The New York State Next Generation Mathematics Learning Standards for grades 6 through 8 are designed to build a strong mathematical foundation for students, preparing them for higher-level math and real-world problem-solving. These standards emphasize a balance of conceptual understanding, procedural skills, and practical application.

Key Areas of Focus by Grade:

• Grade 6:

  • Ratios and Proportional Relationships: Understanding and using ratios to solve problems.

  • The Number System: Extending knowledge of number operations to include fractions and decimals.

  • Expressions and Equations: Introducing variables and simple equations.

  • Geometry: Understanding area, surface area, and volume.

  • Statistics and Probability: Developing concepts of statistical variability and data distribution.

• Grade 7:

  • Ratios and Proportional Relationships: Analyzing proportional relationships to solve real-world problems.

  • The Number System: Performing operations with rational numbers, including negative numbers.

  • Expressions and Equations: Solving linear equations and inequalities.

  • Geometry: Working with scale drawings and understanding geometric constructions.

  • Statistics and Probability: Making inferences about populations based on samples.

• Grade 8:

  • The Number System: Exploring irrational numbers and their approximations.

  • Expressions and Equations: Understanding and solving linear equations and systems of equations.

  • Functions: Defining, evaluating, and comparing functions.

  • Geometry: Applying the Pythagorean Theorem and understanding congruence and similarity.

  • Statistics and Probability: Analyzing patterns and associations in bivariate data.

Standards for Mathematical Practice:

Across all grade levels, the standards emphasize eight key practices to develop students' mathematical proficiency:

1. Make sense of problems and persevere in solving them: Encouraging students to understand problems deeply and explore various solution strategies.

2. Reason abstractly and quantitatively: Developing the ability to contextualize and decontextualize mathematical situations.

3. Construct viable arguments and critique the reasoning of others: Fostering skills to create logical arguments and evaluate others' reasoning.

4. Model with mathematics: Applying mathematics to solve problems in everyday life and other disciplines.

5. Use appropriate tools strategically: Selecting and effectively using tools such as calculators, rulers, and software.

6. Attend to precision: Emphasizing accurate calculations, measurements, and clear communication.

7. Look for and make use of structure: Identifying patterns and structures to solve problems more easily.

8. Look for and express regularity in repeated reasoning: Noticing repeated calculations or processes to generalize and find shortcuts.