**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**Algebraic Inequalities**FreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets: 3Study Guides: 1**Introduction to Functions**A function is a rule that is performed on a number, called an input, to produce a result called an output. The rule consists of one or more mathematical operations that are performed on the input. An example of a function is y = 2x + 3, where x is the input and y is the output. The operations of multiplication and addition are performed on the input, x, to produce the output, y. By substituting a number for x, an output can be determined. Read more...iWorksheets: 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**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: 10Study Guides: 2### MN.7.1. Number & Operation

#### 7.1.1. Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.

##### 7.1.1.1. Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

**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**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**Rational and Irrational Numbers**A 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**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**Rational numbers and operations**A 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**Perimeter and area**What 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##### 7.1.1.3. Locate positive and negative rational numbers on a number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

**Coordinates**FreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study 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 :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**Using graphs to analyze data**There 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 :3Study Guides :1##### 7.1.1.4. Compare positive and negative rational numbers expressed in various forms using the symbols <, >, =, less than or equal to, greater than or equal to

**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 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**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##### 7.1.1.5. Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.

**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**Simplify Fractions**Simplifying fractions is the process of reducing fractions and putting them into their lowest terms. 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**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**Rational and Irrational Numbers**A 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**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**Fraction Operations**Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1**Introduction to Percent**What Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1**Numbers and percents**Numbers 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#### 7.1.2. Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

##### 7.1.2.1. Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

**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**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**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 :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**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**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**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**Integer operations**Integer 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 operations**A 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##### 7.1.2.4. Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.

**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**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**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**Applications of percent**Percent 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##### 7.1.2.5. Use proportional reasoning to solve problems involving ratios in various contexts.

**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**Ratios, proportions and percents**Numerical 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 scale**Similarity 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 percents**Numbers 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#### 7.2.1. Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

##### 7.2.1.1. Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy = k or y = k/x).

**Linear relationships**Linear 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**Functions**FreeA function is a rule that is performed on a number, called an input, to produce a result called an output. The rule consists of one or more mathematical operations that are performed on the input. An example of a function is y = 2x + 3, where x is the input and y is the output. The operations of multiplication and addition are performed on the input, x, to produce the output, y. By substituting a number for x, an output can be determined. Read more...iWorksheets :5Study Guides :1##### 7.2.1.2. Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

**Linear relationships**Linear 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### MN.7.2. Algebra

#### 7.2.1 Recognize Proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

##### 7.2.2.1. Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

**Linear relationships**Linear 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##### 7.2.2.2. Solve multi-step problems involving proportional relationships in numerous contexts.

**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**Ratios, proportions and percents**Numerical 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 scale**Similarity 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##### 7.2.2.3. Use knowledge of proportions to assess the reasonableness of solutions.

**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**Ratios, proportions and percents**Numerical 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 scale**Similarity 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 percents**Numbers 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##### 7.2.2.4. Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.

**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 :4Study Guides :1**Solving linear equations**When graphed, a linear equation is a straight line. Although the standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept, linear equations often have both of the variables on the same side of the equal sign. Linear equations can be solved for one variable when the other variable is given. Read more...iWorksheets :5Study Guides :1#### 7.2.3. Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

##### 7.2.3.1. Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.

**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##### 7.2.3.2. Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.

**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#### 7.2.4. Represent real world And mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.

##### 7.2.4.1. Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.

**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 :4Study 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 :6Study Guides :1**Equations and inequalities**An 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 operations**Integer 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**Solving linear equations**When graphed, a linear equation is a straight line. Although the standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept, linear equations often have both of the variables on the same side of the equal sign. Linear equations can be solved for one variable when the other variable is given. Read more...iWorksheets :5Study Guides :1##### 7.2.4.2. Solve equations resulting from proportional relationships in various contexts.

**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**Ratios, proportions and percents**Numerical 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 scale**Similarity 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### MN.7.3. Geometry & Measurement

#### 7.3.1. Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real world and mathematical problems involving circles and related geometric figures.

##### 7.3.1.1. Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.

**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 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**Perimeter and area**What 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##### 7.3.1.2. Calculate the volume and surface area of cylinders and justify the formulas used.

**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**Three dimensional geometry/Measurement**Three-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#### 7.3.2. Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

##### 7.3.2.2. Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.

**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**Ratios, proportions and percents**Numerical 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 scale**Similarity 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##### 7.3.2.3. Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.

**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**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**Similarity and scale**Similarity 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### MN.7.4. Data Analysis & Probability

#### 7.4.1. Use mean, median and range to draw conclusions about data and make predictions.

##### 7.4.1.1. Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.

**Statistics**A statistic is a collection of numbers related to a specific topic. 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**Using graphs to analyze data**There 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 :3Study Guides :1**Collecting and describing data**Collecting 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#### 7.4.2. Display and interpret data in a variety of ways, including circle graphs and histograms.

##### 7.4.2.1. Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

**Graphs**FreeA graph is a diagram that shows information in an organized way. Read more...iWorksheets :10Study 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**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**Using graphs to analyze data**There 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 :3Study Guides :1#### 7.4.3. Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

##### 7.4.3.2. Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.

**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**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**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**Ratios, proportions and percents**Numerical 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**Experimental Probability**FreeExperimental 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 Standards

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