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Multiplying Negatives Demo

Multiplying Negatives Demo
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2020-06-08 03:41
FunctionGeometric Construction
This example demonstrates the geometric interpretation of multiplying negatives using dynamic geometry. It involves core math concepts like negative multiplication rules, number line symmetry, and geometric transformations. GeoGebra commands and objects used include Ellipse, Arc, Translate, Mirror. Suitable for middle school students and introductory calculus education to understand multiplication rules and operations.

GeoGebra Commands & Parameters

  1. Ellipse((a / 2, sqrt(abs(4 - a^(2) / 4))), (a / 2, (-sqrt(abs(4 - a^(2) / 4)))), 2) → c1
  2. Arc(c1, (0, 0), (a, 0)) → left1
  3. Arc(c1, (a, 0), (0, 0)) → right1
  4. Translate(c1, Vector[(a, 0)]) → c2
  5. Translate(c2, Vector[(a, 0)]) → c3
  6. Translate(c3, Vector[(a, 0)]) → c4
  7. Translate(c4, Vector[(a, 0)]) → c5
  8. Arc(c2, ((a * 2), 0), (a, 0)) → right2
  9. Arc(c3, ((a * 3), 0), ((a * 2), 0)) → right3
  10. Arc(c4, ((a * 4), 0), ((a * 3), 0)) → right4
  11. Arc(c5, ((a * 5), 0), ((a * 4), 0)) → right5
  12. Arc(c2, (a, 0), ((2 * a), 0)) → left2
  13. Arc(c3, ((2 * a), 0), ((3 * a), 0)) → left3
  14. Arc(c4, ((3 * a), 0), ((4 * a), 0)) → left4
  15. Arc(c5, ((4 * a), 0), ((5 * a), 0)) → left5
  16. Mirror(c1, x = 0) → c6
  17. Mirror(c2, x = 0) → c7
  18. Mirror(c3, x = 0) → c8
  19. Translate(c8, Vector[((-a), 0)]) → c9
  20. Translate(c9, Vector[((-a), 0)]) → c10
  21. Arc(c10, ((-4 * a), 0), ((-5 * a), 0)) → left10
  22. Arc(c10, ((-5 * a), 0), ((-4 * a), 0)) → right10
  23. Ellipse((a / 2, sqrt(abs(4 - a^(2) / 4))), (a / 2, (-sqrt(abs(4 - a^(2) / 4)))), 4) → c
  24. Arc(c6, ((-a), 0), (0, 0)) → left6
  25. Arc(c7, ((-2 * a), 0), ((-a), 0)) → left7
  26. Arc(c8, ((-3 * a), 0), ((-2 * a), 0)) → left8
  27. Arc(c9, ((-4 * a), 0), ((-3 * a), 0)) → left9
  28. Arc(c6, (0, 0), ((-a), 0)) → right6
  29. Arc(c7, ((-a), 0), ((-2 * a), 0)) → right7
  30. Arc(c8, ((-2 * a), 0), ((-3 * a), 0)) → right8
  31. Arc(c9, ((-3 * a), 0), ((-4 * a), 0)) → right9