Wachusett Regional School District
Wachusett Mountain

District Frameworks - Mathematics

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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.