Mathematical Problem Solving
- Grades 2-3
Can five 20-by-18-foot carpets lying flat with no overlap fit in a 40-by-50-foot room? Can you measure 2 liters of water correctly using only a 4-liter pitcher and a 3-liter pitcher? How many different ways can you add four even, positive numbers to get a sum of 16? Problem-solving in mathematics involves finding a path to a solution, even when there is no clear place to start. In this course, you’ll learn to solve problems using a wide range of approaches like drawing diagrams, making lists, eliminating unreasonable possibilities, identifying patterns, guessing and checking, and manipulating variables. Working individually and in small groups, you’ll learn how to ask questions, choose strategies, and explain your thought processes along the way. You and your classmates will watch demonstrations, do hands-on activities, and play games while becoming critical thinkers and creative problem solvers, strengthening your reasoning skills and preparing for future study in discrete math, probability, and other fields of mathematics.
Typical Class Size: 12
- Explore various strategies for solving mathematical problems, including but not limited to making a list, guess and check, simulations, experiments, diagrams, patterns, and algebraic expressions
- Apply different methods of problem solving to investigate, solve, and justify solutions for simulated and real-world math problems
- Create and share graphs, tables, diagrams, models, and other visual tools to solve problems and justify solutions
- Investigate creative strategies for solving complex problems, including a final project that involves creative applications of the problem-solving strategies learned in class
- Share ideas and solutions to problems, both written and orally, both independently and collaboratively in groups
Summer Dates & Locations
Testing and Prerequisites
|Required Level||CTY-Level||Not required|
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
- 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.
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.