Pennsylvania Core and Academic Standards for Sixth Grade Math

Area and Circumference of Circles
FreeThe circumference of a circle is the distance around the outside. The area of a circle is the space contained within the circumference. It is measured in square units. Read more...iWorksheets: 4Study Guides: 1
Area of Triangles and Quadrilaterals
The area is the surface or space within an enclosed region. Area is expressed in square units. Read more...iWorksheets: 3Study Guides: 1Vocabulary Sets: 2
Coordinates
The use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets: 3Study Guides: 1
Diameter of Circle
The diameter of a circle is a line segment that passes through the center of a circle connecting one side of the circle to the other. Read more...iWorksheets: 3Study Guides: 1
Estimation
Estimation is the process of rounding a number either up or down to the nearest place value requested. Estimation makes it easier to perform mathematical operations quickly. Read more...iWorksheets: 6Study Guides: 1
Evaluate Exponents
Evaluating an expression containing a number with an exponent means to write the repeated multiplication form and perform the operation Read more...iWorksheets: 3Study Guides: 1
Exponents
The exponent represents the number of times to multiply the number, or base. When a number is represented in this way it is called a power. Read more...iWorksheets: 3Study Guides: 1
Exponents to Repeated Multiplication
An exponent is a smaller-sized number which appears to the right and slightly above a number. Read more...iWorksheets: 3Study Guides: 1
Fractions/Decimals
Any fraction can be changed into a decimal and any decimal can be changed into a fraction. Read more...iWorksheets: 3Study Guides: 1
Graphs
A graph is a diagram that shows information in an organized way. Read more...iWorksheets: 6Study Guides: 1
Measurement
FreeThere are many units of measurement: inches, feet, yards, miles, millimeters, meters, seconds, minutes, hours, cups, pints, quarts, gallons, ounces, pounds, etc Read more...iWorksheets: 6Study Guides: 1
Multiple Representation of Rational Numbers
What are multiple representations of rational numbers? A rational number represents a value or a part of a value. Rational numbers can be written as integers, fractions, decimals, and percents.The different representations for any given rational number are all equivalent. Read more...iWorksheets: 3Study Guides: 1
Number Patterns
A number pattern is a group of numbers that are related to one another in some sort of pattern. Finding a pattern is a simpler way to solve a problem. Read more...iWorksheets: 3Study Guides: 1
Ordering Fractions
The order of rational numbers depends on their relationship to each other and to zero. Rational numbers can be dispersed along a number line in both directions from zero. Read more...iWorksheets: 6Study Guides: 1
Percent, Rate, Base
A percent is a way of comparing a number with 100. Percents are usually written with a percent sign. To solve a percent problem, multiply the value by the percent using one of the representations for the percent. Read more...iWorksheets: 3Study Guides: 1
Percentage
The term percent refers to a fraction in which the denominator is 100. It is a way to compare a number with 100. Read more...iWorksheets: 6Study Guides: 1
Perimeter
A perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. Read more...iWorksheets: 3Study Guides: 1
Plotting Points
In a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the vertical axis. Read more...iWorksheets: 4Study Guides: 1Vocabulary Sets: 1
Probability
Probability word problems worksheets. Probability is the possibility that a certain event will occur. An event that is certain to occur has a probability of 1. An event that cannot occur has a probability of 0. Therefore, the probability of an event occurring is always between 0 and 1. The closer a probability is to 1, the more certain that an event will occur. Read more...iWorksheets: 3Study Guides: 1
Repeated Multiplication to Exponents
The result of raising a number to a power is the same number that would be obtained by multiplying the base number together the number of times that is equal to the exponent. Read more...iWorksheets: 3Study Guides: 1
Simplify Fractions
Simplifying fractions is the process of reducing fractions and putting them into their lowest terms. Read more...iWorksheets: 3Study Guides: 1
Statistics
A statistic is a collection of numbers related to a specific topic. Read more...iWorksheets: 6Study Guides: 1
Tables
Tables refer to the different types of diagram used to display data.
There are many types of tables such as data table, frequency table, line chart and stern-and-leaf plot. Read more...
iWorksheets: 3Study Guides: 1
Whole Numbers to Trillions
The number system we use is based on a place value system. Although there are only 10 different digits in this system, it is possible to order them in so many variations that the numbers represented are infinite. Read more...iWorksheets: 3Study Guides: 1

PA.CC.2.1.6. Numbers and Operations

CC.2.1.6.D. Ratios & Proportional Relationships

CC.2.1.6.D.1. Understand ratio concepts and use ratio reasoning to solve problems.
Proportions/Equivalent Fractions
Equivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
Ratio
Ratios are used to make a comparison between two things. Read more...iWorksheets :7Study Guides :1Vocabulary :1
Ratio
A ratio is a comparison of two numbers. The two numbers must have the same unit in order to be compared. Read more...iWorksheets :3Study Guides :1
Simple Proportions
A proportion is a statement that two ratios are equal. A ratio is a pair of numbers used to show a comparison. To solve a proportion, calculate equivalent fractions in order to be sure the two fractions (ratios) are equal. Read more...iWorksheets :3Study Guides :1
Numerical Proportions
Numerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1

CC.2.1.6.E. The Number System

CC.2.1.6.E.1. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Multiply / Divide Fractions
To multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this operation. Read more...iWorksheets :4Study Guides :1
Fraction Operations
Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
CC.2.1.6.E.2. Identify and choose appropriate processes to compute fluently with multi-digit numbers.
Multiplication
Multiplication is a mathematical operation in which numbers, called factors, are multiplied together to get a result, called a product. Multiplication can be used with numbers or decimals of any size. Read more...iWorksheets :3Study Guides :1
Multiplication
Multiplication is one of the four elementary, mathematical operations of arithmetic. Read more...iWorksheets :6Study Guides :1Vocabulary :1
Distributive Property
The distributive property offers a choice in multiplication of two ways to treat the addends in the equation. We are multiplying a sum by a factor which results in the same product as multiplying each addend by the factor and then adding the products. Read more...iWorksheets :3Study Guides :1
Commutative/Associative Properties
The commutative property allows us to change the order of the numbers without changing the outcome of the problem. The associative property allows us to change the grouping of the numbers. Read more...iWorksheets :4Study Guides :1
Division
Division is a mathematical operation is which a number, called a dividend is divided by another number, called a divisor to get a result, called a quotient. Read more...iWorksheets :3Study Guides :1
Division
Divide three-digit numbers by one- and two-digit numbers. Read more...iWorksheets :6Study Guides :1Vocabulary :1
CC.2.1.6.E.3. Develop and/or apply number theory concepts to find common factors and multiples.
Common Factors
Factors are two numbers multiplied together to get a product (an answer to a multiplication problem) Read more...iWorksheets :3Study Guides :1Vocabulary :1
CC.2.1.6.E.4. Apply and extend previous understandings of numbers to the system of rational numbers.
Add/Subtract Fractions
Freeis one of the four basic operations of arithmetic, with the others being subtraction, multiplication and division. The addition of two whole numbers is the total amount of those quantities combined. Read more...iWorksheets :3Study Guides :1
Add/Subtract Fractions
Adding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :7Study Guides :1
Mixed Numbers
A mixed number has both a whole number and a fraction. Read more...iWorksheets :4Study Guides :1
Multiply / Divide Fractions
To multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this operation. Read more...iWorksheets :4Study Guides :1
Adding Fractions
Adding fractions is the operation of adding two or more different fractions. Read more...iWorksheets :3Study Guides :1
Multiply Fractions
Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1
Add/Subtract/Multiply/Divide Decimals
You add/subtract/multiply/divide decimals the same way you add/subtract/multiply/divide whole numbers BUT you also need to place the decimal in the correct spot. When multiplying decimals, the decimals may or may NOT be lined up in the multiplication problem. Read more...iWorksheets :10Study Guides :1Vocabulary :1
Decimal Operations
Decimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
Fraction Operations
Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1

PA.CC.2.2.6. Algebraic Concepts

CC.2.2.6.B. Expressions and Equations

CC.2.2.6.B.1. Apply and extend previous understandings of arithmetic to algebraic expressions.
Algebra
Algebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :4Study Guides :1Vocabulary :1
Order of Operations
A numerical expression is a phrase which represents a number. Read more...iWorksheets :7Study Guides :1
Formulas
The formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
One & Two Step Equations
An algebraic equation is an expression in which a letter represents an unknown number Read more...iWorksheets :3Study Guides :1
Simple Algebra
Simple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Algebraic Equations
FreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
Introduction to Algebra
Algebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :3Study Guides :1
Equations and Inequalities
Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :5Study Guides :1
Algebraic Equations
What are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :4Study Guides :1
Algebraic Inequalities
FreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1
Introduction to Functions
A function is a rule that is performed on a number, called an input, to produce a result called an output. The rule consists of one or more mathematical operations that are performed on the input. An example of a function is y = 2x + 3, where x is the input and y is the output. The operations of multiplication and addition are performed on the input, x, to produce the output, y. By substituting a number for x, an output can be determined. Read more...iWorksheets :5Study Guides :1
Nonlinear Functions and Set Theory
A function can be in the form of y = mx + b. This is an equation of a line, so it is said to be a linear function. Nonlinear functions are functions that are not straight lines. Some examples of nonlinear functions are exponential functions and parabolic functions. An exponential function, y = aˆx, is a curved line that gets closer to but does not touch the x-axis. A parabolic function, y = ax² + bx +c, is a U-shaped line that can either be facing up or facing down. Read more...iWorksheets :4Study Guides :1
CC.2.2.6.B.2. Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems.
Algebra
Algebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :4Study Guides :1Vocabulary :1
One & Two Step Equations
An algebraic equation is an expression in which a letter represents an unknown number Read more...iWorksheets :3Study Guides :1
Algebraic Equations
FreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
Introduction to Algebra
Algebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :3Study Guides :1
Equations and Inequalities
Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :5Study Guides :1
Using Integers
Integers are negative numbers, zero and positive numbers. To compare integers, a number line can be used. On a number line, negative integers are on the left side of zero with the larger a negative number, the farther to the left it is. Positive integers are on the right side of zero on the number line. If a number is to the left of another number it is said to be less than that number. In the coordinate plane, the x-axis is a horizontal line with negative numbers, zero and positive numbers. Read more...iWorksheets :4Study Guides :1
Decimal Operations
Decimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
Fraction Operations
Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
Introduction to Percent
What Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
Algebraic Equations
What are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :4Study Guides :1
Algebraic Inequalities
FreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1

PA.CC.2.3.6. Geometry

CC.2.3.6.A. Geometry

CC.2.3.6.A.1. Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.
Volume
Volume measures the amount a solid figure can hold. Read more...iWorksheets :3Study Guides :1
Area
An area is the amount of surface a shape covers.
An area is measured in inches, feet, meters or centimeters. Read more...
iWorksheets :3Study Guides :1
Formulas
The formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
Area of Coordinate Polygons
Calculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
Standards

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