**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**Coordinates**FreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets: 13Study 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**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**Simplify Fractions**Simplifying fractions is the process of reducing fractions and putting them into their lowest terms. 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: 4Study Guides: 1### N.1. Number and Operations (NCTM)

#### 1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

##### 1.1.1. Work flexibly with fractions, decimals, and percents to solve problems.

**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**Percents**A percentage is a number or ratio expressed as a fraction of 100. Read more...iWorksheets :6Study Guides :1Vocabulary :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**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 :8Study 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**Multiply Fractions**Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1**Subtracting Fractions**Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. First, make sure the denominators are the same, then subtract the numerators. 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**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**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**Adding Fractions**Fractions consist of two numbers. The top number is called the numerator.
The bottom number is called the denominator. To add two fractions with the same denominator: Add the numerators and place the sum over the common denominator. Read more...iWorksheets :3Study 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**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**Applying Percents**Applying percents is a term that refers to the different ways that percents can be used. The percent of change refers to the percent an amount either increases or decreases based on the previous amounts or numbers. Applying percents also means to calculate simple interest using the interest equation, I = P · r · t, where P is the principal; r is the rate and t is the time. Read more...iWorksheets :3Study Guides :1##### 1.1.2. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.

**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**Ordering Decimals**When putting decimals in order from least to greatest, we must look at
the highest place value first. Read more...iWorksheets :6Study Guides :1Vocabulary :1**Compare and Order Fractions**When comparing two fractions that have a common denominator, you can looks at the numerators to decide which fraction is greater Read more...iWorksheets :4Study Guides :1Vocabulary :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**Ordering Fractions**A fraction consists of two numbers separated by a line - numerator and denominator. To order fractions with like numerators, look at the denominators and compare them two at a time. The fraction with the smaller denominator is the larger fraction. Read more...iWorksheets :3Study Guides :1**Fractions/Decimals**How to convert fractions to decimals: Divide the denominator (the bottom part) into the numerator (the top part). Read more...iWorksheets :3Study Guides :1**Exponents, Factors and Fractions**FreeIn a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :8Study Guides :1##### 1.1.3. Develop meaning for percents greater than 100 and less than 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**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##### 1.1.4. Understand and use ratios and proportions to represent quantitative relationships.

**Ratio**Ratios are used to make a comparison between two things. Read more...iWorksheets :9Study 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##### 1.1.5. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.

**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**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**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, Factors and Fractions**FreeIn a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :8Study Guides :1##### 1.1.6. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.

**Common Factors**Factors are two numbers multiplied together to get a product (an answer to a multiplication problem) Read more...iWorksheets :6Study Guides :1Vocabulary :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**Exponents, Factors and Fractions**FreeIn a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :8Study Guides :1##### 1.1.7. Develop meaning for integers and represent and compare quantities with them.

**Positive & Negative Integers**Positive integers are all the whole numbers greater than zero. Negative integers are all the opposites of these whole numbers, numbers that are less than zero. Zero is considered neither positive nor negative Read more...iWorksheets :4Study 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#### 1.2. Understand meanings of operations and how they relate to one another.

##### 1.2.1. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

**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 :8Study 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**Multiply Fractions**Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1**Subtracting Fractions**Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. First, make sure the denominators are the same, then subtract the numerators. 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**Adding Fractions**Fractions consist of two numbers. The top number is called the numerator.
The bottom number is called the denominator. To add two fractions with the same denominator: Add the numerators and place the sum over the common denominator. Read more...iWorksheets :3Study 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##### 1.2.2. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

**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**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##### 1.2.3. Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

**Algebra**Algebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :4Study Guides :1Vocabulary :1#### 1.3. Compute fluently and make reasonable estimates.

##### 1.3.1. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

**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 :8Study 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**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**Multiply Fractions**Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1**Subtracting Fractions**Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. First, make sure the denominators are the same, then subtract the numerators. 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**Adding Fractions**Fractions consist of two numbers. The top number is called the numerator.
The bottom number is called the denominator. To add two fractions with the same denominator: Add the numerators and place the sum over the common denominator. Read more...iWorksheets :3Study 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##### 1.3.2. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

**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 :8Study 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**Multiply Fractions**Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1**Subtracting Fractions**Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. First, make sure the denominators are the same, then subtract the numerators. 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**Adding Fractions**Fractions consist of two numbers. The top number is called the numerator.
The bottom number is called the denominator. To add two fractions with the same denominator: Add the numerators and place the sum over the common denominator. Read more...iWorksheets :3Study Guides :1**Order of Operations**FreeRules of Order of Operations: 1st: Compute all operations inside of parentheses. 2nd: Compute all work with exponents. 3rd: Compute all multiplication and division from left to right. 4th: Compute all addition and subtraction from left to right. Read more...iWorksheets :4Study 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##### 1.3.3. Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

**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##### 1.3.4. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

**Ratio**Ratios are used to make a comparison between two things. Read more...iWorksheets :9Study 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**Geometric Proportions**Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1### N.2. Algebra (NCTM)

#### 2.1. Understand patterns, relations, and functions.

##### 2.1.1. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

**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**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 :6Study Guides :1#### 2.2. Represent and analyze mathematical situations and structures using algebraic symbols.

##### 2.2.1. Develop an initial conceptual understanding of different uses of variables.

**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##### 2.2.2. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

**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 :6Study 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 :5Study Guides :1##### 2.2.3. Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

**Simple Algebra**Simple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study 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 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##### 2.2.4. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

**Algebra**Algebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :4Study Guides :1Vocabulary :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#### 2.3. Use mathematical models to represent and understand quantitative relationships.

##### 2.3.1. Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

**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**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 :5Study Guides :1#### 2.4. Analyze change in various contexts.

##### 2.4.1. Use graphs to analyze the nature of changes in quantities in linear relationships.

**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 :5Study Guides :1### N.3. Geometry (NCTM)

#### 3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

##### 3.1.1. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

**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**Perimeter**A polygon is any 2-dimensional shape formed with straight lines. The perimeter of a polygon is the sum of all its length. Read more...iWorksheets :6Study Guides :1**Polygon Characteristics**A polygon is a plane figure with at least three straight sides and angles, and typically five or more. Read more...iWorksheets :8Study Guides :1Vocabulary :1**Area**Area is the number of square units needed to cover a flat surface. Read more...iWorksheets :3Study Guides :1**Plane Figures: Lines and Angles**Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Adjacent angles are two angles that have a common vertex and a common side but do not overlap. Read more...iWorksheets :3Study Guides :1**Plane Figures: Closed Figure Relationships**Plane figures in regards to closed figure relationships refer to the coordinate plane and congruent figures, circles, circle graphs, transformations and symmetry. Congruent figures have the same size and shape. Transformations are made up of translations, rotations and reflections. A translation of a figure keeps the size and shape of a figure, but moves it to a different location. A rotation turns a figure about a point on the figure. A reflection of a figure produces a mirror image of the figure when it is reflected in a given line. Read more...iWorksheets :3Study Guides :1**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1**Finding Volume**Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1##### 3.1.2. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

**Geometric Proportions**Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1##### 3.1.3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

**Congruent Shapes**Figures are congruent if they are identical in every way except for their
position. Read more...iWorksheets :3Study Guides :1**Geometric Proportions**Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1**Plane Figures: Lines and Angles**Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Adjacent angles are two angles that have a common vertex and a common side but do not overlap. Read more...iWorksheets :3Study Guides :1**Plane Figures: Closed Figure Relationships**Plane figures in regards to closed figure relationships refer to the coordinate plane and congruent figures, circles, circle graphs, transformations and symmetry. Congruent figures have the same size and shape. Transformations are made up of translations, rotations and reflections. A translation of a figure keeps the size and shape of a figure, but moves it to a different location. A rotation turns a figure about a point on the figure. A reflection of a figure produces a mirror image of the figure when it is reflected in a given line. Read more...iWorksheets :3Study Guides :1**The Pythagorean Theorem**Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length
of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :8Study Guides :2#### 3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

##### 3.2.1. Use coordinate geometry to represent and examine the properties of geometric shapes.

**Plot Points**You use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :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##### 3.2.2. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.

**Plot Points**You use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :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#### 3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.

##### 3.4.4. Use geometric models to represent and explain numerical and algebraic relationships.

**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**Volume**Volume measures the amount a solid figure can hold. 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**Area**An area is the amount of surface a shape covers. <br>An area is measured in inches, feet, meters or centimeters. Read more...iWorksheets :3Study Guides :1**Perimeter**A polygon is any 2-dimensional shape formed with straight lines. The perimeter of a polygon is the sum of all its length. Read more...iWorksheets :6Study Guides :1**Volume and Capacity**What is volume? Volume is the 3-dimensional size of an object, such as a box. What is capacity? Capacity is the amount a 3-dimensional object can hold or carry. It can also be thought of the measure of volume of a 3-dimensional object. Read more...iWorksheets :5Study Guides :1**Area**Area is the number of square units needed to cover a flat surface. 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**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**Measurement, Perimeter, and Circumference**There are two systems used to measure objects, the U.S. Customary system and the metric system. The U.S. Customary system measures length in inches, feet, yards and miles. The metric system is a base ten system and measures length in kilometers, meters, and millimeters. 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. To get the perimeter of any figure, simply add up the measures of the sides of the figure. Read more...iWorksheets :3Study Guides :1**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1**Finding Volume**Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1### N.4. Measurement (NCTM)

#### 4.1. Understand measurable attributes of objects and the units, systems, and processes of measurement.

##### 4.1.1. Understand both metric and customary systems of measurement.

**Measurement**Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. Read more...iWorksheets :8Study Guides :1Vocabulary :2##### 4.1.2. Understand relationships among units and convert from one unit to another within the same system.

**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##### 4.1.3. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

**Measurement**Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. Read more...iWorksheets :8Study Guides :1Vocabulary :2**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**Angles**A right angle is an angle that measures 90°. A straight angle is an angle that measures 180°. An obtuse angle is an angle that measures more than 90°. An acute angle is an angle that measures less than 90°. Read more...iWorksheets :10Study Guides :1**Plane Figures: Lines and Angles**Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Adjacent angles are two angles that have a common vertex and a common side but do not overlap. Read more...iWorksheets :3Study Guides :1#### 4.2. Apply appropriate techniques, tools, and formulas to determine measurements.

##### 4.2.2. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

**Volume**Volume measures the amount a solid figure can hold. 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**Area**An area is the amount of surface a shape covers. <br>An area is measured in inches, feet, meters or centimeters. Read more...iWorksheets :3Study Guides :1**Perimeter**A polygon is any 2-dimensional shape formed with straight lines. The perimeter of a polygon is the sum of all its length. Read more...iWorksheets :6Study Guides :1**Measurement**Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. Read more...iWorksheets :8Study Guides :1Vocabulary :2**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**Volume and Capacity**What is volume? Volume is the 3-dimensional size of an object, such as a box. What is capacity? Capacity is the amount a 3-dimensional object can hold or carry. It can also be thought of the measure of volume of a 3-dimensional object. Read more...iWorksheets :5Study Guides :1**Area**Area is the number of square units needed to cover a flat surface. 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**Angles**A right angle is an angle that measures 90°. A straight angle is an angle that measures 180°. An obtuse angle is an angle that measures more than 90°. An acute angle is an angle that measures less than 90°. Read more...iWorksheets :10Study Guides :1**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**Plane Figures: Lines and Angles**Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Adjacent angles are two angles that have a common vertex and a common side but do not overlap. Read more...iWorksheets :3Study Guides :1**Measurement, Perimeter, and Circumference**There are two systems used to measure objects, the U.S. Customary system and the metric system. The U.S. Customary system measures length in inches, feet, yards and miles. The metric system is a base ten system and measures length in kilometers, meters, and millimeters. 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. To get the perimeter of any figure, simply add up the measures of the sides of the figure. Read more...iWorksheets :3Study Guides :1**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1**Finding Volume**Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1##### 4.2.3. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

**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**Area**An area is the amount of surface a shape covers. <br>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**Area is the number of square units needed to cover a flat surface. Read more...iWorksheets :3Study Guides :1**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**Measurement, Perimeter, and Circumference**There are two systems used to measure objects, the U.S. Customary system and the metric system. The U.S. Customary system measures length in inches, feet, yards and miles. The metric system is a base ten system and measures length in kilometers, meters, and millimeters. 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. To get the perimeter of any figure, simply add up the measures of the sides of the figure. Read more...iWorksheets :3Study Guides :1**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1##### 4.2.4. Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

**Volume**Volume measures the amount a solid figure can hold. Read more...iWorksheets :3Study Guides :1**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1**Finding Volume**Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1##### 4.2.5. Solve problems involving scale factors, using ratio and proportion.

**Geometric Proportions**Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1##### 4.2.6. Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

**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### N.5. Data Analysis and Probability (NCTM)

#### 5.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

##### 5.1.1. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

**Data Analysis**Collecting Data. Data = information. You can collect data from other people using polls and surveys. Recording Data. You can record the numerical data you collected on a chart or graph: bar graphs, pictographs, line graphs, pie charts, column charts. Read more...iWorksheets :6Study Guides :1##### 5.1.2. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

**Graphs**A graph is a diagram that shows information in an organized way. Read more...iWorksheets :6Study Guides :1**Analyzing, Graphing and Displaying Data**There are many types of graphs such as, bar graphs, histograms and line graphs. A bar graph compares data in categories and uses bars, either vertical or horizontal. A histogram is similar to a bar graph, but with histograms the bars touch each other where with bar graphs the bars do not touch each other. A line graph is useful for graphing how data changes over time. With a line graph, data is plotted as points and lines are drawn to connect the points to show how the data changes. Read more...iWorksheets :3Study Guides :1#### 5.2. Select and use appropriate statistical methods to analyze data.

##### 5.2.1. Find, use, and interpret measures of center and spread, including mean and interquartile range.

**Statistics**A statistic is a collection of numbers related to a specific topic. Read more...iWorksheets :6Study Guides :1**Statistics**The statistical mode is the number that occurs most frequently in a set of
numbers. Read more...iWorksheets :3Study Guides :1**Data Analysis**Collecting Data. Data = information. You can collect data from other people using polls and surveys. Recording Data. You can record the numerical data you collected on a chart or graph: bar graphs, pictographs, line graphs, pie charts, column charts. Read more...iWorksheets :6Study Guides :1**Organizing Data**The data can be organized into groups, and evaluated. Mean, mode, median and range are different ways to evaluate data. The mean is the average of the data. The mode refers to the number that occurs the most often in the data. The median is the middle number when the data is arranged in order from lowest to highest. The range is the difference in numbers when the lowest number is subtracted from the highest number. Data can be organized into a table, such as a frequency table. Read more...iWorksheets :3Study Guides :1##### 5.2.2. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

**Tables**Tables refer to the different types of diagram used to display data. <br>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**Graphs**A graph is a diagram that shows information in an organized way. Read more...iWorksheets :6Study Guides :1**Graphs and Tables**Using tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1**Analyzing, Graphing and Displaying Data**There are many types of graphs such as, bar graphs, histograms and line graphs. A bar graph compares data in categories and uses bars, either vertical or horizontal. A histogram is similar to a bar graph, but with histograms the bars touch each other where with bar graphs the bars do not touch each other. A line graph is useful for graphing how data changes over time. With a line graph, data is plotted as points and lines are drawn to connect the points to show how the data changes. Read more...iWorksheets :3Study Guides :1#### 5.3. Develop and evaluate inferences and predictions that are based on data.

##### 5.3.2. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

**Analyzing, Graphing and Displaying Data**There are many types of graphs such as, bar graphs, histograms and line graphs. A bar graph compares data in categories and uses bars, either vertical or horizontal. A histogram is similar to a bar graph, but with histograms the bars touch each other where with bar graphs the bars do not touch each other. A line graph is useful for graphing how data changes over time. With a line graph, data is plotted as points and lines are drawn to connect the points to show how the data changes. Read more...iWorksheets :3Study Guides :1#### 5.4. Understand and apply basic concepts of probability

##### 5.4.2. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

**Introduction to Probability**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. Probability word problems worksheets. Read more...iWorksheets :4Study Guides :1##### 5.4.3. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.

**Using Probability**Probability is the possibility that a certain event will occur. Probability is the chance of an event occurring divided by the total number of possible outcomes. Probability is based on whether events are dependent or independent of each other. An independent event refers to the outcome of one event not affecting the outcome of another event. A dependent event is when the outcome of one event does affect the outcome of the other event. Probability word problems. Read more...iWorksheets :3Study Guides :1### N.11. Grade 6 Curriculum Focal Points (NCTM)

#### 11.1. Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimals

##### 11.1.1. Students use the meanings of fractions, multiplication and division, and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and explain why they work. They use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain the procedures for multiplying and dividing decimals. Students use common procedures to multiply and divide fractions and decimals efficiently and accurately. They multiply and divide fractions and decimals to solve problems, including multi-step problems and problems involving measurement.

**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**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#### 11.2. Number and Operations: Connecting ratio and rate to multiplication and division

##### 11.2.1. Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.

**Ratio**Ratios are used to make a comparison between two things. Read more...iWorksheets :9Study 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#### 11.3. Algebra: Writing, interpreting, and using mathematical expressions and equations

##### 11.3.1. Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.

**Algebra**Algebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :4Study Guides :1Vocabulary :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**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**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 :6Study Guides :1### N.12. Connections to the Grade 6 Focal Points (NCTM)

#### 12.1. Number and Operations: Students' work in dividing fractions shows them that they can express the result of dividing two whole numbers as a fraction (viewed as parts of a whole). Students then extend their work in grade 5 with division of whole numbers to give mixed number and decimal solutions to division problems with whole numbers. They recognize that ratio tables not only derive from rows in the multiplication table but also connect with equivalent fractions. Students distinguish multiplicative comparisons from additive comparisons.

**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**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**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#### 12.2. Algebra: Students use the commutative, associative, and distributive properties to show that two expressions are equivalent. They also illustrate properties of operations by showing that two expressions are equivalent in a given context (e.g., determining the area in two different ways for a rectangle whose dimensions are x + 3 by 5). Sequences, including those that arise in the context of finding possible rules for patterns of figures or stacks of objects, provide opportunities for students to develop formulas.

**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**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**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 :6Study Guides :1#### 12.3. Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.

**Volume**Volume measures the amount a solid figure can hold. 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**Area**An area is the amount of surface a shape covers. <br>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**Area is the number of square units needed to cover a flat surface. 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**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**Exploring Area and Surface Area**Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the
base and h is the height. Read more...iWorksheets :4Study Guides :1**Finding Volume**Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1 Standards

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