Lensmire, J: Math Challenge I-C Topics In Algebra

The math challenge curriculum textbook series is designed to help students learn the fundamental mathematical concepts and practice their in-depth problem solving skills with selected exercise problems. Ideally, these textbooks are used together with Areteem Institute's corresponding courses, either taken as live classes or as self-paced classes. According to the experience levels of the students in mathematics, the following courses are offered:

• Fun Math Problem Solving for Elementary School (grades 3-5)
• Algebra Readiness (grade 5; preparing for middle school)
• Math Challenge I-A Series (grades 6-8; intro to problem solving)
• Math Challenge I-B Series (grades 6-8; intro to math contests e.g. AMC 8, ZIML Div M)
• Math Challenge I-C Series (grades 6-8; topics bridging middle and high schools)
• Math Challenge II-A Series (grades 9+ or younger students preparing for AMC 10)
• Math Challenge II-B Series (grades 9+ or younger students preparing for AMC 12)
• Math Challenge III Series (preparing for AIME, ZIML Varsity, or equivalent contests)
• Math Challenge IV Series (Math Olympiad level problem solving)

These courses are designed and developed by educational experts and industry professionals to bring real world applications into the STEM education. These programs are ideal for students who wish to win in Math Competitions (AMC, AIME, USAMO, IMO, ARML, MathCounts, Math League, Math Olympiad, ZIML, etc.), Science Fairs (County Science Fairs, State Science Fairs, national programs like Intel Science and Engineering Fair, etc.) and Science Olympiad, or purely want to enrich their academic lives by taking more challenges and developing outstanding analytical, logical thinking and creative problem solving skills.

Math Challenge I-C is a four-part course designed to bridge the middle school and high school math materials. For students who participate in the American Math Competitions (AMC), there is a big gap in both the fundamental math concepts and the problem-solving techniques involved between the AMC 8 and AMC 10 contests. This course is developed to help students transition smoothly from middle school to high school, and prepare them for high school math competitions including the AMC 10 \& 12, ARML, and ZIML. The full course covers topics and introductory problem solving in algebra, geometry, and finite math. Algebraic topics include linear equations, systems of equations and inequalities, exponents and radicals, factoring polynomials, and solving quadratic equations. Geometric topics include angles in triangles, quadrilaterals, and polygons, congruent and similar polygons, calculating area, and algebraic geometry. Topics in finite math include logic, introductory number theory, and an introduction to probability and statistics. These topics serve as the fundamental knowledge needed for a more advanced problem solving course such as Math Challenge II-A.

The course is divided into four terms:

• Summer, covering Algebra
• Fall, covering covering additional topics in Algebra
• Winter, covering Geometry
• Spring, covering Finite Math

The book contains course materials for Math Challenge I-C: Additional topics in Algebra.

We recommend that students take all four terms starting with the Summer, but students with the required background are welcome to join for later terms in the course, or select suitable terms for self-paced study.

Students can sign up for the course at https://classes.areteem.org for the live online or the self-paced version.

Dr. Kevin Wang is a co-founder and the Academic Director at Areteem Institute, a WASC-accreditted educational organization. He holds a Ph.D. in Mathematics from the Pennsylvania State University, and has broad experiences in academia and industry. With great passion in STEM education, he devotes his efforts in developing curricula and educational systems to not only help the top-performing students, but also bring the less experienced students into the wonderful world of math and science. He has coached many students who eventually reached the very top of major national and international math and science competitions. Dr. Wang himself was a former China Team member for the International Mathematical Olympiad.

Kelly Ren is a co-founder and the Program Director at Areteem Institute. Ms. Ren has a B.S. degree in Physics, and a Master's Degree in Electrical Engineering from Pennsylvania State University. Her visionary and leadership skills led her to positions in business and management in high tech, software and financial services companies. Ms. Ren also teaches math and science courses at Areteem; her logical and clear instruction has resulted in both parents and students coming back for more. She served as Grand Awards Judge at the Intel Science and Engineering Fair, as well as judges at various state and local level science fairs.

John Lensmire is the Curriculum Director at Areteem Institute. John received his Masters of Arts in Mathematics at the UCLA in 2015 and his B.A in Mathematics with high distinction and a Minor in Computer Science at the University of Minnesota, Twin Cities in 2010. In 2011, he participated in a Symposium on Theoretical Aspects of Computer Science held in Dortmund, Germany. John also was in the 11th percentile in North America for the Lowell Putnam Mathematics Competition.

David Reynoso is a dedicated educator and works as an academic specialist developing our math curriculum. He received his Masters in Mathematics from the University of Maryland at College Park and his Bachelors in Mathematics from the University of Guanajuato. Back in middle school he won the Silver medal twice in the Mexican Mathematical Olympiad.

For information about Areteem Institute, visit http://www.areteem.org.