Operations and Algebraic
addition and subtraction with
objects, fingers, mental
images, drawings, sounds , acting out
situations, verbal explanations, expressions, or
CCSS.Math.Content.K.OA.A.2 Solve addition
and subtraction word problems, and add and
subtract within 10, e.g., by using objects or
drawings to represent the problem.
CCSS.Math.Content.K.OA.A.3 Group numbers
less than or equal to 10 into pairs in more than
one way. Can be done by using objects or
drawings, and record each decomposition by a
drawing or equation.
CCSS.Math.Content.K.OA.A.4 For any number
from 1 to 9, find the number that makes 10
when added to the given number by using
objects or drawings, and record the answer with
a drawing or equation.
CCSS.Math.Content.K.OA.A.5 Add and subtract
Students will be able to
represent numbers 1 through
10 using visual aids. They will
be able to add, subtract, and
group these numbers by using
objects or drawings. They will
also be able to solve addition
and subtraction word problems.
Understand addition and understand subtraction
CCSS.Math.Content.1.OA.A.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.
CCSS.Math.Content.1.OA.A.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.
CCSS.Math.Content.1.OA.B.3 Apply properties of operations as
strategies to add and subtract.
CCSS.Math.Content.1.OA.B.4 Understand subtraction as an
CCSS.Math.Content.1.OA.C.5 Relate counting to addition and
CCSS.Math.Content.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, decomposing a
number leading to a ten, using the relationship between addition
and subtraction, and creating equivalent but easier or known
CCSS.Math.Content.1.OA.D.7 Understand the meaning of the
equal sign, and determine if equations involving addition and
subtraction are true or false.
CCSS.Math.Content.1.OA.D.8 Determine the unknown whole
number in an addition or subtraction equation relating three
Students will continue to use
addition and subtraction to
solve word problems and
equations. They will expand
their range from 1 to 20. They
will also learn to apply
properties of operations.
Students will also use a number
of strategies to add and
Represent and solve problems involving addition and
Understand and apply properties of operations and the
relationship between addition and subtraction.
Add and subtract with 20.
Work with addition and subtraction equations.
CCSS.Math.Content.2.OA.A.1 Use addition
and subtraction within 100 to solve one- and
two-step word problems by using drawings
and equations with a symbol for the
unknown number to represent the problem.
CCSS.Math.Content.2.OA.B.2 Add and
subtract within 20 using mental strategies.
By end of Grade 2, know from memory all
sums of two one-digit numbers.
whether a group of objects (up to 20) has
an odd or even number of members; write
an equation to express an even number as
a sum of two equal addends.
CCSS.Math.Content.2.OA.C.4 Use addition
to find the total number of objects arranged
in rectangular arrays with up to 5 rows and
up to 5 columns; write an equation to
express the total as a sum of equal
Students will continue solving
word problems with more
complex numbers (within 100).
Students will also focus on
using mental strategies to add
and subtract within 20.
Students will identify odd and
even numbers and additional
structured in arrays. Students
will also practice writing
equations to demonstrate their
understanding. Students will be
introduced to multiplication.
Represent and solve problems involving addition and
Add and subtract within 20.
Work with equal groups of objects to gain foundations for
products of whole numbers, e.g., interpret 5 7
as the total number of objects in 5 groups of 7
CCSS.Math.Content.3.OA.A.2 Interpret wholenumber quotients of whole
numbers, e.g., interpret 56 8 as the number of
objects in each share when 56 objects are
partitioned equally into 8 shares, or as a
number of shares when 56 objects are
partitioned into equal shares of 8 objects each.
multiplication and division within 100 to solve
word problems in situations involving equal
groups, arrays, and measurement
quantities, e.g., by using drawings and
equations with a symbol for the unknown
number to represent the problem.1
CCSS.Math.Content.3.OA.A.4 Determine the
unknown whole number in a multiplication or
division equation relating three whole numbers.
Third grade focuses on
multiplication and division of
whole numbers. Students will
use multiplication and division
to solve problems involving
equal groups, arrays, and
measurement quantities, etc.
Represent and solve problems involving multiplication and
Understand properties of multiplication and the relationship
between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations and ifentify and
explain patterns in arithmetic.
CCSS.Math.Content.4.OA.A.1 Interpret a
multiplication equation as a comparison.
Represent verbal statements of
multiplicative comparisons as multiplication
CCSS.Math.Content.4.OA.A.2 Multiply or
divide to solve word problems involving
multiplicative comparison, e.g., by using
drawings and equations with a symbol for
the unknown number to represent the
problem, distinguishing multiplicative
comparison from additive comparison.
multistep 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
Students will continue to work
with multiplication and division.
Students will be introduced to
the x variable and be required
to complete whole number
problems in which all
operations are used and
contain an unknown quantity.
Students begin to move away
from drawings and
representations to written
equations with variables for
unknown numbers. Students
begin too generate and analyze
Use the four operations with whole numbers to solve problems.
Gain familiarity with factors and multiples.
Generate and analyze patterns.
parentheses, brackets, or braces in numerical
expressions, and evaluate expressions with
CCSS.Math.Content.5.OA.A.2 Write simple
expressions that record calculations with
numbers, and interpret numerical expressions
without evaluating them.
CCSS.Math.Content.5.OA.B.3 Generate two
numerical patterns using two given rules.
Identify relationships between corresponding
terms. Form ordered pairs consisting of
corresponding terms from the patterns, and
graph the ordered pairs on a grid.
Students will learn the
parentheses, brackets, and
braces and learn how to
accurately solve equations that
have them. Students will write
simple equations without
evaluating them. In
addition, students will learn to
solve problems based on set
“rules” (patterns). Students will
continue to graph the ordered
pairs on a grid.
Write and interpret numerical expressions.
Analyze patterns and relationships.
CCSS.Math.Content.6.RP.A.1 Understand the concept
of a ratio and use ratio language to describe a ratio
relationship between two quantities.
CCSS.Math.Content.6.RP.A.2 Understand the concept
of a unit rate a/b associated with a ratio a:b with b ≠
0, and use rate language in the context of a ratio
CCSS.Math.Content.6.RP.A.3 Use ratio and rate
reasoning to solve real-world and mathematical
CCSS.Math.Content.6.RP.A.3a Make tables of
equivalent ratios relating quantities with wholenumber measurements, find missing values in the
tables, and plot the pairs of values on the
coordinate plane. Use tables to compare ratios.
CCSS.Math.Content.6.RP.A.3b Solve unit rate
problems including those involving unit pricing and
CCSS.Math.Content.6.RP.A.3c Find a percent of a
quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity); solve problems
involving finding the whole, given a part and the
CCSS.Math.Content.6.RP.A.3d Use ratio reasoning
to convert measurement units; manipulate and
transform units appropriately when multiplying or
Content shifts from Operations
and Algebraic Thinking to
Ratios and Proportional
Relationships. Students will
learn about ratios, ratio
terminology, and how ratios are
used in mathematical problems
and every day life. Students will
be able to solve different math
problems using ratios such as
problems involving unit
speed, percent, etc. Students
will also know how to
Understand ratio concepts and use ratio reasoning to solve
Middle School and High School
5th grade, the standards for operations and
algebraic thinking get more specific per grade.
Grade 6 and 7 focus on ratios and proportional
relationships. All of the middle school grades focus
on non-rational numbers and how to
analyze, approximate, and rationalize them. The
high school grades focus primarily on extending the
properties of exponents to rational exponents and
using properties of rational and irrational numbers.