- Math Circle Diaries, Year 1: A Complete Curriculum
- by Anna Burago
Join our math circles for students grades 2 and up!
In a math circle, students explore the fun side of mathematics and go beyond school curriculum. We encourage critical thinking and interactive discussions between teachers and students, while consistently promoting the ideas of rigorous proofs and logical reasoning. Fun puzzles, educational mathematical games, and tournaments are an essential part of our curriculum.
All circles share the same methodology; however, the scope of the presented material and presentation approach will differ.
Beginner Circle is our class for the youngest students, in grade 2. Our main goal in this circle is to develop students' reasoning and creative thinking abilities, and to explore mathematics outside school arithmetic. We will engage kids in discussions, problem solving, hands-on activities, and games. This class is suitable for students who are not only interested in mathematics, but are mature and focused enough to actively participate during the whole duration of the class (one hour).
In this circle, we will work on challenging
word problems and get to explore advanced math concepts and ideas through hands-on
experience. We'll introduce the ideas of mathematical reasoning,
logic and mathematical proof in a fun and engaging way.
The students will learn how to approach logical puzzles, unusual word problems, learn about cryptography and ciphers, binary numbers, fractals, and more.
To view a sample curriculum from this class visit the Archives page.
In this class, the graduates of Junior Circle 1 as well as new students continue to learn creative step-by-step problem analysis, as well as thinking about a problem logically and from multiple perspectives. We’ll explore various topics and problem-solving techniques including logics, parity, word problems, constructive problems, elements of the graph theory, elements of combinatorics, number puzzles. We will do a lot of work on challenging problems that require creativity and out-of-the-box thinking. Math contests, tournaments, and games remain a part of the curriculum as an educational and enjoyable way to engage in problem solving.
To view a sample from this class visit the Archives page.
The circle is about more advanced math concepts and more challenging problems than Junior Circle 2.
The “hands-on” element of the curriculum is balanced with more advanced material required for building a solid foundation for our middle school program.
The students will learn about: logic problems, parity, elements of divisibility theory, weighings and other types of construction problems, creative word problem solvings, visual geometry, combinatorics, smart trial and error, and number theory. While working on these topics and learning new problem-solving solving techniques, the students will be exposed to all elements of mathematical inquiry: creative exploration, rigorous proof and clear explanation. Math tournaments and games such as Math Auction, Math Hockey and Math Dominoes remain a vital part of this circle's curruculum.
To learn more about this class visit the Archives page.
This circle is intended for 6th-7th grade students with or without previous math circle experience. We will explore in more depth: parity, logic problems, divisibility and number theory, combinatorics, constructive problems, cryptography, and game theory. We'll also work on developing of the concepts of math reasoning, justification, proof and the basic ways of logical reasoning. We'll also spend a lot of time working on the challenging problems that mostly require brainpower, creativity and common sense. Some of the classes will be devoted to math contests and competitions – educational ways to get students engaged in active problem solving.
This circle is for the students of grades 7-8 who have already attended a math circle, or are familiar with our Math Circle 1 topics, or are ready to put in extra work to catch up with our Circle 1 program. We'll be expanding our understanding of previous topics, and we will be introducing a wide variety of new topics and problem-solving techniques. We'll be learning proofs by contradiction, necessity and sufficiency, and other proof concepts. The students will get acquainted with elements of graph theory, invariants, colorings, geometry, strategic games, and number systems.
Modern computer science is largely built on branch of mathematics called discrete mathematics – the study of structures that have a discrete nature. Logical statements, graphs, and integer numbers serve as examples of such structures. These mathematical structures find wide application in computing. The course focuses on selected topics in discrete mathematics and their applications in computer science. The students will learn about Boolean logic and logic gates, induction, recursion, number systems, data compression algorithms, and more. This will be a challenging and fast-paced class with plenty of practice and of interesting problem-solving. Enrollment is by the results of the test, by math circle teacher recommendation, or by qualifying math score from Kangaroo (national winner) or AMC exams (at least 18 on AMC 8).
Each circle meets once a week for an hour and a half long session (one hour for our youngest students). A typical session combines class discussion, individual and team problem solving, and for younger students, hands-on exploration. The students regularly have homework consisting of around 5 problems, which are then discussed during next session. Some of the classes are devoted to math competitions and math Olympiads.