Judging event probabilities with a spinning wheel: possible, impossible, certain
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Wahrscheinlichkeitsrechnung - Einführung
This GeoGebra lesson demonstrates how to use a spinning “lucky wheel” to visually determine which statements about stopping positions are correct. Students answer a multiple-choice question by reasoning about which colored sectors the pointer can land on. The key mathematics concepts are event classification (possible / impossible / certain / unlikely), the relationship between the sample space and events, and building probabilistic intuition in a semi-quantitative way. Construction-wise, the example relies on conditional logic and selection: If with SelectedIndex and PointIn to detect which sector the wheel’s pointer lands in, and to trigger correctness checks; geometric construction tools such as Point and Segment (plus line/linePoints) for wheel boundaries and indicator-related graphics; text and math rendering via LaTeX, Join, and Translate for labeling and equation-like annotations; and user interaction components using DropDown and input/selected to drive the multiple-choice flow. Feedback/communication is implemented with elements like RotateText and speech-bubble style annotation, while correctness flags (e.g., correct4–correct11) are represented by the tracked objects. Suitable for grades 7–8 as an introduction to probability and statistics and for guided classroom practice.
GeoGebra Commands & Parameters
If(step < 4, 1, If[step < 6, 2, 3]) → exnumSequence(LineStart + ((m * linesize / 5), 0), m, 0, 5) → linePointsPointIn(Polygon[LineStart, LineStart + (linesize, 0), LineStart + (linesize, Distance[LineStartH, LineStart]), LineStartH]) → H1PointIn(Polygon[LineStart, LineStart + (linesize, 0), LineStart + (linesize, Distance[LineStartH, LineStart]), LineStartH]) → H2PointIn(Polygon[LineStart, LineStart + (linesize, 0), LineStart + (linesize, Distance[LineStartH, LineStart]), LineStartH]) → H3SelectedIndex(DropDown10) → input10SelectedIndex(DropDown11) → input11Point(Line[V1, xAxis]) → V4Point(Line[BH1, xAxis]) → BH2Point(Line[E, xAxis]) → FSegment(LineStart, LineStart + (linesize, 0)) → nZip(Segment[P + (0, -0.2), P + (0, 0.2)], P, linePoints) → lineShortRotateText("\textsf{unmöglich}", 45°) → Text3aRotateText("\textsf{~~~~~~~sehr\\unwahrscheinlich}", 45°) → Text3bRotateText("\textsf{wahrscheinlich}", 45°) → Text3c_{1}RotateText("\textsf{unwahrscheinlich}", 45°) → Text3cRotateText("\textsf{~~~~~~sehr\\wahrscheinlich}", 45°) → Text3dRotateText("\textsf{sicher}", 45°) → Text3ePoint(Line[Bab1, xAxis]) → Bab2SpeechBubbleLeft(A, 10, 2.2) → Vieleck1Point(Line[Mascha1, xAxis]) → Mascha2Point(Line[Flo1, xAxis]) → Flo2Point(Line[Ayla1, xAxis]) → Ayla2LaTeX(step, true, true) → Text4Point(Line[A0, xAxis]) → A1xPoint(Line[A0, xAxis]) → A2xPoint(Line[A0, xAxis]) → A3xPoint(Line[A0, xAxis]) → A5xPoint(Line[A0, yAxis]) → A1yPoint(Line[A0, yAxis]) → A2yPoint(Line[A0, xAxis]) → A4xJoin({Zip[Segment[A, (x(A5x), y(A))], A, {A0, A1y, A2y}], Zip[Segment[(x(A), y(A2y)), A], A, {A0, A1x, A2x, A3x, A4x, A5x}]}) → tabelleJoin({Sequence[(x(A1x) + 0.1, y(A1y) - picsize) + ((m * picsize), 0), m, 0, Distance[A2x, A1x] / picsize - 1], Sequence[(x(A1x), y(A1y) - (2 * picsize)) + ((m * picsize), 0), m, 0, Distance[A2x, A1x] / picsize - 1], Sequence[(x(A1x), y(A1y) - (3 * picsize)) + ((m * picsize), 0), m, 0, Distance[A2x, A1x] / picsize - 1]}) → tabellePoints1aJoin({Sequence[(x(A2x) + 0.1, y(A1y) - picsize - 0.05) + ((m * picsize), 0), m, 0, Distance[A2x, A3x] / picsize - 1], Sequence[(x(A2x), y(A1y) - (2 * picsize)) + ((m * picsize), 0), m, 0, Distance[A2x, A3x] / picsize - 1], Sequence[(x(A2x), y(A1y) - (3 * picsize)) + ((m * picsize), 0), m, 0, Distance[A2x, A3x] / picsize - 1]}) → tabellePoints2aJoin({Sequence[(x(A3x), y(A1y) - picsize) + ((m * picsize), 0), m, 0, Distance[A3x, A4x] / picsize - 1], Sequence[(x(A3x), y(A1y) - (2 * picsize)) + ((m * picsize), 0), m, 0, Distance[A3x, A4x] / picsize - 1], Sequence[(x(A3x), y(A1y) - (3 * picsize)) + ((m * picsize), 0), m, 0, Distance[A3x, A4x] / picsize - 1]}) → tabellePoints3aJoin({Sequence[(x(A4x), y(A1y) - picsize) + ((m * picsize), 0), m, 0, Distance[A4x, A5x] / picsize - 1], Sequence[(x(A4x), y(A1y) - (1.8 * picsize)) + ((m * picsize), 0), m, 0, Distance[A4x, A5x] / picsize - 1], Sequence[(x(A4x), y(A1y) - (3 * picsize)) + ((m * picsize), 0), m, 0, Distance[A4x, A5x] / picsize - 1]}) → tabellePoints4aTranslate(tabellePoints1a, (picsize, 0)) → tabellePoints1bTranslate(tabellePoints2a, (picsize, 0)) → tabellePoints2bTranslate(tabellePoints3a, (picsize, 0)) → tabellePoints3bTranslate(tabellePoints4a, (picsize, 0)) → tabellePoints4bElement({nums1, nums2, nums2}, exnum) → numsJoin({Zip[Text[(("\textsf\small{" * n) * "}"), m + (0, -0.8), true, true, -0, 1], n, {"\bold{Losart\vphantom{g}}", "mit Hai\vphantom{g}", "mit Sonne\vphantom{g}", "mit Regenbogen\vphantom{g}", "mit Smiley\vphantom{g}"}, m, Zip[Midpoint[A, B], A, {A0, A1x, A2x, A3x, A4x}, B, {A1x, A2x, A3x, A4x, A5x}]], Zip[Text[(("\textsf\small{" * n) * "}"), m + (0, -1.6), true, true, -0, 1], n, {"\bold{Anzahl}"}, m, Zip[Midpoint[A, B], A, {A0, A1x, A2x, A3x, A4x}, B, {A1x, A2x, A3x, A4x, A5x}]]}) → tabelleTextTranslate(linePoints, (-1.2, -0.2)) → lineTextPointsElement({17, 15, 15}, exnum) → num
AI Drawing Prompt Reference
Create a probability teaching lucky wheel graphic. The wheel is circular, divided into multiple colored sectors with a fixed pointer at the top indicating the current position. Next to the wheel, five probability labels are arranged from bottom to top at a 45-degree angle, in ascending order: impossible, very unlikely, possible, very likely, and certain. On the right side of the wheel, include a dropdown menu for selecting answers, and below it a table showing the frequency count of different options. Use clean geometric style with clear lines separating wheel sectors and a distinctly colored pointer.
The prompt above was compiled from the original drawing commands and is for reference only.