For 6th and 7th Grade
Introducing Mot_Math in English – a unique course new to Bulgaria that offers an unparalleled opportunity for in-depth math preparation entirely in English. This course is an ideal solution for children born outside Bulgaria, as well as for bilingual students who want to develop their mathematical skills while mastering English terminology.
In Mot_Math, we combine core mathematical and logical topics with English language proficiency. We dive into fascinating concepts like measuring lengths with light, calculating travel time to Mars, juggling negative numbers, understanding progressions, functions, and graphs. We also explore many other interesting practical problems that go beyond the typical middle school curriculum, such as what “mot” is and many other intriguing topics.
The course is specifically designed for general preparation for admission to prestigious educational institutions like the American College of Sofia, Anglo-American School, and other international colleges with English-language programs. Our goal is to provide children with not just mathematical knowledge, but also the confidence to comfortably handle English terms and concepts, fully preparing them for studies in foreign language high schools. This way, we ensure that any potential gaps in Bulgarian language won’t prevent children from mastering and enjoying the beautiful language of mathematics.
Here are the topics we cover:
- Geometry of Plane and Solid Figures: This covers studying circles, polygons (including regular ones), and their lengths and areas. We then move to three-dimensional shapes like prisms, pyramids, cylinders, cones, spheres, and balls, focusing on surface areas and volumes.
- Rational Numbers and Operations: We dive deeper into working with positive and negative numbers, including their representation on the number line, comparison, addition, subtraction, multiplication, and division. We also explore concepts like opposite numbers, absolute value, and algebraic sums.
- Exponents: We learn about exponentiation with natural and zero exponents, the properties of powers with equal bases, and how to exponentiate products, quotients, and powers of powers. This section also includes the standard form of a number.
- Equations and Modeling: We solve linear equations in the form a.x+b=0 and apply rules for solving equations, as well as modeling real-world situations with equations.
- Ratios, Proportions, and Proportionality: We explore ratios and proportions (including their fundamental property and application), direct and inverse proportionality, and how to interpret data using diagrams and graphs.
- Fundamentals of Analytic Geometry: An introduction to the Cartesian coordinate system and coordinates of a point.
- Pythagorean Theorem: Understanding and applying this fundamental theorem for right-angled triangles.
- Introduction to Sets and Probability: We study basic concepts of sets, elements, and subsets, as well as the probability of a random event and statistical data representation (arithmetic mean, tables, graphs).
- Rational Expressions and Monomials: This involves studying rational expressions, variables and constants, and working with monomials (normal form, addition, subtraction, multiplication, exponentiation, and division).
- Polynomials and Shortened Multiplication Formulas: We look at polynomials (normal form, addition, subtraction, multiplication) and thoroughly study shortened multiplication formulas and their applications.
- Factoring Polynomials: Mastering various methods for factoring by extracting a common factor, using shortened multiplication formulas, grouping, and combined methods.
- Equations – Types and Modeling: Working with equivalent and linear equations, including specific types like (ax+b)(cx+d)=0 and |ax+b|=c. We emphasize modeling with linear equations to solve word problems related to motion, work, capital, mixtures, and alloys.
- Basic Geometric Figures and Constructions: An introduction to geometry, fundamental figures and constructions, working with adjacent and opposite angles, perpendicular and parallel lines (properties and criteria).
- Triangles and Congruence: We study the sum of angles and exterior angles in a triangle. A deep dive into congruent triangles (first, second, and third criteria), isosceles, and equilateral triangles. We also cover perpendicular bisectors, angle bisectors, medians, and altitudes, including specific cases for right-angled triangles (median to the hypotenuse, 30-degree angle).
- Inequalities: Working with numerical inequalities and their properties. Solving linear inequalities with one unknown, representing solutions with numerical intervals and graphically, and applying inequalities in geometry (inequalities between sides and angles in a triangle, triangle inequality).
- Parallelograms and Special Types: We study parallelograms (properties and criteria), as well as their special cases – rectangles, rhombuses, and squares.
- Elements of Probability and Statistics: Organizing and presenting data, constructing and interpreting pie charts. Solving probability problems and other practical tasks related to probability and statistics.
Just like our other courses, we work in small groups of up to 8 people, allowing us to provide individual attention to each student. Our approach focuses on building a lasting interest in mathematics in an engaging and inspiring way, within a creative environment that encourages experimentation and development. This helps children not only grasp complex concepts but also develop key skills for solving mathematical challenges that will serve them a lifetime, including mental arithmetic, quick and rational thinking, and the development of logic and deduction.