**Benchmark
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. (2 of 6)
Standard 8-3, page 98, Grades 5-8

Analyze functional relationships to explain how a change in one quantity
results in a change in another
Symbolic equations can be used to summarize how the quantity of something
changes over time or in response to other changes. (4 of 6)
Standard 9-6, page 102, Grades 5-8

Apply algebraic methods to solve a variety of real-world and mathematical
problems
Standard 5-1 page 150, Grades 9-12

Represent situations that involve variable quantities with expressions,
equations, inequalities, and matrices

Symmetry (or the lack of it) may determine properties of many objects,
from molecules and crystals to organisms and designed structures. (5 of
6)
Standard 12-6, page 112, Grades 5-8

Develop an appreciation of geometry as a means of describing the physical
world
Standard 12-3, page 112, Grades 5-8

Explore transformations of geometric figures

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 (6 of 6)
Standard 8-3, page 98, Grades 5-8

Analyze functional relationships to explain how a change in one quantity
results in a change in another
Standard 9-2 page 163, Grades 9-12

Explore periodic real-world phenomena using the sine and cosine functions