Middle School Pre-Algebra (Grade 8)

Segment One

• Define irrational numbers within the real number system and locate an approximate value of a numerical expression involving irrational numbers on a number line
• Plot, order, and compare rational and irrational numbers, represented in various forms
• Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency
• Solve multi-step problems involving the order of operations with rational numbers including exponents and radicals
• Express numbers in scientific notation to represent and approximate very large or very small quantities
• Add, subtract, multiply, and divide numbers expressed in scientific notation with procedural fluency
• Solve problems involving operations with numbers expressed in scientific notation
• Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases
• Apply properties of operations to multiply two linear expressions with rational coefficients
• Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions
• Solve multi-step linear equations in one variable, with rational number coefficients, including equations with variables on both sides
• Determine the real solutions given an equation in the form of x² = p and x³ = q, where p is a whole number and q is an integer
• Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically
• Apply the Pythagorean Theorem to solve problems involving unknown side lengths in right triangles
• Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides
• Use the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides
• Apply the Pythagorean Theorem to solve problems involving the distance between two points in a coordinate plane
• Solve problems involving the relationships between supplementary, complementary, vertical, or adjacent angles
• Solve problems involving the relationships of interior and exterior angles of a triangle
• Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles

Segment Two

• Determine if a linear relationship is also a proportional relationship
• Determine slope given a table, graph, or written description of a linear relationship
• Write an equation in slope-intercept form given a table, graph, or written description of a linear relationship
• Determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph, or an equation in slope-intercept form
• Graph a two-variable linear equation from a written description, a table, or an equation in slope-intercept form
• Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations
• Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution, or infinitely many solutions
• Solve systems of two linear equations by graphing
• Given a set of ordered pairs, a table, a graph, or a mapping diagram, determine whether the relationship is a function.
• Identify the domain and range of the relation
• Analyze a written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant
• Determine whether a function is a linear function given a graph, equation, or input-output table
• Construct a scatter plot or a line graph as appropriate for the context given a set of real-world bivariate numerical data
• Describe patterns of association given a scatter plot within a real-world context
• Informally fit a straight line given a scatter plot with a linear association
• Determine the sample space for a repeated experiment
• Find the theoretical probability of an event related to a repeated experiment
• Solve problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability
• Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship
• Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane
• Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship
• Solve problems involving proportional relationships between similar triangles

To achieve success, students are expected to submit work in each course weekly. Students can learn at their own pace; however, “any pace” still means that students must make progress in the course every week. To measure learning, students complete self-checks, practice lessons, multiple choice questions, projects, discussion-based assessments, and discussions. Students are expected to maintain regular contact with teachers; the minimum requirement is monthly. When teachers, students, and parents work together, students are successful.