Topic: Addition/subtraction 
Mathematics 
 Standard 3. Uses basic and advanced procedures while performing the processes of computation 
  Level PreK (Grade PreK) 
   Benchmark 1.  Knows that the quantity of objects can change by adding or taking away objects 
    Knowledge/skill statements 
     1.  Knows that the quantity of objects in a group can change by adding more objects

     2.  Knows that the quantity of objects in a group can change by taking away some objects 
  Level I (Grade K2) 
   Benchmark 1.  Adds and subtracts whole numbers 
    Knowledge/skill statements 
     1.  Understands the concept of addition 
     2.  Adds whole numbers 
     3.  Subtracts whole numbers 
     4.  Understands the concept of subtraction 
   Benchmark 2.  Solves realworld problems involving addition and subtraction of whole numbers 
    Knowledge/skill statements 
     1.  Determines whether a problem can be solved by subtracting whole numbers 
     2.  Determines whether a problem can be solved by adding whole numbers 
   Benchmark 4.  Understands the inverse relationship between addition and subtraction 
    Knowledge/skill statements 
     1.  Understands that addition and subtraction are inverse relationships 
   Benchmark 5.  Understands strategies for the addition and subtraction of whole numbers 
    Knowledge/skill statements 
     1.  Understands strategies for the addition of whole numbers 
     2.  Understands strategies for the subtraction of whole numbers 
  Level II (Grade 35) 
   Benchmark 2.  Adds, subtracts, multiplies, and divides decimals 
    Knowledge/skill statements 
     1.  Understands the concept of decimal addition 
     2.  Adds decimals 
     3.  Understands the concept of decimal subtraction 
     4.  Subtracts decimals 
     5.  Understands the concept of decimal multiplication 
     6.  Multiplies decimals 
     7.  Understands the concept of decimal division 
     8.  Divides decimals 
   Benchmark 3.  Adds and subtracts simple fractions (i.e., commonly used fractions, fractions with common denominators) 
    Knowledge/skill statements 
     1.  Understands the concept of addition of fractions 
     2.  Adds simple fractions 
     3.  Understands the concept of subtraction of fractions 
     4.  Subtracts simple fractions 
   Benchmark 5.  Performs basic mental computations (e.g., addition and subtraction of whole numbers) 
    Knowledge/skill statements 
     1.  Mentally adds whole numbers 
     2.  Mentally subtracts whole numbers 
     3.  Mentally multiplies whole numbers 
     4.  Mentally divides whole numbers 
   Benchmark 6.  Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers 
    Knowledge/skill statements 
     1.  Determines the effects of addition on the size and order of numbers 
     2.  Determines the effects of division on the size and order of numbers 
     3.  Determines the effects of subtraction on the size and order of numbers 
     4.  Determines the effects of multiplication on the size and order of numbers 
   Benchmark 7.  Understands the properties of and the relationships among addition, subtraction, multiplication, and division (e.g., reversing the order of two addends does not change the sum; division is the inverse of multiplication) 
    Knowledge/skill statements 
     1.  Understands that multiplication and division are inverse operations 
     2.  Understands multiplication as repeated addition 
     3.  Understands division as repeated subtraction 
     4.  Understands effects of reversing order of things added 
     5.  Understands effects of reversing order of things subtracted 
     6.  Understands effects of reversing order of things multiplied 
     7.  Understands effects of reversing order of things divided 
   Benchmark 8.  Solves word problems (e.g., problems that require students to put things into groups or combine things that come in groups)and real world problems involving number operations, including those that specify units (e.g., dollars and cents, hours and minutes, cubic units ) 
    Knowledge/skill statements 
     1.  Solves real world problems involving number operations with money 
     2.  Solves real world problems involving number operations with time 
     3.  Solves real world problems involving operations with volume 
     4.  Determines whether a realworld problem can be solved with computation 
     5.  Solves real world problems involving number operations. 
     6.  Solves word problems involving number operations. 
     7.  Solves word problems that require students to put things into groups 
     8.  Solves word problems that require students to combine things that come in groups 
   Benchmark 9.  Knows the language of basic operations (e.g., "products," "multiplication") 
    Knowledge/skill statements 
     1.  Understands the term "addend" 
     2.  Understands the term "sum" 
     3.  Understands the term "minuend" 
     4.  Understands the term "subtrahend" 
     5.  Understands the term "difference" 
     6.  Understands the term "product" 
     7.  Understands the term "divisor" 
     8.  Understands the term "dividend" 
     9.  Understands the term "quotient" 
  Level III (Grade 68) 
   Benchmark 1.  Adds, subtracts, multiplies, and divides integers, and rational numbers 
    Knowledge/skill statements 
     1.  Adds rational numbers 
     2.  Subtracts rational numbers 
     3.  Multiplies rational numbers 
     4.  Divides rational numbers 
     5.  Adds integers 
     6.  Subtracts integers 
     7.  Multiplies integers 
     8.  Divides integers 
     9.  Understands the concept of integer addition 
     10.  Understands the concept of integer subtraction 
     11.  Understands the concept of integer multiplication 
     12.  Understands the concept of integer division 
   Benchmark 2.  Adds and subtracts fractions with unlike denominators; multiples and divides fractions 
    Knowledge/skill statements 
     1.  Adds fractions with unlike denominators 
     2.  Subtracts fractions with unlike denominators 
     3.  Multiplies fractions 
     4.  Divides fractions 
   Benchmark 4.  Selects and uses appropriate computational methods (e.g., mental, paper and pencil, calculator, computer) for a given situation 
    Knowledge/skill statements 
     1.  Knows when paper/pencil is best method for computation 
     2.  Uses calculator for computations 
     3.  Knows when calculator is best method for computation 
     4.  Knows when mental computation is the best method 
     5.  Uses paper/pencil for computation 
     6.  Uses mental computation 
     7.  Knows when computer is best method for computation 
     8.  Uses a computer for computation 
   Benchmark 5.  Understands the correct order of operations for performing arithmetic computations 
    Knowledge/skill statements 
     1.  Knows the order of operations 
   Benchmark 7.  Understands the properties of operations with rational numbers (e.g., distributive property, commutative and associative properties of addition and multiplication, inverse properties, identity properties) 
    Knowledge/skill statements 
     1.  Understands the associative property of addition 
     2.  Understands the commutative property of multiplication 
     3.  Understands the commutative property of addition 
     4.  Understands the concept of multiplicative inverse 
     5.  Understands the distributive property of multiplication 
     6.  Understands the associative property of multiplication 
     7.  Understands the concept of additive inverse 
     8.  Understands how the properties of operations relate to rational numbers 
     9.  Understands the concept of additive identity 
     10.  Understands the concept of multiplicative identity 
   Benchmark 9.  Understands how different algorithms work for arithmetic computations and operations 
    Knowledge/skill statements 
     1.  Understands how different algorithms work for multiplication 
     2.  Understands how different algorithms work for division 
     3.  Understands how different algorithms work for subtraction 
     4.  Understands how different algorithms work for addition 
  Level IV (Grade 912) 
   Benchmark 1.  Adds, subtracts, multiplies, divides, and simplifies rational expressions 
    Knowledge/skill statements 
     1.  Understands the concept of a rational expressions 
     2.  Adds rational expressions 
     3.  Subtracts rational expressions 
     4.  Multiplies rational expressions 
     5.  Divides rational expressions 
     6.  Simplifies rational expressions 
   Benchmark 2.  Adds, subtracts, multiplies, divides, and simplifies radical expressions containing positive rational numbers 
    Knowledge/skill statements 
     1.  Divides radical expressions with positive rational numbers 
     2.  Adds radical expressions with positive rational numbers 
     3.  Understands concept of radical expression with positive rational numbers 
     4.  Subtracts radical expressions with positive rational numbers 
     5.  Multiplies radical expressions with positive rational numbers 
  Level V (Grade (College Readiness)) 
   Benchmark 1.  Knows properties (e.g., distributive, associative) of complex numbers 
    Knowledge/skill statements 
     1.  Knows how the associative property relates to complex numbers 
     2.  Knows how the distributive property relates to complex numbers 
 Standard 8. Understands and applies basic and advanced properties of functions and algebra 
  Level IV (Grade 912) 
   Benchmark 13.  Adds, subtracts, multiplies, and divides polynomials 
    Knowledge/skill statements 
     1.  Adds polynomials 
     2.  Subtracts polynomials 
     3.  Multiplys polynomials 
     4.  Divides polynomials 