*
Advanced Counting*

*
(two-semester course)*

**
Advanced Counting **course is part of the Classic Math School
Program and is intended for students from **2**^{nd}
to **5**^{th} 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.