About the Course

Geometric and Spatial Reasoning

Geometric and spatial reasoning skills are essential for living in and making sense of the world around us. Everything from solving a jigsaw puzzle to arranging furniture to efficiently packing a bag requires these abilities. Learn and practice these skills as you delve into the mathematical relationships between objects—ones that include congruence and symmetry, reflection and rotation, or expansion and contraction.

Explore the geometric properties of regular polygons and the so-called platonic solids, investigating relationships between area, circumference, and volume in a rigorous fashion.

Exercise hands-on investigation, collaboration, and discussion as you and your classmates physically construct polyhedra while exploring the geometric properties of regular polygons, tessellations, and other tools for studying objects in space.

Fall and Spring Time Commitment: 4-5 hours per week (1-hour of class time, 3-4 hours of independent work).
Summer Time Commitment: 12-15 hours per week (3-hours of class time, 9-12 hours of independent work).

Course Overview

This course is

ungraded.

Classes

Register for an Online course by selecting an open class below. If no open classes are listed, then course enrollment is currently closed. Note: You will need to have an active CTY Account to complete registration through MyCTY

 

This course is not open for enrollment at this time. Please check back later.

Testing and Prerequisites

  Math Verbal
Required Level CTY-Level Not required
Check your eligibility using existing test scores If you do not have existing test scores:

Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.

Sign up for Testing Learn More

Cost and Financial Aid

  • Tuition
    • Varies
  • Application fee
    • Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $20 (outside US only)

CTY Financial Aid Availability for Online Programs

Academic Year 2025-26 (Course start dates July 1, 2025- June 30, 2026): Financial Aid funding is currently available for all eligible students while funding lasts. If interested in applying for financial aid, please select a course with start date of July 1, 2025, or later.

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Course Materials

Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
 

Book Title: The Wright 3
Author: Blue Balliett
ISBN: 978-0439693684

Materials:

  • Hardwood cubes, 100 pack
  • Bullseye Compass
  • (Optional) protractor
  • (Optional) tangrams

Technical Requirements

This course requires a computer with high-speed Internet access and an up-to-date web browser such as Chrome or Firefox. You must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses a virtual classroom for instructor-student communication. The classroom works on standard computers with the Zoom desktop client, and on tablets or handhelds that support the Zoom Mobile app. Recorded meetings can only be viewed on a computer with the Zoom desktop client installed. The Zoom desktop client and Zoom Mobile App are both free to download.

About Mathematics at CTY

Our online Mathematics courses—spanning elementary through high school curricula—cover a wide range of topics, from algebra and geometry to chess, and cryptology and are guided by expert instructors. You’ll join group sessions with classmates to ensure you stay on track with challenging course content. Whether you’re looking for pure math fun and enrichment, to move up the math ladder and advance your academic standing, or to train for mathematics competitions, there’s a CTY course that’s right for you.

Uncover the Exciting World of Cryptology

Unlock the world of secret communication! In Cryptology: Cracking Codes you and your classmates will uncover the logic, patterns, and problem-solving strategies that drive cryptographic systems. Thorugh hands-on activities like encrypting and decrypting messages and creating your own ciphers, you’ll deepen your understanding of how cryptology has developed throughout history to shape our modern encryption systems and secure our digital world.