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# P

##### Prerequisite: Master addition & subtraction problems within 20; understand addition & subtraction within 100

Main Topics:

• Calculation: The concept of multiplication and division; Finding patterns & completing the patterns; Efficient addition & subtraction calculations

• Counting: Real life probability, counting 2D & 3D shapes; The split strategy with/without regrouping

• Combinatorics: Sorting & classifying shapes; Matchstick puzzles; Reflectional (mirror) symmetry; The understanding of odd & even; numeral comparison; fun dice problems; clock angle problems

• Puzzles: Filling in the “plus” and “minus” signs; equation puzzles

• Geometry: The learning of angles; Shape composition/decomposition; 3D shapes; Multi-view—Basic three-view drawings

• Word problem: Measuring lengths with different units; unit conversions; ordinal numbers; two-step multiplication and division word problems

• Number theory: None

# 1

##### Prerequisite: Master addition & subtraction problems within 100; understand the concepts of multiplication and division; multiplication facts fluency

Main Topics:

• Calculation: Efficient addition & subtraction problem calculations; looking for patterns in number sequences; looking for shape patterns (advanced); addition & subtraction equations

• Counting: Counting regular 2D & 3D shapes

• Combinatorics: Odd & even number problems (basic); basic logic reasoning; matchstick puzzles; eulerian path

• Puzzles: Filling signs; vertically stacked shapes puzzle; addition & subtraction puzzles with vertically stacked numbers; Sudoku puzzle

• Geometry: The transformations of 2D shapes; the learning of 2D & 3D shapes; nets for 3D shapes; multi-view—advanced three-view drawings

• Word problem: Measurement; age problems (basic); balance scale; backwards reasoning strategy; sum, difference, & multiple (basic);

• Number theory: Division with no remainder (basic)

# 2

##### Prerequisite: Master the 4 operations

Main Topics:

• Calculation: Efficient multiplication & division problem calculations; the distributive property of multiplication; arithmetic—the 4 operations; the sum of arithmetic sequences

• Counting: The split strategy; enumeration; dendrogram

• Combinatorics: Pigeonhole principle, strategy games for odd & even numbers

• Puzzles: Multiplication & division puzzles with vertically stacked numbers

• Geometry: Calculations of lengths and angles; compose shapes

• Word problem: Sum, difference, & multiple (advanced); profit & loss problems; ancient Chinese puzzle--- chicken & rabbit (basic); ancient Chinese puzzle--- chicken & rabbit (advanced)

• Number theory: Division with no remainder (advanced) ##### Dr. Qin

Retired Wall Street Quant

Ph.D in Statistic at Purdue University

National Math Competition First Prize

Over years of teaching experience with High School and Middle school students

See full profile ##### Ms. King

Master in Mathematics at NYU

Bachelor in Mathematics at Texas A&M

Over years of teaching experience with Elementary students

See full profile ##### Ms. Eileen

Ph.D in Education at Columbia University

Bachelor at Emory University

Over years of teaching experience with Elementary students

See full profile

# 3

##### Prerequisite: Master the 4 operations, some knowledge of fractions, percentages, and decimals

Main Topics:

• Calculation: Efficient multi-digit problem calculations; efficient decimal problem calculations; calculations of number sequences using formulas

• Counting: Addition principle; multiplication principle; formulas for permutations & combinations

• Combinatorics: Analysis of odd & even; problems involving overall planning; logic reasoning; problems involving maximum; strategic games; pigeonhole problems (advanced)

• Puzzles: Advanced vertically stacked calculations; vertically stacked letters; Sudoku puzzle

• Geometry: Area (formula & calculation)

• Word problem: Age problems (advanced); profit & loss problems (advanced); sum, difference & multiple (advanced); distance problems (basic)—motion either in opposite directions or the same direction; distance problems (advanced)— round trip questions; Problems involving arithmetic mean

• Number theory: Prime & composite numbers; common divisor & common multiple

# 4

##### Prerequisite: Master the operations involving fractions, percentages, and decimals; some knowledge of geometry and number theory

Main Topics:

• Calculation: Whole number splitting; fractions & repeating decimals; fraction splitting; equation system solving

• Counting: Inclusion-Exclusion Principle; counting in geometry, number puzzles, and number theory

• Combinatorics: Logical reasoning

• Puzzles: Place value

• Geometry: Area problem solving; area of a circle and a sector (basic); solid geometry

• Word problem: Word problems involving equations; problems involving boats & streams; distance problems (advanced)---ratios; mixture word problems; indefinite equation; the concepts of direct & inverse proportion, with application

• Number theory: Rounding; carrying; remainder

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