Dr. Geo: Exploring Geometry Through Interactive Software

Dr. Geo in the Classroom: Activities and Lesson Plans

Overview

Dr. Geo is free, open-source interactive geometry software (GNU) that lets students create and manipulate geometric constructions and—through an embedded Smalltalk environment—extend or script activities. It’s suited for primary through senior high: basic shape exploration for younger students, transformations and proofs for middle school, and advanced constructions, animations, and numeric experiments for older students.

Ready-to-use activity ideas (5)

1. Exploring Triangle Centers (45–60 min)

   • Tasks: Construct medians, perpendicular bisectors, angle bisectors; locate centroid, circumcenter, incenter, orthocenter.
   • Learning goals: Definitions, loci behavior, relationships between centers.
   • Assessment: Short worksheet: predict how centers move when a vertex is dragged; justify with constructions.

2. Properties of Quadrilaterals (40–50 min)

   • Tasks: Build parallelogram, rectangle, rhombus, square using constraints; measure side lengths/angles; create a classification flowchart.
   • Learning goals: Recognize defining properties, use dynamic manipulation to test invariants.
   • Assessment: Students save two contrasting constructions and write 3 evidence-based statements.

3. Transformations Lab (2 lessons × 45 min)

   • Tasks: Apply translations, rotations, reflections, dilations to shapes; compose transformations; explore symmetry.
   • Learning goals: Effect of each transformation on coordinates and congruence/similarity.
   • Assessment: Create an animation (Smalltalk script optional) showing a composed transformation and explain steps.

4. Coordinate Geometry & Conic Explorations (50–70 min)

   • Tasks: Place points with coordinates, derive equations from constructions (midpoint, slope), construct circle/ellipse via foci.
   • Learning goals: Link geometric construction to algebraic equations; visualize loci.
   • Assessment: Given a construction, students write the corresponding equation or verify a point satisfies it.

5. Intro to Computational Geometry / Scripting (2–3 lessons)

   • Tasks: Use Dr. Geo’s Smalltalk scripting to automate a construction (e.g., regular n-gon generator), animate Newton-Raphson on a function, or create recursive patterns (Fibonacci spiral).
   • Learning goals: Algorithmic thinking, linking geometry and programming, basic debugging.
   • Assessment: Submit the script plus a short comment explaining logic and one classroom demonstration.

Sample 45‑minute lesson plan (Transformations)

• 0–5 min: Objective & demo (show a rotation and translation).
• 5–20 min: Guided construction — students create a triangle and perform one transformation each (teacher circulates).
• 20–35 min: Challenge — students compose two transformations; predict result, then test by dragging.
• 35–42 min: Reflection — students record observations and one real-world example.
• 42–45 min: Quick share + save/export (PNG or Dr. Geo file).

Classroom implementation tips

• Use projector/full-screen mode for whole-class demos.
• Provide starter files (skeleton sketches) so learners focus on exploration rather than setup.
• Encourage “drag testing”: have students manipulate free points to see invariants.
• For mixed-ability classes: offer scaffolded prompts and an extension challenge using scripting.
• Save a gallery of student work for formative assessment and peer critique.

Resources

• Official GNU Dr. Geo site (downloads, user guides, tutorials) — includes example sketches and scripting docs.
• Intro tutorials/articles (e.g., Opensource.com) with step-by-step getting-started guides and classroom tips.