8th Grade Math (Ohio's Learning Standards)

The Number System (8.NS)

• 8.NS.1 Know that real numbers are rational or irrational; rational decimals end or repeat, irrational ones do neither.
• 8.NS.2 Use rational approximations to compare irrational numbers, place them on a number line and estimate expressions.

Expressions and Equations (8.EE)

• 8.EE.1 Use properties of integer exponents to write equivalent numerical expressions, including negative exponents.
• 8.EE.2 Use square and cube roots to solve x² = p and x³ = p, evaluate small roots and know √2 is irrational.
• 8.EE.3 Use a single digit times a power of 10 to estimate very large or small quantities and compare them.
• 8.EE.4 Compute with scientific notation, choose suitable units and read scientific notation from technology.
• 8.EE.5 Graph proportional relationships with the unit rate as slope and compare relationships in different forms.
• 8.EE.6 Use similar triangles to explain why slope is constant and derive y = mx and y = mx + b.
• 8.EE.7 Solve linear equations in one variable.
  • a. Find examples with one, no or infinitely many solutions.
  • b. Solve equations with rational coefficients, distributing and combining like terms.
• 8.EE.8 Analyze and solve pairs of simultaneous linear equations graphically.
  • a. Solutions are the intersection points of the two graphs.
  • b. Estimate solutions by graphing; recognize none, one or infinitely many.
  • c. Solve real problems leading to two linear equations by graphing.

Functions (8.F)

• 8.F.1 Understand a function as a rule giving exactly one output for each input; its graph is a set of ordered pairs.
• 8.F.2 Compare two functions given in different forms, e.g. rates of change from a table and an equation.
• 8.F.3 Know y = mx + b gives a straight line and give examples of nonlinear functions, such as area of a square.
• 8.F.4 Build a linear model from a description or two points, find rate of change and initial value and interpret them.
• 8.F.5 Describe relationships from graphs (increasing, decreasing, linear, nonlinear) and sketch graphs from descriptions.

Geometry (8.G)

• 8.G.1 Verify by experiment the properties of rotations, reflections and translations.
  • a. Lines map to lines and segments to equal segments.
  • b. Angles keep the same measure.
  • c. Parallel lines stay parallel.
• 8.G.2 Understand congruence as a sequence of rigid motions and describe the sequence for two figures.
• 8.G.3 Describe the effect of dilations, translations, rotations and reflections on 2D figures using coordinates.
• 8.G.4 Understand similarity as rigid motions plus dilations and describe the sequence for two figures.
• 8.G.5 Give informal arguments about triangle angle sums, exterior angles, angles with transversals and angle-angle similarity.
• 8.G.6 Analyze and explain an informal proof of the Pythagorean Theorem and its converse.
• 8.G.7 Use the Pythagorean Theorem to find unknown side lengths of right triangles in 2D and 3D problems.
• 8.G.8 Use the Pythagorean Theorem to find the distance between two points on the coordinate plane.
• 8.G.9 Solve problems with the volumes of cones, cylinders and spheres.

Statistics and Probability (8.SP)

• 8.SP.1 Make and interpret scatter plots of bivariate data, noting clusters, outliers and types of association.
• 8.SP.2 Fit a straight line to scatter plots that look linear and judge how well it fits.
• 8.SP.3 Use a linear model's equation to solve problems and interpret slope and intercept in context.
• 8.SP.4 Make two-way tables of categorical data and use relative frequencies to look for association.