Grade 8 is the culmination of the PSSA Math assessment sequence in Pennsylvania, and the content is the most algebraically dense of any PSSA grade. Students tested in Grade 8 are expected to work fluently with linear functions, solve systems of equations, analyze geometric transformations, apply the Pythagorean theorem, interpret bivariate data, and use exponent rules with rational exponents. The Grade 8 PSSA is also the last standardized math assessment Pennsylvania students take before the Keystone Algebra 1 exam — making strong Grade 8 performance a predictor of Keystone success.
This guide covers the major PSSA Grade 8 math topics, sample problems with solutions, common errors, and a four-week study plan.
ViewMath is not affiliated with or endorsed by the Pennsylvania Department of Education. For official PSSA information, visit pa.gov/agencies/education.
Grade 8 PSSA Math: Top Tested Topics
Functions
Understanding functions is the central conceptual goal of Grade 8 math. Students must:
- Understand that a function assigns exactly one output to each input
- Identify functions from tables, graphs, and mappings
- Compare properties of linear and nonlinear functions represented in different forms
- Construct a function rule from a table of values or a verbal description
- Interpret slope and y-intercept in the context of a problem
Linear Equations and Systems
Students solve linear equations in one variable (including those with infinitely many solutions or no solution), solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret solutions in context. PSSA questions in this area often present two scenarios (e.g., two pricing plans or two travel routes) and ask students to find when the outcomes are equal.
Exponents and Scientific Notation
Students apply properties of integer exponents to generate equivalent expressions: product rule, quotient rule, power of a power, negative exponents, and zero exponent. They perform operations with numbers in scientific notation (add, subtract, multiply, divide) and interpret the relative size of numbers expressed in scientific notation.
The Pythagorean Theorem
Students apply the Pythagorean theorem to find missing side lengths of right triangles in both geometric and coordinate-plane contexts. They use the converse to determine whether a triangle with given side lengths is a right triangle. Grade 8 also extends this to finding the distance between two points on the coordinate plane.
Geometric Transformations
Students perform and describe translations, reflections, rotations, and dilations on the coordinate plane. They understand the difference between rigid transformations (which preserve congruence) and dilations (which preserve similarity but change size). PSSA questions often show a pre-image and image and ask students to identify or describe the transformation.
Bivariate Data: Scatter Plots and Trend Lines
Students construct scatter plots, identify patterns of association (positive, negative, linear, nonlinear), draw informal trend lines, and use the trend line to make predictions. They distinguish between correlation and causation in contextual problems.
Sample PSSA Grade 8 Problems
Functions
Which table shows a relationship that is NOT a function?
| Table A | Table B | ||
|---|---|---|---|
| x: 1, 2, 3, 4 | y: 5, 7, 9, 11 | x: 1, 1, 3, 4 | y: 5, 7, 9, 11 |
Answer: Table B is NOT a function because the input x = 1 is paired with two different outputs (5 and 7).
Linear Equations
Solve: 3(2x − 4) = 2x + 8.
Solution: 6x − 12 = 2x + 8. 4x = 20. x = 5. Answer: x = 5.
Exponents
Simplify: (2³ × 2⁻¹)².
Solution: Inside the parentheses: 2³ × 2⁻¹ = 2^(3−1) = 2². Raise to the 2nd power: (2²)² = 2⁴ = 16. Answer: 16.
Pythagorean Theorem
A 10-foot ladder leans against a wall. The base of the ladder is 6 feet from the wall. How high up the wall does the ladder reach?
Solution: h² + 6² = 10². h² = 100 − 36 = 64. h = 8. Answer: 8 feet.
Transformations
Triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 2). After a reflection over the x-axis, what are the new coordinates of vertex A?
Solution: Reflecting over the x-axis changes (x, y) to (x, −y). New A = (1, −2). Answer: (1, −2).
Common PSSA Grade 8 Math Errors
- Function vs. non-function from a graph: Students sometimes use the wrong test. Use the vertical line test: if any vertical line crosses the graph more than once, the relation is not a function.
- Exponent rules: adding instead of multiplying: Students write 2³ × 2⁵ = 2¹⁵ (multiplying the exponents) instead of 2⁸ (adding them). The rule is: same base, multiplication → add exponents; same base, power of power → multiply exponents.
- Pythagorean theorem: using the wrong side as the hypotenuse: Always identify the longest side (opposite the right angle) as c. Then a² + b² = c² where a and b are legs.
- Transformation direction: Students sometimes reverse the direction of a translation (adding x when they should subtract, or moving up when they should move down). Labeling a coordinate grid with positive and negative directions before performing the transformation prevents this.
- Scientific notation operations: When multiplying numbers in scientific notation, students sometimes forget to adjust the exponent after the coefficient product exceeds 10. E.g., (3 × 10⁴)(4 × 10²) = 12 × 10⁶, which must be rewritten as 1.2 × 10⁷.
4-Week PSSA Grade 8 Math Study Plan
Week 1: Functions and Linear Equations
Cover the definition of a function (tables, graphs, mappings, vertical line test). Practice writing function rules from tables and interpreting slope and y-intercept. Solve linear equations with one and two variables, including equations with no solution or infinitely many solutions. Cover systems of linear equations by graphing, substitution, and elimination.
Week 2: Exponents, Scientific Notation, and Irrational Numbers
Review all exponent rules with integer exponents. Practice operations with scientific notation. Cover square roots and cube roots of perfect squares and cubes. Introduce irrational numbers and approximate their location on a number line (e.g., √2 ≈ 1.41 lies between 1 and 2).
Week 3: Geometry
Cover the Pythagorean theorem and its converse. Practice using it in coordinate plane contexts (distance between two points). Cover geometric transformations — translation, reflection, rotation, and dilation — and practice identifying which transformation was applied. Review angle relationships formed by parallel lines and a transversal.
Week 4: Bivariate Data and Full Mixed Practice
Cover scatter plots, association, trend lines, and using trend lines to predict values. Review reading and interpreting two-variable data tables and graphs. Complete a 25-question mixed-topic practice test. Review all errors before the final days before the exam.
Pennsylvania Grade 8 Math Resources
ViewMath offers Grade 8 math books aligned to the PA Core Standards, including practice test collections, study guides, and workbooks with answer keys. Browse the full Grade 8 collection in the sidebar below.
ViewMath is an independent publisher. Our materials are not official PSSA materials and are not affiliated with the Pennsylvania Department of Education.
