Function Machine for Multiplication and Division

① This interactive GeoGebra example visualizes a 'function machine' that takes an input number, applies either multiplication or division, and produces an output, making the operation process tangible. ② Core math concepts include natural number multiplication and division, the inverse relationship between the two operations, and the fundamental idea of a function as a mapping from input to output. ③ Construction details: The applet uses GeoGebra commands such as Random, Segment, Point, Line, Sequence, and Vector to build the machine's visual components (objects like a, A, B, b, C, D, E, c, F), with text objects (text1, text2, etc.) displaying the operation, and sliders (divisionfactor, multordiv) controlling the operation type and factor. Lists list1 and list2 store input/output sequences, and pic1 may serve as a background image. ④ Suitable for upper elementary to middle school students (ages 8-13) to explore multiplication and division, understand function rules, and see how changing the factor alters results; also useful for teachers as a dynamic demonstration tool in classrooms.