Course Overview:
Read, set, go! Grade 8 Pre-Algebra is all about training to run the race of high school math. Students will strengthen their skills in topics like linear relationships, functions, and equations, and learn new skills that prepare them for Algebra 1. This course is designed with interactive learning and real-world activities to strengthen students’ math muscles for the race ahead.
Instructional time for Grade 8 Mathematics: Pre-Algebra will emphasize six areas:
- representing numbers in scientific notation and extending the set of numbers to the system of real numbers, which includes irrational numbers
- generate equivalent numerical and algebraic expressions including using the Laws of Exponents
- creating and reasoning about linear relationships including modeling an association in bivariate data with a linear equation
- solving linear equations, inequalities, and systems of linear equations
- developing an understanding of the concept of a function
- analyzing two-dimensional figures, particularly triangles, using distance, angle, and applying the Pythagorean Theorem
Prerequisites:
Required Materials:
Student-Supplied Resources
You will need the following items to complete this course:
Technical Requirements:
Supported Operating Systems
- Windows 11
- macOS Monterey (12)
- macOS Ventura (13)
- macOS Sonoma (14)
Supported Browsers
You may use recent versions of the following browsers on a technology capable device that supports Java, Flash, and improvements to HTML including HTML5.
- Microsoft Edge
- Mozilla Firefox
- Google Chrome
- Apple Safari
Supported Browser Plugins and Settings
The following plugins and settings may be required to use our courses.
- JavaScript enabled
- Cookies enabled
- Java installed
Syllabus:
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
Module 01: Numerical Expressions
- 01.00 Numerical Expressions Introduction
- 01.01 Irrational Numbers
- 01.02 Laws of Exponents with Integer Exponents
- 01.03 Order of Operations with Radicals
- 01.04 Scientific Notation
- 01.05 Adding and Subtracting with Scientific Notation
- 01.06 Multiplying and Dividing with Scientific Notation
- 01.07 Scientific Notation in the Real World
Module 02: Algebraic Equations and Inequalities
- 02.00 Algebraic Equations and Inequalities Introduction
- 02.01 Equivalent Algebraic Expressions
- 02.02 Multiplying Linear Expressions
- 02.03 Factoring Algebraic Expressions
- 02.04 Multi-Step Linear Equations
- 02.05 Solving Equations Using Square and Cube Roots
- 02.06 Two-Step Linear Inequalities
Module 03: Angles and Triangles
- 03.00 Angles and Triangles Introduction
- 03.01 Pythagorean Theorem
- 03.02 Pythagorean Theorem and the Coordinate Plane
- 03.03 Angle Relationships
- 03.04 Interior and Exterior Angles
- 03.05 Polygon Angle Sums
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
Module 04: Linear Equations
- 04.00 Linear Equations Introduction
- 04.01 Linear Relationships
- 04.02 Slope
- 04.03 Slope-Intercept Form
- 04.04 Graphing Linear Equations
- 04.05 Systems of Linear Equations
Module 05: Statistics and Probability
- 05.00 Statistics and Probability Introduction
- 05.01 Identifying Functions
- 05.02 Linear Functions
- 05.03 Scatter Plots
- 05.04 Line of Fit
- 05.05 Theoretical Probability
- 0.506 Experimental Probability
Module 06: Transformations
- 06.00 Transformations Introduction
- 06.01 Identifying Transformations
- 06.02 Translations
- 06.03 Reflections
- 06.04 Rotations
- 06.05 Dilations
- 06.06 Similar Triangles
