Translating and Solving Real World Inequalities

GeoGebra Commands & Parameters

1. RandomUniform(0, 0.99, 200) → randomSeeds, {0.1933807215627835, 0.3352350439088757, 0.3996118869507219, 0.9055625315825535, 0.5149329054228933, 0.5417824956459422, 0.6738126136561027, 0.11488322313667132, 0.4381145062699758, 0.5222062853409966, 0.799473896948029, 0.7937120952592864, 0.6438007415395809, 0.7359783480420136, 0.19959335507281448, 0.06005889727229728, 0.7040324517285408, 0.1463230487641336, 0.4877489075898688, 0.8133295061757913, 0.5720039897146674, 0.7879888015281103, 0.7750319300394097, 0.1817796435312211, 0.2521925206973072, 0.5428707209911793, 0.39004745716623646, 0.12364429047509364, 0.3656668609447359, 0.5185193895951876, 0.4005101644108796, 0.2010547769225625, 0.32470493649710364, 0.004209625798677974, 0.9720253341385244, 0.292213200207954, 0.4533784161397043, 0.5598190787908002, 0.49514258960224306, 0.37958891770098396, 0.03673016644963624, 0.3042802307043042, 0.6957044365777845, 0.8801339295209042, 0.3905741086655004, 0.19282078172665384, 0.7058865319325252, 0.07768436379165677, 0.32678909621951907, 0.6755955415235222, 0.5241353583688481, 0.6178220506555778, 0.9352573535759386, 0.9846399025863736, 0.7414583669445434, 0.4815157713480963, 0.5933155622924455, 0.6513377328091347, 0.6492063576981022, 0.8958436576615042, 0.1267401493192176, 0.14279850353467888, 0.47961126728512504, 0.42801863741896035, 0.6128804398686567, 0.7626765675385573, 0.6149033080221653, 0.6227955603179913, 0.0465831090859515, 0.3200420645269095, 0.7338286847593535, 0.24313438057710354, 0.7830171657377775, 0.22892635173346548, 0.395825545197877, 0.4597254792868977, 0.5984140677295731, 0.4811161225010281, 0.38298841569860237, 0.046653697888850765, 0.9100784908762345, 0.9256590142570185, 0.23826180528673063, 0.038084431667432736, 0.4508052452462088, 0.010369843587864726, 0.6650520434615655, 0.014400898187810849, 0.9800540251621108, 0.4333900353450858, 0.28863171991977576, 0.7257032195213242, 0.784888567933274, 0.9665539397149994, 0.9533342457803781, 0.4360007793900713, 0.6677781402903323, 0.7769549985185499, 0.29159671706060164, 0.022785586719307728, 0.8058887815383765, 0.5686798725989286, 0.2814067828992591, 0.643970889960516, 0.5274583612408007, 0.3131934230484376, 0.8776456834113066, 0.5474098755404544, 0.9552542156803925, 0.8943077048683874, 0.32019173535459466, 0.09738088241252761, 0.13495328868105663, 0.8220573787061882, 0.2874596419831803, 0.38753166723846955, 0.30756461994813344, 0.6491297552196406, 0.8082989179850137, 0.20082130475380777, 0.5797303523058096, 0.723761842389872, 0.42786032163214044, 0.15397945191264525, 0.6238960415995914, 0.44421711492754945, 0.4641618841228062, 0.7369241499747812, 0.141932666153235, 0.04209434999119708, 0.761647351525512, 0.9364353619570398, 0.0808221873954056, 0.7947964112715472, 0.8160272769055122, 0.8781771185603536, 0.9474849392248608, 0.4115006301793484, 0.3611286254168271, 0.2818936118876236, 0.5317321731048633, 0.02192389732855106, 0.7333524506081959, 0.14127393624971785, 0.09166786734651455, 0.5030638398511678, 0.9826485908234559, 0.49258830264115055, 0.9246441843549017, 0.47592399552932846, 0.3806656689946689, 0.8347428221703932, 0.3490909964775277, 0.36199434608633946, 0.30691914812916804, 0.22788304874362506, 0.23819478271070318, 0.06795969160156189, 0.8924438552207006, 0.9280954569472702, 0.5954934907817419, 0.676747386690173, 0.377457892578212, 0.042114757664927956, 0.8749836388209684, 0.7936016628856591, 0.1750624584500973, 0.17823840576742647, 0.5643025965134942, 0.07738563529946842, 0.08693831779833693, 0.26788336328681844, 0.7289531683538426, 0.8397635892790802, 0.33937215355407163, 0.026389294368958326, 0.3583795669554949, 0.7383039662536846, 0.20875670644327063, 0.591780027202742, 0.010983051710596983, 0.4738707889578426, 0.9349570644480542, 0.79624012812301, 0.1348824927862549, 0.1379337033695103, 0.2186203192160035, 0.027045853187130594, 0.6543790026019208, 0.6816292214468643, 0.914629264316742, 0.961609425210886, 0.6786761055330461, 0.5355432568890967, 0.05846171850451319, 0.19515334088570788, 0.129435759097851, 0.49726215508537724, 0.8252139556146214, 0.5293260187581403}
2. Shuffle(Sequence[7]) → randomCase, {7, 4, 3, 1, 5, 2, 6}
3. If(countQuestion ≟ 0, 1, Element[randomCase, Mod[countQuestion, Length[randomCase]] + 1]) → caseNum
4. Element({{var13, var12, var11}, {var21, var22, 100}, {var31, var32, var33}, {var41, var42, var43}, {var51, var52, var53}, {var61, var62, var63}, {var71, var72, var73}}, caseNum) → currentValues
5. Sequence(If[A ≤ 3, (If[currentValues(A) < 10, 0.4, If[currentValues(A) < 100, 0.6, If[currentValues(A) < 1000, 0.8, 1]]] * boxWidth), (0.5 * boxWidth)], A, 1, numPoints) → widths
6. Sequence(If[A ≟ 1, 0, Sum[Take[widths, 1, A - 1]] + (0.2 * (A - 1)) + widths(A) / 2 - (0.5 * widths(1))], A, 1, numPoints) → homeOffsets
7. Sequence(HomeAnchor + (homeOffsets(A), 0), A, 1, numPoints) → homeLocations
8. Element(movingPoints, movingIndex) → PMove
9. centerBox(widths(10), boxHeight, P10) → box10
10. centerBox(widths(9), boxHeight, P9) → box9
11. centerBox(widths(8), boxHeight, P8) → box8
12. centerBox(widths(7), boxHeight, P7) → box7
13. centerBox(widths(6), boxHeight, P6) → box6
14. centerBox(widths(5), boxHeight, P5) → box5
15. centerBox(widths(4), boxHeight, P4) → box4
16. centerBox(widths(3), boxHeight, P3) → box3
17. centerBox(widths(2), boxHeight, P2) → box2
18. centerBox(widths(1), boxHeight, P1) → box1
19. RemoveUndefined(Zip[If[IsInRegion[PMove, A] ∧ B ≠ movingIndex, B], A, {box1, box2, box3, box4, box5, box6, box7, box8, box9, box10}, B, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]) → overlapBox
20. PixelsToPoint((xMin, yMin), (xMax, yMax), AppDimensions, (16, If[step ≟ 1, 245, 145])) → DestinationAnchor
21. Sequence(If[A ≟ 1, widths(destinationOrder(1)) / 2, widths(destinationOrder(A - 1)) / 2 + widths(destinationOrder(A)) / 2], A, 1, Length[destinationOrder]) → destinationOffsets
22. If(Length[destinationOrder] > 0, Min[Sum[destinationOffsets] + (boxWidth * If[Length[destinationOrder] < destinationSize, destinationSize - Length[destinationOrder], widths(destinationOrder(6)) / 2]), (boxWidth * Sum[widths])], (boxWidth * Sum[widths])) → destinationBoxWidth
23. Join({Zip[("" * A), A, currentValues], {"x", "+", "-", "\gt", "\lt", "\ge", "\le"}}) → allText
24. Element({{2, 1, 3, 4, 5, 6, 7, 8, 9, 10}, {3, 2, 1, 4, 5, 6, 7, 8, 9, 10}, {2, 3, 1, 4, 5, 6, 7, 8, 9, 10}, {3, 2, 1, 4, 5, 6, 7, 8, 9, 10}, {3, 1, 2, 4, 5, 6, 7, 8, 9, 10}, {1, 2, 3, 4, 5, 6, 7, 8, 10, 9}, {1, 2, 3, 4, 5, 6, 7, 8, 10, 9}}, caseNum) → caseVars
25. Sequence(baseVars(IndexOf[destinationOrder(A), caseVars]), A, 1, Length[destinationOrder]) → studentOrder1, {}
26. centerBox(destinationBoxWidth + (2 * x(gapCoords)), boxHeight + (2 * y(gapCoords)), CenterDestination) → frameAnswer
27. Element({var1Ans, var2Ans, var3Ans, var4Ans, var5Ans, var6Ans, var7Ans}, caseNum) → expectedX
28. Zip((("$\text{" * A) * "}$"), A, {"\phantom{\le}", "\le", "\lt", "\ge", "\gt"}) → selectIneq
29. If(SelectedIndex[selectIneq] ≟ 1, -1, SelectedIndex[selectIneq] - 1) → selectedIneq
30. If(step ≟ 1, destinationOrder, {("" * studentAns)}) → inputCurrent
31. If(step ≟ 2, 300, 290) → layoutY
32. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, (xMin, yMin), (xMax, yMax), AppDimensions) → OnboardingTextOffset
33. Element({If[layoutX ≟ 16, layoutX - 5, 11], layoutX - 5}, layoutCase) → layoutHintSolnX
34. If(step ≟ 1 ∨ step ≟ 2 ∧ (¬showsolution), layoutY + 5, layoutY - 50) → layoutFeedbackY
35. Min(studentIneq) → minStudent
36. Max(studentIneq) → maxStudent
37. Element({(((((("x&\le\dfrac{" * var11) * "-") * var12) * "}{") * var13) * "}"), (((("x&\le\dfrac{" * var21) * "-100}{") * var22) * "}"), (((((("x&\le\dfrac{" * var31) * "-") * var32) * "}{") * var33) * "}"), (((((("x&\le\dfrac{" * var41) * "-") * var43) * "}{") * var42) * "}"), (((((("x&\le\dfrac{" * var52) * "-") * var53) * "}{") * var51) * "}"), (((((("x&\ge\dfrac{" * var63) * "-") * var61) * "}{") * var62) * "}"), (((((("x&\ge\dfrac{" * var73) * "-") * var71) * "}{") * var72) * "}")}, caseNum) → solnLine2
38. If(IsInRegion[PMove, frameAnswer], FRAME, HOME) → locationPMove
39. Textfield(studentAns) → input1A
40. Defined(IndexOf[studentOrder1, correctOrderings1]) → correct1
41. Element({(("No more than " * var1Ans) * " people can go to the concert."), (("At most, " * var2Ans) * " people can go on the trip."), (("No more than " * var3Ans) * " people can go to the beach."), (("At most, " * var4Ans) * " people can attend the dance."), (("Up to " * var5Ans) * " boxes can be loaded into the cargo hold."), (("Bella needs to spend at least \$" * var6Ans) * " to earn a free drink."), (("Tyler needs to exercise for at least " * var7Ans) * " minutes to earn the free session.")}, caseNum) → solnSentence
42. Defined(IndexOf[movingIndex, destinationOrder]) → inDestination
43. Sequence(DestinationAnchor + (Sum[Take[destinationOffsets, 1, A]], 0), A, 1, Length[destinationOffsets]) → destinationAnchors
44. Zip(centerBox[A, boxHeight, B], A, widths, B, homeLocations) → allHomeBoxes
45. Sequence(Sequence[If[9 ≤ Element[correctOrderings1, A, B] ≤ 10, -1, Element[correctOrderings1, A, B]], B, 1, 6], A, 1, Length[correctOrderings1]) → correctOrdersNoIneq, {{3, -1, 1, 5, 2, 4}, {3, 6, 2, 4, -1, 1}, {3, 6, 1, -1, 2, 4}, {3, -1, 2, 4, 5, 1}, {1, -1, 3, 6, 2, 4}, {2, 4, 5, 1, -1, 3}, {1, 5, 2, 4, -1, 3}, {2, 4, -1, 3, 6, 1}}
46. IndexOf(Remove[studentOrder1, {7, 8, 9, 10}], correctOrdersNoIneq) → studentMatchNoIneq
47. Sequence(If[7 ≤ studentOrder1(A) ≤ 10, -1, studentOrder1(A)], A, 1, Length[studentOrder1]) → studentOrderNoIneq
48. Sequence(If[studentOrder1(A) < 3, -1, studentOrder1(A)], A, 1, Length[studentOrder1]) → studentOrderNoRateConst
49. Sequence(Sequence[If[1 ≤ Element[correctOrderings1, A, B] ≤ 2, -1, Element[correctOrderings1, A, B]], B, 1, 6], A, 1, Length[correctOrderings1]) → correctOrdersNoRateConst, {{3, 9, -1, 5, -1, 4}, {3, 6, -1, 4, 9, -1}, {3, 6, -1, 9, -1, 4}, {3, 9, -1, 4, 5, -1}, {-1, 10, 3, 6, -1, 4}, {-1, 4, 5, -1, 10, 3}, {-1, 5, -1, 4, 10, 3}, {-1, 4, 10, 3, 6, -1}}
50. centerBox(destinationBoxWidth + (4 * x(gapCoords)), boxHeight + (4 * y(gapCoords)), CenterDestination) → frameAnswerHighlight
51. Sequence((("SetFixed(box" * A) * ",false,enableInput&&step==1)"), A, 1, Length[movingPoints]) → cmdFixBoxes
52. Zip(Text[("\vphantom{\dfrac{1}{2}}" * If[step ≟ 2 ∧ (¬Defined[IndexOf[C, destinationOrder]]), "", ("" * A)]), B + (0, 0.1), true, true, 0, 0], A, allText, B, movingPoints, C, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}) → boxText
53. Sequence(HOME, A, 1, numPoints) → allHome
54. Flatten(RemoveUndefined[Zip[If[IsInRegion[PMove, Element[{box1, box2, box3, box4, box5, box6, box7, box8, box9, box10}, A]] ∧ A ≠ movingIndex, {B, A}], A, destinationOrder, B, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]]) → overlapInfo
55. RemoveUndefined(Sequence[If[¬Defined[IndexOf[A, destinationOrder]], (((("SetValue(P" * A) * ",homeLocations(") * A) * "))"), (((("SetValue(P" * A) * ",destinationAnchors(") * IndexOf[A, destinationOrder]) * "))")], A, 1, numPoints]) → cmdOrganize
56. Sequence((((("SetValue(P" * A) * ",homeLocations(") * A) * "))"), A, 1, numPoints) → cmdSendHome
57. Zip(allText(A), A, Sequence[baseVars(IndexOf[correctOrderings1(4, K), caseVars]), K, 1, Length[correctOrderings1(1)]]) → possibleTiles
58. If(triesPart1 ≤ 1, 0, If[triesPart1 ≤ 2, 1, 2]) → termsToShow
59. centerBox(widths(movingIndex) + (2 * x(gapCoords)), boxHeight + (2 * y(gapCoords)), PMove) → highlightBorder
60. Sequence(((((("Clickable tile: \(" * allText(A)) * "\). Click this tile to append \(") * allText(A)) * "\) to the end of the current expression. ") * altExpression), A, 1, Length[allText]) → altBoxCaptions
61. expandQuad(Vertex[box10, 1], Vertex[box10, 2], Vertex[box10, 3], Vertex[box10, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject
62. If(pulseCurrent > 0.5, 1 - pulseCurrent, pulseCurrent) → pulseOpacity
63. centerBox(widths(1), boxHeight, P1) → box1NoTab
64. centerBox(widths(2), boxHeight, P2) → box2NoTab
65. centerBox(widths(3), boxHeight, P3) → box3NoTab
66. centerBox(widths(4), boxHeight, P4) → box4NoTab
67. centerBox(widths(5), boxHeight, P5) → box5NoTab
68. centerBox(widths(6), boxHeight, P6) → box6NoTab
69. centerBox(widths(7), boxHeight, P7) → box7NoTab
70. centerBox(widths(8), boxHeight, P8) → box8NoTab
71. centerBox(widths(9), boxHeight, P9) → box9NoTab
72. centerBox(widths(10), boxHeight, P10) → box10NoTab
73. centerBox(widths(movingIndex), boxHeight, PMove) → highlightBox
74. Text((("\(" * allText(movingIndex)) * "\)"), PMove + (0, 0.1), true, true, 0, 0) → highlightText
75. Vertex(frameAnswer, 2) → PDestination
76. Take(solnLine1, 1, IndexOf["&", solnLine1] - 1) → test