Grade 6:
* Number Sense and Operations: Working with larger numbers, including decimals, fractions, and percentages. Understanding ratios, rates, and proportions. Beginning to explore integers (positive and negative numbers). Order of operations (PEMDAS/BODMAS).
* Algebraic Thinking: Introduction to variables and simple equations. Representing relationships with tables, graphs, and expressions.
* Geometry: Working with two-dimensional shapes, calculating area and perimeter. Introduction to three-dimensional shapes.
* Measurement: Converting units of measurement (length, weight, volume). Understanding and using formulas for area and volume.
* Data Analysis and Probability: Organizing and interpreting data using tables, charts, and graphs. Introduction to basic probability.
Grade 7:
* Number Sense and Operations: Fluency with operations on rational numbers (fractions, decimals, and integers). Understanding proportional relationships and solving problems involving percentages.
* Algebra: Solving more complex equations and inequalities. Graphing linear equations. Working with expressions and variables.
* Geometry: Understanding similar figures, transformations (rotations, reflections, translations). Calculating circumference and area of circles. Introduction to angles and their relationships.
* Measurement: Converting units of measurement, calculating volume and surface area of three-dimensional shapes.
* Data Analysis and Probability: Interpreting data from various sources, calculating measures of central tendency (mean, median, mode). Probability of simple events.
Grade 8:
* Number Sense and Operations: Working with irrational numbers (e.g., square roots, pi). Scientific notation.
* Algebra: Solving systems of equations. Graphing linear equations and inequalities. Working with exponents and polynomials.
* Geometry: Understanding the Pythagorean theorem. Working with three-dimensional shapes, including volume and surface area calculations. Introduction to geometric proofs (depending on the curriculum).
* Data Analysis and Probability: Working with scatter plots and lines of best fit. Probability of compound events.
* Introduction to Functions: Understanding the concept of a function and its representation.
Essentially, middle school math lays the groundwork for higher-level math in high school, including algebra, geometry, and beyond. It focuses on developing a strong understanding of fundamental concepts and problem-solving skills.