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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.

Performance Objectives:              Performance Objectives:                Performance Objectives:               Performance Objectives:                   Performance Objectives:

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.

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
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.

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)

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.

Performance Objectives:              Performance Objectives:                Performance Objectives:                 Performance Objectives:                   Performance Objectives:

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.
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.
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.

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.

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.

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.

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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