Exploring Reasoning and Proof
 Introduction | Triangular and Square Numbers | Conjecturing with Algebraic Symbols | Proving the Conjecture | Reflection Questions | Summary | Your Journal
 Your task is to use the grid space to create triangular and square numbers. Then we will ask you to prove the following conjecture. "A triangular number plus the next consecutive triangular number is always a square number." For instance, using the figure introduced before, 3 + 6 = 9, a square number. Now use the Interactive Activity below to explore triangular and square numbers. The interactive feature on this page requires the FLASH 5 player/plugin. If you do not see a Flash feature above, or if it is behaving strangely, you should download the player/plugin from the Macromedia web site. (You are seeing this message because you have scripting disabled in your browser and we could not detect the presence of the Flash 5 player/plugin.) Now use the grid to construct an informal proof of the conjecture: "A triangular number plus the next consecutive triangular number is always a square number."
 Teaching Math Home | Grades 9-12 | Reasoning and Proof | Site Map | © |