Putting Essential Understanding into Practice: Geometry, 9–12

Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image, not the whole plane? Do they understand that examples, no matter how many they find, cannot prove a conjecture but one counterexample is sufficient to disprove it?

Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of diagrams and definitions, transformations, and proof. Use the opportunities that these and similar tasks provide to build on their understanding and guide them in taking the next steps in learning.