8th Grade Worksheets

Numbers & Operations (N)

PA.N.1.1 Develop and apply the properties of integer exponents, including a^0 = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions. PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation. PA.N.1.3 Multiply and divide numbers written in scientific notation and express the answer in scientific notation. PA.N.1.4 Compare and order real numbers; locate them on a number line. Identify square roots of perfect squares to 400 or, if not perfect, locate the irrational value between two consecutive positive integers.

Algebraic Reasoning & Algebra (A)

PA.A.1.1 Recognize a function as a relationship between an independent and a dependent variable in which the independent variable determines the value of the dependent variable. PA.A.1.2 Use linear functions to represent and model mathematical situations. PA.A.1.3 Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a non-vertical straight line. PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate between representations. PA.A.2.2 Identify, describe, and analyze linear relationships between two variables. PA.A.2.3 Identify graphical properties of linear functions, including slope and intercepts; know slope equals rate of change and that y-intercept is zero when the function is proportional. PA.A.2.4 Predict how changing slope or y-intercept affects the graph of a linear function; use appropriate tools to examine effects. PA.A.2.5 Solve problems involving linear functions and interpret the results in the original context. PA.A.3.1 Use substitution to simplify and evaluate algebraic expressions. PA.A.3.2 Justify steps in generating equivalent expressions by combining like terms and using order of operations (including grouping symbols); identify properties used (associative, commutative, distributive). PA.A.4.1 Solve problems using one-variable linear equations where there could be one, infinitely many, or no solutions; represent and interpret solutions in context. PA.A.4.2 Represent, write, solve, and graph linear inequalities in one variable of the form px + q > r and px + q < r, where p, q, r are rational numbers. PA.A.4.3 Represent real-world situations using equations and inequalities in one variable.

Geometry & Measurement (GM)

PA.GM.1.1 Justify the Pythagorean theorem using measurements, diagrams, or dynamic software to solve two-dimensional problems involving right triangles. PA.GM.1.2 Use the Pythagorean theorem to find the distance between any two points in the coordinate plane. PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets; use appropriate units (e.g., cm²). PA.GM.2.2 Calculate the surface area of a cylinder, in terms of π and using approximations for π, via decomposition or nets; use appropriate units (e.g., cm²). PA.GM.2.3 Justify why base area (B) and height (h) in V = Bh are multiplied to find the volume of a rectangular prism; use appropriate units (e.g., cm³). PA.GM.2.4 Develop and use V = (πr^2)h and V = Bh to determine volume of right cylinders (in terms of π and with approximations); justify why base area and height are multiplied; use appropriate units (e.g., cm³).

Data & Probability (D)

PA.D.1.1 Describe the impact of inserting or deleting a data point on the mean and median of a data set; create data displays using technology to examine this impact. PA.D.1.2 Explain how outliers affect measures of center and spread. PA.D.1.3 Collect, display, and interpret data using scatter plots; use the shape to informally find a line of best fit, describe average rate of change, and make predictions; use appropriate titles, labels, and units. PA.D.2.1 Calculate experimental probabilities and represent them as percents, fractions, and decimals between 0 and 1; use experimental probabilities to predict relative frequencies when actual probabilities are unknown. PA.D.2.2 Determine how samples are chosen (randomness) to draw and support conclusions about generalizing a sample to a population, including identifying limitations and biases. PA.D.2.3 Define, compare, and contrast the probabilities of dependent and independent events.