About the Course

Geometric and Spatial Reasoning

  • Grades 3-4
  • CTY-Level
  • LIVE

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

Important Dates
Apply by August 30 to start:

Apply by August 30 to start:


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.

9 weeks
5:00 p.m. (ET)

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)

Financial Aid is available

We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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Course Materials

Please acquire all course materials by the course start date. If you have questions about these materials or difficulty locating them, please contact ctyinfo@jhu.edu.

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


  • 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 college-level curricula—cover a wide range of topics, from algebra and geometry to chess, cryptology, and AP Calculus 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 honors and AP (and beyond) academic standing, or to train for mathematics competitions, there’s a CTY course that’s right for you.

New math enrichment courses available!

Explore our new math enrichment courses, including Excursions in Pre-algebra, Mathematical Modeling, and Introduction to Logic and Proofs.

Meet our Mathematics Instructors