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4 1 grades 5 8 by cYevV8B

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									STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS):
                Grade 5                                    Grade 6                                           Grade 7                                   Grade 8
A. Number Sense                          A. Number Sense                                  A. Number Sense                              A. Number Sense
    1. Use real-life experiences,            1. Use real-life experiences, physical           1. Extend understanding of the               1. Extend understanding of the
       physical materials, and                  materials, and technology to                       number system by constructing              number system by constructing
       technology to construct                  construct meanings for numbers                     meanings for the following                 meanings for the following
       meanings for numbers (unless             (unless otherwise noted, all                       (unless otherwise noted, all               (unless otherwise noted, all
       otherwise noted, all indicators          indicators for grade 6 pertain to                  indicators for grade 7 pertain             indicators for grade 8 pertain
       for grade 5 pertain to these             these sets of numbers as well).                    to these sets of numbers as                to these sets of numbers as
       sets of numbers as well).                     o All integers                                well):                                     well):
            o All fractions as part of a             o All fractions as part of a                        o Rational numbers                         o Rational numbers
                 whole, as subset of a                    whole, as subset of a set,                     o Percents                                 o Percents
                 set, as a location on a                  as a location on a number                      o Whole numbers with                       o Exponents
                 number line, and as                      line, and as divisions of                           exponents                             o Roots
                 divisions of whole                       whole numbers                       2. Demonstrate a sense of the                         o Absolute values
                 numbers                             o All decimals                                relative magnitudes of numbers.                  o Numbers represented in
            o All decimals                   2. Recognize the decimal nature of               3. Understand and use ratios,                              scientific notation
    2. Recognize the decimal nature of          United States currency and                         proportions, and percents               2. Demonstrate a sense of the
       United States currency and               compute with money.                                (including percents greater than           relative magnitudes of numbers.
       compute with money.                   3. Demonstrate a sense of the relative                100 and less than 1) in a variety       3. Understand and use ratios,
    3. Demonstrate a sense of the               magnitudes of numbers.                             of situations.                             proportions, and percents
       relative magnitudes of numbers.       4. Explore the use of ratios and                 4. Compare and order numbers of                 (including percents greater than
    4. Use whole numbers, fractions,            proportions in a variety of situations.            all named types.                           100 and less than 1) in a variety
       and decimals to represent             5. Understand and use whole-number               5. Use whole numbers, fractions,                of situations.
       equivalent forms of the same             percents between 1 and 100 in a                    decimals, and percents to               4. Compare and order numbers of
       number.                                  variety of situations.                             represent equivalent forms of              all named types.
    5. Develop and apply number              6. Use whole numbers, fractions, and                  the same number.                        5. Use whole numbers, fractions,
       theory concepts in problem               decimals to represent equivalent              6. Understand that all fractions can            decimals, and percents to
       solving situations.                      forms of the same number.                          be represented as repeating or             represent equivalent forms of the
            o Primes, factors,               7. Develop and apply number theory                    terminating decimals.                      same number.
                 multiples                      concepts in problem solving               B. Numerical Operations                          6. Recognize that repeating
    6. Compare and order numbers.               situations.                                   1. Use and explain procedures for               decimals correspond to fractions
B. Numerical Operations                              o Primes, factors, multiples                  performing calculations with               and determine their fractional
    1. Recognize the appropriate use of              o Common multiples,                           integers and all number types              equivalents.
       each arithmetic operation in                       common factors                           named above with:                                o 5/7 = 0.
       problem situations.                   8. Compare and order numbers.                               o Pencil-and-paper                              714285714285… =
    2. Construct, use, and explain       B. Numerical Operations                                         o Mental math                                   0.714285
       procedures for performing             1. Recognize the appropriate use of                         o Calculator                      7. Construct meanings for common
       addition and subtraction with            each arithmetic operation in                  2. Use exponentiation to find whole             irrational numbers, such as π (pi)
       fractions and decimals with:             problem situations.                                number powers of numbers.                  and the square root of 2.
            o Pencil-and-paper               2. Construct, use, and explain                   3. Understand and apply the              B. Numerical Operations
            o Mental math                       procedures for performing                          standard algebraic order of             1. Use and explain procedures for
            o Calculator                        calculations with fractions and                    operations, including                      performing calculations involving
    3. Use an efficient and accurate            decimals with:                                     appropriate use of parentheses.            addition, subtraction,
       pencil-and-paper procedure for                o Pencil-and-paper                   C. Estimation                                       multiplication, division, and
       division of a 3-digit number by a             o Mental math                        Use equivalent representations of                   exponentiation with integers and
       2-digit number.                               o Calculator                         numbers such as fractions, decimals, and            all number types named above
    4. Select pencil-and-paper, mental       3. Use an efficient and accurate             percents to facilitate estimation.                  with:
       math, or a calculator as the             pencil-and-paper procedure for                                                                      o Pencil-and-paper
       appropriate computational                division of a 3-digit number by a 2-                                                                o Mental math
        method in a given situation                 digit number.                                          o Calculator
        depending on the context and            4.  Select pencil-and-paper, mental             2.   Use exponentiation to find whole
        numbers.                                    math, or a calculator as the appro               number powers of numbers.
    5. Check the reasonableness of              5. priate computational method in a             3. Find square and cube roots of
        results of computations.                    given situation depending on the                 numbers and understand the
    6. Understand and use the various               context and numbers.                             inverse nature of powers and
        relationships among operations          6. Find squares and cubes of whole                   roots.
        and properties of operations.               numbers.                                    4. Solve problems involving
C. Estimation                                   7. Check the reasonableness of                       proportions and percents.
    1. Use a variety of estimation                  results of computations.                    5. Understand and apply the
        strategies for both number and          8. Understand and use the various                    standard algebraic order of
        computation.                                relationships among operations and               operations, including appropriate
    2. Recognize when an estimate is                properties of operations.                        use of parentheses.
        appropriate, and understand the         9. Understand and apply the standard        C. Estimation
        usefulness of an estimate as                algebraic order of operations for the       1. Estimate square and cube roots
        distinct from an exact answer.              four basic operations, including                 of numbers.
    3. Determine the reasonableness of              appropriate use of parentheses.             2. Use equivalent representations of
        an answer by estimating the         C. Estimation                                            numbers such as fractions,
        result of operations.                   1. Use a variety of strategies for                   decimals, and percents to
    4. Determine whether a given                    estimating both quantities and the               facilitate estimation.
        estimate is an overestimate or an           results of computations.                Recognize the limitations of estimation
        underestimate.                          2. Recognize when an estimate is            and assess the amount of error resulting
                                                    appropriate, and understand the         from estimation.
                                                    usefulness of an estimate as
                                                    distinct from an exact answer.
                                                3. Determine the reasonableness of
                                                    an answer by estimating the result
                                                    of operations.
                                                4. Determine whether a given estimate
                                                    is an overestimate or an
                                                    underestimate.

								
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