Mathematics Institute of the Triangle is an “after school” program with classes currently on Sunday afternoons and growing to include Thursdays after school in the 2023-4 school year. Classes are not just for those who excel at math; in fact, especially in Beast Academy, the material is easily approachable and slowly grows in depth. Students who have a curiosity and interest in math and who allocate time to work problems as they do their homework in between classes set themselves up for success.

We use curricula from Art of Problem Solving (AoPS) as well as material each teacher has developed. Our teacher Dilip also teaches at AoPS; another teacher, Kim, uses their curricula in her own classes. We love AoPS because it starts off very accessibly and builds to give richness focused on problem solving that is difficult to find in other curricula – all while maintaining the joy and interconnectedness of mathematics. Our school is not AoPS; there is an AoPS academy in Morrisville, NC and a virtual online one, both of which we highly recommend if we can’t serve your students’ needs.

AoPS starts with Beast Academy for levels 1-5 and then prealgebra. After that the typical sequence is: algebra, geometry, advanced algebra, precalculus, and calculus. Competition math classes are also offered, as is mechanics (which we may offer in the future). As demand grows, we hope to offer all levels through precalculus and calculus. The following are our notes on the levels.

**Math Circle 1/2**

Grades 1-2

A math circle is not like a typical math class but rather helps students to explore and play with mathematical concepts. Parents are encouraged to join their children for a 1-hour weekly session. Topics are wide-ranging, all designed to deepen a student’s interest in the joy of math, and may include playing and designing a game; figuring out what “figurate numbers” like Square and Triangular Numbers are and how to build upon them – and coming up with one’s own such numbers; using a compass and straight edge to construct diagrams illustrating concepts like parallel and perpendicular lines or copying a shape; and looking for and creating patterns in nature, art, at home, and in numbers.

**Math Level 1**

Grade 1

Level 1 lays a foundation that builds upon the abilities to count to at least 20. Fun lessons in patterns, counting, shapes, comparing, adding and subtracting, measurement, and problem solving give students the confidence to build their math skills while having a good time with the colorful books with monsters who enact different learning styles. Details for all the Levels 1-5 including scope and sequence and mapping to Common Core State Standards can be found at beastacademy.com/resources/planning.

**Math Level 2**

Grade 2

Level 2 is a lovely introduction to important problem-solving skills. Students build a deeper understanding of place value, become comfortable with adding and subtracting multi-digit numbers, look at interesting puzzles, consider very big numbers, and consider non-obvious applications of odd and even numbers. There is a very basic introduction to variables but shhh… we don’t tell students that! 3rd graders who need more foundation in math can successfully take Level 2. It’s Dilip’s favorite level! By starting students here, it sets the stage for their continued success in problem solving and mathematics.

**Math Level 3**

Grade 3

Key concepts that are covered include multiplication, division, and using the distributive rule (e.g., 58 x 7 = (60-2)x7 = 60x7 – 2x7 = 420-14 = 406); an introduction to fractions leading up to students’ understanding how to make sophisticated comparisons of fractions; and basic geometry. We grow with use of variables and discuss expressions and equations. Puzzles and word problems are included.

**Math Level 4**

Grade 4-5

Level 4 solidifies multiplication and division and goes on to include decimals, negative numbers, probability and counting, geometry, symmetry, prime numbers, and logic.

**Math Level 5**

Grade 5-7

Level 5 starts with an exciting unit on 3D geometry. We cover a variety of topics such as more geometry, number theory, divisors and multiples (at Mathematics Institute of the Triangle we have some cool additional ways we share for computing GCD and LCM), ratios, counting (e.g., how many numbers are there: 7, 12, 17, 22, …, 227 ?) sequences, fractions and decimals, ways of working with very large numbers, and more.

**Prealgebra**

Grade 6-8

Prealgebra begins with a review of Level 5 but in more detail and with a more comprehensive textbook. In addition we cover counting, probability, and some challenging geometry.

**Algebra**

Grade 7-9

Our algebra (Algebra 1) is more broad and deep than typical high school algebra classes. Topics include more detailed review of material like rates and inequalities from prealgebra followed by solving linear and quadratic equations, graphing, functions, imaginary numbers and the complex plane (we also discuss a fascinating connection to Pythagorean triples), and compound interest. We have some handouts to help demystify factoring, including several techniques that can help. The content is similar to NC public schools’ Math 1 without least squares regression and Math 2 without conditional probability or geometry.

**Geometry**

Grades 8-10

In algebra our students will have been exposed to analytical geometry. Geometry continues and includes trigonometry and basics of precalculus. We feel it is the most challenging class in this set of classes that we offer or plan to offer.

**Advanced Algebra**

Grades 9-11

Advanced algebra (Algebra 2) continues with material learned in algebra, going deeper in areas like optimization with inequalities, series and sequence, and polynomials.

**Precalculus**

Grades 10-12

In precalculus further study is done with trigonometry and complex numbers. Vector spaces are introduced and the foundation is laid for calculus.

**Calculus**

Grades 11-12

Calculus is taught at the level of an introductory college class with traditional topics expected such as L'Hôpital's rule, limits, continuity, chain rule, fundamental theorem of calculus, polar coordinates, power series, derivatives, integrals, and differential equations.

**Competition Math**

Grades 6-12

In competition math, the focus is on deeper understanding and approach to problems that are often tested in competitions like Mathcounts and AMC.

Roughly speaking, Levels 1-5 are supersets of the grade level indicated by the number; e.g., Level 2 is a superset of the 2nd grade NC Math Standard Course of Study. However, our mathematics generally go into more topics and in more detail, so it may be perfectly appropriate, for example, for a 6th or 7th grader to be in Level 5. For those with a foundation of Beast Academy, Prealgebra would come after Level 5, followed by Algebra, Geometry, Advanced Algebra (though it can be taken before Geometry), Precalculus, and Calculus.

Here is a rough mapping of the NC Math Standard Course of Study for high school to the Art of Problem Solving plus our custom curricula.

**Math 1**

Grades 9; 8

AoPS algebra roughly covers Math 1 without least squares regression and Math 2 without conditional probability or geometry.

**Math 2**

Grades 10; 9

AoPS geometry provides more extensive coverage of the geometry topics in Math 2.

**Math 3**

Grades 11; 10

Many of Math 3’s topics are covered in AoPS algebra, such as polynomial and rational expressions, inequalities, building polynomial and exponential functions, and logarithms; topics like trigonometric functions and geometry are covered in AoPS geometry.

**Math 4**

Grades 12; 11

Math 4 topics are a subset of ones in AoPS advanced algebra.

**Precalculus**

Grades 11-12

AoPS precalculus is a superset.

**Calculus**

Grades 11-12

AoPS calculus is a superset.

**Discrete Math**

Grade 12

Many schools do not offer discrete math. AoPS counting and probability classes (introduction and intermediate) cover many of these topics.

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