First Grade CCSS Progressions
Cluster 1: Operations and Algebraic Thinking
K Progression
First Grade CCSS

K.OA.2. Solve addition and
subtraction word problems
and add and subtract
within 10, e.g., by using
objects or drawings to
represent the problem.
See attached “Addition and Subtraction Situations” table
for clarification on developmental progression.

Mastery of Result Unknown,
Total Unknown and Both
Addends Unknown for Add
To, Take From and Put
Together/Take Apart
Situations.
1.OA.1. 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.
2.OA.1. Use addition and
subtraction within 100 to
solve one and two- step
word problems involving
situations 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.

K.OA.2. Solve addition and
subtraction word problems
and add and subtract
within 10, e.g., by using
objects or drawings to
represent the problem.
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.
Solve word problems that
call for subtraction of three
whole numbers whose
difference is less than or
equal to 10, e.g., by using
objects, drawings, and
equations.
Example: There were 16
marbles in a bag. Aki took
out 8 marbles. Then Aki
took out 5 marbles. How
many marbles are left in
the bag? 16 – 8 – 5 = ___
Solve word problems that
involve addition and
subtraction of three whole
numbers with sums to 20
and differences to 10.
Examples: Maria has 9
apples. Corey has 4 fewer
apples than Maria. How
many apples do they have
in all?
Example: There were 9
carrots on a plate. The girls
ate 5 carrots. Mother put 7
more carrots on the plate.
How many carrots are
there now? 9 – 5 + 7 = ___
The zoo had 7 cows and
some horses in the big pen.
There were 15 animals in
the big pen. Then 4 more
horses ran into the big pen.
How many horses are there
now?
1
Progressions
Second Grade CCSS
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama.
Cluster 1: Operations and Algebraic Thinking


K Progression
First Grade CCSS
K.OA.1. Represent
addition and
subtraction with
objects, fingers, mental
images, drawings,
sounds (e.g., claps),
acting out situations,
verbal explanations,
expressions, or
equations.
1.OA.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.)
K.OA.4. For any
number from 1 to 9,
find the number that
makes 10 when added
to the given number,
e.g., by using objects
or drawings, and
record the answer with
a drawing or equation.
1.OA.4 Understand subtraction as
an unknown-addend problem. For
example, subtract 10 – 8 by finding
the number that makes10 when
added to 8. Add and subtract
within 20.
Using the language,
“How many more to
make 10?”
K.OA.1. Represent
addition and subtraction
with objects, fingers,
mental images, drawings,
sounds (e.g., claps),
acting out situations,
verbal explanations,
expressions, or equations.
2
Progressions
“Once students have explored strategic reasoning to
find solutions to basic math facts it is time to engage
students in meaningful practice (short in duration and
frequent) so that they can commit the facts to
memory.”
John SanGiovanni and Susan O’Connell, Mastering the
Basic Math Facts in Addition and Subtraction.
CCPS Basic Fact Website

Resources for 5 A Day Practice

Strategy Assessments

Strategy Games
http://www2.carrollk12.org/instruction/elemcurric/math/tba
sicfacts.HTM
1.OA.5 Relate counting to addition
and subtraction (e.g., by counting
on 2 to add 2).
Counting-on from larger number:
Relate counting (without models) to
addition and subtraction scaffold with
partial models.
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama.
Second Grade
CCSS
2.OA.2 Fluently add
and subtract within 20
using mental
strategies. By end of
grade 2 know from
memory all sums of
two 1-digit numbers.
2.NBT.9. Explain why
addition and
subtraction strategies
work, using place
value and the
properties of
operations.
(explanation may be
supported by drawings
or objects)
Cluster 1: Operations and Algebraic Thinking

K Progression
First Grade CCSS
K.OA.3. Decompose
numbers less than or equal
to 10 into pairs in more than
one way, e.g., by using
objects or drawings, and
record each
decomposition by a
drawing or equation (e.g.,
5 = 2 + 3 and 5 = 4 + 1).
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 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).
Subitize 11 to 20 on a
double tens frame,
recognizing groups of 5 or
10.
1.OA.7 Understand the
meaning of the equal sign,
and determine if equations
involving addition and
subtraction are true or
false. For example, which of
the following equations are
true and which are false? 6
= 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4
+ 1 = 5 + 2.
MASTERED
K.OA.5. Begins to fluently
add and subtract within 5.

K.OA.3. Decompose
numbers less than or equal
to 10 into pairs in more than
one way, e.g., by using
objects or drawings, and
record each
decomposition by a
drawing or equation (e.g.,
5 = 2 + 3 and 5 = 4 + 1).
Progressions
Second Grade CCSS
Use tens frames to help
students visualize addition
combinations, moving
toward mental arithmetic.
+
Visualize addition and
subtraction using a 20’s
chart. Knowing that 7 + 11
is 7 + 10 + 1

3
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama.
2.OA.2 Fluently add and
subtract within 20 using
mental strategies. By end of
grade 2 know from memory
all sums of two 1-digit
numbers.
Cluster 1: Operations and Algebraic Thinking
K Progression
First Grade CCSS

K.OA.4. For any number
from 1 to 9, find the number
that makes 10 when added
to the given number, e.g.,
by using objects or
drawings, and record the
answer with a drawing or
equation.
Mastered

Using the language, “How
many more to make 10?”
1.OA.8 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 = _.

K.MD.3. Classify objects into
given categories; count the
numbers of objects in each
category and sort the
categories by count.
1.MD.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.
Organize, represent, and
interpret data with up to
four 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.
Collect, organize(sort) and
display data in real graphs
(physical objects 1:1 such
as linking cubes, counting
bears, or shapes to display)
Progressions
Second Grade CCSS
Organize, represent, and
interpret data with up to
three or four categories.
Solve simple put together
and take apart problems
using information presented
in the graph.
2.MD.10. Draw a picture
graph and a bar graph
(with single unit scale) to
represent a data set with
up to 4 categories. Solve
simple put together, take
apart and compare
problems using information
presented in a bar graph.
Gather and collect data
to answer questions
(yes/no)
Use vocabulary words more
and fewer in relation to
interpreting graphs


Addition and Subtraction Situations (by grade level)
Results Unknown
Change Unknown
4
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama.
Start Unknown
Add to A bunnies sat on the grass. B more
bunnies hopped there. How many
bunnies are on the grass now? K Mastery

A bunnies were sitting on the grass.
Some more bunnies hopped there. Then
there were C bunnies. How many
bunnies hopped over to the first A
bunnies? 1st Mastery
A+B=
A+
Take from C apples were on the table. I ate B
apples. How many apples are on the
table now? K Mastery
C-B=
C-
Total Unknown
=A
A+B=
Addend Unknown

A+
Difference Unknown
Compare “How many more?” version. Lucy has A
apples. Julie has C apples. How many
more apples does Julie have than
Lucy?
+ B = C
=C
C–A=
Some apples were on the table. I ate B
apples. Then there were A apples. How
many apples were on the table before?
2nd Mastery
- B = A
C apples are on the table. A are red
Put Together or
A red apples and B green apples are on and the rest are green. How many
Take Apart the table. How many apples are on the
apples are green? 1st Mastery
table? K Mastery
2nd Mastery
=C
C apples were on the table. I ate some
apples. Then there were A apples. How
many apples did I eat? 1st Mastery

Some bunnies were sitting on the grass.
B more bunnies hopped there. Then
there were C bunnies. How many
bunnies were on the grass before?

Both Addends Unknown
Grandma has C flowers. How many can
she put in her red vase and how many
in her blue vase? 1 Mastery
C =
+
Bigger Unknown
Smaller Unknown
“More” version suggests operation. Julie
has B more apples than Lucy. Lucy has
A apples. How many apples does Julie
have? 1st Mastery
“Fewer” version suggests operation.
Lucy has B fewer apples than Julie. Julie
has C apples. How many apples does
Lucy have? 1st Mastery
“Fewer” version suggests wrong
operation. Lucy has B fewer apples than
Julie. Lucy has A apples. How many
apples does Julie have? 2nd Mastery
“More” version suggests wrong
operation. Julie has B more apples than
Lucy. Julie has C apples. How many
apples does Lucy have? 2nd Mastery
1st Mastery
“How many fewer?” version. Lucy has A
apples. Julie has C apples. How many
fewer apples does Lucy have than
Julie? 1st Mastery
A+
5
=C
C–A=


A+B=
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama.
C-B=
+ B = C