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List of Benchmarks for Mathematics

Standard 9.Understands the general nature and uses of mathematics
  Level Pre-K (Grade Pre-K)
   1. Not appropriate at this level
  Level I (Grade K-2)
   1. Not appropriate for this level
  Level II (Grade 3-5)
   1. Understands that numbers and the operations performed on them can be used to describe things in the real world and predict what might occur
   2. Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically
  Level III (Grade 6-8)
   1. Understands that mathematics has been helpful in practical ways for many centuries
   2. Understands that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent
  Level IV (Grade 9-12)
   1. Understands that mathematics is the study of any pattern or relationship, but natural science is the study of those patterns that are relevant to the observable world
   2. Understands that mathematics began long ago to help solve practical problems; however, it soon focused on abstractions drawn from the world and then on abstract relationships among those abstractions
   3. Understands that in mathematics, as in other sciences, simplicity is one of the highest values; some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived
   4. Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications
   5. Understands that new mathematics continues to be invented even today, along with new connections between various components of mathematics
   6. Understands that science and mathematics operate under common principles: belief in order, ideals of honesty and openness, the importance of review by colleagues, and the importance of imagination
   7. Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments
   8. Understands that the development of computers has opened many new doors to mathematics just as other advances in technology can open up new areas to mathematics
   9. Understands that mathematics often stimulates innovations in science and technology
   10. Understands that mathematicians commonly operate by choosing an interesting set of rules and then playing according to those rules; the only limit to those rules is that they should not contradict each other