A Project-Based Learning Workshop for STEM Curriculum
Aligned with East Baton Rouge Parish School System (EBR) Standards
Students will analyze a single, multi-functional tool that replaces the standard compass, ruler, protractor, parallel rule, and ellipsograph. The central challenge is to deconstruct its mechanisms to connect physical engineering principles with abstract mathematical definitions, thereby fulfilling the **Application** and **Conceptual Understanding** components of the LSSM Guide to Rigor.
(Conceptual sketch showing ruler, compass, and thread components)
Focus: Conceptual Definitions and Foundational Constructions
Activity 1: Circle Definition (Compass Function)
Using the slide ruler, set a fixed radius ($r$) of 5 cm. Draw a circle and mark its center. Draw two more circles of 3 cm and 8 cm. Students will define a circle as the set of all points equidistant from a central point, connecting the physical drawing action to the **GM: G-CO.A.1** definition.
**LSSM Link:** GM: G-CO.A.1 (Conceptual Understanding)
Activity 2: Parallel Line Construction (Ruler/Slide)
Draw a base line ($l$). Use only the instrument's sliding feature to translate the line segment, drawing a parallel line ($m$) 4 cm away. Students must then draw perpendicular segments between $l$ and $m$ at three arbitrary points ($A, B, C$) to prove that the lines remain equidistant ($d_A = d_B = d_C$).
**LSSM Link:** GM: G-CO.D.12 (Construct parallel lines) & 8.G.A.1c (Procedural Skill)
Activity 3: Angle Precision (Protractor Function)
Use the instrument's protractor feature to measure a provided 55° acute angle and a 125° obtuse angle. Record the measurements and calculate the margin of error for each (actual value vs. measured value). Students discuss how tool design limits **procedural fluency**.
**Rigor Focus:** Procedural Skill & Fluency (accurate use of measurement tools).
Deliverable: **Documented calculations and sketches for the three activities, proving foundational geometric definitions.**
Focus: Conic Sections and Verification of Geometric Locus
Activity 1: Fixed Foci & Thread Length
Mark two foci ($F_1$ and $F_2$) 8 cm apart. Determine the length of the string required for a major axis ($2a$) of 12 cm. Fix the thread to the instrument's body using the stem/thread mechanism, setting the constant length ($2a = d_1 + d_2$).
**LSSM Link:** GM: G-GPE.A.3.1 (Setup for deriving conic equations).
Activity 2: Proof of Constant Sum
Draw the ellipse by keeping the thread taut. Select three random points on the resulting curve ($P_1, P_2, P_3$). For each point, use the ruler feature to measure the distance to both foci ($d_1$ and $d_2$). Calculate the sum $S = d_1 + d_2$ for all three points.
**Rigor Focus:** Conceptual Understanding (Verifying the locus definition) & Procedural Skill (Accurate measurement).
Activity 3: Real-World Modeling
Discuss how this mechanical action models Kepler's first law (elliptical planetary orbits) and architectural whispering galleries. Use the measured values to explain how changing the distance between $F_1$ and $F_2$ (the foci) impacts the eccentricity of the ellipse.
**Rigor Focus:** Application (Connecting geometry to physics/engineering).
Deliverable: **A data table showing three points where $d_1 + d_2 \approx 2a$, demonstrating the definition of an ellipse.**
Focus: Engineering Design Process and Mathematical Modeling (SMP 4)
Activity 1: Identify and Define the Constraint
Based on testing in Parts 1 and 2, identify the instrument's primary weakness (e.g., parallax error on the ruler scale, difficulty setting the thread length precisely). Formulate a clear design challenge: **How can we improve the [Specific Function] to enhance [Specific Rigor Component]?**
**Rigor Focus:** Application (Identifying real-world engineering constraints).
Activity 2: Rapid Prototype Sketch & Justification
Sketch a detailed modification (digital or physical). Teams must use geometric terms to explain *how* the modification improves the tool's precision (Procedural Skill) or expands its function (Conceptual Understanding). For example, adding a fine-tune screw mechanism to the compass attachment.
**LSSM Link:** SMP 4 (Model with mathematics) & SMP 5 (Strategically use tools).
Activity 3: Final Pitch & Peer Critique
Each team delivers a short pitch (2 minutes) to justify their innovation, detailing the cost, benefit, and which LSSM standard or rigor component is most enhanced by their design. Peer teams provide constructive feedback on the design's feasibility and mathematical soundness.
**Rigor Focus:** Application (Solving problems) & Collaboration (Critique).
Deliverable: **Annotated conceptual sketch (digital or physical) and a final design presentation slide.**
GM: G-CO.A.1 (Conceptual Definition)
Students will **know precise definitions** of angle, **circle**, **perpendicular line**, and **parallel line** by actively constructing them with the instrument's features.
GM: G-CO.D.12 (Geometric Construction)
Students will **make formal geometric constructions** with a variety of tools and methods (e.g., compass and straightedge, **string**), specifically by constructing parallel lines and circles.
GM: G-GPE.A.3.1 (Conic Section Application)
Students will **derive the equations of ellipses** given the foci by physically demonstrating the property that the sum of the distances from the two fixed points (foci) is constant.
1. Conceptual Understanding
The tool forces students to connect the physical mechanism (the thread's length) directly to the **mathematical definition** of an ellipse.
2. Procedural Skill and Fluency
Achieved by practicing **multiple constructions** (circles, parallel lines, angles) using a single, efficient instrument, emphasizing speed and accuracy in geometric procedures.
3. Application (SMP 4)
Met during the **Design Improvement Phase**, where students use geometry to **model and solve a design problem** (improving the tool's utility/precision).