Introduction to FunctionsA 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: 8Study Guides: 1
Nonlinear Functions and Set TheoryA 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
Plane Figures: Closed Figure RelationshipsPlane 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
Plane Figures: Lines and AnglesPlane 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: 5Study Guides: 1
The Pythagorean TheoremPythagorean 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: 10Study Guides: 2
Analyzing, Graphing and Displaying DataThere 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: 6Study Guides: 1
Rational and Irrational NumbersA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. Read more...iWorksheets: 3Study Guides: 1

### MD.MP. Mathematical Practices

#### MP.1. Make sense of problems and persevere in solving them.

Mathematical processesMathematical processes refer to the skills and strategies needed in order to solve mathematical problems. If one strategy does not help to find the solution to a problem, using another strategy may help to solve it. Problem solving skills refer to the math techniques that must be used to solve a problem. If a problem were to determine the perimeter of a square, a needed skill would be the knowledge of what perimeter means and the ability to add the numbers. Read more...iWorksheets :3Study Guides :1

#### MP.2. Reason abstractly and quantitatively.

Mathematical processesMathematical processes refer to the skills and strategies needed in order to solve mathematical problems. If one strategy does not help to find the solution to a problem, using another strategy may help to solve it. Problem solving skills refer to the math techniques that must be used to solve a problem. If a problem were to determine the perimeter of a square, a needed skill would be the knowledge of what perimeter means and the ability to add the numbers. Read more...iWorksheets :3Study Guides :1

### MD.MA.7.RP. Ratios and Proportional Relationships (RP)

#### Analyze proportional relationships and use them to solve real-world and mathematical problems.

##### 7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like and or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour.
###### 7.RP.1.2. Ability to recognize the difference(s) between a unit rate and a ratio (see 7.G.1).
Numerical ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
##### 7.RP.2. Recognize and represent proportional relationships between quantities.
###### 7.RP.2a.1. Ability to recognize in a given proportional situation that the two “between ratios” and the two “within ratios” are the same.
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioA 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 ProportionsA 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 ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures 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 :7Study Guides :1
Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. 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. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1
###### 7.RP.2a.3. Ability to recognize that two equal ratios represent a proportion.
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioA 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 ProportionsA 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 ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures 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 :7Study Guides :1
Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. 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. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1
###### 7.RP.2b.1. Ability to express unit rates using a variety of representations, given a contextual situation.
Numerical ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
###### 7.RP.2c.1. Ability to recognize that multiplicative relationships are proportional.
Linear relationshipsLinear relationships refer to two quantities that are related with a linear equation. Since a linear equation is a line, a linear relationship refers to two quantities on a line and their relationship to one another. This relationship can be direct or inverse. If y varies directly as x, it means if y is doubled, then x is doubled. The formula for a direct variation is y = kx, where k is the constant of variation. Read more...iWorksheets :3Study Guides :1
###### 7.RP.2d.1. Ability to identify that a proportional relationship intersects (0,0).
Linear relationshipsLinear relationships refer to two quantities that are related with a linear equation. Since a linear equation is a line, a linear relationship refers to two quantities on a line and their relationship to one another. This relationship can be direct or inverse. If y varies directly as x, it means if y is doubled, then x is doubled. The formula for a direct variation is y = kx, where k is the constant of variation. Read more...iWorksheets :3Study Guides :1
##### 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
###### 7.RP.3.1. Ability to build on prior experience with equivalent fractions to solve multi-step problems with ratio and percent (see 6.RP.3c).
Percent, Rate, BaseA 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 PercentWhat 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 PercentsApplying 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
Applications of percentPercent increase or decrease can be found by using the formula: percent of change = actual change/original amount. The change is either an increase, if the amounts went up or a decrease if the amounts went down. If a number changes from 33 to 89, the percent of increase would be: Percent of increase = (89 -33) ÷ 33 = 56 ÷ 33 ≈ 1.6969 ≈ 170% Read more...iWorksheets :4Study Guides :1
###### 7.RP.3.2. Ability to relate “between” ratios and “within” ratios to the cross-product and factor of change algorithms.
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioA 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 ProportionsA 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 ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures 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 :7Study Guides :1
Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. 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. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1

### MD.MA.7.NS. The Number System (NS)

#### Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

##### 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number line diagram.
###### 7.NS.1b.1. Ability to build on prior experience with absolute value (see 6.NS.7).
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
Mixed NumbersA mixed number has both a whole number and a fraction. Read more...iWorksheets :4Study Guides :1
Fraction OperationsFraction 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
Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1
###### 7.NS.1b.2. Knowledge of absolute value to add and subtract rational numbers using a horizontal or a vertical number line.
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
Mixed NumbersA mixed number has both a whole number and a fraction. Read more...iWorksheets :4Study Guides :1
Fraction OperationsFraction 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
Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1
###### 7.NS.1c.1. See the skills and knowledge that are stated in the Standard.
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
Mixed NumbersA mixed number has both a whole number and a fraction. Read more...iWorksheets :4Study Guides :1
Fraction OperationsFraction 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
Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1
###### 7.NS.1d.1. Ability to identify and apply the following properties: Commutative Property of Addition; Associative Property of Addition; Identity Property of Addition.
Commutative/Associative PropertiesThe 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
##### 7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational number.
###### 7.NS.2a.1. Ability to identify and apply the following properties: Multiplicative Inverse; Commutative Property of Multiplication; Associative Property of Multiplication; Identity Property of Multiplication; Recognize that rules for multiplying signed numbers remain the same for all rational numbers.
Commutative/Associative PropertiesThe 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
###### 7.NS.2b.2. Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to extend to multiplication and division.
Using IntegersIntegers 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
Integer operationsInteger operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. Equations with integers are solved using inverse operations. Addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. Read more...iWorksheets :4Study Guides :1
###### 7.NS.2b.3. Ability to use patterns and concrete models to devise a general rule for dividing integers: −(p/q) = -p/q = p/-q.
Using IntegersIntegers 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
Integer operationsInteger operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. Equations with integers are solved using inverse operations. Addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. Read more...iWorksheets :4Study Guides :1
###### 7.NS.2c.1. Ability to identify and apply the following properties: Distributive Property; Associative Properties; Commutative Properties; Identity Properties.
Distributive PropertyThe 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 PropertiesThe 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 IntegersIntegers 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
##### 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
###### 7.NS.3.2. Ability to apply knowledge of Order of Operations.
Order of OperationsA numerical expression is a phrase which represents a number. Read more...iWorksheets :8Study Guides :1
Using IntegersIntegers 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

### MD.MA.7.EE. Expressions and Equations (EE)

#### Use properties of operations to generate equivalent expressions.

##### 7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a+0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
###### 7.EE.2.1. Ability to utilize Properties of Operations in order to rewrite expressions in different forms.
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra 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 :4Study Guides :1
Equations and inequalitiesAn equation is mathematical statement that shows that two expressions are equal to each other. The expressions used in an equation can contain variables or numbers. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Inequalities are also solved by using inverse operations. Read more...iWorksheets :3Study Guides :1
###### 7.EE.2.2. Ability to develop understanding of equivalent forms of numbers, their various uses and relationships, and how they apply to a problem.
Algebraic EquationsWhat 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

#### Solve real-life mathematical problems using numerical and algebraic expressions and equations.

##### 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically; apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making \$25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or \$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
###### 7.EE.3.1. See the skills and knowledge that are stated in the Standard.
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets :9Study Guides :1
Mixed NumbersA mixed number has both a whole number and a fraction. Read more...iWorksheets :4Study Guides :1
Multiply / Divide FractionsFreeTo 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 :6Study Guides :1
Simplify FractionsSimplifying fractions is the process of reducing fractions and putting them into their lowest terms. Read more...iWorksheets :3Study Guides :1
Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets :3Study Guides :1
PercentageThe 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
Multiple Representation of Rational NumbersWhat 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
Decimal OperationsDecimal 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
Exponents, Factors and FractionsFreeIn 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
Fraction OperationsFraction 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 PercentWhat 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
Integer operationsInteger operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. Equations with integers are solved using inverse operations. Addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. Read more...iWorksheets :4Study Guides :1
Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1
Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. 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. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1
##### 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
###### 7.EE.4b.1. Ability to develop correct usage of all four inequality symbols and related terminology (at least, no more than, etc.).
Fractions/DecimalsAny fraction can be changed into a decimal and any decimal can be changed into a fraction. Read more...iWorksheets :3Study Guides :1
Ordering FractionsThe 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
###### 7.EE.4b.2. Ability to solve inequalities to determine the solution set.
Equations and InequalitiesAlgebraic 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 :6Study Guides :1
Algebraic InequalitiesFreeAlgebraic 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
Equations and inequalitiesAn equation is mathematical statement that shows that two expressions are equal to each other. The expressions used in an equation can contain variables or numbers. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Inequalities are also solved by using inverse operations. Read more...iWorksheets :3Study Guides :1
Integer operationsInteger operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. Equations with integers are solved using inverse operations. Addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. Read more...iWorksheets :4Study Guides :1
Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1

### MD.MA.7.G. Geometry (G)

#### Draw, construct, and describe geometrical figures and describe the relationships between them.

##### 7.G.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
###### 7.G.1.1. Ability to describe and identify ratios and proportions (see 7.RP.1 and 7.RP.2).
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioA 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 ProportionsA 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 ProportionsNumerical 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
Ratios, proportions and percentsNumerical proportions compare two numbers. A proportion is usually in the form of a:b or a/b. There are 4 parts to a proportion and it can be solved when 3 of the 4 parts are known. Proportions can be solved using the Cross Product Property, which states that the cross products of a proportion are equal. Read more...iWorksheets :4Study Guides :1
Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures 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 :7Study Guides :1
Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. 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. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1
###### 7.G.1.2. Ability to reproduce scale drawing at a different scale.
Geometric ProportionsGeometric 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
Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures 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 :7Study Guides :1

#### Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

##### 7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
###### 7.G.4.1. Ability to identify and apply the vocabulary for a circle – radius, diameter, chord, circumference, center, pi (π)≈3.14159 and 22/7.
Diameter of CircleThe 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
AreaAn 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
Area and Circumference of CirclesFreeThe 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 CircumferenceThere 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 AreaArea 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
Perimeter and areaWhat Is Perimeter and Area? 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 find the perimeter of any figure, simply add up the measures of the sides of the figure. 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 parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1
###### 7.G.4.2. Ability to use a near-parallelogram to discover the formula for area of a circle.
Diameter of CircleThe 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
AreaAn 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
Area and Circumference of CirclesFreeThe 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 AreaArea 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
Perimeter and areaWhat Is Perimeter and Area? 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 find the perimeter of any figure, simply add up the measures of the sides of the figure. 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 parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1
##### 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (SC 7).
###### 7.G.5.1. Ability to explore the relationship between the angles of intersecting lines and figures.
Finding VolumeVolume 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
##### 7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
###### 7.G.6.1. See the skills and knowledge that are stated in the Standard.
VolumeVolume measures the amount a solid figure can hold. Read more...iWorksheets :3Study Guides :1
Diameter of CircleThe 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
AreaAn 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
Area of Triangles and QuadrilateralsThe area is the surface or space within an enclosed region. Area is expressed in square units. Read more...iWorksheets :7Study Guides :1Vocabulary :2
Area of Coordinate PolygonsCalculate 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 CirclesFreeThe 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 AreaArea 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 VolumeVolume 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
Perimeter and areaWhat Is Perimeter and Area? 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 find the perimeter of any figure, simply add up the measures of the sides of the figure. 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 parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1
Three dimensional geometry/MeasurementThree-dimensional geometry/measurement refers to three-dimensional (3D) shapes and the measurement of their shapes concerning volume and surface area. The figures of prisms, cylinders, pyramids, cones and spheres are all 3D figures. Volume measures the amount a solid figure can hold. Volume is measured in terms of units³ and can be measured in inches, feet, meters, centimeters, and millimeters. Read more...iWorksheets :11Study Guides :1

### MD.MA.7.SP. Statistics and Probability (SP)

#### Use random sampling to draw inferences about a population.

##### 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
###### 7.SP.1.1. Ability to describe and identify population, sample of a population, random sampling, validity, reliability, invalid, inferences.
Collecting and describing dataCollecting and describing data refers to the different ways to gather data and the different ways to arrange data whether it is in a table, graph, or pie chart. Data can be collected by either taking a sample of a population or by conducting a survey. Describing data looks at data after it has been organized and makes conclusions about the data. Read more...iWorksheets :3Study Guides :1
Experimental ProbabilityFreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1
##### 7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
###### 7.SP.2.1. See the skills and knowledge that are stated in the Standard.
Collecting and describing dataCollecting and describing data refers to the different ways to gather data and the different ways to arrange data whether it is in a table, graph, or pie chart. Data can be collected by either taking a sample of a population or by conducting a survey. Describing data looks at data after it has been organized and makes conclusions about the data. Read more...iWorksheets :3Study Guides :1
Experimental ProbabilityFreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1

#### Draw informal comparative inferences about two populations.

##### 7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, mean height of players on the basketball team is. 10 cm greater than mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
###### 7.SP.3.1. Ability to describe and identify deviation, standard deviation, absolute deviation, measures of central tendency, measures of variability.
StatisticsA statistic is a collection of numbers related to a specific topic. Read more...iWorksheets :6Study Guides :1
Organizing DataThe 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
Using graphs to analyze dataThere are different types of graphs and ways that data can be analyzed using the graphs. Graphs are based on the coordinate plane. Data are the points on the plane. If collecting data about the ages of people living on one street, the data is all the ages. The data can then be organized into groups, and evaluated. Mean, mode and median are different ways to evaluate data. Read more...iWorksheets :7Study Guides :1
Collecting and describing dataCollecting and describing data refers to the different ways to gather data and the different ways to arrange data whether it is in a table, graph, or pie chart. Data can be collected by either taking a sample of a population or by conducting a survey. Describing data looks at data after it has been organized and makes conclusions about the data. Read more...iWorksheets :3Study Guides :1

#### Investigate chance processes and develop, use, and evaluate probability models.

##### 7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
###### 7.SP.5.1. Ability to devise models where outcomes are equally likely versus not equally likely.
ProbabilityProbability 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
##### 7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times (SC 7).
###### 7.SP.6.1. See the skills and knowledge that are stated in the Standard.
Introduction to ProbabilityProbability 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
Experimental ProbabilityFreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1
##### 7.SP.7. Develop a probability model and use it to find probabilities of events; compare probabilities from a model to observed frequencies; and if the agreement is not good, explain possible sources of the discrepancy.
###### 7.SP.7a.1. See the skills and knowledge that are stated in the Standard.
Introduction to ProbabilityProbability 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
Theoretical probability and countingProbability word problems worksheets. Theoretical probability is the probability that a certain outcome will occur based on all the possible outcomes. Sometimes, the number of ways that an event can happen depends on the order. A permutation is an arrangement of objects in which order matters. A combination is a set of objects in which order does not matter. Probability is also based on whether events are dependent or independent of each other. Read more...iWorksheets :3Study Guides :1
###### 7.SP.7b.1. Ability to describe and identify possibility versus probability.
Introduction to ProbabilityProbability 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
Experimental ProbabilityFreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1
Theoretical probability and countingProbability word problems worksheets. Theoretical probability is the probability that a certain outcome will occur based on all the possible outcomes. Sometimes, the number of ways that an event can happen depends on the order. A permutation is an arrangement of objects in which order matters. A combination is a set of objects in which order does not matter. Probability is also based on whether events are dependent or independent of each other. Read more...iWorksheets :3Study Guides :1
##### 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
###### 7.SP.8a.1. Ability to compare simple events with compound events.
Using ProbabilityProbability 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
###### 7.SP.8b.1. See the skills and knowledge that are stated in the Standard.
Using ProbabilityProbability 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