Mathematics Frameworks
STANDARDS -- NUMBER AND NUMBER SYSTEMS
Number Sense and Numeration (NCTM Standard 6)
In grades K-4, the mathematics curriculum shall include whole number concepts and skills so that students will:
| construct number meanings through real-world experiences and the use of
physical materials;
| understand our numeration system by relating counting, grouping, and
place-value concepts;
| develop number sense;
| interpret the multiple uses of numbers encountered in the real world. | |
Concepts of Whole Number Operations (NCTM Standard 7)
In grades K-4 mathematics curriculum shall include concepts of addition, subtraction, multiplication, and division of whole numbers so that students will:
| develop meaning for the operations by modeling and discussing a rich
variety of problem situations;
| relate the mathematical language and symbolism of operations to problem
situations and informal language;
| recognize that a wide variety of problem structures can be represented by
a single operation;
| develop operation sense. | |
Fractions and Decimals (NCTM Standard 12)
In grades K-4 the mathematics curriculum shall include fractions and decimals so that students will:
| develop concepts of fractions, mixed numbers, and decimals;
| develop number sense for fractions and decimals;
| use models to relate fractions to decimals and to find equivalent
fractions;
| use models to explore operations on fractions and decimals;
| apply fractions and decimals to problem situations. | |
In grades 5-8, the mathematics curriculum shall include the continued development of number and number relationships so that students will:
| understand, represent, and use numbers in a variety of equivalent forms
(integer, fraction, decimal, percent, exponential, and scientific notation)
in real-world and mathematical problems situations;
| develop number sense for whole numbers, fractions, decimals, integers, and
rational numbers;
| understand and apply ratios, proportions, and percents in a wide variety
of situations;
| investigate relationships among fractions, decimals, and percents;
| represent numerical relationships in one- and two-dimensional graphs. | |
Number Systems and Number Theory (NCTM Standard 6)
In grades 5-8, the mathematics curriculum shall include the study of number systems and number theory so that students will:
| understand and appreciate the need for numbers beyond the whole numbers;
| develop and use order relations for whole numbers, fractions, decimals,
integers, and rational numbers;
| extend their understanding of whole number operations to fractions,
decimals, integers, and rational numbers;
| understand how the basic arithmetic operations are related to one another;
| develop and apply number theory concepts (e.g., primes, factors, and
multiples) in real-world and mathematical problem situations. | |
STANDARDS -- NUMBER AND NUMBER SYSTEMS
In grades 9-12, the mathematics curriculum shall include topics from discrete mathematics so that all students will:
| represent problem situations using discrete structures such as finite
graphs, matrices, sequences, and recurrence relations;
| represent and analyze finite graphs using matrices;
| develop and analyze algorithms;
| solve enumeration and finite probability problems; | |
and, in addition, college-intending students will:
| represent and solve problems using linear programming and difference
equations;
| investigate problem situations that arise in connection with computer
validation and the application of algorithms. | |
Mathematical Structure (NCTM Standard 14)
In grades 9-12, the mathematics curriculum shall include the study of mathematical structure so that all students will:
| compare and contrast the real number system and its various subsystems
with regard to their structural characteristics;
| understand the logic of algebraic procedures;
| appreciate that seemingly different mathematical systems may be
essentially the same; | |
and, in addition, college-intending students will:
| develop the complex number system and demonstrate facility with its
operations;
| prove elementary theorems within various mathematical structures, such as
groups and fields;
| develop an understanding of the nature and purpose of axiomatic systems. | |
ADULT BASIC EDUCATION -- NUMBER AND NUMBER SYSTEMS
In the adult basic education classroom, curriculum design shall include concrete and developmental approaches to teaching numbers, number relationships, operations, and computation which allows the learner to:
| understand, represent, and use numbers in a variety of equivalent forms
and in order relations (integers, fraction, decimal, percent, exponential,
and scientific notation) in real-world, work-related, and mathematical
problem situations;
| compute with whole numbers, fractions, decimals, and integers, using
appropriate algorithms and a variety of techniques including mental math,
paper-and-pencil, calculator, and computer methods;
| analyze and explain procedures for computation and understand how
arithmetic operations are related to one another, particularly the
reversibility of operations;
| use estimation to develop number sense, operation sense, and to check the
reasonableness of results;
| analyze and explain methods for solving proportions;
| select and use in problem solving situations an appropriate method from
among mental arithmetic, paper-and-pencil, calculator, and computer methods;
| use computation, estimation, and proportions to solve problems. | |
Go to Standard I Mathematics as Problem Solving
Go to Standard II Mathematics as Communication
Go to Standard III Mathematics as Reasoning
Go to Standard IV Mathematical Connections
Go to Standard VI Estimation and Computation
Go to Standard VII Patterns, Relations, and Functions
Go to Standard VIII Geometry and Measurement
Go to Standard IX Statistics and Probability
Return to Mathematics Curriculum Frameworks