8th Grade Math (New Jersey NJSLS)

The Number System (8.NS)

• 8.NS.A.1 Know that irrational numbers are not rational; every number has a decimal expansion and repeating decimals can be written as fractions.
• 8.NS.A.2 Approximate irrational numbers with rationals to compare and order them, plot them and estimate values.
• 8.NS.A.3 Know sums and products of rationals are rational, rational + irrational is irrational, and non-zero rational × irrational is irrational.

Expressions and Equations (8.EE)

• 8.EE.A.1 Use the properties of integer exponents to write equivalent numerical expressions.
• 8.EE.A.2 Use √ and ∛ symbols to write solutions of x² = p and x³ = p for a positive rational p.
  • a. Evaluate √ of small perfect squares and ∛ of small perfect cubes; know √2 is irrational.
  • b. Simplify square roots of non-perfect squares, e.g. √8 = 2√2.
• 8.EE.A.3 Estimate very big or very small amounts as a single digit times a power of 10 and compare them.
• 8.EE.A.4 Calculate with numbers in scientific notation, choose suitable units and read scientific notation from technology.
• 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 the same anywhere on a line; derive y = mx and y = mx + b.
• 8.EE.C.7 Solve linear equations in one variable.
  • a. Give examples of linear equations with one, infinitely many or no solutions and show which by rewriting them.
  • b. Solve linear equations with rational coefficients, including expanding brackets and collecting like terms.
• 8.EE.C.8 Analyze and solve systems of two linear equations.
  • a. Know the solution of a system of two linear equations is where their graphs intersect.
  • b. Solve systems of two linear equations algebraically, estimate solutions by graphing and solve simple cases by inspection.
  • c. Solve real and math problems that lead to a pair of linear equations with two unknowns.

Functions (8.F)

• 8.F.A.1 Understand a function as a rule giving exactly one output for each input; its graph is the set of input-output pairs.
• 8.F.A.2 Compare properties of two functions shown in different ways (equation, table, graph, words).
• 8.F.A.3 Know y = mx + b defines a linear function with a straight-line graph; give examples of non-linear functions.
• 8.F.B.4 Build a linear function from a description or two points and interpret its rate of change and initial value.
• 8.F.B.5 Describe how two quantities are related by reading a graph and sketch a graph from a verbal description.

Geometry (8.G)

• 8.G.A.1 Check by experiment the properties of rotations, reflections and translations.
  • a. Lines go to lines and segments to segments of the same length.
  • b. Angles go to angles of the same size.
  • c. Parallel lines go to parallel lines.
• 8.G.A.2 Know two shapes are congruent if one maps to the other by rotations, reflections and translations; describe the sequence.
• 8.G.A.3 Use coordinates to describe what dilations, translations, rotations and reflections do to 2D shapes.
• 8.G.A.4 Know two shapes are similar if one maps to the other by transformations including dilations; describe the sequence.
• 8.G.A.5 Use informal arguments about triangle angle sums, exterior angles, angles from parallel lines and a transversal, and AA similarity.
• 8.G.B.6 Explain why the Pythagorean Theorem and its converse are true.
• 8.G.B.7 Use the Pythagorean Theorem to find unknown sides of right triangles in 2D and 3D problems.
• 8.G.B.8 Find the distance between two points on a coordinate grid using the Pythagorean Theorem.
• 8.G.C.9 Know and use the volume formulas for cones, cylinders and spheres.

Statistics and Probability (8.SP)

• 8.SP.A.1 Make and interpret scatter plots and describe patterns such as clusters, outliers and linear or non-linear association.
• 8.SP.A.2 Fit a straight line informally to a scatter plot with a linear pattern and judge how well it fits.
• 8.SP.A.3 Solve problems with a linear model's equation, interpreting its slope and intercept in context.
• 8.SP.A.4 Use two-way tables of frequencies and relative frequencies to look for association between two categorical variables.