Benchmarks 11B (Common Themes: Models)
Grades K-2, page 268
A model of something is different from the real thing but can be used
to learn something about the real thing.
Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Explain to other students how they go about solving numerical problems.
Benchmarks 2C (The Nature of Mathematics: Mathematical Inquiry)
Grades K-2, page 36
Numbers and shapes can be used to tell about things.
Benchmarks 9E (The Mathematical World: Reasoning)
Grades 6-8, page 233
Sometimes people invent a general rule to explain how something works
by summarizing observations. But people tend to overgeneralize, imagining
general rules on the basis of only a few observations.
Benchmarks 2C page 37 (The Nature of Mathematics: Mathematical
Inquiry)
Grades 6-8
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).
Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Give rough estimates of numerical answers to problems before doing
them formally.
Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades K-2, page 290
Readily give the sums and differences of single-digit numbers in familiar
contexts where the operation makes sense and judge the reasonableness of
the answer.