餐厅选择问题

几何画板及绘图内容加载中，请稍等……

2022-07-04 18:25

所属专题 Arbeiten mit Baumdiagrammen

①本范例演示了如何在餐厅菜单中通过组合不同的选项来计算总的可能性；②涉及的核心数学概念是乘法原理和概率统计中的基本计数方法；③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Polygon（多边形）、SpeechBubbleLeft（左侧文本气泡）、Segment（线段）、Textfield（文本字段）、If（条件判断）；④适合的学段或用途：本范例适合小学高年级（5-6年级）学生学习如何解决排列组合问题，理解乘法原理在生活中的应用。

GeoGebra 命令及参数

Polygon((9.7, -2.2), (9.7, -3.5), (10.6, -3.5), (10.6, -2.2)) → box5_{2}, box3_{23}, box3_{24}, box3_{25}, box3_{26}
Polygon((8.7, -2.2), (8.7, -3.5), (9.6, -3.5), (9.6, -2.2)) → box5_{1}, box3_{27}, box3_{28}, box3_{29}, box3_{30}
Polygon((7.7, -2.2), (7.7, -3.5), (8.6, -3.5), (8.6, -2.2)) → box4_{2}, box3_{13}, box3_{14}, box3_{15}, box3_{16}
Polygon((6.7, -2.2), (6.7, -3.5), (7.6, -3.5), (7.6, -2.2)) → box4_{1}, box3_{17}, box3_{18}, box3_{19}, box3_{20}
Polygon((5.7, -2.2), (5.7, -3.5), (6.6, -3.5), (6.6, -2.2)) → box3_{2}, box3_{7}, box3_{8}, box3_{9}, box3_{10}
Polygon((4.7, -2.2), (4.7, -3.5), (5.6, -3.5), (5.6, -2.2)) → box3_{1}, box3_{31}, box3_{5}, box3_{6}, box3_4
Polygon((8.4, 0.09999999999999998), (8.4, -1.0999999999999994), (10.2, -1.0999999999999994), (10.2, 0.09999999999999998)) → box2_{3}, box2_{12}, box2_{13}, box2_{14}, box2_{15}
Polygon((6.5, 0.09999999999999998), (6.5, -1.0999999999999994), (8.3, -1.0999999999999994), (8.3, 0.09999999999999998)) → box2_{2}, box2_{8}, box2_{9}, box2_{10}, box2_{11}
Polygon((4.6, 0.09999999999999998), (4.6, -1.0999999999999994), (6.4, -1.0999999999999994), (6.4, 0.09999999999999998)) → box2_{1}, box2_{4}, box2_{5}, box2_{6}, box2_{7}
Polygon((1.5, 0.09999999999999998), (1.5, -1.0999999999999994), (3.3, -1.0999999999999994), (3.3, 0.09999999999999998)) → box1_{3}, box1_{12}, box1_{13}, box1_{14}, box1_{15}
Polygon((-0.4, 0.09999999999999998), (-0.4, -1.0999999999999994), (1.4, -1.0999999999999994), (1.4, 0.09999999999999998)) → box1_{2}, box1_{8}, box1_{9}, box1_{10}, box1_{11}
Polygon((-2.3, 0.09999999999999998), (-2.3, -1.0999999999999994), (-0.5, -1.0999999999999994), (-0.5, 0.09999999999999998)) → box1_{1}, box1_{4}, box1_{5}, box1_{6}, box1_{7}
Polygon((-2.6, 0.4), (-2.6, -1.4), (-0.5, -1.4), (-0.5, 0.4)) → val1_1, m, n, p, q
Polygon((-0.45, 0.4), (-0.45, -1.4), (1.45, -1.4), (1.45, 0.4)) → val1_2, r, s, t, b
Polygon((1.5, 0.4), (1.5, -1.4), (3.6, -1.4), (3.6, 0.4)) → val1_3, c, d, e, k_1
Polygon((4.3, 0.4), (4.3, -1.4), (6.4, -1.4), (6.4, 0.4)) → val2_1, l_1, m_1, n_1, p_1
Polygon((6.45, 0.4), (6.45, -1.4), (8.35, -1.4), (8.35, 0.4)) → val2_2, q_1, r_1, s_1, t_1
Polygon((8.4, 0.4), (8.4, -1.4), (10.6, -1.4), (10.6, 0.4)) → val2_3, a_1, b_1, c_1, d_1
SpeechBubbleLeft(Bubble1, 8, 2) → sp1
SpeechBubbleLeft(Bubble1, 9.3, 2) → sp2
SpeechBubbleLeft(Bubble1 + (0, 0.8), 11.8, 2) → sp3
Segment(V, W) → f
Segment(Z, A_1) → g
Segment(B_1, C_1) → h
Segment(V_{1}, W_{1}) → f_{1}
Segment(Z_{1}, A_{2}) → g_{1}
Segment(B_{2}, C_{2}) → h_{1}
SpeechBubbleLeft(Bubble1 + (0, 0.8), 13, 2.2) → sp4
Segment(P_1, Q_1) → i
Segment(R_1, S_1) → j
Segment(P_{2}, Q_{2}) → i_{1}
Segment(R_{2}, S_{2}) → j_{1}
Segment(P_{3}, Q_{3}) → i_{2}
Segment(R_{3}, S_{3}) → j_{2}
Segment(P_{4}, Q_{4}) → i_{3}
Segment(R_{4}, S_{4}) → j_{3}
Segment(P_{5}, Q_{5}) → i_{4}
Segment(R_{5}, S_{5}) → j_{4}
Segment(P_{6}, Q_{6}) → i_{5}
Segment(R_{6}, S_{6}) → j_{5}
SpeechBubbleLeft(Bubble1, 13.5, 3) → sp5
Textfield(bInput) → InputBox2
Textfield(cInput) → InputBox3
Textfield(dInput) → InputBox4
Textfield(eInput) → InputBox5
If((¬Defined[(dInput * eInput)]) ∧ (cInput ≟ 2 ∨ cInput ≟ 3), true, If[cInput ≟ 2 ∧ dInput ≟ 2 ∧ eInput ≟ 3 ∨ cInput ≟ 2 ∧ dInput ≟ 3 ∧ eInput ≟ 2 ∨ cInput ≟ 3 ∧ eInput ≟ 2 ∧ dInput ≟ 2, true, false]) → correct2
If(cInput ≟ 2, dInput ≟ 3 ∨ dInput ≟ 2, If[cInput ≟ 3, dInput ≟ 2]) → correct3
If(cInput ≟ 2 ∧ dInput ≟ 2, eInput ≟ 3, eInput ≟ 2) → correct4
Segment(C_7, D_7) → k
Segment(E_7, F_7) → l
Polygon((4.5, -2), (4.5, -3.7), (5.6, -3.7), (5.6, -2)) → val3_1, e_1, f_2, g_2, h_2
Polygon((9.7, -2), (9.7, -3.7), (10.9, -3.7), (10.9, -2)) → val5_{2}, box3_{11}, box3_{12}, box3_{21}, box3_{22}
Polygon((8.7, -2), (8.7, -3.7), (9.6, -3.7), (9.6, -2)) → val5_{1}, box3_{32}, box3_{33}, box3_{34}, box3_{35}
Polygon((7.7, -2), (7.7, -3.7), (8.6, -3.7), (8.6, -2)) → val4_{2}, box3_{36}, box3_{37}, box3_{38}, box3_{39}
Polygon((6.7, -2), (6.7, -3.7), (7.6, -3.7), (7.6, -2)) → val4_{1}, box3_{40}, box3_{41}, box3_{42}, box3_{43}
Polygon((5.7, -2), (5.7, -3.7), (6.6, -3.7), (6.6, -2)) → val3_{2}, box3_{44}, box3_{45}, box3_{46}, box3_{47}
If(IsInRegion[MidCon3, val3_1] ∧ (IsInRegion[MidDon1, val3_{2}] ∨ IsInRegion[MidDon2, val3_{2}] ∨ IsInRegion[MidDon3, val3_{2}]), true, If[IsInRegion[MidCon3, val3_{2}] ∧ (IsInRegion[MidDon1, val3_1] ∨ IsInRegion[MidDon2, val3_1] ∨ IsInRegion[MidDon3, val3_1]), true, If[IsInRegion[MidCon3, val4_{1}] ∧ (IsInRegion[MidDon1, val4_{2}] ∨ IsInRegion[MidDon2, val4_{2}] ∨ IsInRegion[MidDon3, val4_{2}]), true, If[IsInRegion[MidCon3, val4_{2}] ∧ (IsInRegion[MidDon1, val4_{1}] ∨ IsInRegion[MidDon2, val4_{1}] ∨ IsInRegion[MidDon3, val4_{1}]), true, If[IsInRegion[MidCon3, val5_{1}] ∧ (IsInRegion[MidDon1, val5_{2}] ∨ IsInRegion[MidDon2, val5_{2}] ∨ IsInRegion[MidDon3, val5_{2}]), true, If[IsInRegion[MidCon3, val5_{2}] ∧ (IsInRegion[MidDon1, val5_{1}] ∨ IsInRegion[MidDon2, val5_{1}] ∨ IsInRegion[MidDon3, val5_{1}]), true, false]]]]]) → cone3True
If(IsInRegion[MidCon2, val3_1] ∧ (IsInRegion[MidDon1, val3_{2}] ∨ IsInRegion[MidDon2, val3_{2}] ∨ IsInRegion[MidDon3, val3_{2}]), true, If[IsInRegion[MidCon2, val3_{2}] ∧ (IsInRegion[MidDon1, val3_1] ∨ IsInRegion[MidDon2, val3_1] ∨ IsInRegion[MidDon3, val3_1]), true, If[IsInRegion[MidCon2, val4_{1}] ∧ (IsInRegion[MidDon1, val4_{2}] ∨ IsInRegion[MidDon2, val4_{2}] ∨ IsInRegion[MidDon3, val4_{2}]), true, If[IsInRegion[MidCon2, val4_{2}] ∧ (IsInRegion[MidDon1, val4_{1}] ∨ IsInRegion[MidDon2, val4_{1}] ∨ IsInRegion[MidDon3, val4_{1}]), true, If[IsInRegion[MidCon2, val5_{1}] ∧ (IsInRegion[MidDon1, val5_{2}] ∨ IsInRegion[MidDon2, val5_{2}] ∨ IsInRegion[MidDon3, val5_{2}]), true, If[IsInRegion[MidCon2, val5_{2}] ∧ (IsInRegion[MidDon1, val5_{1}] ∨ IsInRegion[MidDon2, val5_{1}] ∨ IsInRegion[MidDon3, val5_{1}]), true, false]]]]]) → cone2True
If(IsInRegion[MidCon1, val3_1] ∧ (IsInRegion[MidDon1, val3_{2}] ∨ IsInRegion[MidDon2, val3_{2}] ∨ IsInRegion[MidDon3, val3_{2}]), true, If[IsInRegion[MidCon1, val3_{2}] ∧ (IsInRegion[MidDon1, val3_1] ∨ IsInRegion[MidDon2, val3_1] ∨ IsInRegion[MidDon3, val3_1]), true, If[IsInRegion[MidCon1, val4_{1}] ∧ (IsInRegion[MidDon1, val4_{2}] ∨ IsInRegion[MidDon2, val4_{2}] ∨ IsInRegion[MidDon3, val4_{2}]), true, If[IsInRegion[MidCon1, val4_{2}] ∧ (IsInRegion[MidDon1, val4_{1}] ∨ IsInRegion[MidDon2, val4_{1}] ∨ IsInRegion[MidDon3, val4_{1}]), true, If[IsInRegion[MidCon1, val5_{1}] ∧ (IsInRegion[MidDon1, val5_{2}] ∨ IsInRegion[MidDon2, val5_{2}] ∨ IsInRegion[MidDon3, val5_{2}]), true, If[IsInRegion[MidCon1, val5_{2}] ∧ (IsInRegion[MidDon1, val5_{1}] ∨ IsInRegion[MidDon2, val5_{1}] ∨ IsInRegion[MidDon3, val5_{1}]), true, false]]]]]) → cone1True
If(y(SushiLeft2) ≠ -4.5 ∨ y(NudelnLeft2) ≠ -4.6 ∨ y(CurryLeft2) ≠ -4.72, false, true) → movedHauptspeise
If(y(donutLeft3) ≠ -5 ∨ y(coneLeft3) ≠ -5, false, true) → movedNachspeise

AI 绘图提示语参考

绘制一个用于“餐厅选项选择”组合计数的教学图。先在画面下半部分按网格画出多列等高矩形框，形成三行左右的选项区域，并在每个框中预留用于计数的格子。再在上方或中间放置一个用于说明的左侧对话气泡，旁边放置多行输入框用于填写若干选项数量。最后在合适位置画多组连接线段，把各输入项对应到不同的选项区域；并在对话气泡处放置提示信息，配合输入条件判断的结果显示，用于判断所填组合是否正确。

以上提示语为根据原始绘图命令整理而来，仅供参考。