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 Displaying dataDisplaying data refers to the many ways that data can be displayed whether it is on a bar graph, line graph, circle graph, pictograph, line plot, scatter plot or another way. Certain data is better displayed with different graphs as opposed to other graphs. E.g. if data representing the cost of a movie over the past 5 years were to be displayed, a line graph would be best. A circle graph would not be appropriate to use because a circle graph represents data that can add up to one or 100%. 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 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 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 Solving 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. Algebraic inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to, ≥; less than, <; and less than or equal to, ≤. When multiplying or dividing by a negative number occurs, the inequality sign is reversed from the original inequality sign in order for the inequality to be correct. Read more...iWorksheets: 3Study 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 Plane figuresPlane figures refer to points, lines, angles, and planes in the coordinate plane. Lines can be parallel or perpendicular. Angles can be categorized as acute, obtuse or right. Angles can also be complementary or supplementary depending on how many degrees they add up to. Plane figures can also refer to shapes in the coordinate plane. Triangles, quadrilaterals and other polygons can be shown in the coordinate plane. Read more...iWorksheets: 4Study 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 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 Real numbersReal numbers are the set of rational and irrational numbers. The set of rational numbers includes integers, whole numbers, and natural 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. Read more...iWorksheets: 4Study Guides: 1 SequencesA sequence is an ordered list of numbers. Sequences are the result of a pattern or rule. A pattern or rule can be every other number or some formula such as y = 2x + 3. When a pattern or rule is given, a sequence can be found. When a sequence is given, the pattern or rule can be found. Read more...iWorksheets: 5Study Guides: 1 PA.CC.MP. Standards for Mathematical Practice
CC.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 CC.MP.5. 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 PA.CC.2.1.8. Numbers and Operations
CC.2.1.8.E. The Number System
CC.2.1.8.E.1. Distinguish between rational and irrational numbers using their properties.
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 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 CC.2.1.8.E.4. Estimate irrational numbers by comparing them to rational numbers.
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 PA.CC.2.2.8. Algebraic Concepts
CC.2.2.8.B. Expressions and Equations
CC.2.2.8.B.1. Apply concepts of radicals and integer exponents to generate equivalent expressions.
Polynomials and ExponentsFreeA polynomial is an expression which is in the form of ax<sup>n</sup>, where a is any real number and n is a whole number. If a polynomial has only one term, it is called a monomial. If it has two terms, it is a binomial and if it has three terms, it is a trinomial. The standard form of a polynomial is when the powers of the variables are decreasing from left to right. Read more...iWorksheets :6Study Guides :1 CC.2.2.8.B.2. Understand the connections between proportional relationships, lines, and linear equations.
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 :7Study Guides :1 Linear equationsLinear equations are equations that have two variables and when graphed are a straight line. Linear equation can be graphed based on their slope and y-intercept. The standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept. Slope can be found with the formula m = (y2 - y1)/(x2 - x1), which represents the change in y over the change in x. Read more...iWorksheets :6Study Guides :1 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 FunctionsFreeA 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 CC.2.2.8.C. Functions
CC.2.2.8.C.1. Define, evaluate, and compare functions.
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 :7Study Guides :1 FunctionsFreeA 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 CC.2.2.8.C.2. Use concepts of functions to model relationships between quantities.
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 Solving linear equationsWhen 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 PA.CC.2.3.8. Geometry
CC.2.3.8.A. Geometry
CC.2.3.8.A.1. Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
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 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 CC.2.3.8.A.2. Understand and apply congruence, similarity, and geometric transformations using various tools.
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 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 :3Study 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 Patterns in geometryPatterns in geometry refer to shapes and their measures. Shapes can be congruent to one another. Shapes can also be manipulated to form similar shapes. The types of transformations are reflection, rotation, dilation and translation. With a reflection, a figure is reflected, or flipped, in a line so that the new figure is a mirror image on the other side of the line. A rotation rotates, or turns, a shape to make a new figure. A dilation shrinks or enlarges a figure. A translation shifts a figure to a new position. Read more...iWorksheets :3Study 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 CC.2.3.8.A.3. Understand and apply the Pythagorean Theorem to solve problems.
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 Standards
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