8th Grade Math (Arizona Mathematics Standards)

The Number System (NS)

• 8.NS.A.1 Know irrational numbers are not rational; every number has a decimal expansion, and rational decimals repeat; convert repeating decimals to fractions.
• 8.NS.A.2 Use rational approximations to compare and place irrational numbers on a number line and estimate expressions.
• 8.NS.A.3 Know that between any two rational or irrational numbers there is both a rational and an irrational number.

Expressions and Equations (EE)

• 8.EE.A.1 Use the properties of integer exponents to write equivalent numerical expressions.
• 8.EE.A.2 Use square and cube root symbols for solutions to x² = p and x³ = p (p positive rational) and know √2 is irrational.
  • a. Find square roots of perfect squares up to 225.
  • b. Find cube roots of perfect cubes up to 1000.
• 8.EE.A.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.A.4 Calculate with numbers in scientific notation, choose suitable units and read technology output.
• 8.EE.B.5 Graph proportional relationships with the unit rate as slope and compare relationships shown in different ways.
• 8.EE.B.6 Use similar triangles to explain why slope is constant on a line and derive y = mx and y = mx + b.
• 8.EE.C.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 and inequalities with rational coefficients, including expanding and collecting like terms.
• 8.EE.C.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 (F)

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

Geometry (G)

• 8.G.A.1 Check by experiment that rotations, reflections and translations keep lines, segment lengths, angle measures and parallel lines. (being checked)
• 8.G.A.2 Know two figures are congruent if rigid motions (rotations, reflections, translations) map one onto the other, and describe the sequence.
• 8.G.A.3 Use coordinates to describe what dilations and rigid motions do to 2-D figures.
• 8.G.A.4 Know similar figures are linked by rigid motions plus dilations, and describe such a sequence.
• 8.G.A.5 Use informal arguments about triangle angle sums, exterior angles, angles at parallel lines with a transversal, and AA similarity.
• 8.G.B.6 Understand the Pythagorean Theorem and its converse, including using side lengths to decide if a triangle is right.
• 8.G.B.7 Use the Pythagorean Theorem to find unknown sides of right triangles in 2-D and 3-D problems.
• 8.G.B.8 Use the Pythagorean Theorem to find how far apart two points on a coordinate grid are.
• 8.G.C.9 Know and use the volume formulas for cones, cylinders and spheres.

Statistics and Probability (SP)

• 8.SP.A.1 Make and interpret scatter plots and describe patterns such as clusters, outliers and positive, negative or non-linear association.
• 8.SP.A.2 Know straight lines model linear associations; fit a line informally and judge the fit.
• 8.SP.A.3 Use a linear model's equation to solve problems, interpreting slope and intercept.
• 8.SP.A.4 Show association in categorical data with two-way tables of frequencies and relative frequencies.
• 8.SP.B.5 Find probabilities of compound events with lists, tables, tree diagrams and simulation. (being checked)
  • a. Know a compound event's probability is the fraction of the sample space where it happens.
  • b. Show sample spaces with lists, tables and tree diagrams and identify the outcomes in an event.
  • c. Design and use a simulation to estimate compound-event probabilities.