8th Grade Math. Texas Assessments of Academic Readiness (STAAR) Texas Assessments of Academic Readiness (STAAR)

Texas Assessments of Academic Readiness (STAAR) for Eighth Grade Math

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

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

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

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

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

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

TX.STAAR.8. STAAR Grade 8 Mathematics Assessment

Reporting Category 1: Numbers, Operations, and Quantitative Reasoning - The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

(8.1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:

8.1 (A) Compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals. Readiness 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

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

8.1 (C) Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as p, O2). Supporting Standard (STAAR)

Measurement, Perimeter, and CircumferenceThere are two systems used to measure objects, the U.S. Customary system and the metric system. The U.S. Customary system measures length in inches, feet, yards and miles. The metric system is a base ten system and measures length in kilometers, meters, and millimeters. Perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. To get the perimeter of any figure, simply add up the measures of the sides of the figure. Read more...iWorksheets :3Study Guides :1

Exploring Area and Surface AreaArea is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1

Perimeter and areaWhat Is Perimeter and Area? Perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. To find the perimeter of any figure, simply add up the measures of the sides of the figure. Area is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1

8.1 (D) Express numbers in scientific notation, including negative exponents, in appropriate problem situations. Supporting Standard (STAAR)

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

(8.2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:

8.2 (B) Use appropriate operations to solve problems involving rational numbers in problem situations. 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

8.2 (D) Use multiplication by a given constant factor (including unit rate) to represent and solve problems involving proportional relationships including conversions between measurement systems. 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

Similarity and scaleSimilarity refers to similar figures and the ability to compare them using proportions. Similar figures have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :7Study Guides :1

Numbers and percentsNumbers and percents refer to the relationship between fractions, decimals, and percents. A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Fractions and decimals can easily be changed into percent. There are three cases of percent. Read more...iWorksheets :3Study Guides :1

Reporting Category 2: Patterns, Relationships, and Algebraic Reasoning - The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning.

(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:

8.3 (A) Compare and contrast proportional and non-proportional linear relationships. Supporting Standard (STAAR)

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

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

8.3 (B) Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Readiness Standard (STAAR)

(8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to:

8.5 (A) Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations. Readiness Standard (STAAR)

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

8.5 (B) Find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change). Supporting Standard (STAAR)

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

Reporting Category 3: Geometry and Spatial Reasoning - The student will demonstrate an understanding of geometry and spatial reasoning.

(8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:

8.6 (A) Generate similar figures using dilations including enlargements and reductions. Readiness Standard (STAAR)

(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:

8.7 (D) Locate and name points on a coordinate plane using ordered pairs of rational numbers. 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

Reporting Category 4: Measurement - The student will demonstrate an understanding of the concepts and uses of measurement.

(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:

8.8 (A) Find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models). Supporting Standard (STAAR)

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

(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to:

8.9 (A) Use the Pythagorean Theorem to solve real-life problems. Readiness Standard (STAAR)

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

8.9 (B) Use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements. Readiness Standard (STAAR)

(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to:

8.10 (A) Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally. Supporting Standard (STAAR)

Reporting Category 5: Probability and Statistics - The student will demonstrate an understanding of probability and statistics.

(8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:

8.11 (A) Find the probabilities of dependent and independent events. Readiness 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

(8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:

8.12 (B) Draw conclusions and make predictions by analyzing trends in scatterplots. Supporting Standard (STAAR)

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

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

8.12 (C) Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology. Supporting Standard (STAAR)

(8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:

8.13 (A) Evaluate methods of sampling to determine validity of an inference made from a set of data. Supporting Standard (STAAR)

Collecting and describing dataCollecting and describing data refers to the different ways to gather data and the different ways to arrange data whether it is in a table, graph, or pie chart. Data can be collected by either taking a sample of a population or by conducting a survey. Describing data looks at data after it has been organized and makes conclusions about the data. Read more...iWorksheets :3Study Guides :1

Experimental ProbabilityFreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets :3Study Guides :1

8.13 (B) Recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. Readiness Standard (STAAR)

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.

(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:

8.14 (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

8.14 (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)

8.14 (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)

(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:

8.15 (A) Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. (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

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

Introduction to PercentWhat Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1

Integer operationsInteger operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. Equations with integers are solved using inverse operations. Addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. Read more...iWorksheets :4Study Guides :1

Rational numbers and operationsA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. Read more...iWorksheets :3Study Guides :1

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

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

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:

8.16 (A) Make conjectures from patterns or sets of examples and nonexamples. (STAAR)

Standards

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Texas Assessments of Academic Readiness (STAAR) 8th Grade Math Activities