8th Grade Math Standards from the Department of Education
These are the standards defined by the Minnesota Department of Education. These are the concepts that your 8th grade son/daughter should know by the end of the year.
22.214.171.124 Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational.
126.96.36.199 Compare real numbers; locate real numbers on a number line Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers.
188.8.131.52 Determine rational approximations for solutions for problems involving real numbers.
184.108.40.206 Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions.
220.127.116.11 Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.
18.104.22.168 Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notations, such as f(x) to represent such relationships.
22.214.171.124 Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount.
126.96.36.199 Understand that a function is linear if it can be expressed in the form f(x)=mx +b or if its graph is a straight line
188.8.131.52 Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x) = mx + b, where x = 0,1,2,3
184.108.40.206 Understand that a geometric sequence is a non-linear function that can be expressed in the form f(x)=ab^x, where x=0,1,2,3
220.127.116.11 Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.
18.104.22.168 Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.
22.214.171.124 Identify how coefficient changes in the equations f(x)= mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.
126.96.36.199 Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.
188.8.131.52 Represent geometric sequences using equations, tables, graphs and verbal descriptions and use them to solve problems.
184.108.40.206 Evaluate algebraic expressions, including expressions containing radicals and absolute values, as specified values of their variables
220.127.116.11 Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.
18.104.22.168 Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships
22.214.171.124 Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.
126.96.36.199 Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line.
188.8.131.52 Use linear inequalities to represent relationships in various contexts.
184.108.40.206 Solve linear inequalities using properties of inequalities. Graph the solutions on the number line.
220.127.116.11 Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line.
18.104.22.168 Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically.
22.214.171.124 Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.
126.96.36.199 Use the relationship between square roots and squares of a number to solve problems.
188.8.131.52 Use the Pythagorean Theorem to solve problems involving right triangles.
184.108.40.206 Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.
220.127.116.11 Informally justify the Pythagorean Theorm by using measurements, diagrams and computer software.
18.104.22.168 Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine these relationships.
22.214.171.124 Analyze polygons on a coordinate system by determining the slopes of their sides.
126.96.36.199 Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically.
188.8.131.52 Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.
184.108.40.206 Use a line of best fit to make statements about approximate rate of change and to make predictions about values not on the original data set.
220.127.116.11 Assess the reasonableness of predictions using scatterplots by interpreting them in the original context.