Key Math Domains & Topics (Common Core Aligned)
| Domain | Topics Covered |
|---|---|
| Congruence & Proof (G-CO) | – Use rigid transformations (reflection, rotation, translation) to define congruence |
Prove geometric theorems using logical reasoning
Apply deductive proofs, two-column and paragraph proofs |
| Similarity, Right Triangles & Trigonometry (G-SRT) | – Define similarity using dilationsUse similarity to solve for unknown side lengths
Apply the Pythagorean Theorem and its converse
Understand and use basic trigonometric ratios (sine, cosine, tangent) |
| Circles (G-C) | – Define parts of circles: radii, chords, arcs, sectorsUnderstand central and inscribed angles
Apply arc length and area of sectors in radians and degrees |
| Expressing Geometric Properties Algebraically (G-GPE) | – Use coordinates to prove geometric relationships (e.g., parallel/perpendicular lines, distance, midpoint)Find equations of circles on the coordinate plane |
| Geometric Measurement & Dimension (G-GMD) | – Calculate volume and surface area of 3D figures: cones, cylinders, spheresApply density and modeling in real-life problems |
| Modeling with Geometry (G-MG) | – Use geometry to model real-world contextsSolve design and construction-based problems (blueprints, structures, etc.) |
| Publisher | Curriculum Name | Features |
|---|
| Eureka Math (Great Minds) | Geometry Modules | Emphasizes deductive reasoning, proofs, and conceptual rigor |
| Illustrative Mathematics | Geometry Curriculum | Inquiry-based; supports rich discussions and structured exploration |
| Big Ideas Math Geometry | Visual, tech-supported; real-life examples |
| CPM Geometry | Collaborative learning and problem-solving focus |
| Go Math! / enVision Geometry | Textbook and digital versions; scaffolded for ELLs and intervention |
| Open Up Resources | Free, CCSS-aligned materials with lesson plans and guided discovery |
| Type | Description |
|---|---|
| Formative Assessments | Weekly skill checks, diagram labeling, theorem explanation tasks |
| Performance Tasks | Projects that integrate geometric reasoning with real-world models (e.g., city plans, 3D modeling) |
| Summative Unit Tests | Cover congruence, similarity, right triangles, circles, coordinates, and volume |
| State Exams (End-of-Course) | Many states test Geometry (especially if required for graduation): |
| E.g., STAAR (TX), Regents (NY), MCAS (MA), FAST (FL), SBAC (CA) |
| Tool | Purpose |
|---|---|
| Geometric Tools | Protractor, compass, ruler — used for constructions, angle measurement, and transformations |
| Graphing Calculators / Desmos | Coordinate geometry proofs, graphing equations of circles, slope reasoning |
| 3D Models / Nets | Help visualize and calculate volume/surface area |
| Algebra Tiles & Coordinate Grids | Link algebraic and geometric thinking |
| Digital Tools | GeoGebra, Desmos Geometry, Khan Academy, CK-12, IXL, Mathspace |
| State | Notes |
|---|---|
| California | Follows CCSS; Geometry taught after Algebra I; SBAC includes reasoning tasks from Geometry domains |
| Texas | Uses TEKS; STAAR Geometry EOC exam required for high school graduation |
| Florida | Geometry is part of the B.E.S.T. standards; FAST end-of-course exam measures proof and application |
| New York | Culminates in the Geometry Regents Exam; strong emphasis on proofs and coordinate geometry |
| Illinois | Geometry is tested under IAR (or locally chosen tests); CCSS followed closely |
Typical School Year: August to May/June
Instruction Time: 55–75 minutes per day
Instruction is organized into 6–8 units:
Transformations and congruence
Geometric proof and logic
Similarity and triangle properties
Trigonometry
Circles and their properties
Coordinate geometry
Volume and surface area
Real-world applications
Advanced Concepts Introduced in Grade 10
- Formal geometric proofs (2-column, paragraph, flowchart)
- Use of transformations to define congruence and similarity
- Coordinate proofs for slope, distance, and midpoint
- Application of trigonometry to solve triangles
- Modeling real-world geometry problems involving volume, area, and constructions
- Understanding relationships in circles (angles, arcs, sectors)
