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Exploring Solutions of One-Variable Equations: Hot and Cold Activity

Exploring Solutions of One-Variable Equations: Hot and Cold Activity
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2022-12-26 21:24
FunctionCoordinate GeometryGeometric Construction
This example explores one-variable equations by substituting different values, helping students understand the number of solutions (0, 1, or infinite). It covers algebra and equations. Using GeoGebra commands like Shuffle and Join for dynamic demonstrations, it is suitable for 6-8 grade students.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

This is a graphic for displaying solutions of one-variable equations. It includes a number line with a marked point, tick marks on the number line, a dropdown menu with options "One Solution", "One solution", "No solution", "Infinitely many solutions". The graphic also contains labels, text, a table, and circles to indicate the current solution. The graphic uses color selection and dynamic text to indicate the number of solutions.
The prompt above was compiled from the original drawing commands and is for reference only.