
District Frameworks  Mathematics
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Standard 5
Number and Number System Standards
Grades K4
Number Sense and Numeration (NCTM Standard 6)  shall include whole number concepts and skills so that students will:
 Construct number meanings through realworld experiences and the use of physical materials;
 Understand our numeration system by relating counting, grouping, and placevalue concepts;
 Develop number sense;
 Interpret the multiple uses of numbers encountered in the real world.
Concepts of Whole Number Operations (NCTM Standard 7)  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)  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.
Grades 58
Number and Number Relationships (NCTM Standard 5)  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 realworld 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 twodimensional graphs.
Number Systems and Number Theory (NCTM Standard 6)  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 realworld and mathematical problem situations.
Grades 912
Discrete Mathematics (NCTM Standard 12)  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, collegeintending 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)  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, collegeintending 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
Numbers, Operations, and Computations (ABE Standard 6)  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 realworld, workrelated, and mathematical problem situations;
 Compute with whole numbers, fractions, decimals, and integers, using appropriate algorithms and a variety of techniques including mental math, paperandpencil, 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, paperandpencil, calculator, and computer methods;
 Use computation, estimation, and proportions to solve problems.
