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## Pennsylvania Math Standards - 8th Grade

MathScore aligns to the Pennsylvania Math Standards for 8th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

View the Pennsylvania Math Standards at other levels.

## Number, Number Systems, and Number Relationships

2.1.8A. Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, exponents, scientific notation, square roots). (Compare Mixed Values , Compare Mixed Values 2 , Positive Number Line , Number Line , Compare Integers , Fractions to Decimals , Decimals To Fractions , Repeating Decimals , Percentages , Percentage Pictures , Scientific Notation , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Perfect Squares , Simplifying Radical Expressions )
2.1.8B. Simplify numerical expressions involving exponents, scientific notation and using order of operations. (Using Parentheses , Order Of Operations , Scientific Notation 2 , Exponent Basics , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Scientific Notation , Roots Of Exponential Expressions )
2.1.8C. Distinguish between and order rational and irrational numbers.
2.1.8D. Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles. (Unit Cost , Proportions 1 , Proportions 2 , Distance, Rate, and Time , Ratios )
2.1.8E. Simplify and expand algebraic expressions using exponential forms. (Simplifying Algebraic Expressions 2 , Foil Method , Binomial Fraction Simplification , Polynomial Fraction Simplification , Roots Of Exponential Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
2.1.8F. Use the number line model to demonstrate integers and their applications. (Compare Integers )
2.1.8G. Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations. (Missing Factor , Missing Term , Missing Operator , Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Trinomial Factoring , Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )

## Computation and Estimation

2.2.8A. Complete calculations by applying the order of operations. (Order Of Operations )
2.2.8B. Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions. (Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence )
2.2.8C. Estimate the value of irrational numbers. (Estimating Square Roots )
2.2.8D. Estimate amount of tips and discounts using ratios, proportions and percents.
2.2.8E. Determine the appropriateness of overestimating or underestimating in computation.
2.2.8F. Identify the difference between exact value and approximation and determine which is appropriate for a given situation. (Estimated Multiply Divide Word Problems )

## Measurement and Estimation

2.3.8A. Develop formulas and procedures for determining measurements (e.g., area, volume, distance).
2.3.8B. Solve rate problems (e.g., rate × time = distance, principal × interest rate = interest). (Unit Cost , Simple Interest , Distance, Rate, and Time )
2.3.8C. Measure angles in degrees and determine relations of angles. (Identifying Angles , Angle Measurements )
2.3.8D. Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass and angles. (Triangle Area , Parallelogram Area , Perimeter , Rectangular Solids , Circle Area , Circle Circumference , Triangular Prisms , Cylinders , Perimeter and Area of Composite Figures , Trapezoids )
2.3.8E. Describe how a change in linear dimension of an object affects its perimeter, area and volume. (Compare Rectangle Area and Perimeter , Area And Volume Proportions )
2.3.8F. Use scale measurements to interpret maps or drawings.
2.3.8G. Create and use scale models.

## Mathematical Reasoning and Connections

2.4.8A. Make conjectures based on logical reasoning and test conjectures by using counter-examples.
2.4.8B. Combine numeric relationships to arrive at a conclusion. (Patterns: Numbers )
2.4.8C. Use if...then statements to construct simple, valid arguments.
2.4.8D. Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers.
2.4.8E. Distinguish between inductive and deductive reasoning.
2.4.8F. Use measurements and statistics to quantify issues (e.g., in family, consumer science situations).

## Mathematical Problem Solving and Communication

2.5.8A. Invent, select, use and justify the appropriate methods, materials and strategies to solve problems.
2.5.8B. Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams.
2.5.8C. Justify strategies and defend approaches used and conclusions reached.
2.5.8D. Determine pertinent information in problem situations and whether any further information is needed for solution.

## Statistics and Data Analysis

2.6.8A. Compare and contrast different plots of data using values of mean, median, mode, quartiles and range. (Stem And Leaf Plots )
2.6.8B. Explain effects of sampling procedures and missing or incorrect information on reliability.
2.6.8C. Fit a line to the scatter plot of two quantities and describe any correlation of the variables.
2.6.8D. Design and carry out a random sampling procedure.
2.6.8E. Analyze and display data in stem-and-leaf and box-and-whisker plots. (Stem And Leaf Plots )
2.6.8F. Use scientific and graphing calculators and computer spreadsheets to organize and analyze data.
2.6.8G. Determine the validity of the sampling method described in studies published in local or national newspapers.

## Probability and Predictions

2.7.8A. Determine the number of combinations and permutations for an event.
2.7.8B. Present the results of an experiment using visual representations (e.g., tables, charts, graphs).
2.7.8C. Analyze predictions (e.g., election polls).
2.7.8D. Compare and contrast results from observations and mathematical models.
2.7.8E. Make valid inferences, predictions and arguments based on probability.

## Algebra and Functions

2.8.8A. Apply simple algebraic patterns to basic number theory and to spatial relations.
2.8.8B. Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships.
2.8.8C. Create and interpret expressions, equations or inequalities that model problem situations. (Algebraic Sentences 2 , Algebraic Sentences )
2.8.8D. Use concrete objects to model algebraic concepts. (Requires outside materials )
2.8.8E. Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. (Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities )
2.8.8F. Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets. (Requires outside materials )
2.8.8G. Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions )
2.8.8H. Graph a linear function from a rule or table.
2.8.8I. Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions.
2.8.8J. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship. (Linear Equations )

## Geometry

2.9.8A. Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.
2.9.8B. Draw, label, measure and list the properties of complementary, supplementary and vertical angles. (Angle Measurements )
2.9.8C. Classify familiar polygons as regular or irregular up to a decagon.
2.9.8D. Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders. (Quadrilateral Types )
2.9.8E. Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles). (Identifying Angles )
2.9.8F. Distinguish between similar and congruent polygons. (Congruent And Similar Triangles )
2.9.8G. Approximate the value of π (pi) through experimentation.
2.9.8H. Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions.
2.9.8I. Generate transformations using computer software.
2.9.8J. Analyze geometric patterns (e.g., tesselations, sequences of shapes) and develop descriptions of the patterns.
2.9.8K. Analyze objects to determine whether they illustrate tesselations, symmetry, congruence, similarity and scale.

## Trigonometry

2.10.8A. Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships. (Pythagorean Theorem , Solving For Angles , Proportions 2 )
2.10.8B. Solve problems requiring indirect measurement for lengths of sides of triangles.

## Concepts of Calculus

2.11.8A. Analyze graphs of related quantities for minimum and maximum values and justify the findings.
2.11.8B. Describe the concept of unit rate, ratio and slope in the context of rate of change. (Determining Slope )