Benchmark 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. (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