From Earth to Sky Education

Stop Teaching Math in Isolation. Start Teaching It in Action.

What if students didn’t just learn pre-calculus… but used it to design bridges, analyze rocket trajectories, and build real engineering systems?

Pre-Calculus Through Engineering transforms advanced mathematics into a hands-on, real-world experience where every concept is applied with purpose.

This is not a traditional textbook course.
This is mathematics brought to life through engineering.

What Makes This Course Different

Instead of memorizing formulas in isolation, students:

• Apply functions to design load-bearing bridges
• Use trigonometry to model rocket trajectories
• Analyze sinusoidal waves through circuit design
• Model exponential systems in water distribution engineering
• Use vectors and parametrics in gear system design
• Integrate all concepts into a real-world capstone engineering project

Every unit begins with a real engineering challenge, then builds the exact math needed to solve it.

Course Overview

• Full Year Curriculum (36 Weeks)
• High School Level (Ages 15–18)
• 1 Full Math Credit (Pre-Calculus / Advanced Math)
• Honors-Level Rigor with Applied STEM Focus

Students complete 6 major engineering units:

1. Structural Engineering: Bridge Design
2. Aerospace Engineering: Rocket Trajectory
3. Electrical Engineering: Circuit Design
4. Civil Engineering: Water Systems
5. Mechanical Engineering: Gear Systems
6. Capstone: Renewable Energy System Design

Each unit follows a powerful learning cycle:

• Engineering Challenge
• Concept Development
• Guided Practice
• Design & Build
• Testing & Analysis
• Documentation & Reflection

How Students Learn

This course uses a project-based, portfolio-driven approach:

• No busywork
• No meaningless worksheets
• No traditional tests

Instead, students demonstrate mastery by:

• Building real models
• Creating mathematical systems
• Writing engineering reports
• Analyzing real data
• Reflecting on their thinking

By the end of the course, students have a professional-level portfolio showcasing both mathematical and engineering competency.

Built for Homeschool Families

You do not need to be a math expert.

This course is designed so that the parent serves as a facilitator, not a lecturer.

• Clear explanations of all math concepts
• Guided discussion prompts
• Step-by-step project structure
• Built-in assessment rubrics

It empowers you to guide advanced learning with confidence.

What Students Will Master

• Functions (polynomial, exponential, logarithmic, trigonometric)
• Analytic geometry, vectors, and parametrics
• Polar coordinates and conic sections
• Sequences, series, and limits
• Real-world mathematical modeling
• Engineering design thinking

Most importantly, students will understand:

Why math matters.
How math works in the real world.
And how to use it to solve meaningful problems.

Materials Needed

• Graphing calculator (TI-84 recommended)
• Access to Desmos (free)
• Basic building materials (balsa wood, cardboard, etc.)
• Notebook or engineering journal
• Optional: Tinkercad or simple modeling tools

Perfect For

• Homeschool high school students
• STEM-focused learners
• Hands-on, project-based learners
• Students preparing for engineering, science, or technical careers
• Families who want rigorous academics without traditional schooling methods

Why This Course Matters

Most students finish math courses asking:
"When will I ever use this?"

Students in this course finish knowing:
“I already have.”

Give Your Student More Than Math

Give them the ability to:

• Think critically
• Build confidently
• Solve real problems
• Create with purpo