MathPlotAI Logo MathPlotAI

Quiz: Equivalent Rates and Equations for Proportional Relationships

Quiz: Equivalent Rates and Equations for Proportional Relationships
Loading the math board and drawing, please wait…
2022-03-28 19:41
FunctionCoordinate GeometryGeometric ConstructionSlider Animation
In collections Elementary Math Resources
This example demonstrates how to write equivalent rates and equations within proportional relationships. It involves core math concepts like algebra, arithmetic, equations, linear equations, linear functions, ratios, matrices, and fractions. Construction highlights the use of GeoGebra commands/objects such as PointIn, Random, Dilate, Vector, Segment, If, and Textfield. Suitable for middle school and above students for practicing proportional relationships applications.

GeoGebra Commands & Parameters

  1. PointIn(g_1) → D
  2. Random(1, 15) → y_1, 3
  3. Random(1, 15) → x_1, 10
  4. Random(20, 75) → k, 23
  5. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], A) → B'
  6. Vector(B, B') → u
  7. Dilate(A, If[2 < a ≤ 3, 3 - a, 0], (0, y(D))) → A'
  8. Vector(A, A') → v
  9. Dilate(A', If[3 < a ≤ 4, 4 - a, 0], D) → C'
  10. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], (x(D), y(D) + y(A'))) → D'
  11. Dilate(D', If[6 < a ≤ 7, 7 - a, 0], (x(D') + x(D), y(D'))) → E'
  12. Dilate(A, If[8 < a ≤ 9, 9 - a, 0], D) → A'_{1}
  13. Segment(A, A'_{1}) → g
  14. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E) → D'_{1}
  15. Random(-10, 10) → b_1, 4
  16. Random(-10, 10) → n_1, 1
  17. Random(1, 10) → d_1, 4
  18. If(s ≥ 0, "earn", "lose") → text7
  19. If(d > 1, "hours", "hour") → text8
  20. Textfield(p) → InputBox3
  21. Textfield(o) → InputBox1
  22. If(o ≟ n_1 / d_1, "Yes!", "no") → text9
  23. If(p ≟ q, "Yes!", "no") → text10
  24. Vector(A', C') → w
  25. Dilate(D, If[9 < a ≤ 10, 10 - a, 0], E') → D'_{2}
  26. Segment(D, D'_{2}) → h
  27. Textfield(p_1) → InputBox2
  28. Textfield(q_1) → InputBox4
  29. Textfield(k_1) → InputBox5
  30. Textfield(m_1) → InputBox7
  31. Textfield(o_1) → InputBox8
  32. Textfield(l_1) → InputBox6
  33. If(c1, "√", "×") → text21
  34. If(c2, "√", "×") → text20
  35. If(c3, "√", "×") → text22
  36. Textfield(r_1) → InputBox9

AI Drawing Prompt Reference

Draw a coordinate system with point D in the first quadrant. Randomly generate coordinates for points A and B, then use scaling to create points B', A', C', D', and E'. Connect points A and A', D and D', and generate vectors u, v, and w. Finally, add some segments and text boxes to display proportional relationships and equations.
The prompt above was compiled from the original drawing commands and is for reference only.