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Grade 6

20260723.Thu first session - mostly quiz

Patterns/Sequences

20260827.Thu hw
20260829.Sat
Score Pct 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
26.5/36 73.6 c a _ a c c c c d c a d c a _ a c d b c c b c _ _ a a a _ a a _ _ a a a
20260831.Mon Patterns/Sequences - matchstick rearrangement problems



Algebra and Number Theory

1) Divisibility Rules (2, 3, 4, 5, 6, 8, 9, 11)
20260908.Tue hw
202609XX
Score Pct 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
a b c d 111 221 1111 100001 107107 1234554321 1 2 3 4 1 2 3 4 5 6 1 2 3 4
19.5/38 51.3 7 (a,b)∈{(5,2)} (a,b)∈{(5,0),(0,5)} (a,b)∈{(2,0),(7,4)} 3 13.17 11 11 9 3 c 12 No 8 3 4 3 3 0 1 3 2 1 3 3 8 4 c _ c b 529isamultipleof3 a d 5 1230432 2232,2532,2832,2136,2436 1
202609XX
Score Pct 1 2 3
1 2 3 4 1 2 3 4 1 2 3 4
4.25/13 32.7 ? 262,161 196,621 idk 1 7 2 4 ? ? ? ?
202609XX
Score Pct 4 5 6 7 8 9 10 11 12 13
1 2
8.5/12 70.8 a b c 11 withAlx withAlx 25 18,38 62 _ 5

2) Greatest Common Divisor (GCD) & Least Common Multiple (LCM)
3) Powers of Numbers & Exponent Rules
4) Algebraic Equations & Systems of Variables (Most important)
5) Working with Fractions & Ratios (4 involved)
6) Base-10 Structure (1, 10, 100, 1000) (4 involved)
7) Averages & Statistical Mean

Rates and Kinematics

8) Work, Time & Capacity (Working Hours)
9) Velocity & Motion Kinematics
10) Clock Angles & Time Calculation

Combinatorics and Set theory

11) Bipartite Matching (Match People with Things) (Most simple)
12) Venn Diagrams & Overlapping Sets (Really important)
13) Fundamental Counting Principle & Combinatorics
14) Logic of Truth-Telling & Lying Games (Simple) (Can be combined with 11)
15) Pigeonhole Principle & Worst-Case Scenarios

Game Theory and Tournaments

16) Tournament Structure & Results
17) Balance Scale Logic & Weighings
18) Combinatorial Strategy Games (Hard)

Geometry

19) Perimeter & Planar Dissections (Hard)
20) 2D Geometry & Area (Hard)
21) 3D Geometry & Surface Area

Bonus

22) Match Sticks
23) Constructions



Grade 7

Algebra

1) Variables & Expressions
2) Natural Powers & Prime Factorization (including GCD & LCM, Total number of divisors of a number)
3) Divisibility Rules & Properties (including last-digit arithmetic, modular arithmetic/arithmetic of remainders, number formulas e.g., odd n = 2k + 1, Euclidean algorithm)
4) Custom Operations (New/binary operators and custom operations)
5) Set Theory (subsets, equality of two sets, empty sets; operations: union, intersection, set difference, symmetric difference)
6) Number Line & Decimals (The number line, negative numbers, periodic and non-periodic decimals, converting repeating decimals into fractions)
7) Absolute Value (Absolute value (module) of a number)
8) Percentages
9) Proportions (directly proportional and inversely proportional quantities)
10) Averages & Mixture Problems (Solving problems using arithmetic mean)
11) Distributive Property (expanding/opening brackets)
12) Linear Equations
13) Exponent Rules (Natural exponents and properties of powers with natural exponents)
14) Monomials (Monomials, operations on monomials: multiplication, exponentiation/raising to a power, degree of a standard monomial)
15) Polynomials (Polynomials, standard polynomials, degree of a polynomial, operations on polynomials: addition, subtraction, multiplying a monomial by a polynomial, multiplying polynomials)
16) Algebraic Identities (square of sum and difference of two expressions, square of sum of three or more expressions, sum and difference of cubes, sum and difference of $n$-th powers, cube of sum and difference of two expressions)
17) Quadratic Trinomials (completing the square, finding maximum and minimum values)
18) Identities (Proofs of algebraic identities)
19) Polynomial Division
20) Factoring Polynomials factoring out common factors, grouping method, using algebraic identities, a^n - b^n, a^n + b^n, factoring trinomials where a = 1 with rational roots)
21) Cartesian Coordinate System (The coordinate plane, coordinates of a point)
22) Functions & Graphs (Definition of a function, methods of representing functions, function graphs)
23) Linear Functions (position of linear function graphs relative to coordinate axes and each other, parallel and perpendicular lines).
24) Graphical Solution of Equations
25) Linear Equations in Two Variables
26) Systems of Linear Equations (solving systems using substitution and elimination/addition methods).
27) Reducible Systems
28) System Applications (Solving word problems by constructing systems of linear equations)


Geometry

1) Foundations of Geometry: Introduction to geometry (primitive concepts, axioms), relative positions of points and lines, relative positions of lines.
2) Line Segments: Segments, segment construction axiom, segment measurement axiom.
3) Half-Planes: Concept of a half-plane.
4) Rays: Concept of a ray.
5) Angles: Angle measurement, angle measurement axiom.
6) Angle Bisectors
7) Supplementary & Vertical Angles
8) Perpendicular Lines: Angle between two lines, perpendicularity of lines
9) Congruence: Congruence/equality of geometric figures.
10) Parallel Lines: Criteria for parallel lines, properties of parallel lines
11) Triangles: General concepts of triangles
12) Triangle Angle Sum: Sum of angles in a triangle
13) Triangle Cevians: Altitudes, bisectors, and medians of a triangle
14) Triangle Congruence Rules (SAS & ASA & SSS)
15) Isosceles Triangles
16) Perpendicular Bisectors
17) Exterior Angles
18) Triangle Inequality
19) Distance & Right Triangles: Distance from a point to a line, distance between two parallel lines, right triangles, criteria for right triangle congruence.
20) Properties of Right Triangles: Property of a 30 angle's opposite side, property of the median to the hypotenuse, angle bisector properties, angles formed between the altitude, median, and bisector drawn from the right-angle vertex).
21) Circles & Lines: Circles (radius, diameter, chord, tangent line)
22) Perpendicular Diameter Property
23) Intersections of Circles
24) Inscribed & Circumscribed Triangles
25) Arcs & Central Angles
26) Inscribed Angles
27) Intersecting Chords & Secants