小数与分数转换练习：利用GeoGebra进行直观演示

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2023-05-09 19:41

所属专题 Wiederholung II: Erweitern & Kürzen, Darstellungsarten Bruchzahlen in endliche Dezimalzahlen umrechnen

本范例通过GeoGebra工具，帮助学生理解小数与分数之间的转换关系。核心数学概念包括分数与小数的对应、十进制位值表的应用以及错误分析。作图要点涉及使用Shuffle、Element、SpeechBubbleLeft等GeoGebra命令构建动态问题，并利用十进制位值表进行可视化展示。该内容适合小学5-6年级学生，用于培养数感与有理数运算能力。

GeoGebra 命令及参数

Shuffle(Sequence[Random[10, 999], i, 1, 100]) → randomZaehler, {478, 706, 743, 347, 484, 537, 589, 315, 994, 267, 716, 751, 428, 951, 36, 471, 197, 305, 26, 618, 609, 459, 896, 867, 396, 593, 518, 347, 229, 907, 922, 562, 784, 142, 895, 828, 427, 907, 287, 953, 872, 735, 673, 283, 237, 108, 665, 956, 693, 615, 908, 258, 579, 811, 626, 246, 109, 20, 932, 780, 927, 843, 881, 343, 693, 298, 16, 209, 705, 815, 230, 100, 420, 150, 88, 102, 897, 886, 896, 804, 355, 89, 516, 27, 468, 506, 828, 316, 536, 994, 837, 328, 628, 54, 602, 761, 842, 689, 189, 473}
Element(randomZaehler, Mod[questionCount, 100] + 1) → zaehlerZehn
Shuffle(Sequence[Random[10, 99], i, 1, 100]) → randomZaehler2, {14, 70, 81, 57, 91, 37, 19, 56, 15, 42, 21, 70, 77, 19, 37, 93, 81, 38, 74, 87, 45, 14, 29, 50, 95, 55, 35, 67, 33, 89, 80, 54, 44, 30, 40, 50, 75, 10, 78, 86, 16, 11, 82, 14, 39, 41, 35, 50, 50, 54, 60, 31, 80, 22, 19, 62, 51, 35, 10, 90, 75, 60, 65, 41, 64, 26, 46, 32, 75, 89, 79, 47, 29, 26, 36, 30, 70, 14, 87, 54, 43, 73, 34, 30, 30, 37, 34, 49, 47, 94, 81, 44, 32, 94, 15, 22, 85, 67, 78, 19}
Element(randomZaehler2, Mod[questionCount, 100] + 1) → zaehlerHundert
SpeechBubbleLeft(Bubble, BubbleLength(move), BubbleHeight(move)) → bubbleTrixi
If(Mod[questionCount, 2] ≟ 0, If[Mod[zaehlerZehn, 10] ≟ 0, zaehlerZehn + 4, zaehlerZehn], If[Mod[zaehlerHundert, 10] ≟ 0, zaehlerHundert + 4, zaehlerHundert]) → zaehler
If(zaehler < 10, zaehler, If[zaehler < 100, floor(zaehler / 10), If[zaehler < 1000, floor(zaehler / 100)]]) → stelle1
If(zaehler < 100, Mod[zaehler, 10], If[zaehler < 1000, Mod[floor(zaehler / 10), 10]]) → stelle2
If(zaehler ≥ 100, Mod[floor(zaehler), 10]) → stelle3