**Benchmark
2C: The Nature of Mathematics - Mathematical Inquiry**
**(grades 6-8, page 37)**
Mathematicians often represent things with abstract ideas, such as numbers
or perfectly straight lines, and then work with those ideas alone. The
"things" from which they abstract can be ideas themselves(for example,
a proposition about "all equal-sided triangles" or all "odd numbers). (1
of 2)
Standard 2-6 page 78, Grades 5-8

Appreciate the value of mathematical notation and its role in the development
of mathematical ideas
Standard 2-3 page 140, Grades 9-12

Express mathematical ideas orally and in writing

When mathematicians use logical rules to work with representations of things,
the results may or may not be valid for the things themselves. Using mathematics
to solve a problem requires choosing what mathematics to use; probably
making some simplifying assumptions, estimates, or approximations; doing
computations; and then checking to see whether the answer makes sense.
If an answer does not seem to make enough sense for its intended purpose,
then any of these steps might have been inappropriate. (2 of 2)
Standard 3-4 page 81, Grades 5-8

Validate their own thinking