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Advanced Counting

(two-semester course)

Advanced Counting course is part of the Classic Math School Program and is intended for students from 2nd to 5th grade. This course requires the confident use of table of multiplication and certain level of fluency with whole numbers. The scope and depth of the course may vary significantly depending on the actual students’ level and duration of the course.

Interactive Advanced Counting course is designed to be taught in a small group setting using a variety of instructional methods and materials. Hands-on activities, math games and puzzles form an integral part of each class session to enhance students’ understanding and retention.

The topics and problems that are studied in Advanced Counting course may include:

1.      Addition, subtraction, multiplication and division of multi-digit whole numbers. Order of operations. Changing the order of operations using grouping symbols and/or properties. Commutative and association properties for addition and multiplication. Distributive property of multiplication (division) over addition (subtraction). Using the properties for mental math with discretion.

2.      Introduction to the concept of long division with a remainder. Understanding the relationship between the dividend, divisor, quotient, and remainder.

3.      Introduction to the concept of divisibility. Rules of divisibility. Prime numbers. Factoring. Exponential notation. Greatest Common Factor (GCF) and Least Common Multiple (LCM). Relatively prime numbers.

4.      The concept of fractions. Fractions as part of a whole and fractions as part of a set. Proper and improper fractions. Mixed Numbers. Whole numbers as fractions. Converting improper fractions to mixed numbers and backwards.

5.      Comparing fractions. Fractions on the number line. Simplifying fractions. Equivalent fractions. Addition, subtraction, multiplication, and division of fractions and mixed numbers.

6.      Solving and making up word problems that involve operations on fractions. Finding a certain part of a given whole and vice versa.

7.      Introduction to the concept of probability.

8.      The concept of decimals. Different decimal notations for the same numbers. Whole numbers as decimals. Reading and writing decimals.

9.      Comparing decimals. Decimals on the number line. Addition, subtraction, multiplication, and division of decimals. Rounding Decimals.

10.  Converting decimals to fractions (proper, improper, mixed numbers) and backwards. Their relative positions on the number line.

11.  Solving and making up word problems that involve operations on decimals.

12.  Percents as decimals and fractions.

13.  Mixed problems involving fractions, decimals, and percent notations. Understanding the need of conversion. Relative advantages and disadvantages of each notation. The optimum choice for every problem.

14.  The concept of measurement. Identifying appropriate units (metric and US) of measuring length, area, volume, weight/mass, time, and money. Carrying out simple unit conversion within a system of measurements and between the systems. 

15.  Solving and making up money “management” and time “management” problems involving fractions, decimals, percents and unit conversions.

16.  Understanding basic geometric terms (point, line, segment, ray, angle) and their proper notation. Identification and classification of different angles (acute, right, obtuse). Identification and classification of polygons (triangles, quadrilaterals, pentagons, hexagons, etc.) and three dimensional solids (prisms, pyramids, cones, and cylinders). Circles and spheres.

17.  Identification and classification of triangles (equilateral, isosceles, scalene, acute, right, obtuse), and quadrilaterals (square, rectangle, rhombus, parallelogram, kite, trapezoid). Introduction to the concepts of congruency and similarity.

18.  Introduction to the concepts of variable and formula through the simple perimeter and area formulas. Variable (formula) as a convenient device for repetitive calculations. Derivation and application of area formulas for the square, rectangle, triangle, parallelogram, and trapezoid based on area addition postulate.

19.  Two-dimensional coordinate system. Plotting points with given coordinates and finding coordinates of the given points. Translations and rotations of figures.

20.  Introduction to integers. Addition and subtraction of simple integers using the number line.

21.  Finding, describing, and extending patterns of numbers, symbols, and geometric figures.

22.  Solving logic problems by justifying and articulating the reasons.