- Identify, describe, compare, and classify geometric figures
- Visualize and represent geometric figures with special attention to developing spatial sense
- Explore transformations of geometric figures
- Understand and apply geometric properties and relationships
- Develop an appreciation of geometry as a means of describing the physical world
- Represent and solve problems using geometric models

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

Grades K-2, page 223

Shapes such as circles, squares, and triangles can be used to describe
many things that can be seen.

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

Grades K-2, page 26

Patterns can be made by putting different shapes together or taking
them apart.

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

Grades 3-5, page 273

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* 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 3-5, page 223

Length can be thought of as unit lengths joined together, area as a
collection of unit squares, and volume as a set of unit cubes.

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

Grades 3-5, page 223

Areas of irregular shapes can be found by dividing them into squares
and triangles.

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

Grades 6-8, page 224

Lines can be parallel, perpendicular, or oblique.

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

Grades 6-8, page 224

Some shapes have special properties: Triangular shapes tend to make
structures rigid, and found shapes give the least possible boundary for
a given amount of interior area. Shapes can match exactly or have the same
shape in different sizes.

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

Grades K-2, page 26

Circles, squares, triangles, and other shapes can be found in things
in nature and in things that people build.

*Benchmarks* 11D (Common Themes: Scale)

Grades 6-8, page 274

Symmetry (or the lack of it) may determine properties of many objects,
from molecules and crystals to organisms and designed structures.

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

Grades 3-5, page 223

Scale drawings show shapes and compare locations of things very different
in size.

Grades 3-5, page 268

Geometric figures, number sequences, graphs, diagrams, sketches, number lines, maps, and stories can be used to represent objects, events, and processes in the real world, although such representations can never be exact in every detail.

*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 distortion.