| Instructional
programs from prekindergarten through grade 12 should enable
all students to— |
In grades 9–12 all students should— |
| Understand
numbers, ways of representing numbers, relationships among
numbers, and number systems |
| • |
develop a deeper understanding of very large and very
small numbers and of various representations of them;
|
| • |
compare and contrast the properties of numbers and number
systems, including the rational and real numbers, and
understand complex numbers as solutions to quadratic equations
that do not have real solutions; |
| • |
understand vectors and matrices as systems that have some
of the properties of the real-number system; |
| • |
use
number-theory arguments to justify relationships involving
whole numbers. |
|
| Understand
meanings of operations and how they relate to one another |
| • |
judge the effects of such operations as multiplication,
division, and computing powers and roots on the magnitudes
of quantities; |
| • |
develop an understanding of properties of, and representations
for, the addition and multiplication of vectors and matrices;
|
| • |
develop an understanding of permutations and combinations
as counting techniques. |
|
| Compute
fluently and make reasonable estimates |
| • |
develop
fluency in operations with real numbers, vectors, and
matrices, using mental computation or paper-and-pencil
calculations for simple cases and technology for more-complicated
cases. |
| • |
judge
the reasonableness of numerical computations and their
results. |
|
