积极 AI Logo 积极 AI

一元方程解的探索：热与冷活动

一元方程解的探索：热与冷活动
几何画板及绘图内容加载中，请稍等……
2022-12-26 21:24
函数解析几何几何作图
本范例通过代入不同值探索一元方程，帮助学生理解方程解的个数（0、1或无限）。使用了代数、方程等核心概念。通过GeoGebra命令如Shuffle、Join等进行动态演示。适合6-8年级学生学习。

GeoGebra 命令及参数

  1. Shuffle(Sequence[-5, 5]) → sols, {4, 1, -5, 5, 2, -2, -4, -1, 0, -3, 3}
  2. Shuffle(Flatten[Sequence[Sequence[3], kk, 1, 10]]) → solutions, {2, 3, 1, 2, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 3, 1, 3, 1, 1, 2, 2, 3, 3, 2}
  3. Shuffle(Sequence[6]) → formatNums, {5, 2, 4, 3, 1, 6}
  4. Join({{1 / 2, 1 / 5, 2 / 5}, (-1 * {1 / 2, 1 / 5, 2 / 5})}) → allowedFractions
  5. Shuffle(Flatten[{Sequence[-10, 10] \ {0}, allowedFractions}]) → bNums, {-0.5, 0.5, -1, -10, 3, -3, -8, 9, 10, -7, 0.4, 1, 0.2, 4, 5, -5, -0.4, 8, -2, -0.2, 2, -6, -9, 6, 7, -4}
  6. Shuffle(Flatten[{Sequence[-10, 10] \ {0, 1}, allowedFractions}]) → aNums, {-0.4, 3, -10, 0.5, -8, -0.5, 4, -1, 0.4, -6, -9, -4, -2, 5, 10, 6, -7, -0.2, 7, 8, -3, 2, 0.2, 9, -5}
  7. Element(formatNums, Mod[questionCount, Length[formatNums]] + 1) → formatNum
  8. Element(sols, Mod[questionCount + 1, Length[sols]] + 1) → int
  9. Element({-2, -1, 2}, Mod[questionCount, 3] + 1) → aLight
  10. If(formatNum ≥ 4, aLight, Element[aNums, Mod[questionCount, Length[aNums]] + 1]) → a
  11. Shuffle(Flatten[{Sequence[-10, 10] \ {0, 1, a}, allowedFractions}]) → cNums, {10, 7, -6, -10, -4, 3, -0.4, 5, -9, 4, -5, 0.5, 0.4, 9, 6, 0.2, 8, -8, -1, -0.2, -3, 2, -7, -0.5}
  12. If(questionCount ≟ 0, 1, Element[solutions, Mod[questionCount, Length[solutions]] + 1]) → solutionsCurrent
  13. Element(sols, Mod[questionCount, Length[sols]] + 1) → sol
  14. If(solutionsCurrent ≠ 1, Element[bNums, Mod[questionCount, Length[bNums]] + 1], int - (a * sol)) → b
  15. Shuffle(Flatten[{Sequence[-10, 10] \ {0, b}, allowedFractions}]) → dNums, {6, -2, -9, 1, 4, 0.2, 8, -7, -4, 10, 0.4, 2, -1, -6, -0.2, -0.4, -8, -3, 5, 3, 7, -10, 0.5, -0.5, -5}
  16. Segment(LeftEndPoint1, RightEndPoint2) → numberLine2
  17. Point(numberLine2) → A'
  18. Segment(LeftEndPoint, RightEndPoint) → numberLine
  19. If(solutionsCurrent ≟ 3, 1, solutionsCurrent ≟ 2, 4, If[DifX ≥ 10, 4, If[DifX ≥ 5, 3, If[DifX ≠ 0, 2, 1]]]) → colorCase
  20. Element(colors, colorCase) → ColorDyn
  21. Element(cNums, Mod[questionCount, Length[cNums]] + 1) → c1
  22. If(solutionsCurrent ≟ 1, c1, a) → c
  23. Element(dNums, Mod[questionCount, Length[dNums]] + 1) → d1
  24. If(solutionsCurrent ≟ 3, b, solutionsCurrent ≟ 1, int - (c * sol), d1) → d
  25. Element({LeftEval32, LeftEval32, LeftEval22, LeftEval32, LeftEval32, LeftEval42}, formatNum) → RightEval2
  26. Element({LeftEval12, LeftEval22, LeftEval32, LeftEval42, LeftEval42, LeftEval32}, formatNum) → LeftEval2nd
  27. Element({LeftEval3, LeftEval3, LeftEval2, LeftEval3, LeftEval3, LeftEval4}, formatNum) → RightEval
  28. Element({LeftEval1, LeftEval2, LeftEval3, LeftEval4, LeftEval5, LeftEval3}, formatNum) → LeftEval
  29. Corner(5) → AppSize
  30. Element(bNums, Mod[questionCount, Length[bNums]] + 1) → b1
  31. Element({Left1, Left2, Left3, Left4, Left5, Left3}, formatNum) → Left
  32. Element({Left3, Left3, Left2, Left3, Left3, Left4}, formatNum) → Right
  33. Zip((("$\textsf{" * AA) * " }$"), AA, {"\phantom{One Solution}", "One solution", "No solution", "Infinitely many solutions"}) → dropDown
  34. If(correct, "Correct!", "Try again...") → text1
  35. Sequence(Segment[(x(Cor1) + ii, -0.15), (x(Cor1) + ii, 0.15)], ii, 1, 15) → ticks
  36. If(formatNum ≟ 3 ∨ formatNum ≟ 6, fcdEvalText, fabEvalText) → A4
  37. TableText({{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}}, "rclrh") → text3
  38. Text(text3, C, true, true, -1, -1) → text4
  39. meterComplete(MeterCenter, meterRadius, meterNum) → meter_{1}, meter_{2}, meter_{11}, meter_{101}, meter_{102}, meter_{103}, meter_{104}, meter_{105}, meter_{106}, meter_{107}, meter_{108}, meter_{109}, meter_{110}, meter_{12}, meter_{111}, meter_{112}, meter_{113}, meter_{114}, meter_{115}, meter_{116}, meter_{117}, meter_{118}, meter_{119}, meter_{120}, meter_{13}, meter_{121}, meter_{122}, meter_{123}, meter_{124}, meter_{125}, meter_{126}, meter_{127}, meter_{128}, meter_{129}, meter_{130}, meter_{14}, meter_{131}, meter_{132}, meter_{133}, meter_{134}, meter_{135}, meter_{136}, meter_{137}, meter_{138}, meter_{139}, meter_{140}, meter_{15}, meter_{141}, meter_{142}, meter_{143}, meter_{144}, meter_{145}, meter_{146}, meter_{147}, meter_{148}, meter_{149}, meter_{150}, meter_{16}, meter_{151}, meter_{152}, meter_{153}, meter_{154}, meter_{155}, meter_{156}, meter_{157}, meter_{158}, meter_{159}, meter_{160}, meter_{17}, meter_{161}, meter_{162}, meter_{163}, meter_{164}, meter_{165}, meter_{166}, meter_{167}, meter_{168}, meter_{169}, meter_{170}, meter_{18}, meter_{171}, meter_{172}, meter_{173}, meter_{174}, meter_{175}, meter_{176}, meter_{177}, meter_{178}, meter_{179}, meter_{180}, meter_{19}, meter_{181}, meter_{182}, meter_{183}, meter_{20}, meter_{3}, meter_{21}, meter_{22}, meter_{23}, meter_{24}, meter_{25}, meter_{26}, meter_{27}, meter_{28}, meter_{29}, meter_{30}, meter_{4}, meter_{31}, meter_{32}, meter_{33}, meter_{34}, meter_{35}, meter_{36}, meter_{37}, meter_{38}, meter_{39}, meter_{40}, meter_{5}, meter_{41}, meter_{42}, meter_{43}, meter_{44}, meter_{45}, meter_{46}, meter_{47}, meter_{48}, meter_{49}, meter_{50}, meter_{6}, meter_{51}, meter_{52}, meter_{53}, meter_{54}, meter_{55}, meter_{56}, meter_{57}, meter_{58}, meter_{59}, meter_{60}, meter_{7}, meter_{61}, meter_{62}, meter_{63}, meter_{64}, meter_{65}, meter_{66}, meter_{67}, meter_{68}, meter_{69}, meter_{70}, meter_{8}, meter_{71}, meter_{72}, meter_{73}, meter_{74}, meter_{75}, meter_{76}, meter_{77}, meter_{78}, meter_{79}, meter_{80}, meter_{9}, meter_{81}, meter_{82}, meter_{83}, meter_{84}, meter_{85}, meter_{86}, meter_{87}, meter_{88}, meter_{89}, meter_{90}, meter_{10}, meter_{91}, meter_{92}, meter_{93}, meter_{94}, meter_{95}, meter_{96}, meter_{97}, meter_{98}, meter_{99}, meter_{100}
  40. onboardingTextOffset(Corner[onboardingText_{1}, 1], Corner[onboardingText_{1}, 3], onboardingCase_{1}, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset_{1}
  41. circlePixels(A', 9 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject
  42. Sequence(Text[(If[minx + ii - 1 ≥ 0, "\hspace{5}", ""] * (minx + ii - 1)), (x(Cor1) + ii, -0.4), true, true, 0, 0], ii, 1, 15) → l1
  43. Text(((If[x(A) ≥ 0, "\hspace{5}", ""] * LabelPoint) * "\\\\"), A', true, true, 0, 1) → LabelPointPos

AI 绘图提示语参考

这是一个用于展示一元方程解的图形。图形包含一条数轴，上面有一个标记点，数轴上有刻度标记。图形中有一个下拉菜单，选项包括“One Solution”、“One solution”、“No solution”、“Infinitely many solutions”。图形中还有标签、文本、表格和圆圈，用于显示当前解的情况。图形通过颜色选择和动态文本来指示解的数量。
以上提示语为根据原始绘图命令整理而来，仅供参考。