### Standard 8: Patterns and Functions

In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students can:
• Describe, extend, and create a wide variety of patterns
Benchmarks 11C page 273 (Common Themes: Constancy and Change)
Some features of things may stay the same even when other features change. Some patterns look the same when they are shifted over, or turned, or reflected or seen form different directions.

• Describe and represent relationships with tables, graphs, and rules
• Benchmarks 9B (The Mathematical World: Symbolic Relationships)
Tables and graphs can show how values of one quantity are related to values of another.

Benchmarks 11C (Common Themes: Constancy and Change)
Things change in steady, repetitive, or irregular ways or sometimes in more than one way at the same time. Often the best way to tell which kinds of change are happening is to make a table or graph of measurements.

Benchmarks 12D (Habits of Mind: Communication Skills)
Organize information in simple tables and graphs and identify the relationships they reveal.

• Analyze functional relationships to explain how a change in one quantity results in a change in another
• Benchmarks 9B (The Mathematical World: Symbolic Relationships)
Mathematical statements can be used to describe how one quantity changes when another changes. Rates of change can be computed from magnitudes and vice versa.

Benchmarks 11C (Common Themes: Constancy and Change)
Physical and biological systems tend to change until they become stable and then remain that way unless their surroundings change.

Benchmarks 11C (Common Themes: Constancy and Change)
A system may stay the same because nothing is happening or because things are happening but exactly counterbalance one another.

Benchmarks 11C (Common Themes: Constancy and Change)