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8th Grade Math

Utah 8th Grade Math Curriculum

Video lessons and practice for every 8th grade math topic. Aligned to Utah Core Standards so your child keeps up with what Utah schools teach.

Utah 8th Grade Math Curriculum | StudyPugHelp

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ID

Standard

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8.NS.A.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).

8.EE.A.2

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.A.3

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.EE.B.6

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations.

8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

8.G.B.6

Explain a proof of the Pythagorean Theorem and its converse.

8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

8.G.C.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8th Grade Math Topics in Utah

Utah's 8th grade math curriculum follows the Utah Core Standards Math and covers a wide range of topics that bridge middle school math and high school algebra. StudyPug provides video lessons and practice problems for every standard, organized so students can find exactly what they need.

Number Systems and Exponents

Students learn the difference between rational and irrational numbers, understand decimal expansions, and use rational approximations to place irrational numbers on a number line. They apply the properties of integer exponents, work with square roots and cube roots, and perform operations using scientific notation — including converting between decimal and scientific notation forms.

Expressions and Equations

8th grade students solve linear equations in one variable and analyze systems of simultaneous linear equations. They graph proportional relationships and interpret slope, use similar triangles to explain why slope is constant on a line, and derive the equations y = mx and y = mx + b.

Functions

Students are introduced to the concept of a function as a rule assigning exactly one output to each input. They compare functions represented algebraically, graphically, in tables, or in words. They interpret y = mx + b as a linear function, construct functions to model linear relationships, and analyze graphs qualitatively to describe increasing or decreasing behavior.

Geometry

The geometry strand covers transformations — rotations, reflections, translations, and dilations — and their effects on two-dimensional figures. Students distinguish congruence and similarity, use angle relationships in triangles and with parallel lines cut by a transversal, and apply the angle-angle criterion for similar triangles. They also explain and apply the Pythagorean Theorem, use it to find unknown side lengths and distances between points in a coordinate system, and solve real-world volume problems involving cones, cylinders, and spheres.

Statistics and Probability

Students construct and interpret scatter plots, identify patterns of association, informally fit lines to linear scatter plots, and use the equation of a linear model to interpret slope and intercept in context. They also analyze bivariate categorical data using two-way tables and relative frequencies.

  • Irrational numbers and decimal expansions
  • Integer exponents and scientific notation
  • Slope and linear equations
  • Systems of linear equations
  • Functions and linear models
  • Geometric transformations, congruence, and similarity
  • Pythagorean Theorem and its applications
  • Volume of cones, cylinders, and spheres
  • Scatter plots and bivariate data analysis

How StudyPug Helps Utah 8th Graders

StudyPug's video lessons follow the Utah Core Standards Math sequence so students always find content that matches what their teacher is covering. Each lesson is short enough to fit into a homework session and includes practice problems so students can confirm their understanding before moving on. Whether a student is catching up, keeping pace, or getting ahead, StudyPug is available on any device at any time.