# C2 by zhangyun

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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                   Performance                      Performance                  Performance                 Performance                        Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                 Objectives:                        Objectives:
1 Model                      1 Demonstrate the              1 Demonstrate the
through sums                 addition through               using manipulatives
of 10 using                  sums of 20                     with two 3-digit
manipulatives.               using                          whole numbers
(e.g., Say: 2 +              maipulatives.                  using
4 . Student                                                 manipulatives.
models
problem
through use of
manipulatives
)

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                   Performance                      Performance                  Performance                  Performance                        Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                  Objectives:                        Objectives:
2 Model                      2 Demonstrate the              2 Demonstrate the             1 Demonstrate the
subtraction                  process of                     process of                    process of
with minuends                subtraction with               subtraction with              subtraction
of 10 using                  minuends of 20                 two-digit whole               through 3-digit
manipulatives.               using                          numbers using                 whole numbers
(e.g.,Say: 4 -               manipulatives.                 manipulatives.                using
2. Student                                                                                manipulatives .
models
through use of
manipulatives
)

3 Verbal or                    3 Verbal or written
written                        demonstration of
demonstration                  accuracy with basic
with basic                     subtraction facts up
subtraction facts
up to 20 (with
or without a
number line).

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                   Performance                      Performance                  Performance                  Performance                        Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                   Objectives:                       Objectives:
digit whole                    whole numbers                 whole numbers               numbers.
numbers                        with regrouping.              with regrouping.
without
regrouping.
5 Subtract 1- and              5 Subtract 1- and 2-          3 Subtract two              2 Subtract whole
2-digit whole                  digit whole                   3-digit whole               numbers with
numbers                        numbers with or               numbers, with               regrouping.
without                        without regrouping.           regrouping.
regrouping.

operation                   level                          level appropriate             level appropriate           level appropriate                 level appropriate
(+,-) to solve              appropriate                    operation to solve            operation to                operation to solve                operation to solve
word                        operation to                   word problems.                solve word                  word problems.                    word problems.
problems                    solve word                                                   problems.
using                       problems. (e.g.,
numbers 0                   + and -)
through 9.

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.
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                   Performance                      Performance                  Performance                  Performance                       Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                   Objectives:                       Objectives:
4 Solve word                 7 Solve word                   8 Solve word                  6 Solve word                4 Solve word                      2 Solve word
problems                     problems using                 problems using                problems using              problems using                    problems using
orally using                 subtraction of 2-              subtraction of two            appropriate                 appropriate                       appropriate
addition or                  digit whole                    2-digit numbers               operations and              operations and                    operations and
subtraction                  numbers                        with regrouping               numbers.                    numbers.                          numbers.
with whole                   without                        AND two 3-digit
numbers                      regrouping.                    whole numbers
through 9.                                                  without
regrouping.

5 Skip count by             8 Count by                     9 Count by multiples          7 Demonstrate the           5 Multiply 3-digit                3 Multiply 3-digit
10's to 100.                multiples to                   of three.                     process of                  whole numbers by 2-               whole numbers by 3-
show the                                                     multiplication as           digit whole                       digit whole
process of                                                   repeatedly adding           numbers.                          numbers.
multiplication to                                            the same number,                                              (e.g., 426 x 329)
110. (e.g., skip                                             counting by
count by 2 and                                               multiples,
5)                                                           combining equal
sets, and making
arrays.

Italics denote a repetition of a performance objective (learned in an earlier grade).   16              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                   Performance                      Performance                  Performance                   Performance                       Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                    Objectives:                       Objectives:
8 Demonstrate the            6 Divide a 4-digit                4 Divide a 4-digit
process of                   dividend by a 1-                  dividend by a 2-
division with one-           digit divisor (w/ or              digit divisor.
digit divisors               w/out remainders).
(separating
elements of a set
into smaller equal
sets, sharing
equally, or
repeatedly
subtracting the
same number).

9 Demonstrate                                                9 Demonstrate                7 Use division with
families of                                                  families of                  remainders in
equations for                                                equations for                contextual
subtraction                                                  and division
through 18.                                                  through 10s.
(e.g.,                                                       (i.e., fact
7 + 9 = 16,                                                  families)
9 + 7 = 16,
16 - 9 = 7,
16 - 7 = 9)

Italics denote a repetition of a performance objective (learned in an earlier grade).   17               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                   Performance                      Performance                Performance                   Performance                        Performance
Objectives:                  Objectives:                      Objectives:                Objectives:                    Objectives:                       Objectives:
10 State multiplication     10 State                      8 State multiplication
facts ( 2s,5s,10s).         multiplication               and division facts
and division facts           through 12's.
through 10's.

10 Demonstrate                 11 Demonstrate the          11 Demonstrate the            9 Demonstrate the                 5 Demonstrate the
Identity and                   Associative                 Commutative and              Associative                       Distributive
Commutative                    property of                 Identity                     property of                       property of
properties                     addition.                   properties of                multiplication.                   multiplication over
through 18.                    [e.g., (3 + 5) + 4 =        multiplication.                                                addition.
3 + (5 + 4)]                                                                               [e.g., (3*38 =
3(30+8) = (3*30)
+(3*8) ]
11 Identify                                                12 Identify                  10 Use the distributive            6 Demonstrate the
subtraction as                                             and division as              multiplication                    multiplication
inverse                                                    inverse                      problems.                         properties of
operations.                                                operations.                                                    equality (identity
(e.g., 3+4 =                                                                                                              elements).
4+3)

Italics denote a repetition of a performance objective (learned in an earlier grade).   18             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                   Performance                      Performance                Performance                    Performance                       Performance
Objectives:                  Objectives:                      Objectives:                Objectives:                     Objectives:                       Objectives:
appropriate                 level appropriate             appropriate                       appropriate
properties to assist        properties to                 properties to assist              properties to assist
in computation;.            assist in                     in computation;                   in computation;
Associative,                computation;                  Associative,                      Associative,
Commutative                 Associative,                  Commutative,                      Commutative,
Commutative,                  Distributive,                     Distributive,
Identity                      Identity                          Identity

6 Identify the             12 Apply the                   13 Apply the symbols        14 Apply the                  12 Apply the symbols               8 Apply the symbol:
symbols                     symbols (+, -,                 (+,-,                       symbols            • and * ( ) for                   "[ ]" to represent
( +, –, = ).                =).                            x , /, ÷,                   *%and the           multiplication,                   grouping.
<,>,                        grouping symbols              and ≤ and ≥.
%, ≠ ).                     ( ) and " , ".

Italics denote a repetition of a performance objective (learned in an earlier grade).   19              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                   Performance                      Performance                Performance                   Performance                       Performance
Objectives:                   Objectives:                     Objectives:                Objectives:                    Objectives:                       Objectives:
level                        appropriate                    appropriate                 appropriate                  appropriate                       appropriate
appropriate                  mathematical                   mathematical                mathematical                 mathematical                      mathematical
mathematical                 terminology.                   terminology.                terminology.                 terminology.                      terminology.
terminology.                 (e.g.,
subtract,                    greater than or
equals, more,                less than)
less)

10 Simplify fractions to
lowest terms.
fractions with                 fractions with like         denominators                 no regrouping.                    numbers with like
like                           denominators                (halves, thirds,                                               denominators with
denominators                   (halves and fourths)        fourths, fifths,                                               regrouping.
(halves) using                 using models.               sixths, eighths,
models.                                                    and tenths).

Italics denote a repetition of a performance objective (learned in an earlier grade).   20             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                   Performance                      Performance                Performance                   Performance                       Performance
Objectives:                   Objectives:                     Objectives:                Objectives:                    Objectives:                       Objectives:
15 Demonstrate                 16 Demonstrate              17 Subtract fractions        15 Subtract fractions             12 Subtract proper
subtraction of                 subtraction of              with like                    with like                         fractions and mixed
fractions with                 fractions with like         denominators                 denominators, no                  numbers with like
like                           denominators                (halves, thirds,             regrouping.                       denominators with
denominators                   (halves and fourths)        fourths, fifths,                                               regrouping.
(halves) using                 using models.               sixths, eighths,
models.                                                    and tenths).

without                        regrouping through          in contextual                regrouping through                thousandths.
regrouping                     \$5.00 using                 situations,                  \$99.99.
through 99¢                    manipulatives and           through \$20.00.
using                          paper and pencil.
manipulatives
and
pencil/paper, .
17 Subtract money              18 Subtract money           19 Apply                     17 Subtract money                 14 Subtract decimals to
without                        without regrouping          subtraction in               with regrouping                   the thousandths.
regrouping                     through \$5.00               contextual                   through \$99.99.
through                        using manipulatives         situations,
99¢using                       and paper and               through \$20.00.
manipulatives                  pencil..
and
pencil/paper, .

Italics denote a repetition of a performance objective (learned in an earlier grade).   21             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                   Performance                      Performance                  Performance                 Performance                       Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                  Objectives:                       Objectives:
18 Multiply 3-digit               15 Multiply decimals
numbers                           using factors
representing                      through the
money by 1- and 2-                hundredths place.
digit whole
numbers.

19 Divide a 4-digit               16 Divide decimal
dividend                          numbers through the
representing                      hundredths place
money by a 1-                     with whole number
digit divisor (w/out              divisors.
remainders).                      (e.g., 67.2 ÷ 16 =
4.2)
17 Divide decimal
numbers through
the hundredths
place with decimal
divisors. (e.g.,
26.25 ÷ 2.1 = 12.5)

Italics denote a repetition of a performance objective (learned in an earlier grade).   22             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                   Performance                      Performance                  Performance                 Performance                       Performance
Objectives:                  Objectives:                      Objectives:                  Objectives:                  Objectives:                       Objectives:
20 Simplify numerical             18 Simplify numerical
expressions using                 expressions using
the order of                      the order of
operations with                   operations with
operations on                     operations on
number sets.                      number sets.

Italics denote a repetition of a performance objective (learned in an earlier grade).   23             e.g., means for example. This list is not exclusive. Other examples may apply.
15 Identify     15 Identify
one to ten      100 more
more or         or less
less of a       than a
number up       number up
to 100.         to 1,000.
(e.g.., 10      (e.g., 100
more than       more than
50 = 60, 3      862 = 962,
less than       100 less
47 = 44)        than 625 =
525)

10 Construct
equivalent
forms of
whole
numbers,
using any
operation.
(e.g.,
31 = 10 +
10 + 10 +
1;
(10 x 3) +
1;
25 + 6 ;
41 - 10 ;

```
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