District Frameworks - Mathematics
Number and Number System Standards
Number Sense and Numeration (NCTM Standard 6) - 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) - 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.
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 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) - 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.
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, 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) - 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
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 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.