KNS1.0 Students understand the relationship
between numbers and quantities (i.e., that a set of objects has the same
number of objects in different situations regardless of its position or
arrangement).

K.CC: Know number names
and the counting sequence.

K.CC: Count to tell the
number of objects. Compare numbers (Cluster Statement)

KNS1.1 Compare two or more sets of
objects (up to ten objects in each group) and identify which set is equal to,
more than, or less than the other.

K.CC.6: Identify whether
the number of objects in one group is greater than, less than, or equal to
the number of objects in another group, e.g., by using matching and counting
strategies.*

K.CC.7: Compare two
numbers between 1 and 10 presented as written numerals.

KNS1.2 Count, recognize,
represent, name, and order a number of objects (up to 30).and by tens.

K.CC.2: Count forward
beginning from a given number within the known sequence (instead of having to
begin at 1).

K.CC.3: Write numbers
from 020. Represent a number of objects with written numeral 0 -20 (with 0
representing a count of no objects).

K.CC.5: Count to answer
how many? questions about as many as 20 things arranged in a line, a
rectangular array, or a circle, or as many as 10 things in a scattered
configuration; given a number from 1-20, count out that many objects

KNS1.3 Know
that the larger numbers describe sets with more objects in them than the
smaller numbers have a relationship between numbers and quantities; connect counting
to cardinality.

K.CC.4a: When counting
objects, say the number names in the standard order, pairing each object with
one and only one number name and each number name with one and only one
object.

K.CC.4b: Understand
that the last number name said tells the number of objects counted. The
number of objects is the same regardless of their arrangement or the order in
which they were counted.

K.CC.4c: Understand
that each successive number name refers to a quantity that is one larger.

K.CC.6: Identify
whether the number of objects in one group is greater than, less than, or
equal to the number of objects in another group, e.g., by using matching and
counting strategies.*

KNS2.0 Students understand and
describe simple additions and subtractions

K.OA: (Cluster
Statement) Understand addition as putting
together and adding to, and understand subtraction as taking apart and taking
from.

KNS3.0 Students use estimation
strategies in computation and problem solving that involve numbers that use
the ones and tens places.

NO

KNS3.1 Recognize when an estimate
is reasonable

NO

1NS Number
Sense

1NS1.0 Students understand and use
numbers up to 100.

1.NBT:
Extend the counting sequence. (Cluster Statement)

1NS1.1 Count, read, and write whole numbers to 100.

1.NBT.1:
Count to 120, starting at any number less than 120. In this range, read and
write numerals and represent a number of objects with a written numeral.

1NS1.2 Compare and
order whole numbers to 100 by using the symbols for less than, equal to, or
greater than (<, =, >).

1.NBT.3:
Compare two two-digit numbers based on meanings of the tens and ones digits,
recording the results of comparisons with the symbols >, =, and <.

1NS1.3 Represent equivalent forms
of the same number through the use of physical models, diagrams, and number
expressions (to 20) (e.g., 8 may be represented as 4 + 4, 5 + 3, 2 + 2 + 2 +
2, 10 -2, 11 -3).

1.OA.6:
Add and subtract within 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on: making ten (e.g.,
8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten
(e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between
addition and subtraction (e.g., knowing that 8 + 4 = 12, one know 12 8 =
4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by
creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

1NS1.4 Count and group object in
ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 + 4).

1.NBT.2:
Understand that the two digits of a two-digit number represent amounts of
tens and ones. Understand the following as special cases:

1NS2.0 Students demonstrate
the meaning of addition and subtraction and use these operations to solve
problems

1.OA: Represent and solve
problems involving addition and subtraction. (Cluster Statement)

1NS2.1 Know the addition
facts (sums to 20) and the corresponding subtraction facts and commit them to
memory.

1.OA.6: Add and
subtract within 20, demonstrating fluency for addition and subtraction within
10.Use strategies such as counting on:making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a
ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between
addition and subtraction (e.g., knowing that 8 + 4 = 12, one know 12 8 =
4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by
creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

1NS2.2 Use the
inverse relationship between addition and subtraction to solve problems

1.OA.4:
Understand subtraction as an unknown-addend problem..

!NS2.3
Identify one more than, one less than, 10 more than, and 10 less than a
given number.

1.NBT.5:
Given a two-digit number, mentally find 10 more or 10 less that the number,
without having to count: explain the reasoning used.

1NS2.4 Count by 2s,
5s, and 10s to 100. 1.OA.5: Relate counting to
addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.5:
Relate counting to addition and subtraction (e.g., by counting on 2 to add
2).

1NS2.5 Show the
meaning of addition (putting together, increasing) and subtraction (taking
away, comparing, finding the difference).

NO

1NS2.5 Show the
meaning of addition (putting together, increasing) and subtraction (taking
away, comparing, finding the difference).

NO

1NS2.6 Solve
addition and subtraction problems with one-and two-digit numbers (e.g., 5 +
58 = __).

1.NBT.4: Add within
100, including adding a two-digit number, and adding a two-digit number and a
multiple of 10, using concrete models or drawings and strategies based on
place value, properties of operations, and/or the relationship between
addition and subtraction; related the strategy to a written method and
explain the reasoning used. Understand that in adding two-digit numbers, one
adds tens and tens, ones and ones; and sometimes it is necessary to compose a
ten.

1.NBT.6: Subtract
multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90
(positive or zero differences), using concrete models or drawings and
strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; related the strategy to a
written method and explain the reasoning used.

1NS2.7 Find the sum of
three one-digit numbers.

1.OA.2:
Solve word problems that call for addition of three whole numbers whose sum
is less than or equal to 20, e.g., by using objects, drawings, and equations
with a symbol for the unknown number to represent the problem.

1OA.8: Determine the unknown
whole number in an addition or subtraction equation relating to three whole
numbers.

1NS3.0 Students use estimation
strategies in computation and problem solving that involve numbers that use
the ones, tens, and hundreds places.

NO

1NS3.1 Make reasonable estimates
when comparing larger or smaller numbers.

NO

2NS Number Sense

2NS1.0 Students understand the relationship between numbers,
quantities, and place value in whole numbers up to 1,000:

2.NBT: Understand Place Value. Use place value
understanding andproperties
of operations to add and subtract. (Cluster Statement)

2NS1.1*Count, read, and write whole numbers
to 1,000 and identify the place value for each digit.

2.NBT.1: Understand that the three-digit number
representamounts
of hundreds, tens and ones; e.g. 706 equals 7 hundreds, 0tens, and 6 ones. Understand the following as special
cases:

2.NBT.1a: 100 can be thought of as a bundle of ten tens-called
a hundred.

2.NBT.1b: The numbers 100, 200, 300, 400, 500, 600,
700,800, 900
refer to one, two, three, four, five, six, seven, eight, ornine hundreds (and 0 tens and 0
ones).

2.NBT.2: Count within 1000; skip-count by 5s, 10s and
100s.

2.NBT.3: Read and write
numbers to 1000 using base-ten numerals, number names and expanded form.

2NS1.2Use words, models, and expanded
forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).

2.NBT.3: Read and write numbers to 1000 using
base-ten numerals,number names and expanded form.

2NS1.3* Order and compare whole numbers to
1,000 by using the symbols <, =, >.

2.NBT.4: Compare two three-digit numbers based on
meanings of thehundreds,
tens and ones digits, using >, =, and < symbols to recordthe results of the comparisons.

2NS2.0Students estimate, calculate, and solve problems involving addition
and subtraction of two- and three-digit numbers:

2.NBT.1: (Cluster Statement) Use place value
understanding andproperties
of operations to add and subtract.

2NS2.1* Understand and use the inverse
relationship between addition and subtraction (e.g., an opposite number
sentence for 8 + 6 = 14 is 14 6 = 8) to solve problems and check solutions.

2.NBT.5: Fluently add and subtract within 100 using
strategiesbased on
place value, properties of operations, and/or the relationship between
addition and subtraction.

2.NBT.7: Add and subtract within 1000, using concrete
models or drawings and strategies based on place value, properties ofoperations, and/or the
relationship between addition and subtraction;relate the strategy to a written method. Understand that in addingor subtracting three-digit numbers, one adds or
subtracts hundreds andhundreds, tens and
tens, ones and ones; and sometimes it is necessaryto compose or decompose tens or hundreds.

2.NBT.9: Explain why addition and subtraction
strategies work,using
place value and the properties of operations.

2NS2.2*Find the sum or difference of two
whole numbers up to three digits long.

2.NBT.6: Add up to four two-digit numbers using
strategies based onplace
value and properties of operations.

2.NBT.7: Add and subtract within 1000, using concrete
models ordrawings
and strategies based on place value, properties ofoperations, and/or the relationship between addition and
subtraction;relate the strategy to a written
method. Understand that in addingor
subtracting three-digit numbers, one adds or subtracts hundreds andhundreds, tens and tens, ones and ones; and sometimes it
is necessaryto compose or decompose tens or
hundreds.

2NS2.3 Use mental arithmetic to
find the sum or difference of two two-digit numbers. &&&

2.OA.1: Use addition and subtraction within 100
to solveone- and
two-step word problems involving situations of adding to,taking from, putting together, taking apart and comparing,
with unknowns in all positions ,e.g., by using drawing and equations with asymbol for the unknown number to represent the
problem.

2.OA.2: Fluently add and subtract within 20 using
mental strategies.By the end of Grade 2, know from
memory all sums of two one-digit numbers.

2.NBT.5: Fluently add and subtract within 100 using
strategiesbased on
place value, properties of operations, and/or the relationship between
addition and subtraction.

2.NBT.8: Mentally add 10 or 100 to a given number
100-900, andmentally
subtract 10 or 100 from a given number 100-900.

2NS3.0* Students model and solve simple
problems involving multiplication and division:

NO

2NS3.1* Use repeated addition, arrays, and
counting by multiples to do multiplication.

2.OA.4: Use addition to find the total number
of objects arranged inrectangular
arrays with up to 5 rows and up to 5 columns; write anequation to express the total as a sum of equal addends.

2NS3.2* Use repeated subtraction, equal sharing, and forming equal
groups with remainders to do division.

NO

2NS3.3* Know the multiplication tables of
2s, 5s, and 10s (to times 10) and commit them to memory.

NO

2NS4.0 Students understand that fractions
and decimals may refer to parts of a set and parts of a whole:

NO

2NS4.1* Recognize, name, and compare unit fractions from 1/12 to 1/2.

NO

2NS4.2* Recognize fractions of a
whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15
balls).

NO

2NS4.3* Know that when all
fractional parts are included, such as four-fourths, the result is equal to
the whole and to one.

2.G.3: Partition circles and rectangles into two,
three, or four equal shares, describe the shares using words halves, thirds,
half of, a third of, etc., and describe the whole as two halves, three
thirds, four fourths. Recognize that equal shares of identical wholes need
not have the same shape.

2NS5.0 Students model and solve problems by
representing, adding, and subtracting amounts of money:

2.MD: Work with time and
money. (Cluster Statement)

2NS5.1* Solve problems using combinations of coins and bills.

2.MD.8: Solve word problems involving dollar bills,
quarters,dimes,
nickels and pennies, using dollar and cent symbols appropriately.

2NS5.2* Know and use the decimal
notation and the dollar and cent symbols for money.

NO

2NS6.0 Students use estimation
strategies in computation and problem solving that involve numbers

NO

2NS6.1 Recognize when an estimate is reasonable
in measurements (e.g., closest inch).

NO

3NS Number Sense

3NS1.0 Students understand the
place value of whole numbers:

NO -- CCS explains in the
Grade 4 overview: Students generalize their understanding of place value to
1,000,000, understanding the relative sizes of numbers in each place. CCS
does not mention what the place value limit in Grade 3.

3NS1.1 Count, read, and write
whole numbers to 10,000

NO -- 4.NBT.2: Read and write
multi-digit whole numbers using base-ten numerals, number names, and expanded
form. Compare two multi-digit numbers based on meanings of the digits in each
place, using >, =, and < symbols to record the results of comparisons.

NO -- CCS Grade 4 expectations in this domain are
limited to whole numbers

less than or equal to
1,000,000.

3NS1.2 Compare and order whole numbers to
10,000.

NO -- 4.NBT.2: Read
and write multi-digit whole numbers using base-ten numerals, number names,
and expanded form. Compare two multi=digit numbers based on meanings of the
digits in each place, using >, =, and < symbols to record the results
of comparisons.

3NS1.3* Identify the place value
for each digit in numbers to 10,000.

NO -- 4.NBT.1: Recognize
that in a multi-digit whole number, a digit in one place represents ten times
what it represents in the place to its right. CCS adds the comparison of one
place value to the next (x 10).

3NS1.4 Round off numbers to 10,000
to the nearest ten, hundred, and thousand.

Partial -- 4.NBT.3: Use
place value understanding to round multi-digit whole numbers to any place.

3NS1.5* Use expanded notation to represent
numbers (e.g., 3,206 = 3,000 + 200 + 6).

NO

3NS2.0 Students calculate and
solve problems involving addition, subtraction, multiplication, and division:

3.OAT (Cluster Statement) Use place value understanding and
properties of operations to perform multi-digit arithmetic

3NS2.1* Find the sum or difference
of two whole numbers between 0 and 10,000

3.NBT.2: Fluently add and
subtract within 1000 using strategies and algorithms based on place value,
properties of operations, and/or the relationship between addition and
subtraction.

3NS2.2
Memorize to automaticity the multiplication table for numbers between 1 and
10.

3.OA.7: Fluently multiply and
divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 x 5 = 40, one know 40 χ 5 =
8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.

3.NBT.3: Multiply one-digit
whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60)
using strategies based on place value and properties of operations.

3NS2.3* Use the
inverse relationship of multiplication and division to compute and check
results.

3.OA.4: Determine the unknown whole number in a multiplication or
division equation relating three whole numbers

3.OA.7: Fluently multiply and divide within 100, using strategies
such as the

relationship between
multiplication and division (e.g., knowing that 8 x 5 = 40, one know 40
χ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one digit numbers.

3.OA.6: Understand division as an unknown-factor problem

3NS2.4* Solve
simple problems involving multiplication of multi-digit numbers by one-digit
numbers (3,671 Χ 3 = ___).

3.OA.1: Interpret products of
whole number, e.g., interpret 5 x 7 as the total number of objects in 5
groups of 7 objects each.

3.OA.7: Fluently multiply and
divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 x 5 = 40, one know 40 χ 5 =
8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.

3NS2.5 Solve division problems in which a
multi-digit number is evenly divided by a one-digit number (135 χ 5 = ___).

3NS2.6 Understand the special properties of
0 and 1 in multiplication and division.

3NS2.7 Determine the unit cost when given the total cost and number of
units.

3NS2.8 Solve problems that require two or
more of the skills mentioned above.

3NS3.0 Students understand the
relationship between whole numbers, simple fractions, and decimals:

3.NF: (Cluster Statement)
Develop an understanding of fractions as numbers.

CCS does not explicitly describe the relationship between whole
numbers,

simple fractions, and decimals.

4.NF: (Cluster Statement)
Understand decimal notation for fractions, and compare decimal fractions.

3NS3.1 Compare fractions represented by drawings or
concrete materials to show equivalency and to add and subtract simple
fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of
another pizza that is the same size; show that 3/8 is larger than 1/4).

3.NF.3: Explain equivalence offractions in special cases, and

compare fractions by reasoning about their size

3.NF.3a: Understand two
fractions as equivalent (equal) if they are the same size, or the same point
on a number line.

3.NF.3b: Recognize and generate
simple equivalent fractions, e.g., = 2/4, 4/6 = 2/3. Explain why
the fractions are equivalent, e.g., by using a visual fraction model.

3.NF.3c: Express whole numbers
as fractions, and recognize fractions that are equivalent to whole numbers.

3.NF.3d: Compare two fractions with the same numerator or the
same denominator by reasoning

about their size. Recognize
that comparisons are valid only when the two fractions refer to the
samewhole. Record the results of comparisons with the symbols >, =, <,
and justify the conclusions, e.g., by using a visual fraction model

3NS3.2* Add and subtract simple fractions (e.g., determine
that 1/8 + 3/8 is the same as 1/2).

Partial - CCS does not mention adding and subtracting of simple
fractions. However, it is implied in statement 3.NF.2b.

3.NF.2: Understand a fraction
as a number on the number line; represent fractions on a number line diagram.

3.NF.2a: Represent a fraction
1/b on a number line diagram by defining the interval from 0 to 1 as the
whole and partitioning it into b equal parts. Recognize that each part has
size 1/b and that the endpoint of the part based at 0 locates the number 1/b
on the number line.

3.NF.2b: Represent a fraction
a/b on a number line diagram by marking off a length of 1/b from 0. Recognize
that the resulting interval has size a/b and that its endpoint locates the
number a/b on the number line.

3NS3.3* Solve problems involving addition,
subtraction, multiplication, and division of money amounts in decimal
notation and multiply and divide money amounts in decimal notation by using
whole-number multipliers and divisors.

NO -5.NBT.7: Add, subtract, multiply, and

divide decimals to hundredths, using concrete models or drawings
and strategies based on place value,

properties of operations, and/or
the relationship between addition and subtraction; relate the strategy to a
written method and explain the reasoning used.

3NS3.4 Know and
understand that fractions and decimals are two different representations of
the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a
dollar).

NO ---4.NF.6: Use decimal notation for fractions with
denominators 10 or 100.

CCS describes the two different representations with denominators
that are the powers of 10.

4NS Number Sense

4NS1.0Students understand the place value of whole numbers and decimals
to two decimal places and how whole numbers and decimals relate to simple
fractions. Students use the concepts of negative numbers:

4.NBT: Generalize place value

understanding for multi-digit whole
numbers (Cluster Statement).

4.NF Cluster Statement:
Understand decimal notation for fractions, and compare decimal fractions).

4NS1.1* Read
and write whole numbers in the millions.

4.NBT.2: Read and write
multi-digit whole numbers using base-ten numerals, number names, and expanded
form.

Compare two multi-digit numbers based on meaning of the digits in
each place, using >, =, and < symbols to record the results of
comparisons.

CCS expectations for Grade 4 are limited to whole numbers less
than or equal to 1,000,000.

4NS1.2* Order and compare whole numbers and decimals to
two decimal places.

4.NBT.2: Read and write
multi-digit whole numbers using base-ten numerals, number names, and expanded
form.

Compare two multi-digit numbers based on meaning of the digits in
each place, using >, =, and < symbols to record the results of
comparisons.

4.NF.7: Compare two decimals to
hundredths by reasoning about their size. Recognize that comparisons are
valid only when the two decimals refer to the same whole. Record the results of
comparisons with the symbols >, =, <, and justify the conclusions,
e.g., by using a visual model

4NS1.3* Round whole numbers through the millions to the
nearest ten, hundred, thousand, ten thousand, or hundred thousand.

4.NBT.3: Use place value understanding
to round multi-digit whole numbers to any place.

4NS1.4
Decide when a rounded solution is called for and explain why such a solution
may be appropriate

4.OA.3: Solve multi-step word problems posed with whole numbers
and having whole-number answers using the four

operations, including problems in
which remainders must be interpreted. Represent these problems using
equations with a letter standing for the unknown quantity. Assess the

reasonableness of answers using mental
computation and estimation strategies including rounding.

4NS1.5 Explain different interpretations of fractions, for
example, parts of a whole, parts of a set, and division of whole numbers by
whole numbers; explain equivalents of fractions (see Standard 4.0).

NO

4NS1.6 Write tenths and hundredths in decimal and fraction
notations, and know the fraction and decimal equivalents for halves and
fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).

4.NF.6: Use decimal notation
for fractions with denominators 10 or 100.

CCS does not specify other fractions than those with denominators
of powers of 10.

3.NF.3: Explain equivalence of fractions in special cases, and

compare fractions by reasoning
about their size.

3.NF.3a: Understand two
fractions as equivalent (equal) if they are the same size, or the same point
on a number line.

3.NF.3b: Recognize and generate
simple equivalent fractions, e.g.,. = 2/4, 4/6 = 2/3. Explain whey the fractions are equivalent, e.g.,by using a visual fraction model.

3.NF.3c: Express whole numbers
as fractions, and recognize fractions that are equivalent to whole numbers.

3.NF.3d: Compare two fractions with the same numerator or the
same denominator by reasoning

about their size. Recognize
that

comparisons are valid only when the
two fractions refer to the same whole. Record the results of comparisons with
the symbols >, =, or <, and justify the conclusions, e.g., by using a
visual fraction model

4NS1.7 Write
the fraction represented by a drawing of parts of a figure; represent a given
fraction by using drawings; and relate a fraction to a simple decimal on a
number line.

4.NF.5: Express a fraction with

denominator 10 as an equivalent fraction with a denominator 100,
and use this

technique to add two fractions
with respective denominators 10 and 100. Use decimal notation for fractions
with

denominators 10 or 100.

4.NF.7: Compare two decimals to
hundredths by reasoning about their size Recognize that comparisons are valid
only when the two decimals refer to the same whole. Record the results of
comparisons with the symbols >, =, <, and justify the conclusions,
e.g., by using a visual model.

CCS does not ask students to draw a fraction.

CCS does not specify other fractions than those with denominators
of powers of 10.

4NS1.8
Use concepts of negative numbers (e.g., on a number line, in counting, in
temperature, in "owing").

CCS states two numbers on a

number line not explicitly two

negative numbers.

6.NS.7: Understand ordering and
absolute value of rational numbers.

6.NS.7a: Interpret statements of
inequality as statements about the relative position of two numbers on a
number line diagram.

6.NS.b7: Write, interpret, and explain statements of order for

rational numbers in real-world contexts.

6.NS.7c: Understand the absolute value of a rational number
as its distance from 0 on the number line;interpret absolute value as
magnitude for a positive or negative

quantity in a real-world
situation.

6.NS.7d: Distinguish comparisons
of absolute value from statements about order.

4NS1.9* Identify on a number line the relative position of
positive fractions, positive mixed numbers, and positive decimals to two
decimal places.

4.NF.7: Compare two decimals to
hundredths by reasoning about their size.Recognize that comparisons are valid
only when the two decimals refer to the same whole. Record the results of
comparisons with the symbols >, =, <, and justify the conclusions,
e.g., by using a visual model.

3.NF.2: Understand a fraction
as a number on the number line; represent fractions on a number line diagram.

3.NF.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the
whole and partitioning it into b equal parts. Recognize that each part
has size 1/b and that the endpoint of the part based at 0 locates the
number 1/b on the number line.

3.NF.2b: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0
Recognize that the resulting interval has size a/b and that its
endpoint locates the number a/b on the number line.

4NS2.0 Students extend their use
and understanding of whole numbers to the addition and subtraction of simple
decimals:

NO 5.NBT.7: Add, subtract, multiply, and
divide decimals to hundredths,using concrete models or drawings and
strategies based on place value, properties of operations, and/or
relationship between addition and subtraction; relate the strategy to a
written method and explain the reasoning used.

4NS2.1 Estimate and compute the
sum or difference of whole numbers and positive decimals to two places.

5.NBT.7: Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies based on place
value, properties of operations, and/or relationship between addition and
subtraction; relate the strategy to a written method and explain the
reasoning used.

CCS does not reference estimation directly. In the Mathematical
Practice standards, CCS implies a thorough understanding of the concepts so
students could develop strong estimation skills as abypro uct of the depth of

understanding.

4NS2.2 Round two-place decimals to one decimal or the
nearest whole number and judge the reasonableness of the rounded answer.

NO 5.NBT.4: Use place value understanding
to round decimals to any place.

4.NBT: (Cluster Statement) Use place value understanding and
properties of operations to perform multi-digit arithmetic

4NS3.0* Students solve problems involving addition,
subtraction, multiplication, and division of whole numbers and understand the
relationships among the operations:

4.NBT: (Cluster Statement) Use place value understanding and
properties of operations to perform multi-digit arithmetic

4NS3.1* Demonstrate an understanding of, and the ability
to use, standard algorithms for the addition and subtraction of multi-digit
numbers.

4.NBT.4: Fluently add and
subtract multi-digit whole numbers using the standard algorithm.

4NS3.2* Demonstrate an understanding of, and the ability
to use, standard algorithms for multiplying a multi-digit number by a
two-digit number and for dividing a multi-digit number by a one-digit number;
use relationships between them to simplify computations and to check results

PARTIAL 4.NBT.5: Multiply a whole
number of up to four digits by a one-digit whole number, and multiply two
two-digit numbers, using strategies based on place value and the properties
of operations. Illustrate and explain the calculation by using equations,
rectangular arrays, and/or area models.

5.NBT.5: Fluently multiply multi-digit whole numbers using the

standard algorithm.

4.NBT.6: Find whole-number quotients and remainders with up to
four-digit dividends and one-digit divisors, using

strategies based on place value,
the properties of operations, and/or the relationship between multiplication
and division. Illustrate and explain the calculation by using equations, rectangular
arrays, and/or area models.

4NS3.3* Solve problems involving multiplication of multidigit numbers by two-digit numbers.

PARTIAL 4.NBT.5: Multiply a whole number of up to four digits by
a one-digit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations .Illustrate
and explain the calculation by using equations, rectangular arrays, and/or
area models.

5.NBT.5: Fluently multiply multi-digit whole numbers using the

standard algorithm.

4NS3.4* Solve problems involving division of multi-digit
numbers by one-digit numbers.

PARTIAL 4.NBT.6: Find whole-number quotients

and remainders with up to four-digit dividends and one-digit
divisors, using strategies based on place value, the

properties of operations, and/or
the relationship between multiplication and division. Illustrate and explain
the

calculation by using equations, rectangular
arrays, and/or area models.

6.NS.2: Fluently divide
multi-digit numbers using the standard algorithm.

4NS4.0 Students know how to factor small whole numbers:

4.OA: (Cluster Statement) Gain familiarity with factors and
multiples

4NS4.1 Understand that many whole numbers break down in
different ways (e.g., 12 = 4 Χ 3 = 2 Χ 6 = 2 Χ 2 Χ 3).

PARTIAL 4.OA.4: Find all factor pairs for a whole
number in the range 1-100. Recognize that a whole number is a multiple of
each of its factors. Determine whether a given whole number in the range
1-100 is a multiple of a given one-digit number. Determine whether a given
whole number in the range 1-100 is prime or composite.

CCS only mentions factor pairs.

4NS4.2* Know that numbers such as 2, 3, 5, 7, and 11 do
not have any factors except 1 and themselves and that such numbers are called
prime numbers.

4.OA.4: Find all factor pairs
for a whole number in the range 1-100. Recognize that a whole number is a
multiple of each of its factors. Determine whether a given whole number in
the range 1-100 is a multiple of a given one-digit number. Determine whether
a given whole number in the range 1-100 is prime or composite

5NS
Number Sense

5NS1.0 Students compute with very
large and very small numbers, positive integers, decimals, and fractions and
understand the relationship between decimals, fractions, and percents. They
understand the relative magnitudes of numbers:

5NS1.1 Estimate, round, and
manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.

5NS1.2* Interpret percents as a
part of a hundred; find decimal and percent equivalents for common fractions
and explain why they represent the same value; compute a given percent of a
whole number.

5NS1.3 Understand and compute
positive integer powers of nonnegative integers; compute examples as repeated
multiplication.

5NS1.4* Determine the prime
factors of all numbers through 50 and write the numbers as the product of
their prime factors by using exponents to show multiples of a factor (e.g.,
24 = 2 Χ 2 Χ 2 Χ 3 = 23 Χ 3).

5NS1.5* Identify and represent on
a number line decimals, fractions, mixed numbers, and positive and negative
integers.

5NS2.0 Students perform
calculations and solve problems involving addition, subtraction, and simple
multiplication and division of fractions and decimals:

5NS2.1* Add, subtract, multiply,
and divide with decimals; add with negative integers; subtract positive
integers from negative integers; and verify the reasonableness of the
results.

5NS2.2* Demonstrate proficiency
with division, including division with positive decimals and long division
with multi-digit divisors.

5NS2.3* Solve simple problems,
including ones arising in concrete situations, involving the addition and
subtraction of fractions and mixed numbers (like and unlike denominators of
20 or less), and express answers in the simplest form.

5NS2.4 Understand the concept of
multiplication and division of fractions.

5NS2.5 Compute and perform simple
multiplication and division of fractions and apply these procedures to
solving problems.

6NS Number
Sense

6NS1.0 Students compare and order
positive and negative fractions, decimals, and mixed numbers. Students solve
problems involving fractions, ratios, proportions, and percentages:

6NS1.1Compare and order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.

6NS1.2Interpret and use ratios in different contexts (e.g., batting
averages, miles per hour) to show the relative sizes of two quantities, using
appropriate notations (a/b, a to b, a:b).

6NS1.3Use proportions to
solve problems (e.g., determine the value of N if 4/7 = N/21, find the length
of a side of a polygon similar to a known polygon). Use cross-multiplication
as a method for solving such problems, understanding it as the multiplication
of both sides of an equation by a multiplicative inverse.

6NS1.4Calculate given percentages of quantities and solve problems
involving discounts at sales, interest earned, and tips.

6NS2.0*Students calculate and
solve problems involving addition, subtraction, multiplication, and division:

6NS2.1Solve problems
involving addition, subtraction, multiplication, and division of positive
fractions and explain why a particular operation was used for a given
situation.

6NS2.2Explain the meaning of multiplication and division of positive
fractions and perform the calculations (e.g., 5/8 divided by 15/16 = 5/8 Χ
16/15 = 2/3).

6NS2.3*Solveaddition, subtraction, multiplication, and
division problems, including those arising in concrete situations, that use
positive and negative integers and combinations of these operations.

6NS2.4* Determine the least common multiple and the greatest common
divisor of whole numbers; use them to solve problems with fractions (e.g., to
find a common denominator to add two fractions or to find the reduced form
for a fraction).

7NS Number Sense

7NS1.0 Students know the properties of, and compute with, rational
numbers expressed in a variety of forms:

7NS1.1 Read, write, and compare rational
numbers in scientific notation (positive and negative powers of 10) with
approximate numbers using scientific notation.

7NS1.2* Add, subtract, multiply, and divide rational numbers
(integers, fractions, and terminating decimals) and take positive rational
numbers to whole-number powers.

7NS1.3 Convert fractions to decimals and percents and use these
representations in estimations, computations, and applications.

7NS1.4* Differentiate between rational and irrational numbers.

7NS1.5* Know that every rational number is either a terminating or
repeating decimal and be able to convert terminating decimals into reduced
fractions.

7NS1.6 Calculate the percentage of increases and decreases of a
quantity.

7NS1.7* Solve problems that involve discounts, markups, commissions,
and profit and compute simple and compound interest.

7NS2.0 Students use exponents, powers, and roots and use exponents in
working with fractions:

7NS2.1 Understand negative whole-number exponents. Multiply and divide
expressions involving exponents with a common base.

7NS2.2* Add and subtract fractions by using factoring to find common
denominators.

7NS2.3* Multiply, divide, and simplify rational numbers by using
exponent rules.

7NS2.4 Use the inverse relationship between raising
to a power and extracting the root of a perfect square integer; for an
integer that is not square, determine without a calculator the two integers
between which its square root lies and explain why.

7NS2.5* Understand the meaning of the absolute value of a number;
interpret the absolute value as the distance of the number from zero on a
number line; and determine the absolute value of real numbers.

Using Q&A NOTES for
Study

Please adjust your browser width
to view only this column and ____ the answer column on the right. ... For desktops adjust the window
size. ...For tablets or smart-phones pinch-zoom or ____ anywhere in a column
to best see it. ... Adjust settings to make the text easily readable.
... Usually landscape mode works best.

hide,
double-tap

2

In our study sessions let us keep
a loose leaf ____ in which we:

a)
Date the sheets.

2)
Note the questions that are most difficult to answer.

b)
Practice recall of these to end each session.

c)
Summarize in writing what we have learned.

5) Record questions we may have and any answers from our parents, other
students, our teacher.

6)
Do only a little each day.

notebook

3

In our studies we wish to practice
recall of the ____ answers that complete the thought as expressed in the
sentences in this left column.

missing

4

These pages will help us learn
& review what we need to know and do in ____ ____.

mathematics education

5

By repeatedly reviewing these
notes the reader will refresh his/her ____ of the mathematics standards
- including what teachers, tutors, parents and students must know and be able
to do.

understanding

6

When reading the question we want
to reflect on what each sentence says and means - to grasp sentences as ____
____..

complete thoughts

7

These Q&A Notes are written in
a conceptual, ____ style.

interactive

8

We want to intentionally ___ ____ our
reading to ensure comprehension.

slow down

9

These
Q&A Notes afollow a successful note-taking approach to studying: the
____ ____ approach

Cornell Notes

10

In the Cornell Notes we
read and reflect by
summarizing what we are to grasp. Then we ____
ourselves repeatedly until we achieve recall retention.

quiz

11

In our studies we think there are
____ steps worth following.

several

12

First, we want to focus our
working memory ____ on this left column we will
try to complete in our minds each sentence to form a complete thought.

attention

13

Second, when we have difficulty
completing a thought we simply unhide the ____ ____ in the column on the
right.

missing answer

14

Third, ____ any reading items that
are difficult for us and reflect on it while hiding the answer column.

repeat

15

We do this until we can
comfortably ____ the thought implied by the
sentence.

reproduce

16

Finally, we say out loud to ourselves
any difficult thoughts. This gets the ____ ____ involved with both visual and
text cues.

hearing sense

17

When saying the thought aloud we
will be courteous practicing sub-vocally in libraries or public places.

silently

18

We
will learn here:

1)
the ____ that define what we are expected to know and do,

2)
the math concepts needed,

3)
explanations for rules that are called out in each standard, and

4)
guidance in practicing needed skills.

standards

19

We
will learn here:

1)
the standards that define what we are expected to know and do;

2)
the ____ ____ needed;

3)
explanations for rules that are called out in each standard, and

4)
guidance in practicing the needed skills.

math concepts

20

We
will learn here:

1)
the standards that define what we are expected to know and do;

2)
the math concepts needed,

3)
explanations for ____ that are called out in each standard, and

4)
guidance in practicing the needed skills.

rules

21

We will learn here:

1) the
standards that define what we are expected to know and do;

2) the math
concepts needed;

3) explanations for the rules that are called out in each standard; and

4) guidance in practicing the needed
____.

skills

22

Notice the repetition in the above
Q&A Sequence. Must our learning be this ____?

repetitive

23

Yes, we must repeatedly focus ____
____ ____ on concepts in their native thought structures.

working memory attention

24

There will be no ____untilwe change for
the long term the neural circuits in your brain.

learning

25

This repetitive recall procedure
will help us learn by changing the neural circuits in our ____ ____memory.

long term

26

However - before ____ concepts and/or rules you must first understandthem.

memorizing

27

To first understand the ____ used
we must connect or relate them to prior knowledge - knowledge we are
comfortable with.

concepts

28

This is exactly like learning a
new ____, where we MUST first memorize words, repeatedly translate them
and then get experience by using them in a context, in real sentences..

language

29

To best learn mathematics we must
understand the new material in terms of what we ____ ____.
These connections are all-important.

already know

30

We gain experience by using
knowledge in ____ exercises.

doing

31

We need to mix up the exercises to
help us better recognize solution approaches that worked for us.

32

Without a goal to motivate us it
will be difficult to repeatedly ____ your self - to measure and verify
your ability to recall the learned material.

self-quiz

33

We will gain ____ by successfully
repeating this recall process.

confidence

34

We
know that unless we review ____ on a special schedule we will forget almost
half of what we are exposed to within 7 days.

repeatedly

35

To best retain any learned
material, a good ____ ____ for the first week
is on Days 1, 3 and 7 after our first exposure.
Use the schedule from the figure in Frame 34 for mastery
learning.