Magic Eight Times Table: Grid Patterns and Geometric Transformations

① This interactive GeoGebra example demonstrates the multiplication table of 8 (8×1 to 8×10) on a grid, revealing visual patterns and geometric transformations of the products. ② Core math concepts include multiplication, rational numbers, sequences, geometric transformations (translation), variance in numerical distribution, and a cylindrical metaphor for 3D extension. ③ Construction highlights: The applet uses multiple named objects (T1–T10, U1–U10), buttons (button1, button2) to toggle animations or views, text labels (text1, text1_1) for values, and a slider (n) to adjust the multiplier range, enabling translation transformations to expose periodic patterns in the products. ④ Suitable for upper elementary to middle school students, this resource helps explore multiplication patterns, connect arithmetic with geometry, and serves as a dynamic teaching tool for demonstrating how sequences and transformations interrelate.