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# 6th Grade Skills in Math

The 6th Grade Skills below are based on the Common Core Standards For Mathematics. You can find out more about the Common Core Standards here.

You will also find a listing of related math resources (worksheets, charts, etc.) here.

Note: Math standards and curricula can vary by location or school. Check with your child’s school to determine what 6th grade math skills are expected in your location.

## Ratios & Proportional Relationships

Using the concept of ratio to show the relationship between two quantities. e.g. the ratio of boys to girls was 15:17

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.”

### Worksheet

Using ratios to determine unit rates. e.g. if paint is to be mixed in a ratio of 2:3 parts red to blue, there will be 2/3 tins of red paint for each tin of blue.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.” “We paid $75 for 15 hamburgers, which is a rate of$5 per hamburger.”

### Worksheet

Solving real world problems using ratio and rate including by the use of equivalent ratios and by understanding and using the concept of percentages.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.
1. 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.
2. 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?
3. 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.
4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

### Calculator

•  Percentage Calculator

## The Number System

Dividing fractions by fractions to solve word problems.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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?

### Mixed

Dividing multi-digit numbers with fluency.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Fluently divide multi-digit numbers using the standard algorithm.

### Worksheet Generator

Using the four operations fluently with multi-digit decimals.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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

### Worksheet Generator

Finding greatest common factors ( up to 100) and least common multiples (for numbers to 12) and using distributive property to rewrite expressions. e.g. 48 + 40 as 8(6 + 5)

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Recognizing how negative and positive numbers can be used to indicate quantities in opposite directions. e.g. money saved and money owed, temperature above and below zero.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Identifying and showing negative values graphically. e.g. on number lines and on all 4 quadrants of the coordinate system.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.
1. 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.
2. 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.
3. 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.

### Coordinate Geometry

Understanding the absolute value of rational numbers. e.g. recognizing that – 8 is to the left of -4 on a horizontal number line and that -4 degrees is warmer than -8 degrees, recognizing that a rational number’s absolute value is its distance from zero on a number line.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Understand ordering and absolute value of rational numbers.
1. 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.
2. 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.
3. 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.
4. 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.

### Worksheet

Graphing ordered pairs on the 4 quadrants of the coordinate system and using absolute values to find the distance between points (horizontally or vertically – no Pythagoras required)

## Expressions & Equations

Evaluating numeric expressions that include exponents. e.g. 42 + 53

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Write and evaluate numerical expressions involving whole-number exponents.

### Powers and exponents

Reading, writing, and evaluating expressions that include numbers and letters

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Write, read, and evaluate expressions in which letters stand for numbers.
1. 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.
2. 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.
3. 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.

### Simple Equations

Generating equivalent expressions by using the properties of operations. e.g. 5(2x + 3) = 10x + 15 and 12b + 18c = 6(2b + 3c)

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet Generator

Recognize two equivalent expressions.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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. Reason about and solve one-variable equations and inequalities.

### Simplifying Expressions

Recognizing that equations and inequalities can solved by finding the value or set or values that make them true.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Example/Guidance

Writing expressions to solve real-world problems using variables in place of unknown numbers.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Matching Game

Writing and solving equations to solve real-world problems.
e.g. a + b = c and xy = z

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet Generator

Writing inequalities given specified conditions in real-world problems.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Writing equations that include both dependent and independent variables and examining the relationship between these two variables using graphs and tables. e.g. for a car traveling at a constant speed of 85 km/ h, the distance traveled (‘d’) can be shown as d = 85t where ‘t’ represents time in hours.

## Geometry

Finding the area of triangles and other polygons and doing so to solve real-world problems.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Finding the volume of a rectangular cuboids.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Drawing polygons by plotting their vertices on the coordinate system and determining the length of horizontal and vertical sides.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Coordinate Geometry

Finding the surface area of 3-D shapes using nets of rectangles and triangles.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

## Statistics & Probability

Distinguishing questions that are statistical from those that are not based on whether they anticipate variability. e.g. What age is my teacher? is not statistical whereas What ages are my teachers? is.
Recognizing that data gathered in response to a statistical question can be described by its center, its range, and it’s shape.
Understanding that, for numeric data, a measure of center is a single number that is a summary of all values unlike a measure of variation which is a single number that describes how the values vary.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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.

### Worksheet

Displaying numeric data on histograms, dot plots, and box plots.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

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

### Worksheet

Summarizing sets of numeric data including the numbers, nature, units of measurement, appropriate measures of center (mean/ median, mode) and of variability.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Summarize numerical data sets in relation to their context, such as by:
1. Reporting the number of observations.
2. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
3. 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.
4. 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.

### Example/Guidance

Browse for skills and worksheets at other grade levels by clicking in the table below.