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CCSS Operations and Algebraic
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Thinking (OA)
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Unpacking the Standards
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Grade 1
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Operations and Algebraic Thinking: Represent and solve problems involving addition and
subtraction.
Math Practices:
Related CA Standard AF 1.1 Write and solve number sentences from
Standard: 1. OA. 1
problem situations MR 1.1 Determine the approach, materials, and strategies
MP 1, 2, 3, 4, 5, 6, 8
1.2 Use tools to model problems. 2.1 Explain the reasoning 2.2 Make precise
Cluster: major (m)
calculations
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.
Essential Skills/Concepts
-
-
-
Understand addition and
subtraction concepts
Understand symbols +, -, =
Symbols are introduced in 1st
grade, add/sub concepts were
learned in kinder
Understand that there are
different types of addition and
subtraction problems (see
framework, p. 9)
Understand that there are
different strategies to solve
addition and subtraction
problems (counting on, making
ten, doubles, doubles plus one
etc.)
-Comparing problems are introduced
in first grade. Ex. Sam has 9 balls.
Jake has 3 balls. How many more
balls does Sam have than Jake?
Teaching Notes/Strategies
-
Have students explain, write
and reflect on their problem
solving strategies. Partner
Share
-
Board Math Stems: Compare:
How many more, how many less,
how many fewer…
Methods for solving single digit
addition/subtraction problems
(Framework, p. 7):
Level 1 (kinder): Direct Modeling by
Counting All or Taking Away: Use
objects, drawings or fingers to
represent a problem
Level 2 (1st grade): Counting on: Use
one addend and count on. Some
method of keeping track (fingers,
objects, mentally imaged objects,
body motions) is used to monitor the
count
Resources
www.cde.ca.gov Mathematics
Framework, Appendix F (more
defined methods for solving singledigit addition and subtraction
problems)
Board Math Frames
Number Line
Hundreds Chart
Math Workmats
District Problem-Solving Poster
Caution: Comparing problems are
difficut because many students
“hear” the part of the sentence of
who has “more” but do not initiatlly
hear the part about how many more”.
Level 3 (1st/2nd grade): Convert to an
easier problem
Example: Compare Problems.
Using objects to represent two
sets of balls
Abel has 5 balls. Susan has 3 balls.
How many more balls does Abel
have than Susan?
Teachers can also ask the related
question, “How many fewer balls
does Susan have than Abel?”
Academic Vocabulary: add, adding
to, taking from, putting together,
taking apart, comparing, unknown,
sum, less than, equal to, minus,
subtract, the same amount as, and
Comparison Bars:
Rather than representing the actual
objects with manipulatives or
drawings, they use the numbers in
the problem to represent the
quantities.
(to describe (+) symbol), counting
on, making ten, doubles, equation
*NOTE: Subtraction names a missing
part. Therefore, the minus sign should be
read as “minus” or “subtract” but not as
“take away”. Although “take away” has
been a typical way to define subtraction, it
is a narrow and incorrect definition.
5 balls
?? balls
3 balls
Number Bond Diagrams:
OOOOO (5)
OOO (3)
?
Operations and Algebraic Thinking: Represent and solve problems involving addition and
subtraction.
Related CA Standard
Standard: 1. OA. 2
Math Practices:
NS 2.7 Find the sum of three one-digit
numbers, MR 1.1, 1.2, 2.1, 2.2
MP 1, 2, 3, 4, 5, 6, 8
Cluster: major (m)
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.
(Similar to 1.OA.1… just with three numbers.)
Essential Skills/Concepts
-
-
Understand addition concepts
Understand symbols +, =
Understand that there are
different types of addition
problems
Understand that there are
different strategies to solve
addition problems
Example: Mrs. Smith has 4 oatmeal raisin
cookies, 5 chocolate chip cookies, and 6
gingerbread cookies. How many cookies
does Mrs. Smith have?
Academic Vocabulary: add, adding
to, unknown, sum, total, in all,
altogether, equal to, the same
amount as, and (to describe (+)
symbol), counting on, making ten,
doubles, equation
Teaching Notes/Strategies
-
Have students explain, write
and reflect on their problem
solving strategies. Partner
Share
Focus on Level 2/3 Methods:
Level 2 (1st grade): Counting on: Use
one addend and count on. Some
method of keeping track (fingers,
objects, mentally imaged objects,
body motions) is used to monitor the
count.
Level 3 (1st/2nd grade): Convert to an
easier problem
Resources
Board Math Frames
Number Line
Hundreds Chart
Math Workmats
District Problem-Solving Poster
Operations and Algebraic Thinking: Understand and apply properties of operations and the
relationship between addition and subtraction.
Related CA Standard
Standard: 1. OA. 3
NS 1.3 represent equivalent forms of the same
Math Practices:
MP
2, 7, 8
Cluster: major (m)
number 2.2 Use the inverse relationship MR 2.1
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).
Essential Skills/Concepts
-
Understand the concept of
related facts: 4 + 6 = 10, 6 + 4 =
10, 10- 4 = 6, 10 – 6 =4
-
Apply properties of operations
as strategies to add and
subtract (students don’t need
to know the names, but need to
understand the concepts)
Commutative: 4 + 5 = 5 + 4
Associative (it doesn’t
matterwhich numbers you add
together first) 3 + (9+1) = (3+9)
+ 1 = 12 + 1 = 13
-
Academic Vocabulary: add, subtract,
unknown addend, order, first, second
Teaching Notes/Strategies
Students build a tower of 8 green
cubes and 3 yellow cubes, and
another tower of 3 yellow and 8
green cubes to show that order
does not change the result in the
operation of addition.
Students can also use cubes of 3
different colors to demonstrate
that (2 + 6) + 4 is equivalent to 2 + (6
+ 4) and then to prove 2 + (6 + 4) = 2
+ 10.
Board Math Stems
Make Ten
Resources
Board Math Frames
Number Line
Hundreds Chart
Math Workmats
Ten Frame
Operations and Algebraic Thinking: Understand and apply properties of operations and the
relationship between addition and subtraction.
Related CA Standard
Standard: 1. OA. 4
Math Practices:
NS 2.2 Use the inverse
relationship MR 2.1
MP 2, 7, 8
Cluster: major (m)
Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the
number that makes 10 when added to 8.
Essential Skills/Concepts
See 1. OA. 3
-
-
Understand the connection
between addition and
subtraction
Think-Addition: uses known
addition facts to solve for the
unknown part or quantity within
a problem. When students use
this strategy, they think, “What
goes with this part to make the
total?” The think-addition
strategy is particularly helpful
for subtraction facts with sums
of 10 or less
Academic Vocabulary:
See 1.OA.3
Teaching Notes/Strategies
Resources
See 1. OA. 3
See 1.OA. 3
Teacher Share (games)
Subtraction problems are missing
addend problems: Restate
subtraction as an unknown addend
and solve by counting on: “7-3 means
3+ ? = 7, so 4,5,6,7, I counted on 4
more to get to 7, so 4”
Board Math examples:
- What number sentence can you
use to check the answer for 12
+ 6 = 18
- What is the inverse of 9 + 6 =
15
- Write the related facts for 3,
5, 8
Games: “Figure out how many I
took away”
Ten frame partially filled in…
Operations and Algebraic Thinking: Add and subtract within 20
Standard: 1. OA. 5
Math Practices:
Cluster: major (m)
MP 7, 8
Related CA Standard
NS 2.4 Count by 2s, 5s,
and 10s
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2)
Essential Skills/Concepts
-
Connect “Counting on” and
“counting back” to adding and
subtracting
Academic Vocabulary: addition,
putting together, subtraction,
taking apart, taking from,
equivalent, sum, unknown, equal,
equation, counting on, counting
back
Teaching Notes/Strategies
Resources
-
Hold the start number in your
head and count forward.
See Above
-
Subtraction problems are
missing addend problems:
Restate subtraction as an
unknown added and solve by
counting on: “7-3 means 3+ ? =
7, so 4,5,6,7, I counted on 4
more to get to 7, so 4”
-
Board Math Stems
Operations and Algebraic Thinking: Add and Subtract within 20.
Standard: 1. OA. 6
Cluster: major (m)
Math Practices:
MP 2, 7, 8
Related CA Standard
NS 1.3 Represent equivalent forms
of the same number 2.1 Know
addition/subtraction facts (up to
sums of 20) fluently MR 2.1
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).
Essential Skills/Concepts
- Understand addition/subtraction
and number concepts within 20
- Understand concept of fluency
- Understand different strategies
for adding/subtracting:
*decomposing a number to
make ten
*related facts (relationship
between addition and subtraction),
*creating equivalent but easier
known sums (doubles, doubles plus
one etc.)
Academic Vocabulary: strategy,
fluency, addition, subtraction, sum,
unknown, equal, equation, make ten,
related fact, doubles
Teaching Notes/Strategies
Math facts timed quizzes
Flash Cards
Partner practice
Student success charts
Homework Practice
Addition/Subtraction games
Computer Games
Examples of different strategies:
Sam has 8 red marbles and 7 green marbles.
How many marbles does Sam have in all?
Making 10 and Decomposing a Number
I know that 8 plus 2 is 10, so I broke up
(decomposed) the 7 up into a 2 and a 5.
First I added 8 and 2 to get 10, and then
added the 5 to get 15.
7=2+5
8 + 2 = 10
10 + 5 = 15
Resources
See above
Computer
www.commoncoresheets.com
Creating an Easier Problem with Known
Sums
I broke up (decomposed) 8 into 7 and 1. I
know that 7 and 7 is 14. I added 1 more to
get 15.
8=7+1
7 + 7 = 14
14 + 1 = 15
There were 14 birds in the tree. 6 flew away.
How many birds are in the tree now?
Relationship between Addition &
Subtraction
I thought, ‘6 and what makes 14?’. I know
that 6 plus 6 is 12 and two more is 14.
That’s 8 altogether. So, that means that 14
minus 6 is 8.
6 + 8 = 14
14 – 6 = 8
Board Math Stems:
“Use the strategy of ‘Making a Ten’
to solve this addition problem.
8+6=
Related CA Standard
AF 1.2 Understand the
meaning
of the symbols +, −, =. MR 1.1,
Operations and Algebraic Thinking: Work with addition and subtraction equations.
2.1
Standard: 1. OA. 7
Math Practices:
MP 2, 3, 6, 7
Cluster: major (m)
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.
Essential Skills/Concepts
Teaching Notes/Strategies
Resources
- Understand that the
quantity on one side of the
equal sign must be the
same quantity on the other
side of the equal sign.
-
Interchange language:
“equal to”, “is the same as”
“not equal to” “is not the
same as”
Academic Vocabulary: equation,
equal, sign/operation, the same
amount/quantity as, true, false,
unknown, value, sum, difference
Board Math Stems:
- Find the difference.
15 – 6 =
- Is this equation true? Why or
Why not?
5 + 6= 2 + 8
- What operation will make this
number sentence true?
13 _ 5 = 8
- Which of these equations are
true or false? Explain your
thinking.
10 = 3+7
12-2=4+6
4+5+1=5+4+1
- Number talks (mental math,
explain reasoning)
- Estimation may be used as a
strategy: 3 + 4 = 3 + 3 +2
“There are 3s on both sides, but the
right side has 3 + 2 and the left side
has 4, which is less than 3+ 2”
See Above
Operations and Algebraic Thinking: Work with addition and subtraction
equations.
Standard: 1. OA. 8
Math Practices:
MP 2, 6, 7
Cluster: major (m)
Related CA Standard
NS 2.6
Solve addition and subtraction
problems with one- and two-digit
numbers MR 2.1
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 = __
Essential Skills/Concepts
Use skills and concepts from 1.OA.4
and 1.OA.6
Teaching Notes/Strategies
Board Math Stems:
- What number makes this
equation true?
7 = ____ - 5
- Determine the unknown number.
5 = ____ - 2
___ + 9 = 17
-
Academic Vocabulary: equation,
equal, sign/operation, the same
amount/quantity as, true, false,
unknown, value, addend, sum,
difference
Use symbol for unknown/
Unknown in different spots
4+
= 5+4
+3= 2+3
Resources
See above