DoDEA CCRSM Gap Analysis
OPERATIONS AND ALGEBRAIC THINKING
DOMAIN
First Grade
College and Career Ready Standards for Mathematics
(CCRSM)
1.OA.A.1
DoDEA Standards
Alignment Notes
CLUSTER: Represent and solve problems involving addition and subtraction.
Express the concepts of onedigit whole number addition
"Within 20" and "one-digit" seem very close, but
1.M.1e and subtraction using objects, composition and decomposition missing. 2.M.2c
drawings, number sentences,
needed to get variables.
and verbal explanations.
This standard specifically names 5 different
problem situations and “unknowns in all positions”
refers to 3 additional types of problems. There are
st
15 problem types in all, all of which 1 grade
Use addition and subtraction within 20 to solve
students have to solve/understand/make sense of.
Explain and use the inverse
word problems involving situations of adding to,
These problem types, and their cognitive
relationship
between
addition
taking from, putting together, taking apart, and
1.M.1f
load/difficulty are described in Table 1 in the
and
subtraction
to
solve
comparing, with unknowns in all positions, e.g.,
problems and check solutions. Glossary, which the standard refers to in a
by using objects, drawings, and equations with a
footnote. DoDEA standards don’t address the
symbol for the unknown number to represent
differences between “add to” and “put together”
the problem.
problems, and they don’t mention “compare”
problems at all.
1.M.1g
Select, explain, and use
addition and subtraction
strategies to solve real-world
problems.
1.M.2d
Write equations using
mathematical symbols.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
1.OA.A.1
1.OA.A.2
Use addition and subtraction within 20 to solve
word problems involving situations of adding to,
taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g.,
by using objects, drawings, and equations with a
symbol for the unknown number to represent
the problem.
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.
DoDEA Standards
1.M.2e
Model and describe problem
situations using
representations, such as
words, objects, number
phrases, or sentences.
2.M.2c
Use symbols to represent
unknown quantities and
identify values for symbols.
2.M.1g
Solve multi-step problems
involving addition and
subtraction.
2.M.2c
Use symbols to represent
unknown quantities and
identify values for symbols.
Alignment Notes
Grade 2 DoDEA standard deals with much greater
numbers.
CLUSTER: Understand and apply properties of operations and the relationship between addition and subtraction.
1.OA.B.3
Apply properties of operations as strategies to
add and subtract. Examples: If 8 + 3 = 11 is
known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6
+ 4, the second two numbers can be added to
make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
1.M.1g
Select, explain, and use
addition and subtraction
strategies to solve real-world
problems.
1.M.2c
Solve open sentences using
the commutative property of
addition.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
DoDEA standard does not specify properties of
operations. The properties of operations are
addressed in CCRSM.
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
1.OA.B.3
1.OA.B.4
DoDEA Standards
Apply properties of operations as strategies to
add and subtract. Examples: If 8 + 3 = 11 is
known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6
+ 4, the second two numbers can be added to
make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
Understand subtraction as an unknown-addend
problem. For example, subtract 10 - 8 by finding
the number that makes 10 when added to 8.
2.M.2e
Solve open sentences by
representing an expression in
more than one way using the
associative property of
addition.
1.M.1e
Express the concepts of onedigit whole number addition
and subtraction using objects,
drawings, number sentences,
and verbal explanations.
1.M.1f
Explain and use the inverse
relationship between addition
and subtraction to solve
problems and check solutions.
Alignment Notes
Missing addend strategy not specified.
CLUSTER: Add and subtract within 20.
1.OA.C.5
Relate counting to addition and subtraction (e.g.,
by counting on 2 to add 2).
1.OA.C.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
1.M.1g
1.M.1e
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Select, explain, and use
addition and subtraction
strategies to solve real-world
problems.
Counting on is not specifically mentioned as a
strategy in DoDEA standards. Counting on is
conceptually challenging for 1st graders as they are
still working on developing conservation of
number. It is not a “procedure” but the conceptual
underpinning for their understanding of the
number system.
Express the concepts of onedigit whole number addition
and subtraction using objects,
drawings, number sentences,
and verbal explanations.
Definition of fluency--skill in carrying out
procedures flexibly, accurately, efficiently, and
appropriately--suggests more than following a set
procedure. DoDEA standards do not reference the
full range of strategies.
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
that 8 + 4 = 12, one knows 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).
1.OA.D.7
1.OA.D.8
DoDEA Standards
1.M.1f
Explain and use the inverse
relationship between addition
and subtraction to solve
problems and check solutions.
1.M.1g
Elect, explain, and use
addition and subtraction
strategies to solve real-world
problems.
2.M.1c
Show equivalent
representations for whole
numbers by using addition
and subtraction facts.
Alignment Notes
CLUSTER: Work with addition and subtraction equations.
Understand the meaning of the equal sign, and
DoDEA standards include the use of equal signs
determine if equations involving addition and
and equivalence but do not refer to true/false.
not aligned
subtraction are true or false. For example, which
Understanding the equals sign is one of the major
of the following equations are true and which
shifts students must make in this grade level are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 +
equivalence as balance not as action.
2.
Determine the unknown whole number in an
addition or subtraction equation relating three
whole numbers. For example, determine the
unknown number that makes the equation true
in each of the equations
8 + ? = 11, 5 = _ - 3, 6 + 6 = _.
1.M.2c
Solve open sentences using
the commutative property of
addition.
2.M.2c
Use symbols to represent
unknown quantities and
identify values for symbols.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
DoDEA Grade 2 standards use larger numbers.
DODEA standards don’t specify “relating 3 whole
numbers”.
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
DoDEA Standards
Alignment Notes
CLUSTER: Extend the counting sequence.
1.NBT.A.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.
1.M.1a
Count and group objects into
ones and tens up to 100.
CCRSM goes to 120, DoDEA goes to 100. Grade 2
includes numbers to 1,000 but does not specify
counting. Reading and writing numerals are not
included in DoDEA standards.
NUMBERS AND OPERATIONS IN BASE TEN
CLUSTER: Understand place value.
1.NBT.B.2
Understand that the two digits of a two-digit
number represent amounts of tens and ones.
Understand the following as special cases:
1.M.1a
Count and group objects into
ones and tens up to 100.
CCRSM list gets very specific, but all the parts seem
to be included in DoDEA standard.
This group of 4 CCRSM is at a higher
conceptual/cognitive level than the 2 matched to it
from DODEA (which are more focused on
strategies)
1.NBT.B.2.A
10 can be thought of as a bundle of ten ones —
called a "ten."
1.M.1a
Count and group objects into
ones and tens up to 100.
1.NBT.B.2.B
The numbers from 11 to 19 are composed of a
ten and one, two, three, four, five, six, seven,
eight, or nine ones.
1.M.1a
Count and group objects into
ones and tens up to 100.
1.NBT.B.2.C
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90
refer to one, two, three, four, five, six, seven,
eight, or nine tens (and 0 ones).
1.M.1a
Count and group objects into
ones and tens up to 100.
3.M.1e
Compare whole numbers, up
to 10,000, using mathematical
symbols (>, <, =) and words
(greater than, less than, equal
to) and arrange them in
numerical order.
1.NBT.B.3
Compare two two-digit numbers based on
meanings of the tens and ones digits, recording
the results of comparisons with the symbols >, =,
and <.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
DoDEA introduces inequality symbols much later in
its standards.
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
1.NBT.C.4
1.NBT.C.5
DoDEA Standards
Alignment Notes
CLUSTER: Use place value understanding and properties of operations to add and subtract.
Explain and demonstrate
addition and subtraction for
The phrase "explain and demonstrate" is
Add within 100, including adding a two-digit
considered equivalent to "relate the strategy to the
two-digit numbers without
number and a one-digit number, and adding a
written method and explain the reasoning." The
2.M.1d regrouping, e.g., doubling,
two-digit number and a multiple of 10, using
variety of representations in CCRSM is not present
making jumps of ten, partial
concrete models or drawings and strategies
sums or differences, counting in DoDEA standards.
based on place value, properties of operations,
up or back.
and/or the relationship between addition and
subtraction; relate the strategy to a written
Explain and demonstrate
method and explain the reasoning used.
addition and subtraction for
DODEA standards do not address “using the
Understand that in adding two-digit numbers,
two-digit numbers with
relationship between addition and subtraction”,
one adds tens and tens, ones and ones; and
2.M.1e regrouping, e.g., doubling,
properties of operations, relating strategies to
sometimes it is necessary to compose a ten.
making jumps of ten, partial
written methods.
sums or differences, counting
up or back.
Explain and demonstrate
addition and subtraction for
two-digit numbers without
CCRSM is very specific and is contained in the
2.M.1d regrouping, e.g., doubling,
broader DoDEA standards.
making jumps of ten, partial
sums or differences, counting
Given a two-digit number, mentally find 10 more
up or back.
or 10 less than the number, without having to
count; explain the reasoning used.
Explain and demonstrate
NBT.C.5-6:DODEA standards do not address “using
addition and subtraction for
the relationship between addition and
two-digit numbers with
subtraction”, properties of operations, relating
2.M.1e regrouping, e.g., doubling,
strategies to written methods. This cluster aims for
making jumps of ten, partial
students to generalize the characteristics/structure
sums or differences, counting
of the number system.
up or back.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
1.NBT.C.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; relate the
strategy to a written method and explain the
reasoning used.
DoDEA Standards
2.M.1d
Explain and demonstrate
addition and subtraction for
two-digit numbers without
regrouping, e.g., doubling,
making jumps of ten, partial
sums or differences, counting
up or back.
2.M.1e
Explain and demonstrate
addition and subtraction for
two-digit numbers with
regrouping, e.g., doubling,
making jumps of ten, partial
sums or differences, counting
up or back.
Alignment Notes
CCRSM is very specific and is contained in the
broader DoDEA standards.
MEASUREMENT AND DATA
CLUSTER: Measure lengths indirectly and by iterating length units.
1.MD.A.1
K.M.4a
Compare and order objects
according to length, capacity,
weight, and temperature by
using descriptors, e.g., longer,
taller, and heavier.
1.M.4b
Measure and differentiate
objects using both
comparative terms and
standard units of measure,
e.g., inches, centimeters.
Order three objects by length; compare the
lengths of two objects indirectly by using a third
object.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Although DoDEA Grade 1 standards go farther in
terms of using measurement units and
quantification, neither standard looks at the
indirect measure with reference to a third object.
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DOMAIN
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
1.MD.A.2
DoDEA Standards
Express the length of an object as a whole
number of length units, by laying multiple copies
of a shorter object (the length unit) end to end;
understand that the length measurement of an
object is the number of same-size length units
that span it with no gaps or overlaps. Limit to
contexts where the object being measured is
spanned by a whole number of length units with
no gaps or overlaps.
K.M.4d
Use non-standard
measurement tools to
estimate and verify results.
1.M.4c
Estimate and measure a
variety of attributes of objects
using standard and
nonstandard units.
Alignment Notes
DoDEA standards include more attributes and also
include estimation as part of the standard
statements. See also 2.M.4e: use repetition of a
single unit to measure something larger than the
unit.
For first graders, this is more than just “following a
procedure”. CCRSM is worded to move students
toward generalizing this concept of length (no
gaps, no overlaps) for its later critical application to
the number line, rational number understanding,
etc.
CLUSTER: Tell and write time.
1.MD.B.3
Tell and write time in hours and half-hours using
analog and digital clocks.
1.M.4e
Tell time to the hour and half
hour using digital and analog
timepieces.
Writing time is not specified in DoDEA standards.
CLUSTER: Represent and interpret data.
1.MD.C.4
Organize, represent, and interpret data with up
to three categories; ask and answer questions
about the total number of data points, how
many in each category, and how many more or
less are in one category than in another.
1.M.5b
Collect, organize, represent,
and interpret data using
concrete objects, pictures,
tallies, and graphs.
1.M.5d
Construct questions and make
predictions that can be
answered by using
information from a graph or
table.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
DoDEA standards are broader, including data
collection and prediction. Data standards have
been reduced (in number and in level of
conceptual understanding) in order to allow for
more time in the instructional year to focus on
number, numeracy, the number system and the
meaning of addition/subtraction. Data and
measurement standards “prop” up the Number
Base Ten and Operations/Algebraic Thinking
domains.
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DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
GEOMETRY
1.G.A.1
1.G.A.2
1.G.A.3
DoDEA Standards
CLUSTER: Reason with shapes and their attributes.
Identify and compare twodimensional shapes and
Distinguish between defining attributes (e.g.,
three-dimensional objects
triangles are closed and three-sided) versus nonusing attributes and
defining attributes (e.g., color, orientation,
3.M.3a
properties, e.g., sides and
overall size); build and draw shapes to possess
angles in two-dimensional
defining attributes.
shapes, faces and edges in
three-dimensional objects.
Compose two-dimensional shapes (rectangles,
squares, trapezoids, triangles, half-circles, and
Create new shapes by
quarter-circles) or three-dimensional shapes
1.M.3b combining, cutting, or taking
(cubes, right rectangular prisms, right circular
apart existing shapes.
cones, and right circular cylinders) to create a
composite shape, and compose new shapes from
the composite shape.
Partition circles and rectangles into two and four
equal shares, describe the shares using the
words halves, fourths, and quarters, and use the
phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the
shares. Understand for these examples that
decomposing into more equal shares creates
smaller shares.
1.M.1i
Recognize wholes and parts of
wholes, i.e., 1/2, 1/3, and,
1/4.
2.M.1j
Use words, numerals, and
physical models to represent
fractions and their
relationship to the whole.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Alignment Notes
DoDEA standard is just a small part of CCRSM
standard and is two grade levels higher.
Shape in DoDEA standard was assumed to include
two and three dimensions.
The relationship between denominator and size of
pieces in CCRSM is not included in DoDEA
standards.
Page 33
DoDEA CCRSM Gap Analysis
First Grade Alignment Sorted by DoDEA Standards
X = grade level with similar alignment to current DoDEA standards
Gray shading = no alignment with CCRSM at specified grade levels
DoDEA Standards
First Grade
1.M.1a: count and group objects into ones and tens up to 100
CCRSM
K
1
X
X
2
3
1.M.1b: position and identify the order of objects using ordinal numbers up to 10
1.M.1c: identify the number of tens and ones in numbers less than 100
1.M.1d: identify and generate equivalent forms of the same number using concrete objects and
number statements
1.M.1e: express the concepts of one-digit whole number addition and subtraction using objects,
drawings, number sentences, and verbal explanations
1.M.1f: explain and use the inverse relationship between addition and subtraction to solve problems
and check solutions
1.M.1g: select, explain, and use addition and subtraction strategies to solve real-world problems
X
X
X
X
X
1.M.1h: describe using their own words an estimate of the number of objects in groups up to 100 and
verify the results
1.M.1i: recognize wholes and parts of wholes
X
1.M.2a: sort, classify, and order objects by two or more attributes and explain how objects were sorted
X
1.M.2b: identify, describe, extend, and create repeating patterns and number sequences
1.M.2c: solve open sentences using the commutative property of addition
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
X
X
X
Page 34
DoDEA CCRSM Gap Analysis
DoDEA Standards
First Grade
CCRSM
K
1
1.M.2d: write equations using mathematical symbols
X
1.M.2e: model and describe problem situations using representations, such as words, objects, number
phrases, or sentences
X
1.M.2f: model equivalency between sets using concrete materials
X
1.M.3a: identify triangles, rectangles, squares, and circles as the faces of three-dimensional objects
1.M.3b: create new shapes by combining, cutting, or taking apart existing shapes
2
3
X
X
X
1.M.3c: give and follow directions to find a place or object
1.M.3d: identify and determine whether two-dimensional shapes are congruent, i.e., same shape and
size; or similar, i.e., same shape and proportional size
X
1.M.3e: identify symmetry in objects and figures
1.M.3f: identify geometric shapes and structures in the environment
X
1.M.4a: identify common instruments used for measurement, i.e., rulers, scales, measuring cups
X
1.M.4b: measure and differentiate objects using both comparative terms and standard units of
measure, e.g., inches, centimeters
X
X
1.M.4c: estimate and measure a variety of attributes of objects using standard and nonstandard units
X
X
X
1.M.4d: identify repeating patterns of time, e.g., days of the week, months of the year
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 35
DoDEA CCRSM Gap Analysis
DoDEA Standards
First Grade
1.M.4e: tell time to the hour and half hour using digital and analog timepieces
CCRSM
K
1
2
3
X
1.M.4f: order a sequence of events that occur over time
1.M.4g: make estimates about the passage of time in events, e.g., tasks being completed, living things
growing, etc.
1.M.5a: use interviews and observations to gather data about themselves and their surroundings
1.M.5b: collect, organize, represent, and interpret data using concrete objects, pictures, tallies, and
graphs
X
1.M.5c: compare and contrast similar data sets
1.M.5d: construct questions and make predictions that can be answered by using information from a
graph or table
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
X
Page 36