8th Grade Math (Utah Core Standards)

The Number System (8.NS)

• 8.NS.1 Know irrational numbers are not rational; every number has a decimal expansion, and rational decimals repeat; convert repeating decimals to fractions.
• 8.NS.2 Use rational approximations to compare and place irrational numbers on a number line and estimate expressions.
• 8.NS.3 Work with radicals and simplify radical expressions, focusing on square roots.

Expressions and Equations (8.EE)

• 8.EE.1 Use the properties of integer exponents to write equivalent numerical expressions.
• 8.EE.2 Use square and cube root symbols for solutions to x² = p and x³ = p; know small perfect squares and cubes and that √2 is irrational.
• 8.EE.3 Use one digit times a power of 10 to estimate huge or tiny quantities and say how many times bigger one is.
• 8.EE.4 Calculate with numbers in scientific notation, choose suitable units and read technology output.
• 8.EE.5 Graph proportional relationships with the unit rate as slope and compare relationships shown in different ways.
• 8.EE.6 Use similar triangles to explain why slope is constant on a line and derive y = mx and y = mx + b.
• 8.EE.7 Solve linear equations and inequalities in one variable.
  • a. Give examples of linear equations with one, infinitely many or no solutions and show which by simplifying.
  • b. Solve linear equations with rational coefficients, including expanding and collecting like terms.
  • c. Solve absolute value equations in one variable, finding all solutions.
• 8.EE.8 Analyze and solve systems of two linear equations.
  • a. Know a system's solutions are the intersection points of the graphs.
  • b. Solve systems of two linear equations algebraically, estimate by graphing and solve simple cases by inspection.
  • c. Solve real-world and math problems that lead to two linear equations in two variables.

Functions (8.F)

• 8.F.1 Know a function assigns exactly one output to each input, and its graph is the set of input-output pairs.
• 8.F.2 Compare properties of two functions shown in different ways (equation, graph, table, words).
• 8.F.3 Know y = mx + b defines a linear function with a straight-line graph and give examples of non-linear functions.
• 8.F.4 Build a linear function to model a relationship, find its rate of change and initial value, and interpret them.
• 8.F.5 Describe a relationship from a graph (increasing, decreasing, linear, non-linear) and sketch graphs from descriptions.

Geometry (8.G)

• 8.G.1 Check by experiment the properties of rotations, reflections and translations.
  • a. Lines map to lines and segments to segments of equal length.
  • b. Angles map to angles of equal measure.
  • c. Parallel lines map to parallel lines.
• 8.G.2 Know two figures are congruent if rigid motions (rotations, reflections, translations) map one onto the other, and describe the sequence.
• 8.G.3 Use coordinates to describe what dilations and rigid motions do to 2-D figures.
• 8.G.4 Know similar figures are linked by rigid motions plus dilations, and describe such a sequence.
• 8.G.5 Use informal arguments about triangle angle sums, exterior angles, angles at parallel lines with a transversal, and AA similarity.
• 8.G.6 Explain why the Pythagorean Theorem and its converse are true.
• 8.G.7 Use the Pythagorean Theorem to find unknown sides of right triangles in 2-D and 3-D problems.
• 8.G.8 Use the Pythagorean Theorem to find how far apart two points on a coordinate grid are.
• 8.G.9 Know and use the volume formulas for cones, cylinders and spheres.

Statistics and Probability (8.SP)

• 8.SP.1 Make and interpret scatter plots and describe patterns such as clusters, outliers and positive, negative or non-linear association.
• 8.SP.2 Know straight lines model linear associations; fit a line informally and judge the fit.
• 8.SP.3 Use a linear model's equation to solve problems, interpreting slope and intercept (finding the model's equation is not expected in grade 8).
• 8.SP.4 Show association in categorical data with two-way tables of frequencies and relative frequencies.