"Bridge Dreams: Complex Numbers Unleashed!"

11th Grade

Project
1 week

"Bridge Dreams: Complex Numbers Unleashed!"

Molly Howell

Purpose

This project aims to immerse students in the practical application of complex numbers through the lens of bridge engineering. By collaborating with a professional engineer, students will gain insights into real-world challenges and apply mathematical concepts to design and construct a small-scale bridge model. The experience will enhance their problem-solving skills and deepen their understanding of how mathematical theories translate into tangible engineering solutions. Through hands-on experimentation and teamwork, students will explore the dynamic relationship between mathematics and structural design, preparing them for future STEM endeavors.

Learning goals

Students will learn to apply complex number operations, including addition, subtraction, multiplication, and powers, to real-world engineering scenarios. They will develop skills in collaborative problem-solving and critical thinking by designing and constructing a small-scale bridge model. Through interaction with a visiting engineer, students will gain insights into the practical applications of mathematics in engineering, enhancing their understanding of structural integrity and optimization. The project will culminate in a hands-on assessment where students demonstrate their ability to use complex numbers to predict and analyze the behavior of bridge components under various stress conditions.

Standards

Common Core - CCSS.MATH.CONTENT.HSN.CN.A.1: Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.
Common Core - CCSS.MATH.CONTENT.HSN.CN.A.2: Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
NGSS - HS-ETS1-2: Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

Products

Students will design and construct a small-scale bridge model, applying complex number calculations to ensure optimal structural integrity. They will engage in a lab session to experiment with powers of complex numbers, analyzing how various bridge components behave under stress. The final product will be a collaboratively built bridge model, informed by insights from a visiting engineer and real-world data, demonstrating their understanding and application of complex number operations in engineering.

Launch

Kick off the project with an interactive session led by the visiting engineer, who will present real-world bridge design challenges and the role of complex numbers in solving them. Students will engage in a hands-on activity where they simulate stress tests on simple bridge models, observing how different forces affect structural integrity. This session will set the stage for students to explore how mathematical concepts apply to engineering, sparking curiosity and laying the groundwork for the week-long project.

Exhibition

At the end of the project, students will host a Bridge Design Expo where they present their small-scale bridge models to the class, the visiting engineer, and other invited guests such as parents and school staff. Each team will showcase their design process, explaining how they utilized complex numbers to enhance structural integrity and address real-world engineering challenges. The engineer will provide feedback and insights, fostering a dialogue about the practical applications of mathematics in engineering. This expo will serve as a platform for students to demonstrate their problem-solving skills and creativity in applying mathematical concepts to tangible projects.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Project Launch and Engineer Presentation - Kick off the project with an interactive session led by a visiting engineer, who presents real-world bridge design challenges and the role of complex numbers in solving them. (20 min) Hands-On Stress Test Simulation - Students engage in a hands-on activity simulating stress tests on simple bridge models to observe how different forces affect structural integrity, sparking curiosity for the project. (25 min)	Introduction to Complex Numbers - Students learn about the basics of complex numbers, including addition, subtraction, and multiplication, using real-world examples related to bridge structures. (20 min) Collaborative Problem-Solving Session - In small groups, students apply complex number operations to hypothetical bridge scenarios, discussing their findings with peers and refining their understanding. (25 min)	Lab Session: Powers of Complex Numbers - Students explore powers of complex numbers through experimentation, creating and analyzing models of bridge components to predict behavior under stress. (25 min) Data Analysis and Application - Using real-world data provided by the visiting engineer, students work in teams to apply their findings to optimize bridge structural integrity. (20 min)	Bridge Design Planning - Students begin planning their small-scale bridge model, incorporating complex number calculations to ensure structural integrity, facilitated by insights from the engineer. (20 min) Team Collaboration and Design Sketching - Teams collaborate to sketch their bridge designs, discussing how complex number operations will be integrated into their models. (25 min)	Model Construction - Students construct their small-scale bridge models using their design sketches and calculations, focusing on structural integrity and real-world application. (30 min) Reflection and Feedback - Students reflect on their learning and receive feedback from the visiting engineer, preparing to present their models at the Bridge Design Expo. (15 min)
Deliverables	1. Completed small-scale bridge model demonstrating application of complex number calculations. 2. Presentation for the Bridge Design Expo, showcasing the design process and mathematical applications.
Preparation	1. Coordinate with the visiting engineer to ensure their availability and prepare their presentation materials. 2. Prepare simple bridge model kits for stress test simulations on Day 1. 3. Gather and distribute real-world data sets for complex number operations practice. 4. Set up lab materials and equipment for experiments with powers of complex numbers. 5. Ensure availability of construction materials for small-scale bridge models (e.g., balsa wood, glue, etc.). 6. Organize a space and necessary technology for the Bridge Design Expo.