Middle school math in New Hampshire for grades 6-8, aligned with state standards and the Common Core, focuses on developing a strong foundation in mathematical concepts and problem-solving skills:

Grade 6

Ratios and Proportional Relationships: Understanding and applying ratios, rates, and percentages in various contexts.

Number System: Extending knowledge of numbers to include negative numbers and operations with fractions and decimals.

Geometry: Introduction to basic geometric shapes, area, surface area, and volume.

Expressions and Equations: Developing skills in writing, interpreting, and using expressions and equations.

Grade 7

Ratios and Proportional Relationships: Deepening understanding of proportional relationships and applying them to real-world problems.

Number System: Mastery of operations with fractions, decimals, and integers.

Geometry: Exploring the properties of shapes and solving problems involving scale drawings, area, volume, and surface area.

Expressions and Equations: Solving real-world mathematical problems using algebraic expressions, linear equations, and inequalities.

Grade 8

Functions: Introduction to the concept of functions and using them to model relationships between quantities.

Number System: Working with irrational numbers and understanding their properties.

Geometry: Delving into the Pythagorean Theorem and exploring transformations, congruence, and similarity.

Expressions and Equations: Analyzing and solving linear equations, systems of equations, and understanding linear functions.

Throughout these grades, the focus is on developing mathematical reasoning, critical thinking, and the ability to apply math concepts to solve real-life problems, preparing students for high school mathematics.