Geometric Demo of Adding Negatives: Understanding Integer Addition via Vectors

This example uses a plane-geometry setup to demonstrate that adding a negative number corresponds to a displacement in the opposite direction, making integer addition visually intuitive. It centers on integer addition and the meaning of signs, as well as vector direction and length (vector addition as equivalent to chaining displacements). The construction also leverages coordinate-geometry curve elements—such as circles/ellipses/parabolas—to provide a visual “carrier” for changes and patterns during interaction. In GeoGebra, it is built using commands like Vector and Segment to create directed displacements and connecting pieces, Random to generate points/parameters, and Textfield/InputBox1 plus button1/button2 with ans/ans1 and text1 to manage user interaction and display results. Key objects include variables/points such as a, b, C, B, D, k, A, j, E, F, f, g, h, L, m, along with interface elements for computed outputs. Suitable for middle-school to early high-school learners and for lessons that connect number sense with vectors and coordinate geometry.