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.
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.