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Utah Standards

Utah 8th Grade Math Standards

All 37 Utah math standards for 8th grade, each explained in plain English. The official wording is in Utah State Board of Education's document, linked at the end of this page.

37 standards

Mathematical Practices

8 standards
8.MP.1
Analyze constraints and goals in problems like systems or functions, make conjectures, monitor progress, connect equations, tables, and graphs, and check solutions by another method.
8.MP.2
Translate real situations into linear equations and back, like y = 15x + 40 for a phone plan, manipulate the symbols fluently, and explain what the answer means.
8.MP.3
Build logical arguments from definitions and theorems, like why a triangle with sides 5, 12, and 13 is a right triangle, defend conclusions, and critique the reasoning of others.
8.MP.4
Model real data and situations with functions or scatter plots and lines of fit, make approximations, interpret results in context, and improve the model if it falls short.
8.MP.5
Choose tools strategically, like graphing technology, tracing paper for transformations, or a calculator for scientific notation, weighing what each reveals and where it falls short.
8.MP.6
Use precise definitions and state what symbols mean, label units and axes on graphs, calculate accurately, and give answers like square roots to a sensible precision.
8.MP.7
See structure in equations and figures, like noticing 2x + 6 = 2x + 9 has no solution or that slope triangles on a line are similar, and use it to reason.
8.MP.8
Notice repeated calculations, like the same rise over run between any two points on a line, generalize them into rules like slope, and track details while checking intermediate results.

Number System

3 standards
8.NS.1
Tell rational numbers from irrational ones, show that a fraction's decimal ends or repeats, and turn a repeating decimal like 0.333... back into 1/3.
Common Core 8.NS.1
8.NS.2
Pin down an irrational number with decimals, like the square root of 2 is between 1.4 and 1.5, to compare such numbers and place them on a number line.
Common Core 8.NS.2
8.NS.3
Carry out operations with radicals and simplify them, focusing on square roots, like simplifying √50 to 5√2.

Expressions and Equations

8 standards
8.EE.1
Use the exponent rules, like 2³ × 2² = 2⁵ or 3⁻² = 1/9, to rewrite expressions with whole-number and negative exponents.
Common Core 8.EE.1
8.EE.2
Solve equations like x² = 25 or x³ = 8 with square and cube roots, find the roots of small perfect squares and cubes, and know that the square root of 2 is irrational.
Common Core 8.EE.2
8.EE.3
Estimate very large or very small amounts as a single digit times a power of 10, and compare them, like 6 x 10⁸ being 200 times 3 x 10⁶.
8.EE.4
Add, subtract, multiply and divide numbers in scientific notation, mix them with ordinary decimals, and pick sensible units for very large or very small measurements.
Common Core 8.EE.4
8.EE.5
Graph a proportional relationship, read its unit rate as the slope, and compare two such relationships shown in different ways, like a graph against an equation.
Common Core 8.EE.5
8.EE.6
Explain with similar triangles why a line's slope is the same between any two of its points, and derive the equations y = mx and y = mx + b.
Common Core 8.EE.6
8.EE.7
Solve linear equations, inequalities, and absolute value equations in one variable, using distribution and like terms, and tell when there are one, none, or infinitely many solutions.
8.EE.8
Solve a pair of linear equations in two variables by graphing or algebra, knowing the solution is where the two lines cross, and use such pairs to solve word problems.
Common Core 8.EE.8

Functions

5 standards
8.F.1
Explain that a function gives exactly one output for each input, and that its graph is the set of input-output pairs, without needing function notation.
8.F.2
Compare two functions given in different ways, like one as a table and one as an equation, to see which has the greater rate of change.
Common Core 8.F.2
8.F.3
Recognize y = mx + b as a linear function whose graph is a straight line, and give examples of nonlinear ones, like the area of a square A = s².
Common Core 8.F.3
8.F.4
Write a linear function for a real situation, find its rate of change and starting value from a description, table, graph or two points, and explain what they mean.
Common Core 8.F.4
8.F.5
Describe what a graph shows about two quantities, like where it rises, falls or curves, and sketch a graph from a verbal description.
Common Core 8.F.5

Geometry

9 standards
8.G.1
Check with tracing paper or software that sliding, turning or flipping a figure keeps its side lengths, angles and parallel lines unchanged.
Common Core 8.G.1
8.G.2
Know that two figures are congruent when one can be moved onto the other by slides, turns and flips, and describe the moves that do it.
Common Core 8.G.2
8.G.3
Describe how translations, rotations, reflections, and dilations change a figure on the coordinate plane, and notice that only reflections flip its orientation.
8.G.4
Know that two figures are similar when slides, turns, flips and a resize can map one onto the other, and describe the sequence that does it.
Common Core 8.G.4
8.G.5
Argue informally why a triangle's angles add to 180 degrees, which angles match when a line crosses parallel lines, and why two equal angles make triangles similar.
Common Core 8.G.5
8.G.6
Work through and explain why the Pythagorean Theorem and its converse are true, like by rearranging four right triangles inside a square.
8.G.7
Use the Pythagorean theorem to find a missing side of a right triangle in real problems, flat or in three dimensions, like the diagonal of a box.
Common Core 8.G.7
8.G.8
Find the distance between two points on a coordinate grid by treating it as the long side of a right triangle.
Common Core 8.G.8
8.G.9
Use the volume formulas for cylinders, cones and spheres to solve real problems, like how much a can or an ice cream cone holds.
Common Core 8.G.9

Statistics and Probability

4 standards
8.SP.1
Make a scatter plot of two measurements, like height and shoe size, and describe clusters, outliers and whether the points trend up, down, in a line or in a curve.
Common Core 8.SP.1
8.SP.2
Draw a straight line of best fit by eye through a scatter plot that looks linear, and judge how well it fits by how close the points sit to it.
Common Core 8.SP.2
8.SP.3
Use the equation of a line fit to two-variable data to solve problems and explain what the slope and intercept mean, like 2 cm of growth per week.
8.SP.4
Organize yes-or-no data about two things, like curfews and chores, in a two-way table and use row or column percentages to see whether the two are linked.
Common Core 8.SP.4

The official Utah documents

The plain-English lines on this page are EMStudio's own explanations of Utah's standards, not the official wording, which Utah State Board of Education publishes in the documents above. Codes and strand names identify each standard.