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Intuitive Introduction to Gradient (Slope)

Intuitive Introduction to Gradient (Slope)
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2019-04-11 10:25
FunctionCoordinate GeometryGeometric ConstructionSlider Animation
An active, student-centered, color-coded discovery lesson that helps students independently explore the concept of slope (and the four main types of slope). ①This example demonstrates the process of calculating slope through the coordinates of two points. ②Core mathematical concepts involved include coordinates, difference and slope, division, piecewise functions, similarity transformation, arithmetic operations, and confidence intervals. ③Construction highlights derived from GeoGebra commands: GCD (Greatest Common Divisor), If (Conditional Statement), OrthogonalLine (Perpendicular Line), Intersect (Intersection Point), Line (Line Segment), Polygon (Polygon), Distance (Distance Measure), Segment (Line Segment), Angle (Angle Measure), Slope (Slope Calculation). ④Suitable for middle school and above mathematics learners, especially for introductory teaching of analytical geometry.

GeoGebra Commands & Parameters

  1. GCD(deltaY, deltaX) → GCDm
  2. GCD(numerYint, deltaX) → GCDy
  3. If(sgn(deltaY / deltaX) ≥ 0, "", "-") → textSignN
  4. If(sgn(numerYint / deltaX) > 0, "+", "-") → textSign
  5. If(deltaXR ≟ 1, textSignN + deltaYR, textSignN + "\, \frac{" + deltaYR + "}{" + deltaXR + "}") → textslopeN
  6. If(denomYintR ≟ 1, textSign + numerYintR, textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textYint
  7. If(denomYintR ≟ 1, If[numerYintR ≟ 1, textSign, textSign + numerYintR], textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textMID
  8. OrthogonalLine(B, xAxis) → a_2
  9. OrthogonalLine(A, yAxis) → c
  10. Intersect(a_2, c) → C
  11. Line(A, B) → d
  12. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  13. Distance(B, C) → distanceBC
  14. Distance(A, C) → distanceAC
  15. Intersect(a_2, c) → D
  16. Segment(A, D) → e
  17. Segment(C, B) → f
  18. GCD(deltaY_1, deltaX_1) → GCDm_1
  19. If(sgn(deltaY_1 / deltaX_1) ≥ 0, "", "-") → textSignN_1
  20. If(deltaXR_1 ≟ 1, textSignN_1 + deltaYR_1, textSignN_1 + "\, \frac{" + deltaYR_1 + "}{" + deltaXR_1 + "}") → textslopeN_1
  21. Line(A_1, B_1) → d_1
  22. Angle(B, D, A) → α
  23. Segment(A, B) → g
  24. GCD(deltaY_2, deltaX_2) → GCDm_2
  25. If(sgn(deltaY_2 / deltaX_2) ≥ 0, "", "-") → textSignN_2
  26. If(deltaXR_2 ≟ 1, textSignN_2 + deltaYR_2, textSignN_2 + "\, \frac{" + deltaYR_2 + "}{" + deltaXR_2 + "}") → textslopeN_2
  27. Line(A_2, B_2) → d_2
  28. Segment(A_2, B_2) → g_1
  29. GCD(deltaY_3, deltaX_3) → GCDm_3
  30. If(sgn(deltaY_3 / deltaX_3) ≥ 0, "", "-") → textSignN_3
  31. If(deltaXR_3 ≟ 1, textSignN_3 + deltaYR_3, textSignN_3 + "\, \frac{" + deltaYR_3 + "}{" + deltaXR_3 + "}") → textslopeN_3
  32. Line(A_3, B_3) → d_3
  33. Segment(A_3, B_3) → g_2
  34. Slope(g) → h