Ablesen am Thermometer：有理数比较与数轴表示的GeoGebra教学范例

GeoGebra 命令及参数

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