Grade 8 math

Repeating Decimals to Fractions

Convert repeating decimals into fractions in lowest terms.

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Multiplying Decimals by Exponents (Hard)

Challenging problems that combine decimal multiplication with powers of 10, negative exponents, and scientific notation.

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Dilations & Scale Factor

Dilate points and figures about the origin, find the scale factor of a dilation, and find the new side lengths.

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Proportional Relationships & Unit Rate

Read the unit rate (slope) from graphs, tables and equations of proportional relationships, and compare two relationships.

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Rate of Change & Initial Value

Find the rate of change and initial value of a linear function from a story, two data points, a table or a graph, and write its equation.

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Rational & Irrational Numbers

Classify numbers as rational or irrational, and locate square roots between consecutive integers.

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Estimating Square Roots

Estimating square roots of numbers that are not perfect squares only: between which two whole numbers √50 lies, then the nearest whole number, larger numbers, and rounding to the nearest tenth.

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Laws of Integer Exponents (Mixed Review)

Use the product, quotient, power, zero and negative exponent rules to simplify and evaluate expressions.

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Square Roots & Cube Roots (Mixed Review)

Evaluate square and cube roots of perfect squares and cubes, and solve equations like x^2 = p and x^3 = p.

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Square Roots of Perfect Squares

Square roots of perfect squares only: √49 and √144 first, then -√ and larger squares, equations like x^2 = 81, and square roots of decimals and fractions like √0.25 and √(9/16).

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Zero and Negative Exponents

Evaluate powers with zero and negative exponents only: 7^0 first, then 5^-1, 3^-2, (-2)^-3, (2/3)^-2, 1/(2^-3) and sums like 2^-1 + 2^-2.

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Exponents & Scientific Notation (Mixed Review)

Apply exponent rules and convert numbers to scientific notation.

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Simplifying Expressions

Combine like terms to simplify each expression.

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Solving One- & Two-Step Equations

Solve linear equations for x.

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Systems of Equations (Intro)

Solve simple systems of equations using substitution.

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Comparing & Estimating with Scientific Notation

Compare numbers in scientific notation, find how many times as large one is, estimate with powers of 10 and write numbers in standard form.

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Dividing in Scientific Notation

Division of numbers in scientific notation only: (8 × 10^7) ÷ (2 × 10^3) first, then quotients that need adjusting, decimals, negative exponents and very large or small numbers.

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Equations with Variables on Both Sides

Solve multi-step linear equations with the variable on both sides, including the distributive property.

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Multi-Step Equations with the Distributive Property

Solve multi-step equations with parentheses, like terms and fractions, such as 3(x − 4) + 2x = 13, x/3 + 5 = 9 and (2x + 1)/5 = 3.

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Multiplying in Scientific Notation

Multiplication of numbers in scientific notation only: (2 × 10^3) × (4 × 10^5) first, then products that need adjusting, decimals, negative exponents and three factors.

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One, No, or Infinitely Many Solutions

Decide whether a linear equation has one solution, no solution, or infinitely many solutions.

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Power Rule of Exponents

Raising a power to a power, only ((x^a)^b = x^(ab)): (2^3)^2 first, then letters, powers of powers of powers, negative exponents, and monomials like (-2a^3 b)^3.

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Operations with Scientific Notation (Mixed Review)

Multiply, divide, add and subtract numbers written in scientific notation.

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Converting Scientific Notation to Standard Form

Conversion from scientific notation to standard form only: 3 × 10^3 = 3,000 first, then 4.5 × 10^4, 4 × 10^-3, 5.2 × 10^-4, very large and very small numbers, and 3.4567 × 10^3.

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Solving Systems by Elimination

Solve systems of two linear equations by adding or subtracting the equations (multiplying first when needed).

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Solving Systems of Equations by Substitution

Solve systems of two linear equations by substituting an expression for one variable, including systems where a variable must be isolated first.

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Writing Linear Equations

Write the equation y = mx + b of a line from its slope and y-intercept, a point and the slope, two points, a graph or a table.

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Writing Numbers in Scientific Notation

Conversion from standard form to scientific notation only: 3,000 = 3 × 10^3 first, then 45,000, 0.004, 0.00052, very large and very small numbers, and decimals like 3456.7.

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Graphing Points & Linear Relationships

Identify coordinate points and evaluate simple linear relationships.

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Introduction to Functions

Determine whether a relation is a function and evaluate functions given as a table.

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Slope & Linear Equations

Find the slope between two points and evaluate linear equations.

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Comparing Functions

Compare the rates of change and initial values of two linear functions shown in different ways (equation, table, graph or words).

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Function Graphs: Increasing & Decreasing

Read a function from its graph: find outputs for given inputs, tell where it is increasing, decreasing or constant, and find its rate of change on a piece.

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Linear & Nonlinear Functions

Decide whether a function given by an equation, a table or a graph is linear or nonlinear.

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Slope from a Graph, Table or Two Points

Find the slope of a line from its graph, from a table of values, or from two points, including fractional, zero and undefined slopes.

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Solving Systems by Graphing

Read the solution of a system of two linear equations from where their graphs cross, and recognize parallel lines (no solution).

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Pythagorean Theorem (Intro)

Find the hypotenuse of a right triangle given its legs.

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Transformations on the Coordinate Plane

Find the image of a point after a translation, reflection, or rotation.

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Volume of Cylinders, Cones & Spheres

Find the volume of cylinders, cones, and spheres using π ≈ 3.14.

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Distance on the Coordinate Plane

Find the distance between two points using the Pythagorean theorem.

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All Angle Relationships: Mixed Review

Mixed practice with complementary, supplementary, vertical, adjacent and linear-pair angles, angles around a point, and parallel-line angles: name each pair, find missing angles, and solve for x.

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Congruence & Similarity with Transformations

Identify the transformation that maps one figure onto another, describe translations, follow a sequence of transformations, and decide whether figures are congruent or similar.

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Cube Roots of Perfect Cubes

Cube roots of perfect cubes only: ∛27 and ∛125 first, then negative cubes like ∛(-64), equations like x^3 = -8, larger cubes, and cube roots of fractions and decimals like ∛(8/27) and ∛0.125.

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Lines of Best Fit & Predictions

Use the equation of a trend line to make predictions and interpret its slope and y-intercept, and write the equation of a trend line from a graph.

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Parallel Lines & Transversals

Name angle pairs formed by parallel lines and a transversal and use them to find missing angle measures.

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Converse of the Pythagorean Theorem

Use the converse of the Pythagorean theorem to decide whether three side lengths form a right triangle.

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Reflections on the Coordinate Plane

Flip triangles and quadrilaterals across the x-axis, y-axis, y = x, y = −x and other lines, and find the coordinates of the image.

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Angle-Angle Similarity & Similar Triangles

Use the angle-angle rule to decide whether two triangles are similar, find matching angles, and use proportions to find missing sides of similar triangles.

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Surface Area of Cones

Surface area of cones only: the circle base plus the curved side (πr² + πrl), with π ≈ 3.14, diameters, answers in terms of π, and finding the slant height from the height.

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Surface Area of Cylinders

Surface area of cylinders only: two circles plus the curved side (2πr² + 2πrh), with π ≈ 3.14, diameters, answers in terms of π, and word problems.

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Surface Area of Spheres

Surface area of spheres only: 4πr², with π ≈ 3.14, diameters, answers in terms of π, and word problems.

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Translations on the Coordinate Plane

Slide triangles and quadrilaterals on the coordinate plane, find image coordinates, and write translation rules (x, y) → (x + a, y + b).

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Triangle Angle Sum & Exterior Angles

Use the triangle angle sum (180°) and the exterior angle theorem to find missing angles and solve for x.

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Volume: Changing Radius & Height

See how the volume of cylinders, cones and prisms changes when the height or radius changes, compare cones with cylinders, and solve volume formulas for a missing height.

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Scatter Plots & Association

Describe the association in a scatter plot (positive, negative or none; linear or nonlinear) and find outliers.

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Two-Way Tables & Relative Frequency

Read and complete two-way tables and find relative frequencies as fractions and percents.

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Product Rule of Exponents

Multiplication of powers with the same base, only (x^a · x^b = x^(a+b)): 3^4 · 3^2 first, then letters, three factors, negative exponents, and monomials like (3x^4 y)(-5x^2 y^3).

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Quotient Rule of Exponents

Division of powers with the same base, only (x^a / x^b = x^(a-b)): 5^7 / 5^3 first, then letters, bigger and negative exponents, and monomials like 12x^7 y^5 / 4x^2 y^3.

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Word Problems

Linear equation word problems.

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Pythagorean Theorem: Missing Legs & Word Problems

Use the Pythagorean theorem to find a missing leg, solve real-world problems, and find the diagonal of a box.

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Systems of Equations Word Problems

Write and solve a system of two linear equations to answer real-world questions.

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