Common Core State Standards for
Mathematics Grade 6 
Domain 6.RP  Ratios and
Proportional Relationships 
Understand ratio concepts and use ratio reasoning to solve problems. 
Lessons 
6.RP.1 
Understand the concept of a ratio and use ratio
language to describe a ratio relationship between two quantities. For
example, “The ratio of wings to beaks in the bird house at the zoo was
2:1, because for every 2 wings there was 1 beak.” “For every vote
candidate A received, candidate C received nearly three votes.” 
Writing Fractions as Percents
Writing Percents as Fractions 
6.RP.3 
Use ratio and rate reasoning to solve realworld and mathematical
problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 
Percent and Proportions 

6.RP.3.a 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. 
Meaning of Percent 

6.RP.3.c 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 percent. 
Percent and Proportions
Percent Change
Discount and Sale Price
Practice Exercises for Consumer Math
Challenge Exercises for Consumer Math 
Domain 6.NS  The Number System 
Apply and extend previous understandings of multiplication and division to divide fractions by fractions 
Lessons 
6.NS.1 
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between
multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 3/4cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2
square mi? Compute fluently with multidigit numbers and find common factors and multiples. 
Dividing Fractions
Dividing Mixed Numbers
Reciprocals
Solving Word Problems
Practice Exercises for Unit 17
Challenge Exercises for Unit 17 
Compute fluently with multidigit numbers and find common factors and multiples. 
Lessons 
6.NS.2 
Fluently divide multidigit numbers using the standard
algorithm. 
Divisibility Rules 
6.NS.3 
Fluently add, subtract, multiply, and divide
multidigit decimals using the standard algorithm for each operation. 
Adding Decimals
Subtracting Decimals
Multiplying Decimals
Dividing Decimals 
6.NS.4 
Find the greatest common factor of two whole numbers
less than or equal to 100 and the least common multiple of two whole
numbers less than or equal to 12. Use the distributive property to
express a sum of two whole numbers 1–100 with a common factor as a
multiple of a sum of two whole numbers with no common factor. For
example, express 36 + 8 as 4 (9 + 2). Apply and extend previous
understandings of numbers to the system of rational numbers. 
Greatest Common Factor
Least Common Multiples
Number Theory Worksheets 
Apply and extend previous understandings of numbers to the system of rational numbers. 
Lessons 
6.NS.5 
Understand that positive and negative numbers are used
together to describe quantities having opposite directions or values
(e.g., temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in realworld contexts,
explaining the meaning of 0 in each situation. 
Introduction to Integers
Absolute Value
Comparing and Ordering Integers
Integer Addition
Integer Subtraction
Integer Multiplication
Integer Division
Operations with Integers
Practice Exercises for Integers
Challenge Exercises for Integers 
6.NS.6 
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 
Introduction to Integers 

6.NS.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line;
recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. 
Introduction to Integers
Absolute Value
Integer Addition
Integer Subtraction 
6.NS.7 
Understand ordering and absolute value of rational numbers. 


6.NS.7.a Interpret statements of inequality as
statements about the relative position of two numbers on a number line
diagram. For example, interpret –3 > –7 as a statement that –3 is
located to the right of –7 on a number line oriented from left to right. 
Comparing and Ordering Integers 

6.NS.7.b Write, interpret, and explain statements
of order for rational numbers in realworld contexts. For example,
write –3 ^{o}C > –7 ^{o}C to express the fact that –3
^{o}C is warmer than –7 ^{o}C. 
Comparing and Ordering Integers 

6.NS.7.c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret
absolute value as magnitude for a positive or negative quantity in a realworld situation.
For example, for an account balance of –30 dollars, write –30 = 30 to describe the size of the debt in dollars. 
Absolute Value 

6.NS.7.d Distinguish comparisons of absolute
value from statements about order. For example, recognize that an
account balance less than –30 dollars represents a debt greater than 30 dollars. 
Introduction to Integers 
Domain 6.EE  Expressions and Equations 
Apply and extend previous understandings of numbers to the system of rational numbers. 
Lessons 
6.EE.1 
Write and evaluate numerical expressions involving wholenumber exponents. 
Exponents
Patterns and Exponents
Order of Operations With Exponents 
6.EE.2 
Write, read, and evaluate expressions in which letters stand for numbers. 
Topics In PreAlgebra 

6.EE.2.a Write expressions that record operations
with numbers and with letters standing for numbers. For example, express
the calculation “Subtract y from 5” as 5 – y. 
Writing Algebraic Expressions 

6.EE.2.b Identify parts of an expression using
mathematical terms (sum, term, product, factor, quotient, coefficient);
view one or more parts of an expression as a single entity. For
example, describe the expression 2 (8 + 7) as a product of two factors;
view (8 + 7) as both a single entity and a sum of two terms. 
Writing Algebraic Expressions 

6.EE.3.c Evaluate expressions at specific values
of their variables. Include expressions that arise from formulas used in
realworld problems. Perform arithmetic operations, including those
involving wholenumber exponents, in the conventional order when there
are no parentheses to specify a particular order (Order of Operations).
For example, use the formulas V = s^{3} and A = 6 s^{2} to find the volume
and surface area of a cube sides of length s = 1/2. 
Area of a Rectangle 
Reason about and solve onevariable equations and inequalities. 
Lessons 
6.EE.5 
Understand solving an equation or inequality as a process of answering a question: which values from a
specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set
makes an equation or inequality true. 
Writing Algebraic Equations 
6.EE.6 
Use variables to represent numbers and write expressions when solving a realworld or mathematical problem;
understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 
Writing Algebraic Equations
Math and Climate Worksheet 
Domain 6.G  Geometry 
Solve realworld and mathematical problems involving area, surface area, and volume. 
Lessons 
6G.1 
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
Area of a Rectangle
Area of a Parallelogram
Area of a Triangle
Area of a Trapezoid
Practice Exercises for Perimeter & Area
Challenge Exercises for Perimeter & Area 
Domain 6.SP  Statistics and Probability 
Develop understanding of statistical variability. 
Lessons 
6.SP.1 
Recognize a statistical question as one that anticipates variability in
the data related to the question and accounts for it in the answers.
For example, “How old am I?” is not a statistical question, but “How old
are the students in my school?” is a statistical question because one
anticipates variability in students’ ages. 
The Range of a Set of Data 
6.SP.2 
Understand that a set of data collected to answer a statistical question
has a distribution which can be described by its center, spread, and overall shape. 
Introduction to Probability
Certain and Impossible Events
Sample Spaces
The Complement of an Event
Mutually Exclusive Events
Independent Events
Dependent Events
Conditional Probability 
6.SP.3 
Recognize that a measure of center for a numerical data set summarizes
all of its values with a single number, while a measure of variation
describes how its values vary with a single number. 
Arithmetic Mean
The Median of a Set of Data
The Mode of a Set of Data 
Summarize and describe distributions. 
Lessons 
6.SP.4 
Display numerical data in plots on a number line, including dot plots,
histograms, and box plots. 
Data and Line Graphs
Data and Bar Graphs
Data and Circle Graphs 
6.SP.5 
Summarize numerical data sets in relation to their context, such as 


6.SP.5.a Reporting the number of observations. 
The Range of a Set of Data
Arithmetic Mean
NonRoutine Mean
The Median of a Set of Data
The Mode of a Set of Data
Practice Exercises for Unit 8
Challenge Exercises for Unit 8 

6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of
measurement. 
Constructing Line Graphs
Constructing Bar Graphs
Constructing Circle Graphs 

6.SP.5.c Giving quantitative measures of center
(median and/or mean) and variability (interquartile range and/or mean
absolute deviation), as well as describing any overall pattern and any
striking deviations from the overall pattern with reference to the
context in which the data were gathered. 
Data and Graphs Worksheets 

6.SP.5.d Relating the choice of measures of
center and variability to the shape of the data distribution and the
context in which the data were gathered. 
Comparing Graphs 