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Snail Race: Opposites & Absolute Value (Fraction Input)

Snail Race: Opposites & Absolute Value (Fraction Input)
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2024-12-16 19:46
In collections Gegenzahl und Betrag einer rationalen Zahl
This GeoGebra example uses a “snail race” animation on the number line to help students compare and interpret absolute value as distance from 0, and to connect it with opposites (additive inverses). The key math ideas are absolute value (|a| as the distance from a to 0), the symmetry of opposites about 0, and the fact that opposite numbers share the same absolute value. Construction and interactio

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[i, i, 1, 30]) → ind, {9, 6, 30, 2, 22, 27, 1, 12, 29, 19, 24, 4, 7, 17, 3, 20, 16, 8, 18, 26, 13, 5, 21, 15, 23, 25, 10, 14, 11, 28}
  2. Shuffle(Sequence[Shuffle[1…10], i, 1, 100]) → inds, {{7, 10, 9, 1, 3, 5, 2, 8, 6, 4}, {7, 5, 1, 8, 2, 10, 6, 9, 3, 4}, {4, 7, 8, 9, 1, 3, 5, 10, 6, 2}, {3, 6, 5, 7, 1, 10, 9, 8, 4, 2}, {3, 8, 2, 4, 7, 10, 1, 6, 9, 5}, {3, 4, 2, 9, 8, 6, 10, 1, 5, 7}, {2, 3, 10, 8, 1, 7, 5, 6, 4, 9}, {6, 10, 3, 1, 7, 5, 2, 9, 8, 4}, {2, 10, 9, 7, 1, 3, 6, 8, 5, 4}, {7, 4, 2, 8, 9, 6, 5, 10, 3, 1}, {4, 10, 5, 9, 8, 3, 7, 2, 1, 6}, {3, 5, 10, 1, 9, 4, 2, 8, 6, 7}, {9, 5, 3, 10, 8, 6, 7, 1, 2, 4}, {10, 7, 8, 6, 2, 9, 4, 3, 1, 5}, {3, 1, 2, 7, 6, 4, 9, 8, 10, 5}, {3, 9, 7, 1, 8, 6, 10, 5, 2, 4}, {2, 5, 10, 1, 7, 8, 9, 6, 4, 3}, {9, 6, 7, 10, 3, 1, 2, 8, 4, 5}, {1, 7, 9, 5, 4, 6, 2, 3, 10, 8}, {6, 8, 10, 4, 7, 5, 1, 2, 3, 9}, {2, 4, 1, 9, 5, 7, 8, 3, 6, 10}, {4, 5, 1, 10, 8, 3, 6, 7, 2, 9}, {9, 3, 2, 8, 4, 1, 5, 6, 7, 10}, {8, 9, 1, 6, 10, 4, 5, 2, 7, 3}, {9, 7, 6, 1, 4, 2, 8, 5, 10, 3}, {8, 2, 7, 9, 3, 10, 5, 1, 4, 6}, {9, 1, 2, 6, 10, 4, 8, 3, 7, 5}, {5, 1, 6, 7, 3, 2, 10, 8, 4, 9}, {9, 8, 7, 1, 6, 3, 10, 5, 4, 2}, {2, 6, 1, 4, 9, 7, 5, 3, 8, 10}, {3, 4, 6, 5, 7, 10, 8, 9, 2, 1}, {2, 9, 8, 4, 1, 3, 10, 6, 7, 5}, {10, 7, 2, 5, 8, 4, 9, 1, 3, 6}, {10, 7, 6, 2, 8, 9, 1, 5, 4, 3}, {10, 8, 6, 1, 3, 4, 2, 7, 9, 5}, {9, 5, 1, 4, 7, 8, 6, 2, 10, 3}, {9, 10, 8, 6, 5, 4, 1, 3, 2, 7}, {1, 10, 7, 3, 4, 6, 5, 8, 2, 9}, {8, 1, 2, 10, 9, 6, 4, 7, 5, 3}, {10, 2, 1, 7, 5, 8, 3, 6, 9, 4}, {8, 3, 7, 6, 10, 2, 5, 1, 9, 4}, {6, 5, 1, 4, 10, 2, 3, 7, 9, 8}, {6, 1, 8, 5, 3, 10, 9, 4, 7, 2}, {6, 7, 9, 2, 3, 8, 4, 10, 1, 5}, {3, 7, 10, 1, 8, 9, 4, 5, 6, 2}, {1, 7, 10, 2, 9, 4, 5, 8, 6, 3}, {9, 5, 7, 4, 10, 1, 8, 6, 3, 2}, {9, 8, 4, 10, 6, 3, 5, 2, 7, 1}, {9, 10, 2, 4, 3, 5, 6, 1, 8, 7}, {4, 2, 1, 6, 10, 3, 7, 5, 8, 9}, {8, 6, 3, 1, 9, 2, 4, 5, 7, 10}, {9, 4, 1, 8, 2, 10, 6, 7, 5, 3}, {9, 8, 6, 7, 10, 5, 3, 2, 4, 1}, {7, 4, 6, 3, 10, 2, 1, 5, 8, 9}, {6, 8, 9, 10, 7, 2, 5, 1, 3, 4}, {6, 3, 4, 7, 2, 9, 10, 8, 5, 1}, {1, 2, 4, 5, 6, 3, 9, 8, 10, 7}, {6, 7, 5, 8, 3, 1, 4, 10, 2, 9}, {4, 1, 8, 2, 5, 6, 9, 7, 10, 3}, {8, 3, 7, 5, 4, 10, 6, 2, 9, 1}, {4, 7, 8, 6, 10, 9, 3, 2, 1, 5}, {9, 5, 2, 3, 10, 1, 8, 6, 4, 7}, {7, 3, 8, 4, 10, 2, 1, 9, 6, 5}, {5, 4, 10, 7, 8, 1, 2, 9, 3, 6}, {2, 8, 10, 5, 9, 7, 3, 4, 1, 6}, {5, 10, 9, 4, 3, 6, 1, 2, 7, 8}, {7, 3, 9, 6, 1, 8, 2, 5, 10, 4}, {8, 10, 3, 2, 7, 9, 5, 6, 1, 4}, {4, 5, 2, 1, 6, 10, 9, 3, 8, 7}, {8, 5, 2, 4, 3, 7, 1, 10, 9, 6}, {1, 5, 6, 4, 10, 3, 9, 7, 2, 8}, {9, 5, 3, 10, 1, 6, 7, 8, 2, 4}, {4, 5, 8, 6, 1, 2, 3, 10, 7, 9}, {10, 9, 5, 3, 2, 8, 6, 4, 7, 1}, {3, 6, 8, 4, 5, 10, 2, 7, 1, 9}, {3, 6, 2, 1, 9, 4, 7, 10, 5, 8}, {2, 3, 4, 8, 5, 1, 10, 7, 9, 6}, {6, 2, 5, 9, 10, 1, 4, 3, 7, 8}, {6, 1, 7, 4, 10, 3, 2, 5, 8, 9}, {5, 1, 3, 4, 6, 8, 2, 7, 10, 9}, {5, 4, 8, 6, 2, 9, 10, 7, 3, 1}, {8, 5, 3, 9, 7, 10, 1, 2, 6, 4}, {1, 6, 10, 5, 7, 8, 9, 2, 3, 4}, {6, 2, 3, 1, 5, 10, 9, 8, 7, 4}, {5, 8, 10, 2, 9, 6, 4, 3, 7, 1}, {2, 10, 5, 6, 9, 8, 4, 1, 3, 7}, {6, 2, 1, 7, 8, 10, 3, 5, 9, 4}, {10, 2, 4, 8, 7, 3, 5, 6, 9, 1}, {8, 3, 1, 7, 9, 2, 10, 5, 6, 4}, {7, 9, 10, 2, 6, 5, 8, 4, 1, 3}, {5, 7, 6, 1, 9, 8, 3, 10, 4, 2}, {7, 5, 10, 2, 9, 3, 4, 1, 8, 6}, {9, 6, 7, 8, 4, 1, 2, 5, 10, 3}, {1, 10, 3, 6, 2, 4, 7, 9, 5, 8}, {6, 5, 8, 3, 10, 2, 4, 9, 1, 7}, {8, 4, 10, 7, 9, 5, 2, 1, 6, 3}, {1, 5, 7, 2, 9, 6, 4, 8, 3, 10}, {4, 8, 7, 2, 3, 1, 6, 9, 5, 10}, {8, 1, 6, 5, 10, 2, 9, 7, 4, 3}, {5, 9, 8, 3, 1, 4, 7, 6, 10, 2}}
  3. Textfield(studAns) → InputBox1
  4. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNose4, {6, 10, 2, 10, 6, 3, 2, 6, 7, 3, 8, 3, 8, 2, 2, 8, 9, 7, 7, 3, 8, 2, 5, 10, 2, 2, 9, 6, 2, 8, 10, 8, 8, 2, 7, 7, 4, 2, 10, 5, 7, 3, 9, 3, 8, 8, 2, 9, 4, 3, 2, 6, 2, 9, 8, 2, 6, 8, 8, 9, 8, 4, 7, 8, 6, 5, 9, 6, 7, 3, 7, 7, 8, 4, 10, 4, 10, 8, 6, 10, 7, 9, 10, 4, 10, 6, 5, 4, 6, 10, 3, 10, 3, 10, 9, 6, 4, 10, 5, 6}
  5. Element(randomNose4, Mod[count, 100] + 1) → e4
  6. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosc2, {9, 9, 2, 8, 9, 9, 5, 5, 4, 7, 3, 3, 9, 8, 3, 10, 8, 7, 8, 10, 7, 5, 8, 8, 9, 2, 8, 9, 5, 10, 3, 7, 8, 2, 10, 8, 9, 4, 7, 2, 9, 9, 3, 10, 2, 9, 8, 3, 2, 5, 7, 6, 2, 5, 2, 8, 7, 7, 3, 7, 7, 5, 5, 4, 7, 3, 9, 3, 9, 3, 7, 9, 5, 9, 10, 3, 5, 2, 6, 7, 10, 7, 8, 2, 8, 9, 7, 7, 7, 5, 7, 9, 9, 8, 3, 7, 9, 8, 3, 2}
  7. Element(randomNosc2, Mod[count, 100] + 1) → c2
  8. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosc1, {8, 8, 3, 8, 5, 10, 7, 9, 3, 7, 10, 9, 4, 9, 4, 4, 8, 3, 9, 4, 3, 7, 8, 6, 9, 2, 5, 9, 4, 5, 9, 4, 3, 2, 5, 3, 2, 2, 6, 9, 2, 6, 7, 5, 9, 8, 7, 3, 2, 10, 5, 10, 8, 2, 6, 9, 2, 3, 6, 4, 9, 7, 9, 4, 8, 5, 5, 9, 3, 7, 9, 6, 6, 8, 4, 10, 10, 10, 7, 10, 6, 8, 8, 7, 10, 3, 2, 4, 9, 3, 3, 6, 7, 3, 10, 7, 10, 5, 6, 6}
  9. Element(randomNosc1, Mod[count, 100] + 1) → c1
  10. Shuffle(Sequence[Random[9, 30], i, 1, 100]) → randomNose2, {20, 26, 26, 23, 12, 28, 16, 26, 23, 26, 18, 16, 15, 28, 25, 22, 24, 14, 16, 27, 13, 21, 25, 25, 9, 12, 28, 9, 12, 14, 10, 27, 28, 9, 20, 26, 14, 16, 10, 23, 11, 25, 9, 14, 12, 17, 11, 27, 22, 29, 27, 9, 14, 15, 26, 23, 14, 15, 13, 23, 27, 28, 27, 27, 10, 21, 29, 21, 24, 19, 12, 23, 13, 27, 21, 28, 9, 16, 15, 18, 13, 13, 28, 16, 10, 19, 19, 9, 12, 23, 30, 17, 27, 19, 18, 25, 11, 19, 13, 12}
  11. Element(randomNose2, Mod[count, 100] + 1) → e2
  12. Shuffle(Sequence[Random[20, 50], i, 1, 100]) → randomNosa2, {45, 43, 21, 38, 47, 23, 45, 34, 23, 49, 22, 33, 28, 29, 36, 30, 49, 42, 47, 24, 22, 38, 28, 41, 31, 40, 25, 37, 38, 22, 35, 50, 23, 44, 21, 33, 34, 50, 45, 44, 44, 22, 29, 42, 44, 27, 32, 35, 49, 24, 23, 30, 32, 27, 29, 38, 20, 29, 41, 47, 28, 43, 46, 34, 28, 40, 30, 28, 37, 20, 44, 44, 37, 37, 43, 25, 31, 30, 29, 34, 45, 49, 21, 29, 35, 48, 28, 35, 38, 44, 42, 28, 46, 32, 21, 24, 31, 24, 27, 23}
  13. Element(randomNosa2, Mod[count, 100] + 1) → a2
  14. Shuffle(Sequence[Random[2, 30], i, 1, 100]) → randomNosa1, {15, 27, 15, 19, 13, 24, 17, 28, 29, 18, 6, 4, 29, 13, 10, 18, 29, 4, 14, 7, 24, 15, 26, 30, 8, 12, 25, 22, 16, 27, 17, 4, 28, 29, 12, 4, 16, 5, 14, 5, 25, 30, 21, 9, 25, 8, 28, 18, 6, 18, 13, 20, 2, 2, 10, 23, 17, 4, 25, 19, 17, 7, 12, 23, 30, 2, 23, 3, 6, 8, 21, 24, 26, 2, 16, 9, 11, 25, 9, 30, 19, 9, 19, 21, 28, 26, 18, 14, 8, 5, 24, 27, 29, 29, 16, 8, 5, 19, 23, 8}
  15. Element(randomNosa1, Mod[count, 100] + 1) → a1
  16. Shuffle(Sequence[Random[10, 40], i, 1, 100]) → randomNosb2, {14, 30, 19, 18, 34, 31, 16, 40, 25, 40, 32, 12, 29, 15, 17, 15, 21, 12, 25, 31, 22, 17, 39, 21, 17, 11, 28, 22, 36, 26, 30, 27, 18, 13, 36, 16, 36, 21, 17, 10, 37, 15, 32, 11, 11, 22, 32, 38, 27, 19, 10, 23, 29, 12, 29, 33, 34, 22, 33, 30, 37, 18, 36, 16, 21, 32, 33, 38, 34, 40, 14, 10, 34, 33, 12, 21, 38, 40, 31, 18, 17, 17, 25, 11, 27, 29, 37, 39, 10, 37, 24, 13, 18, 14, 37, 23, 32, 25, 26, 11}
  17. Element(randomNosb2, Mod[count, 100] + 1) → b2
  18. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosd2, {9, 5, 4, 3, 3, 8, 2, 4, 9, 5, 7, 5, 3, 5, 10, 4, 6, 10, 5, 10, 5, 6, 4, 9, 2, 10, 5, 2, 6, 8, 9, 2, 5, 4, 8, 10, 4, 8, 3, 7, 9, 2, 6, 7, 10, 5, 3, 6, 8, 10, 7, 2, 2, 8, 4, 8, 3, 7, 5, 10, 7, 6, 2, 9, 8, 3, 9, 5, 3, 9, 6, 4, 3, 7, 6, 5, 4, 4, 4, 2, 10, 6, 10, 4, 9, 8, 8, 4, 4, 8, 8, 8, 5, 4, 6, 5, 9, 4, 6, 8}
  19. Element(randomNosd2, Mod[count, 100] + 1) → d2
  20. Element(calcTexts, Element[ind, step]) → text5
  21. Shuffle(Sequence[i, i, -100, 100]) → NumListGanzeHelper, {62, -78, -22, -9, -23, 30, 98, 65, -38, -43, 76, -3, -73, 15, 5, 58, 50, 96, 47, 12, -53, 17, 35, -81, -77, -72, 60, -57, -84, -98, 74, 13, 79, 86, 77, -67, -51, 70, 66, 11, 7, 89, -94, -70, 2, -12, -31, 1, 38, 95, 20, -92, 52, -34, -19, 26, -64, -39, 92, -6, 3, 67, -8, -36, 32, 97, 53, 55, 24, 8, 93, -21, 39, -18, 56, 100, -17, 71, 88, 14, 82, 27, 0, -63, -96, 33, 75, 81, -83, -5, 59, 23, -44, 34, 44, -11, -48, -85, -60, -93, 57, -26, 94, 37, -59, 99, 9, -90, -27, 69, 64, 40, -46, -76, -62, -29, -68, 28, 48, -20, 22, 10, -25, -10, 29, -89, 83, 4, -35, -66, 90, -1, -50, 91, -33, 73, -61, 46, -74, -97, -58, -87, 16, 54, -49, -79, 68, -45, 19, 41, -91, -30, -7, -32, -100, 43, 85, 49, -86, -15, -24, -52, -99, -13, -80, -41, 61, -40, -42, 80, 6, -37, -71, -56, 72, -16, 63, 36, -95, 31, 45, -88, -4, 51, 42, -65, -28, -47, 87, -14, -75, 78, 18, 21, -2, -54, 84, -55, -69, -82, 25}
  22. Shuffle(Sequence[i, i, -200, 200]) → NumListDeziRaw, {-81, -62, 87, -166, -167, -199, -11, -170, -155, 136, 98, -193, -29, -52, -106, 7, -63, -59, -85, -79, 187, 92, -127, 112, -7, 125, 40, -111, 61, 100, 70, -53, 199, -74, -34, -108, 130, 60, -2, 86, 68, -131, -28, -132, -77, 54, 44, 161, -98, -41, 140, 165, -101, 118, 186, 114, -118, -114, 52, 147, 89, -130, -20, 191, 117, -136, -21, 11, -92, 106, 64, -146, -30, 26, -135, 195, 184, -187, -70, -24, 16, -33, 139, -185, 4, 155, -160, -178, 200, 3, -163, -44, -18, 143, -35, 0, 171, 55, 23, -188, 99, 113, -12, 12, 28, 39, 145, 173, -186, 76, 14, -75, -67, -99, -173, -76, -57, -142, -88, -68, 38, 167, 153, -8, -78, 95, 58, -91, -138, 72, 24, 120, 158, -174, -45, -158, -93, 20, 148, -89, -100, 128, 93, -112, -161, 75, -73, -154, 25, -46, -65, 53, 168, 81, -102, 36, -171, -86, 19, 32, -175, -180, 193, 80, 176, 65, 194, -192, 178, -129, 48, -22, 15, 110, 49, -103, -37, -14, 34, -122, 69, -97, 133, 41, 127, -9, 188, 159, -80, -168, -64, 142, 22, -116, 189, 122, -164, -176, -151, -156, -50, 183, -124, -23, -182, -84, -143, -147, -144, 157, 50, 56, -119, -172, -195, 198, 182, -179, -10, 29, -69, 88, 131, 169, 47, -83, -54, 149, -58, 105, 8, -196, -25, -55, -60, 123, 192, -191, 162, 79, 177, -26, 57, 84, -197, -17, -183, 37, -115, -16, -27, 180, -133, 115, -107, 144, -32, -123, 163, -189, -134, -87, 1, 107, 172, -94, -3, 59, -169, -49, 74, 30, 151, 31, -90, 63, 102, -51, -126, 175, 154, 135, 91, 82, -71, 33, 42, -39, 35, 13, -105, 137, -198, -139, 166, -128, 116, -96, -109, 108, 85, -141, -150, -148, -72, 197, 185, 134, 51, 45, 66, 196, 83, 5, -82, -152, 164, -36, 156, -13, 94, -165, -4, -1, 43, 146, 109, -184, -149, -42, -56, 27, -153, 10, -104, 174, 141, -121, -110, -137, 78, -47, -95, -40, 9, -145, 67, 179, -194, 103, -61, -177, -120, -190, -48, -38, 46, 170, -31, -181, -113, 77, -200, 97, -140, 124, 2, 138, 62, 152, 96, 111, 150, 121, 181, -157, 101, -125, 132, -5, 17, -162, 6, 21, -66, -43, -6, 71, -15, 73, 190, -19, 160, -117, 126, 104, 90, 18, 129, 119, -159}
  23. Shuffle({2, 3, 4, 5, 6, 8, 10}) → NumListFracNenner, {2, 5, 4, 10, 6, 8, 3}
  24. Shuffle(Sequence[i, i, Max[1, (-2 * nenner)], (2 * nenner)]) → NumListFracZaehler, {3, 2, 4, 1}
  25. Shuffle({1, 2, 3}) → NumListMod, {1, 3, 2}
  26. If(mod ≟ 1, NumListGanze(1), mod ≟ 2, NumListDezi(1), mod ≟ 3, NumListFracZaehler(1) / NumListFracNenner(1)) → xvalue
  27. Shuffle({1, 2}) → ExStyleList, {1, 2}
  28. Text(InputBox1) → InputText
  29. TextToUnicode(InputText) → InputUnicode
  30. Segment((0, 0.7), (40, 0.7)) → f
  31. Segment((0, -9.3), (40, -9.3)) → g
  32. Polygon(E, F, G, H) → v1, e, f_1, g_1, h
  33. OrthogonalLine(A_1, xAxis) → i
  34. Sequence(Translate[Element[salat1, i], Vector[SalatPos1 + ((i - 1) * (dxFolge, 0))]], i, 1, 3) → showSalat1
  35. Sequence(Translate[Element[salat2, i], Vector[SalatPos2 + ((i - 1) * (dxFolge, 0))]], i, 1, 3) → showSalat2
  36. Sequence(Translate[Element[salat3, i], Vector[SalatPos3 + ((i - 1) * (dxFolge, 0))]], i, 1, 3) → showSalat3
  37. If(turboschnecke, (1 / 3 * 0.7), regenbogenschnecke, (1 / 6 * 0.8), (1 / 6 * 0.6)) → speed2
  38. Defined(studAns) → fixed
  39. Text(MasterAngabeHelper, MasterAngabePos, false, true, -1, 0) → Text1