Magic Digit Sum: Divisibility by 3 and Finding Extremes

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2024-01-23 15:03

In collections Teilbarkeitsregeln

This GeoGebra example uses an interactive, question-driven setup to help students explore the relationship between a number’s digit sum and its divisibility by 3 (e.g., analyzing given numbers like 621 and 702561, deciding which numbers are divisible by 3, explaining the correct “divisibility by 3” condition, and asking for the smallest/largest three-digit numbers that are divisible by 3). Key math concepts include the definition of digit sum, the divisibility rule for 3 (an integer is divisible by 3 iff its digit sum is divisible by 3), reasoning with necessary-and-sufficient conditions, and simple optimization within the three-digit range. Construction/interaction is supported by GeoGebra tools reflected in the construction summary: Textfield/InputBox objects for student input, SpeechBubbleRight for guided explanations, Circle/Polygon (Vieleck) as visual elements for the learning interface, Shuffle for randomizing steps/choices, Mod for the modular arithmetic check of divisibility, SelectedIndex for multiple-choice selection, and step/StepAnzeige plus buttons (btnStart/btnCont/btnAgain/btnBack/btnSol/DevReset/DevSol) to manage the walkthrough and feedback. Suitable for grades ~5–6 and classroom practice focused on number sense, factors/multiples, and conceptual justification.

GeoGebra Commands & Parameters

Textfield(input1) → InputBox1
Textfield(input2) → InputBox2
Textfield(input3) → InputBox3
Textfield(input4) → InputBox4
SpeechBubbleRight(C, 8, 2) → Vieleck1
SpeechBubbleRight(A, 8, 2) → Vieleck2
Text(Text4, ZMBesch, false, true, 0, 0) → ZMBeschAction
Circle(B, 1) → WandCheckCirc
Corner(Bild1, 4) → WandCheckPos
SelectedIndex(DropDown) → Index1
Polygon(D, F, I, H, J, E, G) → Vieleck3, d, f, i, h, j, e, g
SpeechBubbleRight(M, 10, 2.2) → Vieleck4
Shuffle(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 Drawing Prompt Reference

Create an interactive learning interface with input boxes for students to enter numbers, right-side speech bubbles explaining the relationship between digit sums and divisibility by 3, use circles and hexagons to visualize example numbers, randomly display multiple three-digit numbers and all three-digit numbers (excluding multiples of 3), and use buttons to control steps. Show the units digit on the left and the modulo 10 result on the right to verify the divisibility rule for 3.

The prompt above was compiled from the original drawing commands and is for reference only.