- Describe, extend, and create a wide variety of patterns

- Describe and represent relationships with tables, graphs, and rules
- Analyze functional relationships to explain how a change in one quantity results in a change in another
- Use patterns and functions to represent and solve problems

Grades 3-5

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.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 3-5, page 218

Tables and graphs can show how values of one quantity are related to
values of another.

*Benchmarks* 11C (Common Themes: Constancy and Change)

Grades 3-5, page 273

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)

Grades 6-8, page 297

Organize information in simple tables and graphs and identify the relationships
they reveal.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 6-8, page 219

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)

Grades 6-8, page 274

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)

Grades 6-8, page 274

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)

Grades 6-8, page 274

Things that change in cycles, such as the seasons or body temperature,
can be described by their cycle length or frequency, what the highest and
lowest values are, and when they occur. Different cycles range from many
thousands of years down to less than a billionth of a second.

*Benchmarks* 2A (The Nature of Mathematics: Patterns and Relationships)

Grades 3-5, page 27

Mathematics is the study of many kinds of patterns, including numbers
and shapes and operations on them. Sometimes patterns are studied because
they help to explain how the world works or how to solve practical problems,
sometimes because they are interesting in themselves.

*Benchmarks* 9C (The Mathematical World: Shapes)

Grades 6-8, page 219

Graphs can show a variety of possible relationships between two variables.
As one variable increases uniformly, the other may do one of the following:
always keeps the same proportion to the first, increase or decrease steadily,
increase or decrease faster and faster, get closer and closer to some limiting
value, reach some intermediate maximum or minimum, alternately increase
and decrease indefinitely, increase or decrease in steps, or do something
different from any of these.