8th Grade Math

Students begin with the real number system. They classify rational, irrational, and real numbers; classify square roots and cube roots as rational or irrational; write repeating decimals as fractions; approximate square roots and cube roots; compare and order real numbers; and estimate expressions involving irrational numbers.

The course then develops exponents and scientific notation. Students evaluate expressions with zero and negative exponents, apply the product, quotient, power, power-of-product, and power-of-quotient rules, and combine exponent rules. They write and compare numbers in scientific notation, convert between scientific and standard notation, perform operations with scientific notation, estimate and compare real-world quantities, and use units to interpret formulas and rates of change.

Students next study radicals. They evaluate square roots and cube roots, identify surds, approximate radical expressions, simplify and operate with radicals, rationalize denominators, connect radicals to fractional exponents, apply product and quotient rules for radicals, solve equations using square and cube roots, and use roots to find side lengths of squares and cubes from area or volume.

Students also study number theory. They use divisibility tests for common factors and multiples, distinguish prime and composite numbers, find prime factors, apply the fundamental theorem of arithmetic, use prime factorization to find greatest common factors and lowest common multiples, and connect rational numbers to finite and repeating decimal forms.

Students then move into linear equations. They analyze equations with one solution, no solution, or infinitely many solutions; model situations with two-variable linear equations; interpret unit rates, slopes, and intercepts from graphs; graph linear equations; write equations of horizontal, vertical, and sloped lines; solve systems of linear equations using graphs, substitution, and elimination; interpret the number of solutions to a system; solve real-world problems with systems; and solve multi-step linear equations in one variable.

The course continues with functions. Students learn to identify functions from rules, tables, graphs, and visual representations. They describe increasing and decreasing behavior, identify maximum and minimum values, interpret real-world functional relationships from graphs, distinguish linear and nonlinear functions, model real-world situations with linear equations, interpret rate of change and initial value in context, and compare functions represented in different ways.

Students next study geometry through transformations, congruence, and similarity. They solve angle problems involving parallel lines and transversals, triangle angle sums, exterior angles, the triangle inequality, the isosceles triangle theorem, and polygon angles. Students translate, reflect, and rotate figures in the coordinate plane; verify that rigid motions preserve length, angle measure, and parallelism; apply sequences of rigid motions; use rigid motions to determine congruence; dilate figures; analyze similarity through scale factors and corresponding parts; use the angle-angle criterion for similar triangles; connect similar triangles to slope; and describe transformation sequences between figures.

The course then develops the Pythagorean theorem and volume. Students understand and explain the Pythagorean theorem, apply it to find missing side lengths, use its converse to identify right triangles, solve real-world distance problems, derive and use the distance formula, apply the Pythagorean theorem in three-dimensional contexts, and calculate volumes of cylinders, cones, and spheres.

The course concludes with statistics and bivariate data. Students read and interpret scatter plots, describe patterns of association, identify clustering and outliers, use trend lines, informally assess model fit, make predictions from trend lines, interpret slopes and intercepts in context, complete two-way tables, calculate relative frequencies, and identify patterns of association in categorical data.

The Real Number System

• Classify decimals as rational or irrational.
• Classify irrational and real numbers.
• Place real numbers within the real number system.
• Classify square roots and cube roots as rational or irrational.
• Write repeating decimals as fractions.
• Approximate square roots and cube roots.
• Identify unit and decimal intervals for irrational roots.
• Compare rational and irrational numbers.
• Order lists of real numbers.
• Estimate expressions involving pi, square roots, and multiple irrational numbers.

Exponents & Scientific Notation

• Evaluate expressions with zero exponents.
• Evaluate expressions with negative exponents.
• Apply the product rule, quotient rule, and power rule for exponents.
• Apply the power-of-product and power-of-quotient rules.
• Combine exponent rules to simplify expressions.
• Write numbers greater than ten, less than one, and negative numbers in scientific notation.
• Convert numbers from scientific notation to standard notation.
• Compare numbers written in scientific notation.
• Add and subtract numbers in scientific notation.
• Add and subtract numbers in scientific notation with different powers of ten.
• Multiply and divide numbers in scientific notation.
• Estimate real-world quantities using scientific notation.
• Compare real-world quantities using scientific notation.
• Express how many times as much one quantity is as another.
• Determine units in formulas.
• Select appropriate units for rates of change.

Radicals

• Evaluate square roots of perfect squares.
• Square square roots.
• Evaluate cube roots of perfect cubes.
• Identify square root and cube root surds.
• Approximate square root and cube root surds.
• Simplify expressions containing radicals.
• Evaluate numerical expressions containing radicals.
• Add and subtract radicals.
• Rationalize denominators.
• Convert between radicals and fractional exponents.
• Apply the product rule and quotient rule for radicals.
• Solve equations using square roots.
• Solve radical equations using the squaring method.
• Solve equations using cube roots.
• Solve radical equations using the cubing method.
• Find side lengths of squares and cubes from area or volume.

Number Theory

• Use divisibility tests for 2, 3, 4, 5, 6, 7, 8, 9, and 10.
• Determine whether a rational number has a finite or repeating decimal expansion.
• Identify prime and composite numbers.
• Find prime factors and write prime factorizations.
• Apply the fundamental theorem of arithmetic.
• Use prime factorization to find greatest common factors and lowest common multiples.

Linear Equations

• Identify linear equations with infinitely many solutions.
• Identify linear equations with no solutions.
• Solve for unknown parameters in equations with no solutions or infinitely many solutions.
• Model situations with two-variable linear equations.
• Model totals using two-variable linear equations.
• Interpret unit rates and intercepts from graphs.
• Fit graphs to given information.
• Graph linear equations using tables and points.
• Write and identify equations of horizontal and vertical lines.
• Calculate slopes from points and graphs.
• Interpret slope as a unit rate in proportional relationships.
• Write equations of lines in slope-intercept form.
• Use slope-intercept form to find slopes, intercepts, and equations of lines.
• Solve systems of linear equations from graphs.
• Solve systems of linear equations using substitution.
• Solve systems of linear equations using elimination.
• Identify whether a system has one solution, no solution, or infinitely many solutions.
• Solve real-world problems using systems of linear equations.
• Solve multi-step linear equations.
• Solve linear equations using the distributive property.
• Determine the number of solutions of a linear equation.

Functions

• Identify functions from rules, tables, graphs, and visual representations.
• Interpret graphs of functions.
• Identify where a function is increasing or decreasing.
• Identify maximum and minimum values of a function.
• Describe functional relationships between two quantities from a graph.
• Sketch graphs from verbal descriptions of real-world relationships.
• Distinguish linear functions from nonlinear functions using graphs, equations, and tables.
• Model real-world situations with linear equations.
• Interpret rate of change and initial value in context.
• Compare properties of functions represented algebraically, graphically, verbally, and in tables.

Geometry: Transformations, Congruence, & Similarity

• Solve angle problems involving corresponding angles.
• Solve angle problems involving alternate interior and alternate exterior angles.
• Solve angle problems involving consecutive angles.
• Use angle criteria to determine when lines are parallel.
• Use the triangle angle sum to find missing angles.
• Use exterior angle relationships in triangles.
• Solve multi-step problems involving angles of triangles.
• Apply the triangle inequality.
• Use the isosceles triangle theorem.
• Use interior and exterior angle relationships in polygons.
• Translate points and polygons in the coordinate plane.
• Reflect points and polygons across axes and diagonal lines.
• Rotate points and polygons about the origin.
• Verify that rigid motions preserve length, angle measure, and parallelism.
• Apply sequences of rigid motions.
• Determine congruence through rigid motions.
• Dilate figures and identify scale factors, centers, enlargements, and contractions.
• Dilate figures in the coordinate plane.
• Identify similar polygons using side lengths and angle measures.
• Calculate missing side lengths, angle measures, and perimeters of similar polygons.
• Determine similarity through sequences of transformations.
• Use the angle-angle criterion for similar triangles.
• Use similar triangles to explain slope.
• Describe sequences of transformations that map one figure onto another.

The Pythagorean Theorem & Volume

• Understand and explain the Pythagorean theorem.
• Apply the Pythagorean theorem to find missing side lengths.
• Use the converse of the Pythagorean theorem to determine whether a triangle is right.
• Identify Pythagorean triples.
• Solve real-world problems using the Pythagorean theorem.
• Find the distance between two points using the Pythagorean theorem.
• State and use the distance formula.
• Connect the distance formula to the Pythagorean theorem.
• Apply the Pythagorean theorem to three-dimensional figures.
• Find diagonal lengths in rectangular boxes.
• Find slant heights of pyramids and cones.
• Calculate volumes of cylinders.
• Calculate volumes of cones.
• Calculate volumes of spheres.
• Solve real-world problems involving volumes of cylinders, cones, and spheres.

Statistics: Bivariate Data

• Read and interpret scatter plots.
• Describe positive, negative, or no association in scatter plots.
• Describe linear and nonlinear association in scatter plots.
• Identify clustering and outliers in scatter plots.
• Identify and estimate trend lines.
• Determine equations of trend lines.
• Informally assess how well a trend line fits a scatter plot.
• Use trend lines and trend line equations to make predictions.
• Interpret slopes and y-intercepts of trend lines in context.
• Complete joint frequency tables.
• Deduce joint and marginal frequencies.
• Solve word problems using joint frequency tables.
• Calculate relative frequencies from two-way tables.
• Calculate row and column relative frequencies.
• Identify patterns of association from two-way tables.
• Draw conclusions from two-way tables in real-world contexts.