Geometry and transformations: a learning progression
Connect geometric properties with coordinates, transformations, circles, and logical arguments.
Before you begin
Recognize shapes and angles and plot points on a coordinate plane.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Describe figures using properties that do not depend on orientation.
- Track coordinates through translations, reflections, rotations, and dilations.
- Use coordinate relationships to find distances, midpoints, and equations.
- Reason about circles, congruence, constructions, and proofs.
What grade is this taught?
Our catalog includes this progression from grade 1 through grade 10. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.