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

This course is

ungraded.

Summer Dates & Locations

Registration deadline:

After May 2, 2025, registration is available upon request pending eligibility and seat availability. To request placement, email [email protected] after submitting a program application.

Session One

Birdseye view image of the campus of Mirman School
Mirman School
Los Angeles, California
-
Day cost: $3,959
Enroll
Image of Gilman School Baltimore
The Gilman School
Baltimore, Maryland
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Day cost: $3,149
Enroll
Image of Speyer School in New York City
Speyer School
New York, New York
-
Day cost: $3,959
Enroll

Session Two

Birdseye view image of the campus of Mirman School
Mirman School
Los Angeles, California
-
Day cost: $3,959
Enroll
Image of Speyer School in New York City
Speyer School
New York, New York
-
Day cost: $3,959
Enroll

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 - $55 (Waived for financial aid applicants)
    • Nonrefundable International Fee - $250 (outside US only)

We have concluded our financial aid application review process for 2025 On-Campus Programs. We encourage those who may need assistance in the future to apply for aid as early as possible. We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.

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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. Younger students build foundational skills by exploring shape, scale, and proportion in Geometry and Spatial Sense. Middle School students delve into real-world applications of lines and analyze data with curves that follow uniform, symmetric, bell-shaped, or skewed patterns in Data and Chance. Advanced students unveil the deep interplay between numbers and shapes, investigating how triangular, square, and polygonal numbers create patterns that bridge geometry and algebra in Number Theory. By examining these elegant number patterns and symmetries, students discover how mathematics captures the intricate beauty and underlying structure of the natural world.

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