District Frameworks - Mathematics Go to: Mathematics as Problem Solving - Standard 1 Mathematics as Communication - Standard 2 Mathematics as Reasoning - Standard 3 Mathematical Connections - Standard 4 Estimation and Computation - Standard 6 Patterns, Relations and Functions - Standard 7 Geometry and Measurement - Standard 8 Statistics and Probability - Standard 9 Standard 5 Number and Number System Standards Grades K-4 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.  Grades 5-8 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.  Grades 9-12 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. Wachusett Regional School District 1745 Main Street | Jefferson MA 01522 | Telephone: 508-829-1670 | Fax: 508-829-1680 Superintendent - Darryll McCall, Ed.D.