Full Curriculum Materials
Free, Building Thinking Classrooms–aligned materials specifically curated for secondary geometry teachers.
Unit 3 - Proof and Congruence
After building early tools of proof and making some convincing arguments, this unit introduces a clear, formal technique for writing proofs. Students use triangle congruence shortcuts as trusted tools in their reasoning so they can focus on explaining why geometric results must be true.
Unit 4 - Triangle Theorems
Unit 4 develops triangle theorems as tools students can actually prove and use. Across six lessons, they move from conjecturing triangle and polygon angle sums to building the missing constructions, then proving the base angles and bisector theorems and using them in problems. The Advanced work is intentionally proof‑heavy: students experience what it means to carry an open conditional, close a deductive chain, and treat theorems as reliable tools rather than memorized facts.
Unit 5 - Quadrilaterals
Unit 5 turns quadrilaterals into triangle proofs in disguise. Students use diagonals, congruence, and coordinate tools to uncover properties of parallelograms, special quadrilaterals, trapezoids, and kites. The focus is on hierarchy, inheritance, and seeing every new fact as a consequence of earlier theorems—not a list to memorize.
Unit 6 – Similarity and Scaling
Build a precise framework for similarity that ties together proportional reasoning, triangle structure, and measurement. Students move from shadows and photographs to triangle shortcuts and indirect measurement, then use scaling laws to explain why perimeter, area, and volume grow differently — and why nature can’t simply “scale things up.”
Unit 7 – Trigonometry: Ratios With a Story
Trigonometry here is not a side quest. It’s what happens when students name the side ratios that similarity guarantees and treat them as functions of an angle. Building on similarity, proportional reasoning, and right triangles from earlier units, students first discover and invert the basic trig ratios, then prove exact values for special angles, and finally extend trig beyond right triangles with the Laws of Sines and Cosines. Along the way, classroom stories, algebraic missteps, and the Everest problem keep the focus on real student thinking and on trig as a natural outgrowth of geometry, not a separate course.
Unit 8 – Circles
Students build a full circle toolkit, starting from the definition (all points the same distance from a center) and showing how nearly every circle fact flows from that one idea. Across seven lessons they connect similarity, arcs and sectors, central and inscribed angles, tangents, and trigonometry, ending with the Law of Sines as a circle theorem in disguise and a synthesis of Units 6–8.