Standard 4: Mathematical Connections
In grades 58, the mathematics curriculum should include the investigation
of mathematical connections so that students can:

See mathematics as an integrated whole
Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 68, page 28
Logical connections can be found between different parts of mathematics.

Explore problems and describe results using graphical, numerical, physical,
and verbal mathematical models or representations
Benchmarks 11B (Common Themes: Models)
Grades 35, 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.

Use a mathematical idea to further their understanding of other mathematical
ideas
Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 35, page 27
Mathematical ideas can be represented concretely, graphically, and
symbolically.

Apply mathematical thinking and modeling to solve problems that arise in
other disciplines, such as art, music, psychology, science, and business
Benchmarks 11B (Common Themes: Models)
Grades 68, page 269
Different models can be used to represent the same thing. What kind
of a model to use and how complex it should be depends on its purpose.
The usefulness of a model may be limited if it is too simple or if it is
needlessly complicated. Choosing a useful model is one of the instances
in which intuition and creativity come into play in science, mathematics,
and engineering.
Benchmarks 11B (Common Themes: Models)
Grades 68, page 269
Models are often used to think about processes that happen too slowly,
too quickly, or on too small a scale to observe directly, or that are too
vast to be changed deliberately, or that are potentially dangerous.

Value the role of mathematics in our culture and society
Benchmarks 2B (The Nature of Mathematics: Mathematics, Science,
and Technology)
Grades 68, page 32
Mathematics is helpful in almost every kind of human endeavor from
laying bricks to prescribing medicine or drawing a face. In particular,
mathematics has contributed to progress in science and technology for thousands
of years and continues to do so.