Pennsylvania State Standards for Mathematics: Grade 8

PA.2.1.8. Numbers, Number Systems and Number Relationships: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.1.8.A. Model and compare values of integers and rational numbers.

2.1.8.B. Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, exponents, scientific notation, square roots, absolute values).

2.1.8.C. Use ratio and proportion to model relationships between quantities.

2.1.8.D. Extend place value concepts to represent large numbers using exponential, scientific, and calculator notation.

2.1.8.E. Apply concepts of prime and composite numbers to calculate GCFs (Greatest Common Factor) and LCMs (Least Common Multiple) of numbers.

2.1.8.F. Understand the concepts of exponents and roots and use the inverse relationships between exponents and roots to determine unknown quantities in equations.

2.1.8.G. Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations.

PA.2.2.8. Computation and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.2.8.A. Intentionally Blank

2.2.8.B. Add, subtract, multiply, and divide different kinds and forms of rational numbers including integers, decimal fractions, percents, and proper and improper fractions.

2.2.8.C. Use the order of operations to evaluate numerical expressions

2.2.8.D. Estimate the values of irrational numbers and the results from calculations with basic operations of fractions and percents and check the reasonableness of those estimates.

2.2.8.E. Determine the appropriateness of overestimating or underestimating in computation.

2.2.8.F. Identify the difference between exact value and approximation and determine which is appropriate for a given situation.

PA.2.3.8. Measurement and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.3.8.A. Intentionally Blank

2.3.8.B. Develop strategies for determining areas and volumes of compound shapes and solids.

2.3.8.C. Calculate volume, surface area, and degrees of angles; calculate circumference and area of circles, and use a measurement formula to solve for a missing quantity.

2.3.8.D. Perform conversions within the metric system and within the customary system including scale measurements, between units of time and between units of temperature.

2.3.8.E. Describe how a change in linear dimension of an object affects its perimeter, area and volume.

2.3.8.F. Estimate and verify measurements of rate and mass.

2.3.8.G. Create and use scale models.

PA.2.4.8. Mathematical Reasoning and Connections: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.4.8.A. Draw inductive and deductive conclusions within mathematical contexts.

2.4.8.B. Use if...then statements to construct simple valid arguments.

2.4.8.C. Use if...then statements to construct simple, valid arguments.

2.4.8.D. Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers.

2.4.8.E. Distinguish between inductive and deductive reasoning.

2.4.8.F. Use measurements and statistics to quantify issues (e.g., in family, consumer science situations).

PA.2.5.8. Mathematical Problem Solving and Communication: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.5.8.A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, apply estimation skills as appropriate, check whether the plan makes sense, and explain how the problem was solved in grade appropriate contexts.

2.5.8.B. Use precise mathematical language, notation, and representations, including numerical tables and equations, simple algebraic equations, and formulas, charts, graphs and diagrams to explain and interpret results.

2.5.8.C. Justify strategies and defend approaches used and conclusions reached.

2.5.8.D. Determine pertinent information in problem situations and whether any further information is needed for solution.

PA.2.6.8. Statistics and Data Analysis: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.6.8.A. Understand and apply sampling techniques to gather data including simple random sampling and convenience sampling.

2.6.8.B. Organize and display one-variable data using appropriate data display, such as stem and- leaf and box-and whisker plots, and two variable data with scatterplots.

2.6.8.C. Calculate quartiles for one-variable data and describe the correlation coefficient for two-variable data displayed in a scatterplot.

2.6.8.D. Compare data sets graphically using double-bar and double-line graphs and numerically using mean, median, mode, range, and quartiles.

2.6.8.E. Determine the effect of extreme values on numerical summaries and calculate estimates based on survey results or graphs.

2.6.8.F. Use scientific and graphing calculators and computer spreadsheets to organize and analyze data.

2.6.8.G. Determine the validity of the sampling method described in studies published in local or national newspapers.

PA.2.7.8. Probability and Predictions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.7.8.A. Calculate the probability of an event involving ''and'', ''or'' or ''not''.

2.7.8.B. Intentionally Blank

2.7.8.C. Determine the number of combinations and permutations for an event.

2.7.8.D. Intentionally Blank

2.7.8.E. Find the experimental or theoretical probability of the outcomes of a simple or compound event.

PA.2.8.8. Algebra and Functions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.8.8.A. Use the concept of equality to demonstrate understanding of the inverse properties of numbers and the addition and multiplication properties of equality.

2.8.8.B. Evaluate and simplify algebraic expressions and solve and graph linear equations and inequalities.

2.8.8.C. Find the missing elements and recognize, describe, and extend patterns to include linear, exponential, and simple quadratic equations.

2.8.8.D. Create a table or graph from a functional rule.

2.8.8.E. Use combinations of symbols and numbers to create expressions and equations in one or two variables, and inequalities in one variable that model problem situations.

2.8.8.F. Interpret the results of solving equations in one or two variables and inequalities in one variable in the context of the situation that motivated the model.

2.8.8.G. Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules.

2.8.8.H. Graph a linear function from a rule or table.

2.8.8.I. Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions.

2.8.8.J. 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.

PA.2.9.8. Geometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.9.8.A. Name, describe and apply geometric relations for 1- dimensional shapes and 2- dimensional shapes and 3- dimensional solids.

2.9.8.B. Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) of a 3- dimensional shape.

2.9.8.C. Plot ordered pairs and 2-dimensional shapes that satisfy given conditions on a 2- dimensional coordinate system.

2.9.8.D. Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.

2.9.8.E. Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles).

2.9.8.F. Distinguish between similar and congruent polygons.

2.9.8.G. Approximate the value of p (pi) through experimentation.

2.9.8.H. Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions.

2.9.8.I. Generate transformations using computer software.

2.9.8.J. Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of the patterns.

2.9.8.K. Analyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale.

PA.2.10.8. Trigonometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.10.8.A. Compute measures of sides and angles using proportions, the Pythagorean Theorem, and right triangle relationships.

2.10.8.B. Intentionally Blank

PA.2.11.8. Concepts of Calculus: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.11.8.A. Analyze graphs of related quantities for minimum and maximum values and justify the findings.

2.11.8.B. Describe the concept of unit rate, ratio, and slope in the context of rate of change.

2.11.8.C. Intentionally Blank