Benchmarks 9C (The Mathematical World: Shapes)
Grades 3-5, page 223
Many objects can be described in terms of simple plane figures and
solids. Shapes can be compared in terms of concepts such as parallel and
perpendicular, congruence, similarity, and symmetry. Symmetry can be found
by reflection, turns, or slides.
Benchmarks 9C (The Mathematical World: Shapes)
Grades 6-8, page 224
It takes two numbers to locate a point on a map or any other flat surface.
The numbers may be two perpendicular distances from a point, or an angle
and a distance from a point.
Benchmarks 9C (The Mathematical World: Shapes)
Grades 6-8, page 224
Shapes on a sphere like the earth cannot be depicted on a flat surface
without some distortion.
Benchmarks 9C (The Mathematical World: Shapes)
Grades 9-12, page 225
Geometric shapes and relationships can be described in terms of symbols
and numbers -and vice versa. For example, the position of any point on
a surface can be specified by two numbers; a graph represents all the values
that satisfy an equation; and if two equations have to be satisfied at
the same time, the values that satisfy them both will be found where their
graphs intersect.
Benchmarks 11C (Common Themes: Constancy and Change)
Grades 9-12, page 275
Graphs and equations are useful (and often equivalent) ways for depicting
and analyzing patterns of change.