[BText42, 3]) → BPos42
  8. Midpoint(Corner[BText51, 1], Corner[BText51, 3]) → BPos51
  9. Midpoint(Corner[BText53, 1], Corner[BText53, 3]) → BPos53
  10. Midpoint(Corner[BText61, 1], Corner[BText61, 3]) → BPos61
  11. Midpoint(Corner[BText62, 1], Corner[BText62, 3]) → BPos62
  12. Midpoint(Corner[BText63, 1], Corner[BText63, 3]) → BPos63
  13. Midpoint(Corner[BText81, 1], Corner[BText81, 3]) → BPos81
  14. Polygon(E, G, F, H) → VR, e, g, f, h
  15. Length({Mod[counterVL1, 2] ≟ 1, Mod[counterVL2, 2] ≟ 1, Mod[counterVL3, 2] ≟ 1, Mod[counterVL4, 2] ≟ 1, Mod[counterVL5, 2] ≟ 1, Mod[counterVL6, 2] ≟ 1} \ {false}) → vlactivated
  16. Length({Mod[counterVR1, 2] ≟ 1, Mod[counterVR2, 2] ≟ 1, Mod[counterVR3, 2] ≟ 1, Mod[counterVR4, 2] ≟ 1, Mod[counterVR5, 2] ≟ 1, Mod[counterVR6, 2] ≟ 1} \ {false}) → vractivated
  17. Sequence(I + (i * Vector[I, J] / nenner1), i, 0, nenner1) → Q1PO
  18. Sequence(L + (i * Vector[I, J] / nenner1), i, 0, nenner1) → Q1PU
  19. Sequence(M + (i * Vector[I, J] / nenner2), i, 0, nenner2) → Q2PO
  20. Sequence(P + (i * Vector[I, J] / nenner2), i, 0, nenner2) → Q2PU
  21. Sequence(Q + (i * Vector[I, J] / nenner2), i, 0, nenner2) → Q3PO
  22. Sequence(T + (i * Vector[I, J] / nenner2), i, 0, nenner2) → Q3PU
  23. Join({{Segment[I, J], Segment[I, L], Segment[L, K], Segment[K, J]}, Sequence[Segment[Q1PO(i), Q1PU(i)], i, 1, Length[Q1PO]]}) → Q1Kanten
  24. Join({{Segment[M, N], Segment[M, P], Segment[P, O], Segment[N, O]}, Sequence[Segment[Q2PO(i), Q2PU(i)], i, 1, Length[Q2PO]]}) → Q2Kanten
  25. Join({{Segment[Q, R], Segment[Q, T], Segment[T, S], Segment[S, R]}, Sequence[Segment[Q3PO(i), Q3PU(i)], i, 1, Length[Q3PO]]}) → Q3Kanten
  26. Polygon(Q, R, S, T) → VRErgebnis, q, r, s, t

AI Drawing Prompt Reference

Draw two fraction-square models to visualize adding fractions with the same denominator. First create a left square frame using four corner points, then place equally spaced division points along its interior and connect them with straight segments to form the fraction-square grid and an activated fill area. Construct a second fraction square on the right with an outer four-corner polygon, using analogous division points and the same step size. Use user-entered numerators to generate the boundary positions by stepping along the grid direction, and connect the corresponding boundary points into grouped side segments. Finally, form a resulting quadrilateral area that represents the shown sum region, allowing visual comparison of the entered fractions.
The prompt above was compiled from the original drawing commands and is for reference only.