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 realnumber system;
 use numbertheory 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 paperandpencil calculations for simple cases and technology for morecomplicated cases.
 judge the reasonableness of numerical computations and their results.


Number & Operations  Algebra  Geometry  Measurement
Data Analysis & Probability  Problem Solving  Reasoning & Proof  Communication
Connections  Representation