8th Grade Math (South Dakota Content Standards)

The Number System (NS)

• 8.NS.1 Know non-rational numbers are irrational, rational decimals end or repeat, and change repeating decimals into fractions.
• 8.NS.2 Use rational approximations to compare irrational numbers, place them on a number line and estimate values such as π².

Expressions and Equations (EE)

• 8.EE.1 Use properties of integer exponents to make equivalent numerical expressions.
• 8.EE.2 Use square and cube root symbols for solutions of x² = p and x³ = p and evaluate small perfect squares and cubes.
• 8.EE.3 Estimate and compare huge or tiny amounts as one digit times a power of ten.
• 8.EE.4 Calculate with scientific notation, including decimals, choose suitable units and read scientific notation from technology.
• 8.EE.5 Graph proportional relationships, read the unit rate as the slope and compare two proportional relationships shown differently.
• 8.EE.6 Use similar triangles to show slope is the same between any two points on a non-vertical line and derive y = mx and y = mx + b.
• 8.EE.7 Solve linear equations in one variable.
  • 8.EE.7a Give examples of equations with one, no or infinitely many solutions and show which by simplifying.
  • 8.EE.7b Solve linear equations with rational coefficients, including distributing and combining like terms.
• 8.EE.8 Analyze and solve systems of two linear equations.
  • 8.EE.8a Know a system's solution is where the two graphs intersect, as it satisfies both equations.
  • 8.EE.8b Solve systems of two linear equations algebraically, estimate by graphing and solve simple cases by inspection.
  • 8.EE.8c Solve real and mathematical problems that lead to two linear equations.

Functions (F)

• 8.F.1 Understand a function as giving exactly one output for each input, its graph being the set of input–output pairs.
• 8.F.2 Compare two functions shown in different ways, e.g. which has the greater rate of change.
• 8.F.3 Know y = mx + b defines a linear function with a straight-line graph, and that some functions are not linear.
• 8.F.4 Build a function for a linear relationship and find its rate of change and starting value from a description, points, a table or a graph.
• 8.F.5 Describe how two quantities relate from a graph (increasing or decreasing, linear or not) and sketch a graph from a description.

Geometry (G)

• 8.G.1 Check by experiment that rotations, reflections and translations keep figures' key properties.
  • 8.G.1a Lines go to lines and segments to segments of the same length.
  • 8.G.1b Angles go to angles of the same measure.
  • 8.G.1c Parallel lines go to parallel lines.
• 8.G.2 Know 2D figures are congruent if rotations, reflections and translations map one onto the other, and describe such a sequence.
• 8.G.3 Use coordinates to show how dilations, slides, turns and flips change 2D figures.
• 8.G.4 Know 2D figures are similar if rotations, reflections, translations and dilations map one onto the other, and describe the sequence.
• 8.G.5 Use informal arguments about triangle angle sums, exterior angles, parallel lines cut by a transversal and angle-angle similarity.
• 8.G.6 Explain why the Pythagorean theorem and its converse are true.
• 8.G.7 Use the Pythagorean theorem to find missing sides of right triangles in real, 2D and 3D problems.
• 8.G.8 Find how far apart two points in the coordinate plane are with the Pythagorean theorem.
• 8.G.9 Know the volume formulas for cylinders, cones and spheres and use them to solve problems.

Statistics and Probability (SP)

• 8.SP.1 Make and read scatter plots of two measured quantities, noting clusters, outliers and linear or nonlinear patterns.
• 8.SP.2 Fit a straight line to a linear pattern on a scatter plot and judge how well it fits.
• 8.SP.3 Solve real problems with a linear model's equation and explain its slope and y-intercept.
• 8.SP.4 Build a two-way table for two categorical variables and use relative frequencies to look for association.