8th Grade Math (Minnesota Academic Standards)

Strand 1: Number & Operation

• 8.1.1.1 Classify real numbers as rational or irrational, including roots of non-perfect squares.
• 8.1.1.2 Compare and place real numbers on a number line; place square roots between consecutive integers.
• 8.1.1.3 Find rational approximations of real-number solutions to problems.
• 8.1.1.4 Use rules of positive and negative integer exponents to write equivalent expressions.
• 8.1.1.5 Use scientific notation for very large and small numbers, multiplying and dividing with suitable precision.

Strand 2: Algebra

• 8.2.1.1 Understand a function as an input–output relationship and use notation such as f(x).
• 8.2.1.2 Understand linear functions: equal changes in input give equal multiples of change in output.
• 8.2.1.3 Recognize linear functions as f(x) = mx + b or straight-line graphs.
• 8.2.1.4 Understand arithmetic sequences as linear functions of whole-number inputs starting at zero.
• 8.2.1.5 Understand geometric sequences as exponential functions of the form ab^x.
• 8.2.2.1 Move between tables, words, symbols, equations and graphs for linear functions.
• 8.2.2.2 Identify slope as rate of change and the intercepts; proportional relationships have y-intercept 0.
• 8.2.2.3 Explore with graphing tools how m and b change the graph of f(x) = mx + b.
• 8.2.2.4 Represent arithmetic sequences with equations, tables, graphs and words and solve problems.
• 8.2.2.5 Represent geometric sequences in several forms and solve problems.
• 8.2.3.1 Evaluate expressions with radicals and absolute values for given values.
• 8.2.3.2 Justify steps in rewriting expressions by naming properties, including grouping symbols.
• 8.2.4.1 Represent constant-rate situations with linear equations, proportional or not.
• 8.2.4.2 Solve multi-step one-variable equations, solve for one variable in terms of others and justify steps.
• 8.2.4.3 Write lines in slope-intercept, point-slope and standard form and convert between them.
• 8.2.4.4 Use linear inequalities to represent relationships in various contexts.
• 8.2.4.5 Solve linear inequalities using their properties and graph the solutions on a number line.
• 8.2.4.6 Represent problems with absolute value equations and inequalities and solve and graph them.
• 8.2.4.7 Represent situations with systems of two linear equations and solve symbolically, graphically and numerically.
• 8.2.4.8 Relate the number of solutions of a system to intersecting, parallel or identical lines; check by substitution.
• 8.2.4.9 Use the relationship between squares and square roots to solve problems.

Strand 3: Geometry & Measurement

• 8.3.1.1 Use the Pythagorean Theorem to solve right-triangle problems.
• 8.3.1.2 Find distances between points on a grid using horizontal, vertical or Pythagorean reasoning.
• 8.3.1.3 Justify the Pythagorean Theorem informally using measurement, diagrams and software.
• 8.3.2.1 Understand slopes of parallel and perpendicular lines, exploring with graphing software.
• 8.3.2.2 Analyze polygons on the coordinate plane by finding slopes of their sides.
• 8.3.2.3 Find equations of lines parallel or perpendicular to a line through a given point.

Strand 4: Data Analysis & Probability

• 8.4.1.1 Make scatterplots with labeled axes and estimate lines of best fit with technology.
• 8.4.1.2 Use lines of best fit to estimate rates of change and make predictions beyond the data.
• 8.4.1.3 Judge the reliability of predictions from scatterplots in real contexts.