Grade 8 Math Help
Step-by-step Grade 8 math videos, unit overviews, new terminology, lesson summaries, practice support, and helpful resources for students, parents, teachers, tutors, and homeschool families.
Welcome to Grade 8 Math
This page organizes Grade 8 math support by unit. Each unit includes an overview, important vocabulary, an all-lessons practice video or playlist, and short summaries to help students review the main ideas.
Unit 1 — Rigid Transformations and Congruence
Unit Overview
Students learn about translations, rotations, reflections, rigid transformations, congruence, and how figures move on the coordinate plane while preserving size and shape.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.1.1 | plane, measure, vertex, vertices, direction, slide, turn |
| 8.1.2 | clockwise, counterclockwise, reflection, rotation, translation, opposite |
| 8.1.3 | image, angle of rotation, center of rotation, line of reflection |
| 8.1.4 | sequence of transformations, distance, reflect, rotate, translate |
| 8.1.5 | point, segment, coordinates, x-axis, y-axis |
| 8.1.7 | rigid transformation, corresponding, measurements, preserve |
| 8.1.8 | midpoint, segment |
| 8.1.9 | vertical angles, parallel, intersect, distance |
| 8.1.11 | congruent, perimeter, area |
| 8.1.14 | alternate interior angles, transversal, supplementary angles |
| 8.1.17 | tessellation, symmetry |
Key Ideas
Rigid Transformations
Students explore translations, rotations, and reflections and describe how figures move.
Coordinate Plane Transformations
Students use coordinates to describe transformations and images of figures.
Congruence and Angles
Students connect rigid transformations to congruence, angle relationships, and geometric reasoning.
Unit 2 — Dilations, Similarity, and Introducing Slope
Unit Overview
Students study dilations, scale factors, similarity, slope triangles, and how similar figures help explain slope and linear relationships.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.2.1 | scale factor, scaled copy, scaling |
| 8.2.2 | dilation, center of a dilation, dilate, radius |
| 8.2.4 | center of a dilation, scale factor |
| 8.2.6 | similar, dilate |
| 8.2.7 | dilation |
| 8.2.9 | quotient |
| 8.2.10 | similar, slope, slope triangle |
| 8.2.11 | similarity, x-coordinate, y-coordinate, equation of a line, quotient |
| 8.2.13 | estimate, approximate, approximately |
Key Ideas
Dilations
Students learn how dilations enlarge or reduce figures using a center and scale factor.
Similarity
Students connect dilations to similar figures and proportional side lengths.
Introducing Slope
Students use slope triangles and similar triangles to understand slope as a constant rate of change.
Unit 3 — Linear Relationships
Unit Overview
Students learn about linear relationships, rate of change, slope, vertical intercepts, horizontal intercepts, equations, graphs, and solutions with two variables.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.3.1 | represent, scale, label, constant of proportionality |
| 8.3.2 | equation |
| 8.3.3 | rate of change, constant of proportionality, equation |
| 8.3.5 | linear relationship, constant rate, slope |
| 8.3.6 | vertical intercept, y-intercept |
| 8.3.7 | initial value, initial amount, constant rate |
| 8.3.9 | horizontal intercept, x-intercept |
| 8.3.10 | intersection point, rate of change, vertical intercept, y-intercept |
| 8.3.11 | constraint, horizontal line, vertical line |
| 8.3.12 | solution to an equation with two variables, variable, combination, set of solutions |
Key Ideas
Rate of Change and Slope
Students identify slope and rate of change in graphs, tables, equations, and contexts.
Intercepts
Students interpret vertical intercepts, horizontal intercepts, and initial values.
Equations with Two Variables
Students represent and interpret solutions to linear equations with two variables.
Unit 4 — Linear Equations and Linear Systems
Unit Overview
Students solve linear equations, work with equivalent expressions, identify different types of solutions, and solve systems of equations using reasoning and substitution.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.4.1 | representation |
| 8.4.2 | expression |
| 8.4.3 | solution of an equation, distribute |
| 8.4.4 | substitute, equation |
| 8.4.5 | term, like terms, distributive property, factor |
| 8.4.6 | term, like terms, distribute, common denominator |
| 8.4.7 | no solution, one solution |
| 8.4.8 | constant term, coefficient, linear equation, infinitely many solutions, expression, variable |
| 8.4.11 | ordered pair |
| 8.4.12 | system of equations, solution of a system of equations |
| 8.4.13 | substitution, no solution, one solution, infinitely many solutions |
| 8.4.14 | algebraically |
Key Ideas
Solving Linear Equations
Students solve equations by using structure, distribution, like terms, and substitution.
Types of Solutions
Students distinguish between no solution, one solution, and infinitely many solutions.
Systems of Equations
Students solve systems and interpret solutions as ordered pairs that satisfy both equations.
Unit 5 — Functions and Volume
Unit Overview
Students learn about functions, inputs, outputs, independent and dependent variables, linear functions, models, and volume formulas for cylinders, cones, and spheres.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.5.1 | input, output |
| 8.5.2 | function, depends on |
| 8.5.3 | independent variable, dependent variable |
| 8.5.5 | prediction |
| 8.5.7 | cube, volume, sphere |
| 8.5.8 | functional relationship, linear function |
| 8.5.9 | mathematical model, prediction |
| 8.5.10 | piecewise linear function, linear function, constant rate |
| 8.5.11 | cylinder, three-dimensional |
| 8.5.12 | dimension, cube, sphere, cylinder, cubic centimeter, rectangular prism |
| 8.5.13 | base of a cylinder, base of a cone, approximation for pi |
| 8.5.15 | cone |
| 8.5.19 | hemisphere |
| 8.5.21 | spherical, volume |
| 8.5.22 | approximate range |
Key Ideas
Functions
Students use inputs, outputs, variables, and rules to understand functions.
Linear Functions and Models
Students use linear functions and models to make predictions and represent relationships.
Volume
Students calculate and reason about volume for cylinders, cones, and spheres.
Unit 6 — Associations in Data
Unit Overview
Students analyze bivariate data using scatterplots, associations, fitted lines, linear models, outliers, clusters, two-way tables, and relative frequency.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.6.1 | scatterplot |
| 8.6.2 | data display, attribute, numerical data, categorical data |
| 8.6.4 | predict, overpredict, underpredict, linear model |
| 8.6.5 | negative association, positive association, linear association |
| 8.6.6 | nonlinear association, no association, fitted line, outlier |
| 8.6.7 | cluster |
| 8.6.8 | independent variable, dependent variable, negative association, positive association, linear association |
| 8.6.9 | segmented bar graph, relative frequency, two-way frequency table |
| 8.6.11 | scatterplot, outlier, cluster, numerical data, categorical data |
Key Ideas
Scatterplots
Students use scatterplots to display and interpret bivariate data.
Associations and Models
Students identify positive, negative, linear, nonlinear, and no association.
Two-Way Tables
Students use two-way tables, segmented bar graphs, and relative frequency to analyze categorical data.
Unit 7 — Exponents and Scientific Notation
Unit Overview
Students extend their understanding of exponents to include powers, powers of 10, zero exponents, negative exponents, and scientific notation.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.7.1 | power, exponent, factor, reciprocal, repeated multiplication |
| 8.7.2 | powers of 10 |
| 8.7.3 | powers of powers, base of an exponent |
| 8.7.4 | expanded, positive exponent, zero exponent |
| 8.7.5 | negative exponent, positive exponent |
| 8.7.6 | power, exponent, base of an exponent, zero exponent |
| 8.7.7 | evaluate, factor, reciprocal, powers of powers, negative exponent |
| 8.7.8 | square of a number |
| 8.7.9 | billion, trillion, multiple of |
| 8.7.10 | integer |
| 8.7.13 | scientific notation, integer |
| 8.7.15 | scientific notation |
Key Ideas
Exponent Rules
Students work with powers, bases, exponents, reciprocals, and powers of powers.
Negative and Zero Exponents
Students make sense of zero exponents and negative exponents.
Scientific Notation
Students use powers of 10 and scientific notation to write very large and very small numbers.
Unit 8 — Pythagorean Theorem and Irrational Numbers
Unit Overview
Students study square roots, cube roots, irrational numbers, decimal approximations, the Pythagorean Theorem, and applications involving right triangles.
New Terminology
| Lesson | New Vocabulary |
|---|---|
| 8.8.2 | square root, square of a number |
| 8.8.3 | irrational number, square root symbol, rational number |
| 8.8.4 | diagonal, decimal approximation |
| 8.8.5 | square root, square root symbol |
| 8.8.6 | Pythagorean Theorem, hypotenuse, legs, right triangle |
| 8.8.9 | converse of the Pythagorean Theorem, Pythagorean Theorem |
| 8.8.10 | edge length, hypotenuse, legs |
| 8.8.12 | cube root |
| 8.8.13 | cube root, edge length |
| 8.8.14 | decimal representation, infinite decimal expansion |
| 8.8.15 | irrational number, repeating decimal |
Key Ideas
Square Roots and Irrational Numbers
Students use square roots, decimal approximations, and irrational numbers.
Pythagorean Theorem
Students use the Pythagorean Theorem and its converse to solve right triangle problems.
Cube Roots and Decimal Representations
Students connect cube roots, edge lengths, and decimal expansions.
Helpful Grade 8 Math Tools
Use these tools to check answers and review common Grade 8 math topics.
Printable and Digital Resources
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