魔法数位和:用3的整除规则判断与最值
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所属专题
Teilbarkeitsregeln
该范例通过交互式题目让学生观察并验证“数位和”与“3的整除性”之间的关系(如给定数字621、702561等判断能否被3整除,并回答关于整除条件与最小/最大三位数)。核心数学概念包括:数位和定义、3的整除规则(一个整数可被3整除当且仅当其各位数字之和可被3整除)、整除的充分必要条件、三位数范围内的最值搜索(如最小/最大三位数中满足可被3整除的数)。作图与交互要点来自构造摘要所示的组件:使用Textfield与InputBox等用于输入数字/文本,SpeechBubbleRight用于提示与叙述,Circle与Polygon(以及Vieleck1/2)用于视觉元素或“魔法”效果的几何呈现,利用Shuffle打乱或随机化步骤/选项,并用Mod实现“取模判断”(对应整除性验证),同时通过SelectedIndex控制选择题答案、StepAnzeige/step与按钮btnStart/btnCont/btnAgain/btnBack/btnSol/DevReset/DevSol进行分步流程与反馈。适合5-6学段(小学中高年级到初中衔接)用于数感与整除规则的探究、练习与课堂互动。
GeoGebra 命令及参数
Textfield(input1) → InputBox1Textfield(input2) → InputBox2Textfield(input3) → InputBox3Textfield(input4) → InputBox4SpeechBubbleRight(C, 8, 2) → Vieleck1SpeechBubbleRight(A, 8, 2) → Vieleck2Text(Text4, ZMBesch, false, true, 0, 0) → ZMBeschActionCircle(B, 1) → WandCheckCircCorner(Bild1, 4) → WandCheckPosSelectedIndex(DropDown) → Index1Polygon(D, F, I, H, J, E, G) → Vieleck3, d, f, i, h, j, e, gSpeechBubbleRight(M, 10, 2.2) → Vieleck4Shuffle(Sequence[(3 * i), i, 34, 333]) → NumList3, {453, 789, 480, 522, 636, 369, 792, 372, 141, 675, 426, 531, 144, 921, 798, 879, 666, 891, 795, 777, 729, 861, 918, 969, 711, 840, 276, 612, 909, 957, 639, 462, 642, 831, 768, 255, 537, 477, 813, 483, 111, 174, 306, 684, 360, 705, 441, 567, 210, 723, 168, 108, 321, 576, 726, 201, 474, 546, 123, 423, 429, 825, 699, 837, 645, 993, 741, 189, 399, 534, 402, 447, 759, 774, 591, 207, 924, 183, 258, 810, 336, 990, 618, 930, 594, 816, 621, 540, 390, 147, 363, 915, 654, 573, 681, 864, 312, 165, 606, 153, 120, 561, 162, 270, 237, 315, 117, 261, 732, 996, 222, 603, 597, 240, 678, 933, 657, 936, 564, 345, 159, 351, 663, 852, 585, 888, 948, 150, 267, 822, 408, 738, 282, 951, 519, 414, 420, 771, 285, 195, 204, 651, 393, 579, 945, 807, 702, 843, 132, 177, 318, 225, 783, 858, 975, 753, 279, 288, 906, 243, 555, 291, 972, 468, 396, 327, 246, 885, 903, 357, 264, 960, 489, 231, 375, 804, 432, 801, 342, 465, 747, 693, 750, 834, 138, 954, 252, 672, 513, 939, 942, 381, 330, 366, 894, 615, 999, 249, 630, 384, 105, 228, 456, 648, 498, 696, 339, 765, 495, 627, 324, 411, 786, 216, 438, 114, 171, 720, 444, 744, 717, 213, 558, 870, 300, 192, 978, 297, 450, 180, 273, 333, 528, 819, 762, 303, 234, 471, 435, 600, 624, 876, 348, 387, 609, 897, 669, 516, 708, 417, 633, 102, 780, 156, 714, 966, 984, 846, 507, 504, 867, 525, 309, 873, 405, 552, 126, 510, 981, 660, 963, 378, 927, 900, 135, 219, 198, 501, 756, 828, 882, 588, 912, 987, 582, 492, 543, 849, 570, 690, 129, 549, 294, 687, 486, 855, 186, 354, 735, 459}Shuffle(Sequence[i, i, 100, 999] \ Sequence[(3 * i), i, 34, 333] \ {num1, num2}) → NumListAll, {938, 166, 970, 910, 364, 410, 211, 160, 877, 697, 187, 683, 158, 359, 919, 598, 301, 566, 229, 443, 895, 263, 373, 182, 145, 283, 620, 148, 698, 845, 922, 647, 475, 457, 460, 328, 466, 860, 292, 959, 529, 425, 347, 296, 601, 631, 640, 304, 463, 713, 281, 136, 448, 878, 340, 758, 911, 133, 485, 958, 130, 908, 299, 502, 808, 272, 661, 140, 250, 983, 169, 743, 893, 214, 883, 215, 230, 896, 676, 694, 295, 310, 724, 452, 412, 265, 481, 509, 322, 115, 998, 184, 143, 728, 490, 439, 673, 701, 391, 595, 862, 940, 200, 695, 854, 260, 154, 920, 652, 385, 286, 161, 421, 454, 946, 829, 499, 269, 635, 905, 505, 830, 874, 716, 262, 458, 925, 164, 974, 208, 752, 274, 599, 611, 370, 221, 527, 722, 142, 575, 568, 559, 268, 634, 188, 613, 551, 167, 838, 436, 731, 857, 125, 103, 497, 823, 137, 491, 557, 641, 926, 955, 293, 655, 901, 757, 404, 449, 191, 532, 118, 149, 307, 844, 769, 989, 617, 899, 302, 770, 688, 610, 446, 628, 389, 464, 430, 887, 176, 256, 442, 704, 514, 764, 971, 839, 193, 799, 247, 733, 592, 943, 257, 850, 239, 766, 100, 671, 226, 994, 712, 244, 539, 238, 338, 740, 931, 607, 512, 335, 484, 988, 664, 362, 538, 650, 275, 800, 178, 523, 608, 785, 467, 419, 112, 767, 541, 356, 227, 668, 209, 977, 907, 545, 349, 500, 106, 242, 107, 805, 478, 175, 194, 508, 787, 596, 334, 964, 245, 950, 196, 842, 235, 400, 706, 346, 190, 637, 763, 146, 572, 376, 802, 773, 305, 152, 488, 437, 319, 524, 542, 113, 325, 692, 550, 734, 686, 736, 826, 418, 917, 517, 401, 760, 560, 121, 721, 205, 719, 179, 962, 433, 323, 847, 544, 518, 353, 109, 254, 548, 869, 271, 413, 406, 589, 649, 866, 479, 629, 473, 935, 586, 101, 202, 929, 217, 680, 685, 332, 482, 932, 818, 110, 530, 875, 416, 185, 415, 748, 224, 266, 952, 707, 791, 781, 422, 428, 737, 569, 682, 739, 503, 233, 944, 587, 197, 368, 172, 749, 341, 965, 775, 367, 520, 131, 313, 622, 916, 863, 811, 656, 836, 427, 344, 253, 571, 806, 331, 223, 751, 700, 155, 623, 403, 980, 496, 365, 644, 506, 827, 881, 157, 995, 371, 902, 440, 424, 982, 116, 259, 251, 536, 565, 746, 151, 646, 554, 784, 824, 754, 848, 643, 212, 653, 181, 703, 812, 890, 526, 689, 817, 832, 632, 383, 884, 638, 772, 515, 392, 865, 434, 809, 803, 892, 409, 941, 455, 937, 914, 521, 973, 379, 562, 853, 820, 851, 662, 139, 290, 761, 394, 614, 326, 619, 923, 241, 583, 535, 374, 104, 898, 715, 593, 710, 472, 382, 380, 361, 779, 343, 337, 976, 997, 277, 880, 352, 793, 563, 388, 287, 616, 992, 470, 461, 320, 487, 377, 355, 913, 284, 494, 358, 961, 991, 605, 979, 398, 727, 967, 248, 778, 886, 871, 986, 236, 667, 604, 794, 289, 218, 782, 206, 122, 329, 574, 511, 553, 386, 580, 602, 556, 985, 451, 745, 311, 859, 625, 755, 308, 776, 658, 889, 407, 232, 493, 856, 670, 547, 947, 679, 127, 278, 835, 815, 317, 280, 395, 445, 170, 578, 709, 626, 953, 821, 163, 841, 314, 796, 476, 134, 725, 797, 833, 469, 203, 590, 581, 949, 674, 124, 934, 742, 677, 220, 904, 968, 298, 173, 577, 665, 718, 659, 868, 128, 928, 956, 316, 533, 730, 199, 584, 872, 350, 397, 790, 814, 119, 431, 788, 691}Mod(num1, 10) → num1stelle3
AI 绘图提示语参考
画一个交互式学习界面,包含输入框供学生输入数字,右侧有气泡解释数字之和与被3整除的关系,用圆形和六边形可视化示例数字,随机展示多个三位数和所有三位数(排除3的倍数),并用按钮控制步骤。左侧显示数字的个位数,右侧显示该位数的模10结果,用于验证被3整除的规则。
以上提示语为根据原始绘图命令整理而来,仅供参考。