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 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 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 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 TX.STAAR.7. STAAR Grade 7 Mathematics Assessment
Reporting Category 1: Numbers, Operations, and Quantitative Reasoning - The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.
(7.1) Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms. The student is expected to:
7.1 (A) Compare and order integers and positive rational numbers. Supporting Standard (STAAR)
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 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 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 7.1 (B) Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator. Readiness Standard (STAAR)
Simplify FractionsSimplifying fractions is the process of reducing fractions and putting them into their lowest terms. 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 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 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 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 7.1 (C) Represent squares and square roots using geometric models. Supporting Standard (STAAR)
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 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 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 (7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to:
7.2 (A) Represent multiplication and division situations involving fractions and decimals with models, including concrete objects, pictures, words, and numbers. Supporting Standard (STAAR)
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 Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. 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 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 7.2 (B) Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Readiness Standard (STAAR)
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 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 Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. 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 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 7.2 (C) Use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms. Supporting Standard (STAAR)
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 7.2 (D) Use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio. Supporting Standard (STAAR)
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 7.2 (E) Simplify numerical expressions involving order of operations and exponents. Supporting Standard (STAAR)
Evaluate ExponentsEvaluating 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 ExponentsThe 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 ExponentsThe 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 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 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 Reporting Category 2: Patterns, Relationships, and Algebraic Reasoning - The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning.
(7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to:
7.3 (A) Estimate and find solutions to application problems involving percent. Readiness Standard (STAAR)
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 7.3 (B) Estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Readiness Standard (STAAR)
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 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 (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to:
7.4 (A) Generate formulas involving unit conversions within the same system (customary and metric), perimeter, area, circumference, volume, and scaling. Supporting Standard (STAAR)
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 MeasurementFreeThere 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 FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1 Area of Coordinate 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 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 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 (7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to:
7.5 (A) Use concrete and pictorial models to solve equations and use symbols to record the actions. Supporting Standard (STAAR)
FormulasThe 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 AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1 Algebraic EquationsFreeWhat 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 7.5 (B) Formulate problem situations when given a simple equation and formulate an equation when given a problem situation. Readiness Standard (STAAR)
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 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 Reporting Category 3: Geometry and Spatial Reasoning - The student will demonstrate an understanding of geometry and spatial reasoning.
(7.6) Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. The student is expected to:
7.6 (A) Use angle measurements to classify pairs of angles as complementary or supplementary. Supporting Standard (STAAR)
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 7.6 (B) Use properties to classify triangles and quadrilaterals. Supporting Standard (STAAR)
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 7.6 (C) Use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders. Supporting Standard (STAAR)
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 7.6 (D) Use critical attributes to define similarity. Readiness Standard (STAAR)
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 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 (7.7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to:
7.7 (A) Locate and name points on a coordinate plane using ordered pairs of integers. Supporting Standard (STAAR)
CoordinatesFreeThe 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 PointsIn 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 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 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 Reporting Category 4: Measurement - The student will demonstrate an understanding of the concepts and uses of measurement.
(7.9) Measurement. The student solves application problems involving estimation and measurement. The student is expected to:
7.9 (B) Connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders. Supporting Standard (STAAR)
VolumeVolume measures the amount a solid figure can hold. Read more...iWorksheets :3Study 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 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 Reporting Category 5: Probability and Statistics - The student will demonstrate an understanding of probability and statistics.
(7.10) Probability and statistics. The student recognizes that a physical or mathematical model (including geometric) can be used to describe the experimental and theoretical probability of real-life events. The student is expected to:
7.10 (B) Find the probability of independent events. Supporting Standard (STAAR)
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 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 (7.11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to:
7.11 (A) Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection. Supporting Standard (STAAR)
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 (7.12) Probability and statistics. The student uses measures of central tendency and variability to describe a set of data. The student is expected to:
7.12 (A) Describe a set of data using mean, median, mode, and range. Supporting Standard (STAAR)
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 Underlying Processes and Mathematical Tools: These skills will not be listed under a separate recording category. Instead, they will be incorporated into at least 75% of the test questions in reporting categories 1-5 and will be identified along with content standards.
(7.13) Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
7.13 (A) Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. (STAAR)
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 7.13 (B) Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. (STAAR)
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 7.13 (C) Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. (STAAR)
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 7.13 (D) Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (STAAR)
EstimationEstimation is the process of rounding a number either up or down to the nearest place value requested. Estimation makes it easier to perform mathematical operations quickly. Read more...iWorksheets :6Study Guides :1 (7.14) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to:
7.14 (A) Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. (STAAR)
MultiplicationMultiplication is a mathematical operation in which numbers, called factors, are multiplied together to get a result, called a product. Multiplication can be used with numbers or decimals of any size. Read more...iWorksheets :3Study Guides :1 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 Fractions/DecimalsAny fraction can be changed into a decimal and any decimal can be changed into a fraction. Read more...iWorksheets :3Study Guides :1 Whole Numbers to TrillionsThe number system we use is based on a place value system. Although
there are only 10 different digits in this system, it is possible to order them in so many variations that the numbers represented are infinite. Read more...iWorksheets :4Study Guides :1 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 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 Evaluate ExponentsEvaluating 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 ExponentsThe 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 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 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 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 EstimationEstimation is the process of rounding a number either up or down to the nearest place value requested. Estimation makes it easier to perform mathematical operations quickly. Read more...iWorksheets :6Study Guides :1 ExponentsThe 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 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 Number PatternsA number pattern is a group of numbers that are related to one another in some sort of pattern. Finding a pattern is a simpler way to solve a problem. Read more...iWorksheets :3Study Guides :1 DivisionDivision is a mathematical operation is which a number, called a dividend
is divided by another number, called a divisor to get a result, called a
quotient. Read more...iWorksheets :3Study Guides :1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 (7.15) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:
7.15 (A) Make conjectures from patterns or sets of examples and nonexamples. (STAAR)
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 Standards
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