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Equivalent Linear Equations Self-Practice

Equivalent Linear Equations Self-Practice
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2020-02-29 20:39
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① This example is a self-practice activity designed to help students master the concept of equivalent linear equations, generating random problems and providing instant feedback. ② The core mathematical concept is equivalent linear equations, meaning equations that share the same solution set, typically obtained through algebraic manipulations such as adding, subtracting, multiplying, dividing, or rearranging terms. ③ Construction highlights: The GeoGebra construction uses random generation (Random, RandomElement), text processing (TextToUnicode, Join, Expand), conditional logic (If, CountIf), and interactive components (Textfield, Button) to dynamically create questions and check answers; objects include counters, variables a, b, c, and multiple text display areas. ④ Suitable for middle school to high school students, this can be used for classroom practice, self-study, or as a teacher's demonstration tool for illustrating equivalent equation transformations.

GeoGebra Commands & Parameters

  1. If(counter < 2, RandomElement[{-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}], If[counter < 3, RandomElement[{-6, -4, -2, 2, 4, 6}], If[counter < 4, RandomElement[{-9, -6, -3, 3, 6, 9}], RandomElement[{-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7}]]]) → a
  2. If(counter < 2, 1, If[counter < 3, 2, If[counter < 4, 3, RandomElement[{1, 2, 3, 4, 5, 6}]]]) → b
  3. If(counter < 2, Random[-7, 9], If[counter < 3, RandomElement[{-10 - 8, -6, -4, -2, 2, 4, 6, 8, 10}], If[counter < 4, RandomElement[{-15, -12, -9, -6, -3, 3, 6, 9, 12, 15}], Random[-7, 9]]]) → c_1
  4. GCD({a, b, c_1}) → c_h
  5. TextToUnicode(Text[h]) → l3
  6. Sequence(32, k, 1, CountIf[x ≟ 32, TextToUnicode[Text[h_1]]]) → l3_s
  7. Remove(l3, l3_s) → l3_c
  8. TextToUnicode(textl32) → l32
  9. Sequence(32, k, 1, CountIf[x ≟ 32, l32]) → l32_s
  10. Remove(l32, l32_s) → l32_c
  11. TextToUnicode(textl22) → l22
  12. Sequence(32, k, 1, CountIf[x ≟ 32, l22]) → l22_s
  13. Remove(l22, l22_s) → l22_c
  14. Expand(Simplify[((-(x(g) / y(g))) * x) - z(g) / y(g)]) → f_1
  15. TextToUnicode(Text[f_1]) → l1
  16. Sequence(32, k, 1, CountIf[x ≟ 32, TextToUnicode[Text[f_1]]]) → l1_s
  17. Join({TextToUnicode["y="], Remove[l1, l1_s]}) → l1_c
  18. TextToUnicode(Text[g]) → l2
  19. If(counter < 5, 1, If[counter < 8, 2, 3]) → type
  20. Random(-6, 7) → c
  21. GCD({a, b, c}) → c_g
  22. Sequence(32, k, 1, CountIf[x ≟ 32, TextToUnicode[Text[g_1]]]) → l2_s
  23. Remove(l2, l2_s) → l2_c
  24. TextToUnicode(Text[textanswera]) → la
  25. Sequence(32, k, 1, CountIf[x ≟ 32, la]) → la_s
  26. Remove(la, la_s) → la_c
  27. TextToUnicode(Text[eqb]) → lbb
  28. Sequence(32, k, 1, CountIf[x ≟ 32, lbb]) → lbb_s
  29. Remove(lbb, lbb_s) → lbb_c
  30. TextToUnicode(Text[eqa]) → laa
  31. Sequence(32, k, 1, CountIf[x ≟ 32, laa]) → laa_s
  32. Remove(laa, laa_s) → laa_c
  33. TextToUnicode(Text[textanswerb]) → lb
  34. Sequence(32, k, 1, CountIf[x ≟ 32, lb]) → lb_s
  35. Remove(lb, lb_s) → lb_c
  36. RandomElement({-5, -4, -3, -2, 1, 0, 1, 2, 3, 4, 5, 1 / 2, 1 / 3, 1 / 4, 3 / 4, 1 / 5, 2 / 3, 1 / 5, 2 / 5, 3 / 5, 4 / 5, -1 / 2, -1 / 3, -1 / 4, -3 / 4, -1 / 5, -2 / 3, -1 / 5, -2 / 5, -3 / 5, -4 / 5}) → m
  37. Expand(Simplify[(m * x) + c]) → f
  38. If(type < 2, la_c ≟ l2_c ∨ la_c ≟ l22_c, If[type ≟ 2, la_c ≟ l3_c ∨ la_c ≟ l32_c, la_c ≟ l1_c]) → answeracorrect
  39. If(type ≟ 1, m, If[type ≟ 2, m_d, m_d]) → m_s
  40. If(type ≟ 1, c, c_d) → c_s
  41. If(type < 2, lb_c ≟ l3_c ∨ lb_c ≟ l32_c, If[type ≟ 2, lb_c ≟ l1_c ∨ lb_c ≟ l1_c, lb_c ≟ l2_c ∨ lb_c ≟ l22_c]) → answerbcorrect
  42. Textfield(textanswera) → InputBox1
  43. Textfield(textanswerb) → InputBox2
  44. Expand(Simplify[(m_s * x) + c_s]) → f_s
  45. CountIf(x ≟ 32, {32, 32, 35, 34, 56}) → d
  46. Point(g, 0.3) → B
  47. Point(g, 0.7) → A

AI Drawing Prompt Reference

Create an interactive graphic showing the equivalence of randomly generated linear equations. Include sliders to control parameters, dynamically generating and displaying the equations. Key elements: graphs of two linear equations, parameter sliders, text areas for equations, input boxes for answers, and a button to check answers. First, plot the graphs of the two linear equations, then use sliders to adjust parameters and observe changes in the graphs, finally displaying the equations and answers in text areas.
The prompt above was compiled from the original drawing commands and is for reference only.