Lateral Moves Activity: Polygon/Triangle Build for Translation and Riemann Sums

This example demonstrates “lateral moves” by constructing polygonal (triangle-based) geometric pieces that visually approximate an area or accumulated quantity. It highlights how upper and lower sums arise from splitting an interval into smaller parts and using side-by-side translated shapes to estimate the target. The core math concepts include Translation, the idea of Upper/Lower Sum (Riemann Sum), and representing local contributions with triangles/polygons. Construction-wise, the GeoGebra setup centers on the Polygon command, using objects D, E, F together with parameter/control objects t1, c, a, and b to position and shape the pieces; here, a and b serve as interval endpoints, t1 controls the partition/parameter position, and c acts as an offset/height or variable quantity. Suitable for advanced high school and early calculus courses, especially for teaching Riemann sums via geometric intuition and interactive visualization.