2 - DoDEA

DoDEA CCRSM Gap Analysis
Second Grade
College and Career Ready Standards for Mathematics
(CCRSM)
DoDEA Standards
Alignment Notes
CLUSTER: Represent and solve problems involving addition and subtraction.
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.
DoDEA standards do not specify all the meanings
for addition and subtraction listed in CCRSM.
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.
For 2.OA.A.1:This standard specifically names 5
different problem situations and “unknowns in
all positions” refers to 3 additional types of
problems. There are 15 problem types in all, all
of which 2nd grade students have to master.
These problem types, and their cognitive
load/difficulty, are described in Table 1 in the
Glossary, which the standard refers to in a
footnote. They don’t address the differences
between “add to” and “put together” problems,
and they don’t mention “compare” problems at
all.
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.
2.M.2f
Model and describe a problem
situation using symbols and
operations.
OPERATIONS AND ALGEBRAIC THINKING
2.M.1d
2.OA.A.1
Use addition and subtraction within 100 to solve
one- 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
drawings and equations with a symbol for the
unknown number to represent the problem.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 37
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
DoDEA Standards
Alignment Notes
CLUSTER: Add and subtract within 20.
2.OA.B.2
2.OA.C.3
NUMBER AND OPERATIONS IN BASE
TEN
2.OA.C.4
2.NBT.A.1
2.NBT.A.1.A
Note that the expectation for fact memory is two
years earlier for addition and subtraction in
Fluently add and subtract within 20 using
CCRSM. DoDEA standard includes four
mental strategies. By end of Grade 2, know from 4.M.1m
operations. CCRSM also explicitly includes use of
memory all sums of two one-digit numbers.
mental strategies. Using mental strategies is not
mentioned in DODEA standard.
CLUSTER: Work with equal groups of objects to gain foundations for multiplication.
Determine whether a group of objects (up to
Identify numbers as even or odd
20) has an odd or even number of members,
numbers and determine
DoDEA standard does not include the writing of
2.M.1b whether a set of objects has an
e.g., by pairing objects or counting them by 2s;
an equation.
write an equation to express an even number as
odd or even number of
a sum of two equal addends.
elements.
Use addition to find the total number of objects
DoDEA standard goes further in terms of size and
Model and demonstrate
arranged in rectangular arrays with up to 5 rows
variety of representation but does not include
2.M.1i multiplication and division
and up to 5 columns; write an equation to
writing the equation as repeated addends and
problems.
express the total as a sum of equal addends.
the emphasis on arrays.
CLUSTER: Understand place value.
Demonstrate mastery in sums
to 20 and related subtraction
facts and multiplication through
12X12 and related division facts.
Understand that the three digits of a three-digit
number represent amounts of hundreds, tens,
and ones; e.g., 706 equals 7 hundreds, 0 tens,
and 6 ones. Understand the following as special
cases:
100 can be thought of as a bundle of ten tens —
called a "hundred."
2.M.1a
Use place value to represent
whole numbers through 1000
using numerals, words, and
physical models.
2.M.1a
Use place value to represent
whole numbers through 1000
using numerals, words, and
physical models.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
DoDEA standards do not specify all the key ideas
in CCRSM, but general wording should contain all
these parts. The DoDEA standard includes
multiple representations.
Page 38
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
2.NBT.A.1.B
2.NBT.A.2
2.NBT.A.3
2.NBT.A.4
2.NBT.B.5
DoDEA Standards
Alignment Notes
The numbers 100, 200, 300, 400, 500, 600, 700,
800, 900 refer to one, two, three, four, five, six,
seven, eight, or nine hundreds (and 0 tens and 0
ones).
Count within 1000; skip-count by 5s, 10s, and
100s.
Use place value to represent
whole numbers through 1000
2.M.1a
using numerals, words, and
physical models.
Count by twos, fives, and tens to DoDEA standard only goes to 100 and does not
2.M.1h
100.
include counting by hundreds.
Use place value to represent
Reading is considered a part of representation.
whole numbers through 1000
2.M.1a
DODEA standards do not require nor specify
using numerals, words, and
“expanded form.”
physical models.
Read and write numbers to 1000 using base-ten
Identify and generate
numerals, number names, and expanded form.
equivalent representations for
the same number by
DODEA standard does not specify “based on the
4.M.1b
decomposing and composing
meanings of hundreds, tens, ones”.
the whole number up to
1,000,000.
Compare whole numbers, up to
10,000, using mathematical
Compare two three-digit numbers based on
The DoDEA standard is a year later, but goes to
symbols (>, <, =) and words
meanings of the hundreds, tens, and ones digits,
3.M.1e
10,000.
(greater than, less than, equal
using >, =, and < symbols to record the results of
to) and arrange them in
comparisons.
numerical order.
CLUSTER: Use place value understanding and properties of operations to add and subtract.
Explain and demonstrate
addition and subtraction for
Separate DoDEA standards combine to give the
Fluently add and subtract within 100 using
two-digit numbers without
full range of cases. CCRSM aims at students
strategies based on place value, properties of
mastering their understanding of addition and
2.M.1d regrouping, e.g., doubling,
operations, and/or the relationship between
making jumps of ten, partial
subtraction using strategies, properties, and
addition and subtraction.
sums or differences, counting
relationships within the number system.
up or back.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 39
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
2.NBT.B.5
Fluently add and subtract within 100 using
strategies based on place value, properties of
operations, and/or the relationship between
addition and subtraction.
2.NBT.B.6
Add up to four two-digit numbers using
strategies based on place value and properties
of operations.
2.NBT.B.7
Add and subtract within 1000, 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. Understand that in adding or
subtracting three-digit numbers, one adds or
subtracts hundreds and hundreds, tens and
tens, ones and ones; and sometimes it is
necessary to compose or decompose tens or
hundreds.
2.NBT.B.8
Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a
given number 100-900.
2.NBT.B.9
Explain why addition and subtraction strategies
work, using place value and the properties of
operations.
DoDEA Standards
Alignment Notes
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.
CCRSM not just asking for a procedure but for
the use of varying strategies based on
understanding place value and properties.
DODEA standard can be interpreted as
procedure only without the specificity of CCRSM.
2.M.1g
Solve multi-step problems
involving addition and
subtraction.
DoDEA standards do not specify four addends,
but the CCSSM would be included in the set of
multistep problems. This CCRSM is aimed at
generalization of the properties, the number
system and their relationship to abstract
symbols.
3.M.1g
Explain and solve problems
involving the sum or difference
of two whole numbers up to
10,000.
DoDEA standard, although a year later, does go
to 10,000. Mental strategies require use of the
number system to construct meaning.
2.M.1e
3.M.1g
3.M.1g
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Explain and solve problems
involving the sum or difference
of two whole numbers up to
10,000.
Explain and solve problems
involving the sum or difference
of two whole numbers up to
10,000.
Mental strategies are not included in DoDEA
standards.
Although "explain" is included in DoDEA
standard, the "why" is not. Justification present
in CCRSM is not clearly present in DoDEA
standard.
Page 40
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
MEASUREMENT AND DATA
2.MD.A.1
2.MD.A.2
2.MD.A.3
2.MD.A.4
2.MD.B.5
DoDEA Standards
CLUSTER: Measure and estimate lengths in standard units.
Identify common instruments
1.M.4a used for measurement, i.e.,
rulers, scales, measuring cups.
Measure the length of an object by selecting
Measure and differentiate
and using appropriate tools such as rulers,
objects using both comparative
yardsticks, meter sticks, and measuring tapes.
1.M.4b terms and standard units of
measure, e.g., inches,
centimeters.
Decide which unit of measure is
2.M.4c
appropriate in a given situation.
Measure the length of an object twice, using
length units of different lengths for the two
not aligned
measurements; describe how the two
measurements relate to the size of the unit
chosen.
Estimate and measure a variety
Estimate lengths using units of inches, feet,
1.M..4c of attributes of objects using
centimeters, and meters.
standard and nonstandard units.
Measure and differentiate
Measure to determine how much longer one
objects using both comparative
object is than another, expressing the length
1.M.4b terms and standard units of
difference in terms of a standard length unit.
measure, e.g., inches,
centimeters.
CLUSTER: Relate addition and subtraction to length.
Use addition and subtraction within 100 to solve
word problems involving lengths that are given
Solve multi-step problems
in the same units, e.g., by using drawings (such
2.M.1g involving addition and
as drawings of rulers) and equations with a
subtraction.
symbol for the unknown number to represent
the problem.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Alignment Notes
Combined, these seem to give tools and units.
Appropriate unit helps with choice of tool.
DoDEA standards in K-4 are silent on how unit
size and number of units reported are related.
Metric and customary units are included in
DoDEA Grade 1 standards.
DoDEA standard also includes comparative
terms.
The length context is not mentioned in the
DoDEA standards specifically. This aspect of
length is not represented in DODEA standards in
terms of addition and subtraction.
Page 41
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
2.MD.B.5
2.MD.B.6
DoDEA Standards
Use addition and subtraction within 100 to solve
word problems involving lengths that are given
in the same units, e.g., by using drawings (such
as drawings of rulers) and equations with a
symbol for the unknown number to represent
the problem.
2.M.2c
Use symbols to represent
unknown quantities and identify
values for symbols.
2.M.2f
Model and describe a problem
situation using symbols and
operations.
Represent whole numbers as lengths from 0 on
a number line diagram with equally spaced
points corresponding to the numbers 0, 1, 2, ...,
and represent whole-number sums and
differences within 100 on a number line
diagram.
not aligned
Alignment Notes
Positioning fractions and decimals on a number
line is found in DoDEA 4.M.1l.
CLUSTER: Work with time and money.
2.MD.C.7
Tell and write time from analog and digital
clocks to the nearest five minutes, using a.m.
and p.m.
2.M.4a
Tell time in five-minute
intervals.
DoDEA standard does not include a.m. and p.m.
or writing time. DODEA standard indicates a
procedure to be followed.
2.MD.C.8
Solve word problems involving dollar bills,
quarters, dimes, nickels, and pennies, using $
and ¢ symbols appropriately. Example: If you
have 2 dimes and 3 pennies, how many cents do
you have?
4.M.4j
Know the process for counting
coins and bills using standard
money notations.
Example with the DoDEA standard confirmed the
idea that money context would involve practical
application.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 42
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
DoDEA Standards
Alignment Notes
CLUSTER: Represent and interpret data.
2.MD.D.9
2.MD.D.10
Generate measurement data by measuring
lengths of several objects to the nearest whole
unit, or by making repeated measurements of
the same object. Show the measurements by
making a line plot, where the horizontal scale is
marked off in whole-number units.
Draw a picture graph and a bar graph (with
single-unit scale) to represent a data set with up
to four categories. Solve simple put-together,
take-apart, and compare problems using
information presented in a bar graph.
1.M.4c
Estimate and measure a variety
of attributes of objects using
standard and nonstandard units.
3.M.5b
Translate information from one
data representation to a graph
or table, e.g., frequency table,
bar graph, picture graph, line
plot.
2.M.5b
Collect, organize, represent, and
interpret data using
pictographs, bar graphs, and
tables.
2.M.5d
Read and interpret graphs and
tables to identify main ideas,
draw conclusions, and make
predictions.
CCRSM problem types specified are not included
in DoDEA standards.
GEOMETRY
CLUSTER: Reason with shapes and their attributes.
2.G.A.1
Recognize and draw shapes having specified
attributes, such as a given number of angles or a
given number of equal faces. Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.
K.M.3a
Name, describe, sort, compare,
and draw two-dimensional
shapes.
K.M.3b
Identify and compare threedimensional objects.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Shape identification and comparison seems to
span the grades. Explicit focus on attributes
begins in DoDEA Grade 3. Creating or drawing a
figure from attributes does not seem to be
included in DoDEA standard statements.
Page 43
DoDEA CCRSM Gap Analysis
College and Career Ready Standards for Mathematics
(CCRSM)
DoDEA Standards
1.M.3a
2.G.A.1
Recognize and draw shapes having specified
attributes, such as a given number of angles or a
given number of equal faces. Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.
1.M.3d
3.M.3a
2.G.A.2
2.G.A.3
Partition a rectangle into rows and columns of
same-size squares and count to find the total
number of them.
Partition circles and rectangles into two, three,
or four equal shares, describe the shares using
the 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.
Identify triangles, rectangles,
squares, and circles as the faces
of three-dimensional objects.
Identify and determine whether
two-dimensional shapes are
congruent, i.e., same shape and
size; or similar, i.e., same shape
and proportional size.
Identify and compare twodimensional shapes and threedimensional objects using
attributes and properties, e.g.,
sides and angles in twodimensional shapes, faces and
edges in three-dimensional
objects.
not aligned
2.M.1j
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Alignment Notes
Use words, numerals, and
physical models to represent
fractions and their relationship
to the whole.
Seems like a pre-area readiness activity, but was
not found in DoDEA standards.
DoDEA standard does not include the reference
to equal shares not necessarily being the same
shape.
Page 44
DoDEA CCRSM Gap Analysis
Second 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
Second Grade
2.M.1a: use place value to represent whole numbers through 1000 using numerals, words,
and physical models
2.M.1b: identify numbers as even or odd numbers and determine whether a set of objects
has an odd or even number of elements
2.M.1c: show equivalent representations for whole numbers by using addition and
subtraction facts
2.M.1d: explain and demonstrate addition and subtraction for two-digit numbers without
regrouping
2.M.1e: explain and demonstrate addition and subtraction for two-digit numbers with
regrouping
2.M.1f: estimate and verify answers in addition and subtraction problems with two-digit
numbers
CCRSM
Kdg
Gr 2
Gr 3
Gr 4
X
X
X
2.M.1g: solve multi-step problems involving addition and subtraction
2.M.1h: count by twos, fives, and tens to 100
Gr 1
X
X
X
X
X
X
X
X
X
2.M.1i: model and demonstrate multiplication and division problems
X
2.M.1j: use words, numerals, and physical models to represent fractions and their
relationship to the whole
X
X
2.M.2a; create and describe patterns with multiple attributes
2.M.2b: identify and extend a linear pattern by its rules
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 45
DoDEA CCRSM Gap Analysis
DoDEA Standards
Second Grade
CCRSM
Kdg
Gr 1
Gr 2
2.M.2c; use symbols to represent unknown quantities and identify values for symbols
X
X
2.M.2d: represent equivalence and extend the concept to situations involving symbols
X
2.M.2e: solve open sentences by representing an expression in more than one way using the
associative property of addition
X
2.M.2f: model and describe a problem situation using symbols and operations
Gr 3
Gr 4
X
2.M.2g: describe qualitative changes
2.M.2h: describe quantitative changes, especially those involving addition and subtraction
2.M.3a: predict the results of putting together and taking apart two-dimensional shapes
X
X
2.M.3b: find and name locations using simple relationships and in coordinate systems
2.M.3c: identify shapes that have been rotated (turned), reflected (flipped), and translated
(slide). Describe direction of translation
2.M.3d: identify and create shapes with symmetry
2.M.4a: tell time in five-minute intervals
X
X
2.M.4b: describe and compare relationships of time
2.M.4c: decide which unit of measure is appropriate in a given situation
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
X
X
Page 46
DoDEA CCRSM Gap Analysis
DoDEA Standards
Second Grade
CCRSM
Kdg
Gr 1
Gr 2
Gr 3
2.M.4d: make and use estimates of measurement, including time volume, weight, and area.
Verify result
X
2.M.4e: use repetition of a single unit to measure something larger than the unit
X
2.M.5a: develop categories for sorting a collection of materials
2.M.5b: collect, organize, represent, and interpret data using pictographs, bar graphs, and
tables
2.M.5c: generate questions, collect and organize data to address the questions, and draw
conclusions
2.M.5d: read and interpret graphs and tables to identify main ideas, draw conclusions, and
make prediction
Gr 4
X
X
X
2.M.5e: describe events that are more likely, least likely, or equally likely to happen
2.M.5f: use physical models and pictures to represent possible arrangements of two or three
objects
2.M.5g: identify events that can have more than one outcome
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
Page 47
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