Common Core State Standards for
Mathematics Grade 4 
Domain 4.OA  Operations and Algebraic Thinking 
Use the four operations with whole numbers to solve problems. 
Lessons 
4.OA.1 
Interpret a multiplication equation as a comparison,
e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as
7 and 7 times as many as 5. Represent verbal statements of
multiplicative comparisons as multiplication equations. 
Writing Algebraic Equations
Challenge Exercises for Perimeter & Area 
4.OA.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. 
Writing Algebraic Equations
Multiplying Decimals and Whole Numbers
Multiplying Decimals
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals
Solving More Decimal Word Problems 
4.OA.3 
Solve multistep word problems posed with whole numbers
and having wholenumber 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 including rounding. 
Divisibility
Order of Operations
Order of Operations with Exponents
Order of Operations with Integers
Writing Algebraic Equations
NonRoutine Mean
Estimating Decimal Sums
Estimating Decimal Differences
Estimating Decimal Products
Estimating Decimal Quotients

Gain familiarity with factors and multiples. 
Lessons 
4.OA.4 
Find all factor pairs for a whole number in the range
1100. Recognize that a whole number is a multiple of each of its
factors. Determine whether a given whole number in the range 1100 is a
multiple of a given onedigit number. Determine whether a given whole
number in the range 1100 is prime or composite. 
Factors and GCF
Multiples and LCM
Prime and Composite Numbers
Practice Exercises for Number Theory
Challenge Exercises for Number Theory
The Sieve of Eratosthenes Worksheet & Answer Key 
Generate and analyze patterns. 
Lessons 
4.OA.5 
Generate a number or shape pattern that follows a given
rule. Identify apparent features of the pattern that were not explicit
in the rule itself. For example, given the rule "Add 3" and the starting
number 1, generate terms in the resulting sequence and observe that the
terms appear to alternate between odd and even numbers. Explain
informally why the numbers will continue to alternate in this way. 
Exponents
Patterns and Exponents
Practice Exercises for Number Theory
Challenge Exercises for Number Theory
Multiplying Decimals and Whole Numbers
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals 
Domain 4.NBT  Number and
Operations in Base Ten 
Generalize place value understanding for multidigit whole numbers. 
Lessons 
4.NBT.1 
Recognize that in a multidigit whole number, a digit
in one place represents ten times what it represents in the place to
its right. For example, recognize that 700
÷ 70 = 10 by applying concepts of place value and division. 
Introduction to Decimals
Reading and Writing Decimals
Multiplying Decimals and Whole Numbers
Dividing Decimals by Whole Numbers 
4.NBT.2 
Read and write multidigit whole numbers using
baseten numerals, number names, and expanded form. Compare two
multidigit numbers based on meanings of the digits in each place, using
>, =, and < symbols to record the results of comparisons. 
Introduction to Decimals
Reading and Writing Decimals
Comparing Decimals 
4.NBT.3 
Use place value understanding to round multidigit
whole numbers to any place. 

Use place value understanding and properties of operations to perform multidigit arithmetic. 
Lessons 
4.NBT.5 
Multiply a whole number of up to four digits by a
onedigit whole number, and multiply two twodigit numbers, using
strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular
arrays, and/or area models. 
Area of a Rectangle
Area of a Parallelogram
Order of Operations

4.NBT.6 
Find wholenumber quotients and remainders with up to
fourdigit dividends and onedigit divisors, using strategies based on
place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models. 
Factors and GCF
Divisibility
Dividing Decimals by Whole Numbers
Dividing Decimals by Decimals 
Domain 4.NF  Number and
Operations  Fractions 
Extend understanding of fraction equivalence and ordering. 
Lessons 
4.NF.1 
Explain why a fraction a/b is equivalent to a fraction
(n x a)/(n x b) by using visual fraction models, with attention to how
the number and size of the parts differ even though the two fractions
themselves are the same size. Use this principle to recognize and
generate equivalent fractions. 
Introduction to Fractions
Classifying Fractions
Equivalent Fractions 
4.NF.2 
Compare two fractions with different numerators and
different denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when the two fractions refer
to the same whole. Record the results of comparisons with symbols >,
=, or <, and justify the conclusions, e.g., by using a visual
fraction model. 
Comparing Fractions
Ordering Fractions 
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 
Lessons 
4.NF.3 
Understand a fraction
a/b with
a > 1 as a sum of fractions 1/b. 
Adding and
Subtracting Fractions and Mixed Numbers 

4.NF.3a Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole. 
Adding Fractions with Like Denominators
Subtracting Fractions with Like Denominators 

4.NF.3b Decompose a fraction into a sum of fractions with
the same denominator in more than one way, recording each decomposition
by an equation. Justify decompositions, e.g., by using a visual
fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2
1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 
Converting Fractions to Mixed Numbers
Converting Mixed Numbers to Fractions 

4.NF.3c Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the relationship
between addition and subtraction. 
Adding Mixed Numbers
Subtracting Mixed Numbers 

4.NF.3d
Solve word problems involving addition and subtraction of fractions
referring to the same whole and having like denominators, e.g., by using
visual fraction models and equations to represent the problem. 
Adding Fractions with Like Denominators
Subtracting Fractions with Like Denominators
Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers 
4.NF.4 
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 
Multiplying and Dividing Fractions and Mixed Numbers 

4.NF.4a Understand a fraction a/b as a multiple of
1/b. For example, use a visual fraction model to represent 5/4 as
the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5
x (1/4). 
Multiplying Fractions 

4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3
x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general,
n x (a/b) = (n x a)/b.) 
Multiplying Fractions By Cancelling Common Factors 

4.NF.4c Solve word problems involving multiplication of a
fraction by a whole number, e.g., by using visual fraction models and
equations to represent the problem. For example, if each person at a
party will eat 3/8 of a pound of roast beef, and there will be 5 people
at the party, how many pounds of roast beef will be needed? Between what
two whole numbers does your answer lie? 
Multiplying Fractions
Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers 
Understand decimal notation for fractions, and compare decimal fractions. 
Lessons 
4.NF.5 
Express a fraction with denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two fractions with
respective denominators 10 and 100. For example, express
3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 
Writing Fractions as Percents 
4.NF.6 
Use decimal notation for fractions with denominators 10 or 100. For
example, rewrite 0.62 as 62/100; describe a length as 0.62 meters;
locate 0.62 on a number line diagram. 
The Meaning of Percent
Writing Percents as Decimals
Percents Less Than 1 or Greater Than 100
Introduction to Decimals
Read and Write Decimals 
4.NF.7 
Compare two decimals to hundredths by reasoning about their size.
Recognize that comparisons are valid only when the two decimals refer to
the same whole. Record the results of comparisons with the symbols >, =,
or <, and justify the conclusions, e.g., by using a visual model. 
Comparing Decimals
Ordering Decimals
Solving Decimal Word Problems
Practice Exercises for Decimals Part I
Challenge Exercises for Decimals Part I 
Domain 4.MD  Measurement and Data 
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 
Lessons 
4.MD.1 
Know relative sizes of measurement units within one
system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min,
sec. Within a single system of measurement, express measurements in a
larger unit in terms of a smaller unit. Record measurement equivalents
in a twocolumn table. 
Converting Mixed Numbers to Fractions 
4.MD.2 
Use the four operations to solve word problems
involving distances, intervals of time, liquid volumes, masses of
objects, and money, including problems involving simple fractions or
decimals, and problems that require expressing measurements given in a
larger unit in terms of a smaller unit. Represent measurement quantities
using diagrams such as number line diagrams that feature a measurement
scale. 
Comparing Fractions
Adding Decimals
Subtracting Decimals
Multiplying Decimals and Whole Numbers
Dividing Decimals by Decimals 
4.MD.3 
Apply the area and perimeter formulas for rectangles
in real world and mathematical problems. For example, find the width of a
rectangular room given the area of the flooring and the length, by
viewing the area formula as a multiplication equation with an unknown
factor. 
Area of a Rectangle
Challenge Exercises for Perimeter & Area 
Geometric measurement: understand concepts of angle and measure angles. 
Lessons 
4.MD.5 
Recognize angles as geometric shapes that are formed
wherever two rays share a common endpoint, and understand concepts of
angle measurement: 


4.MD.5.a An angle is measured
with reference to a circle with its center at the common endpoint of
the rays, by considering the fraction of the circular arc between the
points where the two rays intersect the circle. An angle that turns
through 1/360 of a circle is called a
"onedegree angle," and can be used to measure angles. 
Constructing Circle Graphs 

4.MD.5.b An angle that turns through n onedegree angles is said to have an angle measure of n degrees. 
Constructing Circle Graphs 
4.MD.6 
Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 
Constructing Circle Graphs 
Domain 4.G  Geometry 
Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 
Lessons 
4.G.1 
Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel lines. Identify
these in twodimensional figures. 
Geometry and the Circle
Area of a Parallelogram
Area of a Trapezoid 
4.G.2 
Classify twodimensional figures based on the
presence or absence of parallel or perpendicular lines, or the presence
or absence of angles of a specified size. Recognize right triangles as a
category, and identify right triangles. 
Area of a Triangle
Geometry and a Shoebox 