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					                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                             7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:               Performance Objectives:                   Performance Objectives:

       1 Add whole numbers.                                                                                               1 Add integers.

       2 Subtract whole                                                                                                   2 Subtract integers.
         numbers with
         regrouping.
       3 Select grade level                 1 Select grade level                    1 Select grade level                  3 Select appropriate                    1 Select appropriate
         appropriate                          appropriate operation                   appropriate operation                 operation to solve word                 operation to solve word
         operation to solve                   to solve word                           to solve word                         problems involving                      problems.
         word problems.                       problems.                               problems.                             integers.
       4 Solve word problems                2 Solve word problems                   2 Solve word problems                 4 Solve word problems                   2 Solve word problems
         using grade level                    using grade level                       using appropriate                     using appropriate                       using appropriate
         appropriate                          appropriate                             operations and                        operations and numbers.                 operations and numbers.
         operations and                       operations and                          numbers.                              (integers)
         numbers.                             numbers. (mental
                                              computation,
                                              estimation,
                                              calculators, and
                                              paper and pencil)

       5 Multiply up to 3-digit             3 Multiply up to 3-digit                                                      5 Multiply integers.                    3 Determine the square of
         numbers by 2-digit                   numbers by 3-digit                                                                                                    an integer.
         whole numbers.                       whole numbers. (e.g.,
                                              426 * 329)




   Italics denote a repetition of a performance objective (learned in an earlier grade).       8              e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                                7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:                  Performance Objectives:                   Performance Objectives:

       6 Divide a 4-digit                   4 Divide a 4-digit                      3 Calculate multiplication               6 Divide integers.                      4 Determine the square
         dividend by a 1-digit                dividend by a 2-digit                   and division with two-                                                           root of an integer.
         divisor (w/ or w/out                 divisor.                                digit divisors and
         remainders).                                                                 remainders. (e.g.
                                                                                      percentages and money)


       7 Use division with
         remainders in
         contextual
         situations.
       8 State multiplication
         and division facts
         through 12's.
       9 Demonstrate the                    5 Demonstrate the
         Associate property of                Distributive property
         multiplication.                      of multiplication over
                                              addition. [e.g., 3*38 =
                                              3(30 + 8) = (3*30) +
                                              (3 * 8)]




   Italics denote a repetition of a performance objective (learned in an earlier grade).        9                e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                                  7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:                    Performance Objectives:                   Performance Objectives:

      10 Use Distributive                   6 Demonstrate the                                                                                                          5 Identify squaring and
         property to solve                    addition and                                                                                                               finding square roots as
         multiplication                       multiplication                                                                                                             inverse operations.
         problems.                            properties of equality.
                                              (identity elements)

      11 Apply grade-level                  7 Apply grade-level                     4 Apply grade-level                        7 Apply grade-level                     6 Apply grade-level
         appropriate                          appropriate                             appropriate properties                     appropriate properties                  appropriate properties
         properties to assist in              properties to assist in                 to assist in                               to assist in computation.               to assist in computation.
         computation.                         computation.                            computation.                               Associative,                            Associative,
         Associative,                         Associative,                            Associative,                               Commutative,                            Commutative,
         Commutative,                         Commutative,                            Commutative,                               Identity,                               Identity,
         Identity to assist in                Identity to assist in                   Identity.                                  Distributive.                           Distributive.
         computation.                         computation.

      12 Apply the symbol: •                8 Apply the symbol                      5 Apply the symbols for                    8 Apply the symbols + and               7 Apply the symbols "√" to
         and ( ) and * for                    "[ ]" to represent                      "…" or "____" to                           - to represent positive                 represent square root, "±"
         multiplication, and ≥                grouping.                               represent non-                             and negative numbers,                   to represent roots, and
         and ≤ .                                                                      terminating and                            and "| |" to represent                  "{ }" as grouping
                                                                                      repeating decimals and                     absolute value.                         symbols.
                                                                                      " : " to represent ratios,
                                                                                      superscripts as
                                                                                      exponents.




   Italics denote a repetition of a performance objective (learned in an earlier grade).         10                e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                               7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:                 Performance Objectives:                   Performance Objectives:

      13 Use grade-level                    9 Use grade-level                       6 Use grade-level                       9 Use grade-level                       8 Use grade-level
         appropriate                          appropriate                             appropriate                             appropriate                             appropriate
         mathematical                         mathematical                            mathematical                            mathematical                            mathematical
         terminology.                         terminology.                            terminology.                            terminology.                            terminology.
                                           10 Simplify fractions to                 7 Simplify fractions to
                                              lowest terms.                           lowest terms.
      14 Add fractions with                11 Add proper fractions                  8 Add proper fractions
         like denominators, no                and mixed numbers                       and mixed numbers
         regrouping.                          with like denominators                  with unlike
                                              with regrouping.                        denominators with
                                                                                      regrouping.
      15 Subtract fractions                12 Subtract proper                      9 Subtract proper
         with like                            fractions and mixed                    fractions and mixed
         denominators, no                     numbers with like                      numbers with unlike
         regrouping.                          denominators with                      denominators with
                                              regrouping.                            regrouping.
                                                                                  10 Add mixed numbers.
                                                                                  11 Subtract mixed
                                                                                     numbers.
                                                                                  12 Demonstrate the
                                                                                     process of
                                                                                     multiplication of proper
                                                                                     fractions using models.




   Italics denote a repetition of a performance objective (learned in an earlier grade).        11              e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                               7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:                 Performance Objectives:                   Performance Objectives:

                                                                                  13 Determine a fractional
                                                                                     part of a whole
                                                                                     number greater than
                                                                                     1. ( e.g., 1/6 of 24 or
                                                                                     2/5 of 200).

                                                                                  14 Multiply proper
                                                                                     fractions.
                                                                                  15 Divide proper fractions.

                                                                                  16 Multiply mixed
                                                                                     numbers.
                                                                                  17 Divide mixed numbers.

                                                                                  18 Demonstrate that
                                                                                     division is the inverse
                                                                                     of multiplication with
                                                                                     fractions and decimals.




   Italics denote a repetition of a performance objective (learned in an earlier grade).       12               e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                             7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:               Performance Objectives:                   Performance Objectives:

      16 Add money with                    13 Add decimals to the                 19 Solve problems
         regrouping through                   thousandths.                           involving fractions or
         $99.99.                                                                     decimals (including
                                                                                     money) in contextual
                                                                                     situations.

      17 Subtract money with               14 Subtract decimals to
         regrouping through                   the thousandths.
         $99.99.
      18 Multiply 3-digit                  15 Multiply decimals                   20 Multiply decimals
         numbers                              using factors through                  using factors through
         representing money                   the hundredths place.                  the thousandths place.
         by 1- and 2- digit
         whole numbers.

      19 Divide a 4-digit                  16 Divide decimal                      21 Calculate common                    10 Calculate percent of a                9 Find any missing values
         dividend                             numbers through the                    percent of a given                     given number.                           in percent calculations (is
         representing money                   hundredths place with                  number. (e.g., 10%,                                                            part / of whole = % /
         by a 1-digit divisor                 whole number                           25%, 33%, 50%, 75%)                                                            100).
         (w/out remainders).                  divisors.
                                              (e.g., 67.2 ÷ 16 = 4.2)




   Italics denote a repetition of a performance objective (learned in an earlier grade).       13             e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                            7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:              Performance Objectives:                   Performance Objectives:

                                           17 Divide decimal                      22 Divide decimal
                                              numbers through the                    numbers through the
                                              hundredths place                       thousandths place by
                                              with decimal                           decimal divisors.
                                              divisors. (e.g., 26.25
                                              ÷2.1 = 12.5)
                                                                                                                        11 Convert numbers                     10 Convert standard
                                                                                                                           expressed in standard                  notation to scientific
                                                                                                                           notation to scientific                 notation and vice versa
                                                                                                                           notation and vice versa                (introduce negative
                                                                                                                           (positive exponents                    exponents, but mastery
                                                                                                                           only).                                 expectation is for positive
                                                                                                                                                                  exponents only).


      20 Simplify numerical                18 Simply numerical                    23 Simplify numerical                 12 Simplify numerical                  11 Evaluate and simplify
         expressions using the                expressions using the                  expressions using the                 expressions using order                numerical expressions
         order of operations                  order of operations                    order of operations                   of operations, including               using order of operation
         with grade-                          with grade-                            rule on number sets                   exponents.                             rules on number sets
         appropriate                          appropriate                            using                                                                        (including exponents).
         operations on                        operations on number                   ( ), x, ÷ , + , -
         number sets.                         sets.




   Italics denote a repetition of a performance objective (learned in an earlier grade).      14             e.g. - means for example. This list is not exclusive. Other examples may apply.
                                                                   Strand 1: Numeration and Process Strands
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are
 needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the
                                                                  teaching and learning of mathematical strands.

                                                                         Concept 2: Numerical Operations
                                                     Understand and apply numerical operations and their relationship to one another.

         4th Grade                             5thGrade                               6th Grade                         7th Grade                                 8th Grade
  Performance Objectives:              Performance Objectives:                Performance Objectives:           Performance Objectives:                   Performance Objectives:

                                                                                                                     13 Solve a simple                      12 Evaluate algebraic
                                                                                                                        proportion using proper                absolute value
                                                                                                                        terminology. (product of               expressions.
                                                                                                                        means = product of
                                                                                                                        extreme, i.e., cross
                                                                                                                        products)




   Italics denote a repetition of a performance objective (learned in an earlier grade).    15            e.g. - means for example. This list is not exclusive. Other examples may apply.
C1:PO1       Describe how to use a
(Struc/Log   proportion to solve a
ic)          problem in context
C3:PO11      Use ratios and           C2:PO6   Simplify algebraic
(Patrn &     proportions to solve a            expressions using the
Alg)         given problem (e.g.               Distributive Property
             unit pricing, similar
             figures, scale drawings)

C1:PO1 Use ratios and                         Evaluate algebraic
                                    C3:PO1 (Patrn & Alg)
(Struc/Log proportions to express             expressions, including
ic)        mathematical                       absolute value and square
           relationships                      roots


                                               Select appropriate
                                               operations and solve word
                                               problems

C3:PO11 Solve a simple                     Solve proportions which
                                 C3:PO11 (Patrn & Alg)
(Patrn & algebraic proportion              generate linear equations
Alg)     using proper
         terminology (product of
         the means equals
         products of the
         extremes) (e.g. 3:4 =
         6:8…4 & 6 = mean, 3
         & 8 = extremes)

				
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posted:10/31/2011
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