Foundation Building:
Recognize and understand basic number concepts (counting, place value).
Identify patterns and sequences in numbers and shapes.
Begin to develop basic problem-solving skills through simple addition and subtraction problems.
Introduce basic logic concepts such as "if-then" statements in simple contexts.

Exploring Patterns and Relationships:
Explore more complex patterns and sequences in numbers and shapes.
Introduce multiplication and division concepts and their relationships.
Begin to solve simple word problems involving multiple steps.
Introduce basic geometric concepts and properties.
Start exploring logical puzzles and games to develop deductive reasoning skills.

Logical Problem-Solving:
Develop fluency in arithmetic operations (addition, subtraction, multiplication, division).
Solve multi-step word problems involving all four operations.
Explore fractions and decimals, understanding their relationships and operations.
Introduce algebraic thinking and simple equations.
Engage in logical reasoning activities such as Sudoku, logic puzzles, and deductive reasoning games.

Introduce basic concepts of geometry including angles, perimeter, area, and volume.
(Advanced Logical Thinking):
Apply logical problem-solving skills to more complex mathematical problems.
Develop fluency in operations with fractions, decimals, and percentages.
Solve equations and inequalities, understanding their solutions.
Explore more advanced geometric concepts such as congruence, similarity, and transformations.
Introduce basic concepts of probability and statistics, and analyze data using logical reasoning.
Engage in more challenging logical puzzles and games to further develop deductive reasoning skills.

Mastery and Application:
Apply logical thinking skills to real-world situations and interdisciplinary contexts.
Develop advanced problem-solving strategies for complex mathematical problems.
Master algebraic concepts including functions and systems of equations.
Apply logical reasoning to mathematical proofs and arguments.
Engage in research projects and mathematical modeling activities that require logical thinking and deductive reasoning.