Kindergarten math standards typically focus on building a strong foundation in essential mathematical concepts and skills. These standards emphasize hands-on activities, visual aids, and interactive learning to make math engaging and accessible for young learners. The goal is to develop a positive attitude towards mathematics while fostering critical thinking and problem-solving skills.  

First grade math standards build on the foundational skills developed in kindergarten, focusing on deeper understanding and application of mathematical concepts. These standards emphasize hands-on activities, collaborative learning, and real-world applications to make math relevant and engaging for first graders, while encouraging critical thinking and problem-solving skills. 

Second grade math standards build upon the skills developed in first grade, encouraging students to deepen their understanding of mathematical concepts and apply them in various contexts. These standards emphasize hands-on learning, problem-solving, and real-world applications to make math engaging and relevant, fostering a positive attitude towards mathematics and developing critical thinking skills.  

Third-grade math standards build upon the concepts introduced in earlier grades and introduce students to more complex operations, such as multiplication and division, while strengthening their understanding of fractions, geometry, and measurement. These skills set the foundation for more advanced math concepts in later grades. 

The 4th-grade math curriculum builds on the skills from previous grades, introducing more complex concepts such as multi-digit arithmetic, fractions, and geometry. Students also solidify their understanding of multiplication and division. The goal is to enhance students' critical thinking and problem-solving abilities across various mathematical domains. 

The 5th-grade math standards emphasize deepening students' understanding of operations with fractions, decimals, and whole numbers while introducing more advanced concepts in geometry and data analysis. Students also strengthen their ability to solve more complex multi-step problems. These topics help prepare students for middle school math. 

The 6th-grade math standards introduce more abstract mathematical concepts, laying a foundation for algebra and higher-level math. Students explore ratios, division of fractions, negative numbers, and begin formal statistical thinking. 

The 7th-grade math standards expand on previous knowledge and introduce more advanced topics, such as proportional relationships, linear equations, operations with rational numbers, and basic probability and statistics. These concepts prepare students for algebra and more complex problem-solving in higher grades. 

In 8th grade, students deepen their understanding of linear equations, functions, and geometry while exploring new topics such as irrational numbers and the Pythagorean Theorem. These skills prepare students for high school math, particularly Algebra I and Geometry, and lay the foundation for more advanced problem-solving in real-world contexts. 

Algebra I introduces students to a wide range of foundational mathematical concepts. Students develop skills in solving equations, manipulating expressions, analyzing functions, and interpreting data. These topics are critical as they form the basis for more advanced math courses, including Geometry, Algebra II, and Calculus. Algebra I emphasizes both the abstract manipulation of algebraic expressions and their practical applications in real-world problem-solving. 

Geometry focuses on understanding shapes, transformations, and the relationships between different geometric figures. Students explore both theoretical and practical applications of geometry, learning how to prove theorems, solve problems, and apply concepts in the real world. Key topics include congruence, similarity, right triangles, trigonometry, and the properties of circles. Through the study of Geometry, students develop logical reasoning skills and the ability to model real-world situations using geometric principles. 

Algebra II extends students' understanding of algebraic concepts, focusing on functions, complex numbers, polynomials, logarithms, and trigonometry. It emphasizes both the theoretical aspects of algebra and its practical applications in solving real-world problems. Algebra II prepares students for advanced courses such as Precalculus and Calculus, laying the groundwork for deeper mathematical reasoning and analysis. 

Pre-Calculus consolidates and extends the knowledge of Algebra and Trigonometry, introducing more advanced topics and preparing students for the challenges of Calculus. Key areas include functions, polynomials, rational functions, exponential and logarithmic functions, trigonometry, analytic geometry, vectors, matrices, sequences, series, and an introduction to limits. Pre-Calculus emphasizes both theoretical understanding and practical applications, helping students develop a robust foundation for higher mathematics. 

Calculus AB covers the fundamental principles of calculus, including limits, derivatives, and integrals, and their applications. Students learn to analyze functions, solve problems involving rates of change, find areas and volumes, and apply integration techniques. The course prepares students for the AP Calculus AB exam and provides a foundation for further study in mathematics and related fields. 

Calculus BC extends the concepts from Calculus AB by covering additional topics and techniques, including advanced integration methods, series, and polar and parametric functions. It provides a deeper and more comprehensive understanding of calculus, preparing students for further studies in mathematics and related fields. The course emphasizes problem-solving, mathematical modeling, and the application of calculus concepts to real-world scenarios. 

Statistics provides students with a comprehensive introduction to statistical methods and analysis. Key areas include exploring and describing data, designing surveys and experiments, understanding probability and sampling distributions, performing statistical inference, and using statistical software. The course emphasizes real-world applications, critical thinking, and effective communication of statistical results. It prepares students to analyze data, make informed decisions, and understand the role of statistics in various fields. 

Survey of Math is an introductory college-level course that will prepare students for future mathematics classes and careers by helping them become better mathematical problem solvers. This course will help students develop and use mathematical models to describe and understand real-life situations.