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Gradient Game on Straight Lines

Gradient Game on Straight Lines
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2014-07-14 03:08
VectorFunctionCoordinate GeometryDerivative
In collections Introduction to Linear Functions and Graphs Game Applets (2014 National ICT Presentation)
This example demonstrates the calculation and understanding of gradients of straight lines through an interactive game. Core math concepts include line gradients in coordinate geometry, vector and midpoint calculations. Construction highlights the use of GeoGebra commands/objects like Line, If, Random, Function, Textfield, Vector, Midpoint, Integral for dynamic line generation and gradient computation, suitable for formative assessment, remediation, or student self-study in middle school mathematics.

GeoGebra Commands & Parameters

  1. Line(P, Q) → l_c
  2. If(FractionText[Slope[l_c]] ≟ "?", "undefined", FractionText[Slope[l_c]]) → actualgradient
  3. Random(-6, 6) → c
  4. Random(0, 6) → a
  5. If(gradient_{answer} ≟ Slope[l_c], true, If[gradient_{textanswer} ≟ actualgradient, true, false]) → AnswerCorrect
  6. Function((0 * x) - 1, -3, 3) → f
  7. Textfield(gradient_{answer}) → inputBox1
  8. Vector(Q, N) → vectorhorizontalrun
  9. Vector(N, P) → vectorverticalrun
  10. Midpoint(N, P) → M_{NP}
  11. Midpoint(N, Q) → M_{NQ}
  12. Text(horizontalrun) → texthorizontalrun
  13. Text(verticalrun) → textverticalrun
  14. Function(cos(x) + 2, 0, 31.416) → f_{racepath}
  15. Integral(f_{racepath}, 0, 31.416) → wavebody
  16. Corner(2, 4) → A
  17. Textfield(gradient_{textanswer}) → inputBox2
  18. Function(((-(x(l_c) / y(l_c))) * x) - z(l_c) / y(l_c), -8, 10) → f_{line}

AI Drawing Prompt Reference

Draw a straight line and display its gradient. Randomly generate two points and connect them to form another line. Calculate the gradients of both lines and display the gradient of one line in a text box. Users need to guess the gradient of the other line, and the system will judge the correctness of the guess. At the same time, draw a function graph as the background and calculate the integral area of the function. Mark the two points and their midpoints in the figure, and display the horizontal and vertical vectors.
The prompt above was compiled from the original drawing commands and is for reference only.