OML Search

Common Core Mapping for Grade 6

In Grade 6, instructional time should focus on four critical areas:
(1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
(2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
(3) writing, interpreting, and using expressions and equations
(4) developing understanding of statistical thinking.


Related Topics:
Common Core Math Classroom Resources for all Grades, Common Core Lesson Plans and Worksheets for Grade 6, Common Core for Mathematics

Ratios and Proportional Relationships







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.


Describing ratios

Expressing ratios as fractions

Ratio Games


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 relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. He paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.

Unit Rate

Rate problems

Ratio word problems

Ratio Games


Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Check below



Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Equivalent Ratios

Solving ratio problems with tables

Ratio word problems

Ratio Games


Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Unit Rate Problems

Rate problems

Ratio word problems

Ratio Games


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.

Percents & Ratios

Percent Word Problems

Finding percents

Find Percents

Percentage word problems

Percent Games


Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Convert Measurements


Measurement Games

The Number System







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 3/4-cup 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?.

Divide Fractions

Relationship between Multiplication and Division

Fraction Word Problems

Divide Fractions by Fractions

Divide Fractions and Mixed Numbers

Divide positive fractions

Divide fractions word problems

Divide fractions applications

Understanding dividing fractions by fractions

Fraction Games


Fluently divide multi-digit numbers using the standard algorithm.

Divide Multi-digit Numbers

Multi-digit division

Division Games


Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.


Multiply Decimals

Divide Decimals

Adding decimals

Subtract Decimals

Multiply decimals

Divide decimals

Add and subtracting decimals word problems

Decimal Games


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).


GCF & Distributive Property

Greatest common factor/divisor

Least common multiple

Distributive property

LCM and GCD word problems

Factor Games


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 real-world contexts, explaining the meaning of 0 in each situation.

Positive & Negative Numbers

Integers and the Number Line

Opposite Numbers

Negative number word problems

Integer Games


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.

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.

B. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

C. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Number Opposites on the Number Line

The Opposite of a Number’s Opposite

Ordered Pairs & Coordinate Plane

Rational Numbers on the Number Line

Inequality Statements Involving Rational Numbers

Integers on the number line

Integers on the number line

Fractions on the number line

Number opposites

Graphing points and naming quadrants

Points on the coordinate plane

Reflecting points

Integer Games


Understand ordering and absolute value of rational numbers.

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.

B. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.

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 real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

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.

Absolute Numbers

Absolute Value-Magnitude and Distance

Relate absolute value and order

Ordering negative numbers

Writing numerical inequalities

Finding absolute values

Absolute value word problems

Comparing absolute values

Absolute Value Games


Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Coordinate Plane

Ordered Pairs and the Coordinate Plane

Symmetry on the Coordinate Plane

Points on the Coordinate Plane

Distance on the Coordinate Plane

Problem Solving

Coordinate plane word problems in all four quadrants

Coordinate Plane Games

Expressions and Equations







Write and evaluate numerical expressions involving whole-number exponents.


Understanding Exponents

Positive & zero exponents

Writing numerical expressions with exponents word problems

Exponent Games


Write, read, and evaluate expressions in which letters stand for numbers.

A. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation ԓubtract y from 5Ԡas 5 - y.

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.

C. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Write, Read & Evaluate Expressions

Factoring Expressions

Order of Operations

Replace Letters with Numbers

Replace Numbers with Letters

Writing Addition and Subtraction Expressions

Expand Multiplication Expressions

Distributing Expressions

Writing Division Expressions

Read Expressions in Which Letters Stand for Numbers

Write Expressions in Which Letters Stand for Numbers

Expressions-Multiplication and Division

Expressions - Exponents

Writing expressions

Writing expressions with exponents

Identifying parts of expressions

Evaluating expressions in one variable

Evaluating expressions with variables word problems

Algebraic Expression Games


Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Equivalent Expressions

Distributing Expressions

Combine like terms

Equivalent forms of expressions

Algebraic Expression Games


Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..

Identify Equivalent Expressions

Equivalent forms of expressions

Algebraic Expression Games


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.

Solve Equations & Inequalities

1-Step Equations-Addition, Subtraction

1-Step Equations-Multiplication, Division

Solving equations & inequalities through substitution

Equation Games


Use variables to represent numbers and write expressions when solving a real-world 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.

Algebraic Expressions

Constructing & solving equations in the real world 1

Inequalities in one variable

Algebraic Expression Games


Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which pq and x are all nonnegative rational numbers.

Solving Equations

2-Step Problems

Multi-Step Problems

One step equation intuition

Solve One-step Equations

One-step equations with multiplication

Algebra Games


Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.


From Equations to Inequalities

Writing and Graphing Inequalities in Real-World Problems

Inequalities in one variable

Inequalities on a number line



Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Dependent & Independent Variables

Dependent & independent variables

Algebra Games








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 real-world and mathematical problems.

Area of Regular Polygons & Irregular Polygons

Area of Parallelograms

Area of Triangles

Area of Polygons - Composing and Decomposing

Area in the Real World

Area of parallelograms

Area of quadrilaterals & polygons

Area of trapezoids, rhombi, & kites

Area of triangles

Area problems

Composing & decomposing shapes

Area Games


Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Volume of Rectangular Prisms (Fractional Sides)

Volume with Fractional Lengths

Volume with unit cubes

Volume with fractions

Volume word problems with fractions

Volume Games


Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Polygons in the coordinate plane

Drawing polygons

Polygons in the coordinate plane

Coordinate plane word problems

Coordinate Geometry Games


Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Nets of 3D Figures

Nets of 3D figures

Surface area

Nets of Solids Games

Statistics and Probability







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.

Statistical Questions

Statistical Questions

Statistics Games


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.

Data Distribution

Box plots


Mean, Median & Mode

Statistics Games


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.

Central Tendency & Variance

Describe distributions with center and spread

Statistics Games


Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Dot Plots, Histograms, Box Plots

Creating box and whisker plots

Dot Plots

Statistics Games


Summarize numerical data sets in relation to their context, such as by:

A. Reporting the number of observations.

B. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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.

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.


Reading bar charts 1

Reading bar charts 2

Reading bar charts 3

Reading tables 1

Reading tables 2

Mean, Median & Mode

Pictographs 1

Pictographs 2

Statistics Games

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines