Standard 4: Mathematical Connections

In grades 5-8, 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 6-8, 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 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.
 
• Use a mathematical idea to further their understanding of other mathematical ideas

Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 3-5, 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 6-8, 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 6-8, 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 6-8, 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.