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Ablesen am Thermometer：Rational Number Comparison and Number Line Representation

Ablesen am Thermometer：Rational Number Comparison and Number Line Representation
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2025-01-21 20:15
Coordinate Geometry
In collections Rationale Zahlen & Arbeiten mit der Zahlengerade
This GeoGebra example demonstrates rational number comparison and representation on the number line. Key mathematical concepts include comparing rational numbers, their positions on the number line, and understanding their magnitude. Construction involves using commands like KeepIf, Join, and Sequence to build the number line, along with random number generation for visualization. Suitable for students in grades 7-8 to grasp rational number concepts and number line representation.

GeoGebra Commands & Parameters

  1. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, Element[typMinMaxDist(1), 1], 0 - 0.01, Element[typMinMaxDist(1), 3]]) → randomNumbersTyp1Negativ
  2. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, 0, Element[typMinMaxDist(1), 2], Element[typMinMaxDist(1), 3]] \ {0}) → randomNumbersTyp1Positiv
  3. Join(Sequence[Shuffle[{1, 2, 2}], i, 1, 40]) → randomPosNegNumbers
  4. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, Element[typMinMaxDist(2), 1], 0 - 0.01, Element[typMinMaxDist(2), 3]]) → randomNumbersTyp2Negativ
  5. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, Element[typMinMaxDist(3), 1], 0 - 0.01, Element[typMinMaxDist(3), 3]]) → randomNumbersTyp3Negativ
  6. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, Element[typMinMaxDist(4), 1], 0 - 0.01, Element[typMinMaxDist(4), 3]]) → randomNumbersTyp4Negativ
  7. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, 0, Element[typMinMaxDist(3), 2], Element[typMinMaxDist(3), 3]] \ {0}) → randomNumbersTyp3Positiv
  8. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, 0, Element[typMinMaxDist(2), 2], Element[typMinMaxDist(2), 3]] \ {0}) → randomNumbersTyp2Positiv
  9. KeepIf(Mod[(a * 10), 10] ≠ 0, a, Sequence[i, i, 0, Element[typMinMaxDist(4), 2], Element[typMinMaxDist(4), 3]] \ {0}) → randomNumbersTyp4Positiv
  10. Join({{1}, Join[Sequence[Shuffle[{1, 2, 2, 3, 3, 4, 4}], i, 1, 30]]}) → randomTyps
  11. Sequence(RandomElement[Element[randomNumbersPosNeg(randomTyps(i)), randomPosNegNumbers(i)]], i, 1, Length[randomQuestions]) → randomNumbers, {-0.5, -1.5, 2.6000000000000005, -1.3999999999999995, -0.6000000000000001, 0.25, 1.3000000000000003, -0.75, -1.25, -0.20000000000000007, -0.9, 1.3000000000000003, -1.75, 0.5, -1.8, 0.4, -1.7999999999999998, -0.5, -2.5, -0.6000000000000001, 2.5, -1.2000000000000002, -2.5, 1.9000000000000008, -0.5, 2.4000000000000004, -0.8, -1.6999999999999997, 0.5, -0.5, 1.4, -0.6000000000000001, -0.25, -0.20000000000000015, -0.8, 1.75, -2.5, -1.75, 2.25, -2.4, 0.30000000000000004, -0.4000000000000001, -1.3999999999999995, 0.7999999999999999, -0.4000000000000001, -1.6, 1.7000000000000006, -1.5, -1.25, -0.5, 1.7999999999999998, -1.5, 1.2, -0.8, 0.25, -1.7999999999999998, -1.75, -2.1999999999999997, 2.6000000000000005, -1.25, -2.5, 0.30000000000000004, -1.6999999999999997, -2.5, 0.25, -0.6000000000000001, 0.8, -0.30000000000000016, -0.75, -0.20000000000000007, -0.5, 2.5, -1.6, 0.5, -1.5, 1.7000000000000006, -1.6, -0.7000000000000001, 2.5, -2.5, -0.6000000000000001, -1.2000000000000002, 1.6000000000000005, -0.7000000000000001, 1.75, -0.5, -1.5, -1.6, 0.5, -1.2999999999999994, -0.5000000000000001, 0.4, -0.6000000000000001, -1.5, -0.75, 1.7999999999999998, -2.5, -0.7000000000000001, 0.4, -2.5}
  12. Element(randomNumbers, Mod[questionCount - 1, Length[randomQuestions]] + 1) → actualRandomNumber
  13. Defined(input) → clickableBtnValidate
  14. Textfield(input) → inputBox
  15. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  16. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  17. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  18. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-0.010000000000097327, 12.020000000000158), (0.9925094102884998, 12.020000000000158), (1.9950188205770971, 12.020000000000158), (2.997528230865694, 12.020000000000158), (4.000037641154291, 12.020000000000158), (5.002547051442889, 12.020000000000158), (6.005056461731486, 12.020000000000158), (7.007565872020083, 12.020000000000158), (8.01007528230868, 12.020000000000158), (9.012584692597278, 12.020000000000158), (10.015094102885875, 12.020000000000158), (11.017603513174473, 12.020000000000158), (12.020112923463069, 12.020000000000158), (13.022622333751666, 12.020000000000158), (14.025131744040264, 12.020000000000158), (15.027641154328862, 12.020000000000158), (16.030150564617458, 12.020000000000158)}, {(-0.010000000000097327, 11.01664991624805), (0.9925094102884998, 11.01664991624805), (1.9950188205770971, 11.01664991624805), (2.997528230865694, 11.01664991624805), (4.000037641154291, 11.01664991624805), (5.002547051442889, 11.01664991624805), (6.005056461731486, 11.01664991624805), (7.007565872020083, 11.01664991624805), (8.01007528230868, 11.01664991624805), (9.012584692597278, 11.01664991624805), (10.015094102885875, 11.01664991624805), (11.017603513174473, 11.01664991624805), (12.020112923463069, 11.01664991624805), (13.022622333751666, 11.01664991624805), (14.025131744040264, 11.01664991624805), (15.027641154328862, 11.01664991624805), (16.030150564617458, 11.01664991624805)}, {(-0.010000000000097327, 10.01329983249594), (0.9925094102884998, 10.01329983249594), (1.9950188205770971, 10.01329983249594), (2.997528230865694, 10.01329983249594), (4.000037641154291, 10.01329983249594), (5.002547051442889, 10.01329983249594), (6.005056461731486, 10.01329983249594), (7.007565872020083, 10.01329983249594), (8.01007528230868, 10.01329983249594), (9.012584692597278, 10.01329983249594), (10.015094102885875, 10.01329983249594), (11.017603513174473, 10.01329983249594), (12.020112923463069, 10.01329983249594), (13.022622333751666, 10.01329983249594), (14.025131744040264, 10.01329983249594), (15.027641154328862, 10.01329983249594), (16.030150564617458, 10.01329983249594)}, {(-0.010000000000097327, 9.009949748743832), (0.9925094102884998, 9.009949748743832), (1.9950188205770971, 9.009949748743832), (2.997528230865694, 9.009949748743832), (4.000037641154291, 9.009949748743832), (5.002547051442889, 9.009949748743832), (6.005056461731486, 9.009949748743832), (7.007565872020083, 9.009949748743832), (8.01007528230868, 9.009949748743832), (9.012584692597278, 9.009949748743832), (10.015094102885875, 9.009949748743832), (11.017603513174473, 9.009949748743832), (12.020112923463069, 9.009949748743832), (13.022622333751666, 9.009949748743832), (14.025131744040264, 9.009949748743832), (15.027641154328862, 9.009949748743832), (16.030150564617458, 9.009949748743832)}, {(-0.010000000000097327, 8.006599664991722), (0.9925094102884998, 8.006599664991722), (1.9950188205770971, 8.006599664991722), (2.997528230865694, 8.006599664991722), (4.000037641154291, 8.006599664991722), (5.002547051442889, 8.006599664991722), (6.005056461731486, 8.006599664991722), (7.007565872020083, 8.006599664991722), (8.01007528230868, 8.006599664991722), (9.012584692597278, 8.006599664991722), (10.015094102885875, 8.006599664991722), (11.017603513174473, 8.006599664991722), (12.020112923463069, 8.006599664991722), (13.022622333751666, 8.006599664991722), (14.025131744040264, 8.006599664991722), (15.027641154328862, 8.006599664991722), (16.030150564617458, 8.006599664991722)}, {(-0.010000000000097327, 7.003249581239614), (0.9925094102884998, 7.003249581239614), (1.9950188205770971, 7.003249581239614), (2.997528230865694, 7.003249581239614), (4.000037641154291, 7.003249581239614), (5.002547051442889, 7.003249581239614), (6.005056461731486, 7.003249581239614), (7.007565872020083, 7.003249581239614), (8.01007528230868, 7.003249581239614), (9.012584692597278, 7.003249581239614), (10.015094102885875, 7.003249581239614), (11.017603513174473, 7.003249581239614), (12.020112923463069, 7.003249581239614), (13.022622333751666, 7.003249581239614), (14.025131744040264, 7.003249581239614), (15.027641154328862, 7.003249581239614), (16.030150564617458, 7.003249581239614)}, {(-0.010000000000097327, 5.999899497487505), (0.9925094102884998, 5.999899497487505), (1.9950188205770971, 5.999899497487505), (2.997528230865694, 5.999899497487505), (4.000037641154291, 5.999899497487505), (5.002547051442889, 5.999899497487505), (6.005056461731486, 5.999899497487505), (7.007565872020083, 5.999899497487505), (8.01007528230868, 5.999899497487505), (9.012584692597278, 5.999899497487505), (10.015094102885875, 5.999899497487505), (11.017603513174473, 5.999899497487505), (12.020112923463069, 5.999899497487505), (13.022622333751666, 5.999899497487505), (14.025131744040264, 5.999899497487505), (15.027641154328862, 5.999899497487505), (16.030150564617458, 5.999899497487505)}, {(-0.010000000000097327, 4.996549413735396), (0.9925094102884998, 4.996549413735396), (1.9950188205770971, 4.996549413735396), (2.997528230865694, 4.996549413735396), (4.000037641154291, 4.996549413735396), (5.002547051442889, 4.996549413735396), (6.005056461731486, 4.996549413735396), (7.007565872020083, 4.996549413735396), (8.01007528230868, 4.996549413735396), (9.012584692597278, 4.996549413735396), (10.015094102885875, 4.996549413735396), (11.017603513174473, 4.996549413735396), (12.020112923463069, 4.996549413735396), (13.022622333751666, 4.996549413735396), (14.025131744040264, 4.996549413735396), (15.027641154328862, 4.996549413735396), (16.030150564617458, 4.996549413735396)}, {(-0.010000000000097327, 3.9931993299832875), (0.9925094102884998, 3.9931993299832875), (1.9950188205770971, 3.9931993299832875), (2.997528230865694, 3.9931993299832875), (4.000037641154291, 3.9931993299832875), (5.002547051442889, 3.9931993299832875), (6.005056461731486, 3.9931993299832875), (7.007565872020083, 3.9931993299832875), (8.01007528230868, 3.9931993299832875), (9.012584692597278, 3.9931993299832875), (10.015094102885875, 3.9931993299832875), (11.017603513174473, 3.9931993299832875), (12.020112923463069, 3.9931993299832875), (13.022622333751666, 3.9931993299832875), (14.025131744040264, 3.9931993299832875), (15.027641154328862, 3.9931993299832875), (16.030150564617458, 3.9931993299832875)}, {(-0.010000000000097327, 2.989849246231179), (0.9925094102884998, 2.989849246231179), (1.9950188205770971, 2.989849246231179), (2.997528230865694, 2.989849246231179), (4.000037641154291, 2.989849246231179), (5.002547051442889, 2.989849246231179), (6.005056461731486, 2.989849246231179), (7.007565872020083, 2.989849246231179), (8.01007528230868, 2.989849246231179), (9.012584692597278, 2.989849246231179), (10.015094102885875, 2.989849246231179), (11.017603513174473, 2.989849246231179), (12.020112923463069, 2.989849246231179), (13.022622333751666, 2.989849246231179), (14.025131744040264, 2.989849246231179), (15.027641154328862, 2.989849246231179), (16.030150564617458, 2.989849246231179)}, {(-0.010000000000097327, 1.9864991624790704), (0.9925094102884998, 1.9864991624790704), (1.9950188205770971, 1.9864991624790704), (2.997528230865694, 1.9864991624790704), (4.000037641154291, 1.9864991624790704), (5.002547051442889, 1.9864991624790704), (6.005056461731486, 1.9864991624790704), (7.007565872020083, 1.9864991624790704), (8.01007528230868, 1.9864991624790704), (9.012584692597278, 1.9864991624790704), (10.015094102885875, 1.9864991624790704), (11.017603513174473, 1.9864991624790704), (12.020112923463069, 1.9864991624790704), (13.022622333751666, 1.9864991624790704), (14.025131744040264, 1.9864991624790704), (15.027641154328862, 1.9864991624790704), (16.030150564617458, 1.9864991624790704)}, {(-0.010000000000097327, 0.9831490787269601), (0.9925094102884998, 0.9831490787269601), (1.9950188205770971, 0.9831490787269601), (2.997528230865694, 0.9831490787269601), (4.000037641154291, 0.9831490787269601), (5.002547051442889, 0.9831490787269601), (6.005056461731486, 0.9831490787269601), (7.007565872020083, 0.9831490787269601), (8.01007528230868, 0.9831490787269601), (9.012584692597278, 0.9831490787269601), (10.015094102885875, 0.9831490787269601), (11.017603513174473, 0.9831490787269601), (12.020112923463069, 0.9831490787269601), (13.022622333751666, 0.9831490787269601), (14.025131744040264, 0.9831490787269601), (15.027641154328862, 0.9831490787269601), (16.030150564617458, 0.9831490787269601)}, {(-0.010000000000097327, -0.020201005025148433), (0.9925094102884998, -0.020201005025148433), (1.9950188205770971, -0.020201005025148433), (2.997528230865694, -0.020201005025148433), (4.000037641154291, -0.020201005025148433), (5.002547051442889, -0.020201005025148433), (6.005056461731486, -0.020201005025148433), (7.007565872020083, -0.020201005025148433), (8.01007528230868, -0.020201005025148433), (9.012584692597278, -0.020201005025148433), (10.015094102885875, -0.020201005025148433), (11.017603513174473, -0.020201005025148433), (12.020112923463069, -0.020201005025148433), (13.022622333751666, -0.020201005025148433), (14.025131744040264, -0.020201005025148433), (15.027641154328862, -0.020201005025148433), (16.030150564617458, -0.020201005025148433)}}
  19. Element(randomTyps, Mod[questionCount - 1, Length[randomQuestions]] + 1) → actualRandomTyp
  20. Element(typMinMaxDist, actualRandomTyp) → actualTypMinMaxDist
  21. Sequence(i, i, actualTypMinMaxDist(1), actualTypMinMaxDist(2), actualTypMinMaxDist(3)) → skalaNumbers
  22. Sequence(skalaStart + (0, (Distance[skalaStart, skalaEnd] / (Length[skalaNumbers] - 1) * i)), i, 0, Length[skalaNumbers] - 1) → skalaPoints
  23. RemoveUndefined(Sequence[If[Mod[(skalaNumbers(i) * 10), 10] ≟ 0, skalaPoints(i)], i, 1, Length[skalaPoints]]) → skalaPointsLang
  24. Remove(skalaPoints, Join[{skalaPointsLang, skalaPointsMittel}]) → skalaPointsKurz
  25. Zip(Segment[a - (0.5, 0), a + (0.5, 0)], a, skalaPointsLang) → skalaLinesLang
  26. Zip(Segment[a - (0.4, 0), a + (0.4, 0)], a, skalaPointsMittel) → skalaLinesMittel
  27. Zip(Segment[a - (0.35, 0), a + (0.35, 0)], a, skalaPointsKurz) → skalaLinesKurz
  28. Element(skalaPoints, IndexOf[actualRandomNumber, skalaNumbers]) → thermometerFillingPoint
  29. RemoveUndefined(Sequence[If[Mod[(skalaNumbers(i) * 10), 10] ≟ 0, skalaPoints(i) + (1, 0)], i, 1, Length[skalaPoints]]) → skalaNumbersToShowPoints
  30. RemoveUndefined(Sequence[If[Mod[(skalaNumbers(i) * 10), 10] ≟ 0 ∨ Mod[(skalaNumbers(i) * 10), 5] ≟ 0 ∧ actualRandomTyp ≟ 4, Text["\textsf{\footnotesize{" + (NumberSeparationCommaText[If[sgn(skalaNumbers(i)) ≟ -1, "\(-\)"] + (abs(skalaNumbers(i)))]) + "}}", skalaPoints(i) + (0.85, 0.05), true, true, 0, 0]], i, 1, Length[skalaPoints]]) → skalaNumbersToShowText

AI Drawing Prompt Reference

Draw a thermometer graph with a number line, the number line has negative and positive numbers, the thermometer scale has numbers, the thermometer filling part is filled according to the randomly generated temperature value, the temperature value is marked on the number line at the corresponding position, the thermometer scale has numbers, the thermometer filling part is filled according to the randomly generated temperature value, the temperature value is marked on the number line at the corresponding position, the thermometer scale has numbers, the thermometer filling part is filled according to the randomly generated temperature value, the temperature value is marked on the number line at the corresponding position.
The prompt above was compiled from the original drawing commands and is for reference only.