LabPathCourse replacement path

Geometry LabPath

A replacement-grade Geometry course where students construct, transform, measure, model, and prove. Every theorem becomes a visible invariant and every design decision becomes evidence.

Start first mission Assign to class

10/10replacement gate

10units

30missions

10simulator modes

Day 1

Start with evidence, not a memorized theorem.

Geometry begins by separating what the diagram merely looks like from what the student can prove by construction, measurement, transformation, or coordinate evidence.

geoproof

Definitions Are Tools, Not Decorations

Use points, lines, angles, and distance definitions to justify a geometric claim.

Open mission

Student loop

Every mission makes geometry visible before proof becomes formal.

Teach the geometric idea visually before formal proof language appears.
Ask students to predict what property should stay invariant.
Let students manipulate a construction, transformation, measurement, or design model.
Show the consequence in diagram, measure, coordinate, and proof form.
Require explanation, revision, defense, and transfer before mastery moves.

Representative missions

Proof, construction, transformation, measurement, and modeling.

geoproof

Definitions Are Tools, Not Decorations

Dragging the diagram separates facts that remain true from facts that only looked true.

Try it

buildlab

Inscribed Regular Polygon

A wrong central angle accumulates error and the final vertex misses the start point.

Try it

geoproof

Triangle Similarity Criteria

Valid similarity facts keep ratios consistent; invalid facts break the mapping.

Try it

graphverse

Distance And Midpoint Evidence

Moving points changes distance and midpoint evidence immediately.

Try it

buildlab

Packaging Optimization Challenge

Efficient volume can increase instability; stable design can use more material.

Try it

buildlab

Net To Solid Reasoning

Wrong adjacency predictions become visible when the net folds into the solid.

Try it

Course map

Ten units from definitions to evidence-based design.

Unit 1

Foundations Of Geometry And Proof

How do definitions, diagrams, and logic work together to prove something?

Definitions Are Tools, Not DecorationsUse points, lines, angles, and distance definitions to justify a geometric claim.Conditional Statements And ConversesDistinguish a theorem from its converse and test whether each direction is valid.Proof Chain StudioBuild a complete proof chain from givens to conclusion.

Mastery gate: Student uses definitions, diagrams, and logical steps to defend a claim without relying on appearance alone.

Unit 2

Constructions And Geometric Tools

How can a tool action create a mathematical object with guaranteed properties?

Perpendicular Bisector ConstructionConstruct a perpendicular bisector and prove every point on it is equidistant from endpoints.Angle Bisector As Equal DistanceConstruct an angle bisector and connect the tool action to equal angle measures.Inscribed Regular PolygonConstruct a regular polygon and reason from central angles and equal chords.

Mastery gate: Student constructs geometric objects and explains why the construction guarantees the target property.

Unit 3

Transformations And Congruence

How do transformations prove figures are congruent?

Translate Rotate ReflectUse translations, rotations, and reflections to map a figure onto another.Congruence Criteria LabDecide when SSS, SAS, ASA, AAS, or HL is enough to prove triangles congruent.Transformational Proof ChallengeWrite a proof that a transformation sequence establishes congruence.

Mastery gate: Student uses transformations to show which properties are preserved and why congruence follows.

Unit 4

Similarity And Right Triangle Trigonometry

How do scale, proportion, and angle relationships let us measure what we cannot reach?

Mastery gate: Student uses similarity and trigonometry to solve an indirect measurement problem and defend assumptions.

Unit 5

Circles And Angle Relationships

How do arcs, chords, tangents, and secants control circle geometry?

Inscribed Angles And ArcsRelate inscribed angles to intercepted arcs.Tangents, Radii, And Right AnglesProve a tangent is perpendicular to the radius at the point of tangency.Circle Equation And Coordinate CenterConnect a circle graph to its center-radius equation.

Mastery gate: Student predicts and proves circle angle/length relationships from arcs and intersections.

Unit 6

Coordinate Geometry And Algebraic Proof

How can coordinates turn geometry claims into testable algebra?

Distance And Midpoint EvidenceUse distance and midpoint to verify geometric relationships.Slope As Parallel And Perpendicular EvidenceUse slope to prove lines are parallel or perpendicular.Coordinate Quadrilateral ProofClassify and prove a quadrilateral using coordinate evidence.

Mastery gate: Student uses distance, midpoint, slope, and equation evidence to prove a geometric claim.

Unit 7

Area, Volume, And Design Constraints

How do geometric measures drive real design decisions?

Area By DecompositionDecompose a composite shape and justify total area.Volume And Cross SectionsVisualize cross sections and connect them to volume reasoning.Packaging Optimization ChallengeOptimize a package under volume, material, and stability constraints.

Mastery gate: Student optimizes a design using area, volume, surface area, and constraint evidence.

Unit 8

Geometric Modeling And Applications

How do geometry models support decisions in the real world?

Map Scale And NavigationUse scale and similarity to estimate real distances from a model.Sightline And Shadow ModelUse similar triangles to model shadows, sightlines, or inaccessible height.Design Review With Geometry EvidenceChoose a geometry model and defend a recommendation under constraints.

Mastery gate: Student chooses, tests, and defends a geometry model with limitations.

Unit 9

Probability, Symmetry, And Spatial Reasoning

How do symmetry and spatial structure reveal hidden relationships?

Symmetry As ConstraintUse symmetry to reduce cases and justify geometric relationships.Net To Solid ReasoningFold a net mentally and physically to predict 3D adjacency.Geometric Probability RegionUse area ratios to reason about geometric probability.

Mastery gate: Student uses symmetry and spatial structure to predict outcomes and defend reasoning.

Unit 10

Geometry Capstone: Evidence-Based Design

Can geometry become a trustworthy design argument?

Accessible Ramp DesignDesign a ramp that meets slope, space, and safety constraints.Emergency Coverage MapUse circles, distance, and constraints to decide coverage placement.Geometry Defense PortfolioAssemble a defended Geometry evidence portfolio across proof, measurement, and modeling.

Mastery gate: Student completes a multi-constraint design, explains tradeoffs, defends limitations, and transfers the geometry to a new situation.

TeacherOS

See proof gaps early.

Assign the next Geometry LabPath mission to the class.
See TeacherOS clusters for diagram-trust, theorem misuse, and measurement errors.
Launch a repair mission or Studio assessment for the highest-risk cluster.
Practice the intervention in TeachProof when proof reasoning remains fragile.

Parent and district

Readable growth, serious evidence.

What theorem, construction, or model the student learned this week.
Which misconception was repaired and what evidence proved growth.
A plain-language Learning Evidence Record with proof and design artifacts.
Geometry concept coverage by proof, transformation, coordinate, and modeling strand.
Misconception resolution by class, teacher, and unit.