About the Course

Geometry and Spatial Sense

Spatial understanding is necessary for interpreting, understanding, and appreciating our inherently geometric world. Many everyday tasks such as designing a treehouse, solving a jigsaw puzzle, or laying out a garden require spatial reasoning abilities. This course will help you develop those abilities through discussions and hands-on investigations. You’ll explore mathematical relationships such as congruence, symmetry, and reflection; learn geometric formulas to calculate area, surface area, perimeter, circumference, and volume; and explain your findings using geometric terminology. You and your classmates will explore the geometric properties of regular polygons and create your own polyhedra using paper-folding techniques. By creating two- and three-dimensional drawings and physical models, you’ll study tessellations, similarity, measurement, polygons, and curved shapes. You’ll leave this course with a solid understanding of foundational geometry concepts and a well-developed spatial sense.

Typical Class Size: 12

Course Overview

Summer Dates & Locations

Registration deadline:

Session One

Speyer School
New York, New York
Commuter cost: $3,599

Session Two

Speyer School
New York, New York
Commuter cost: $3,599

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 - $50 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $250 (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.

Learn More

About Mathematics at CTY

Explore the study of shapes

Many of our courses allow students to describe the world around them in basic and profound ways. Our younger students learn about shape, scale, and proportion in Geometry and Spatial Sense. Middle School students explore beautiful real-world applications of lines; analyze data based on curves that fit a uniform, symmetric and bell-shaped, or skewed pattern in Data and Chance. And advanced students explore the underlying mathematics and fundamental characteristics of shapes, distance, and continuous deformations in our proof-based Topology course.

Dive deep into logic and reasoning

Our courses in formal logic give you the tools to question the world around you. Inductive and Deductive Reasoning introduces younger students to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.

Meet our instructors and staff