Grade 8 Mathematics

Syllabus:

Semester 1:

Section 1 – Real Number System

Objectives:

• Evaluate exponential algebraic expressions using exponential rules.
• Perform operations on numbers in scientific notation.
• Apply the use of scientific notation to real world situations. 
• Compare quantities written in scientific notation.
• Use estimation to compare irrational numbers using a number line.
• Solve simple radical equations.

Lessons:

• Rational Numbers
• Powers and Exponents
• Scientific Notation
• Roots

Section 2 – Equations in One Variable 

Objectives:

• Understand when the solution of a linear equation in one variable will give one solution, no solution or many solutions. 
• Solve two step equations with rational coefficients
• Write and solve a linear equation from a real-world problem that involves solving a two-step equation.
• Solve one-variable linear equations that involve the distributive property and gathering like terms
• Solve one-variable linear equations that have the variable on both sides of the equal sign.

Lessons:

• Two-Step Equations
• Writing Two-Step Equations
• Multi-Step Equations
• Equations with Variables on Both Sides

Section 3 – Introduction to Functions 

Objectives:

• Determine if a relation is a function given a set of ordered pairs, a graph, or a table of values.
• Graph functions using a set of ordered pairs.
• Graph and compare proportional relationships.
• Recognize a function as linear or nonlinear
• Analyze and sketch graphs with qualitative relationships.

Lessons:

• Relations and Functions
• Proportional Functions
• Linear and Nonlinear Functions
• Qualitative Functions

Section 4 – Linear Functions 

Objectives:

• Derive the equations of lines.
• Calculate the slope given two points
• Find the slope of a graphed line.
• Know the slopes of vertical and horizontal lines
• Graph lines in slope-intercept and standard form.
• Construct functions that model linear relationships.
• Interpret rate of change and initial value in context.
• Apply linear functions to real world concepts.

Lessons:

• Slope
• Graphing Linear Functions
• Writing Linear Functions
• Modeling with Linear Functions

Section 5 – Systems of Equations 

Objectives:

• Understanding the solution to a system of linear equations is a point that is a solution to all equations in the system.
• Determine the type of solution of a system (no solution, infinite solutions, a point).
• Solve a linear system of equations by graphing.
• Solve a linear system of equations by substitution.
• Create and solve linear systems of equations that model a real-world situation.
• Solve a linear system of equations by elimination.
• Create and solve linear systems of equations that model a real-world situation.

Lessons:

• Solve Linear Systems by Graphing
• Solve Linear Systems by Substitution 
• Solve Linear System by Elimination 
• Applications of Linear Systems

Semester 2:

Section 1 – Transformations 

Objectives:

• Verify the properties of translations
• Identify the rule for translating figures
• Translate figures on a coordinate plane
• Graph the reflection of a pre-image on a coordinate plane.
• State the coordinates of a figure that has been reflected.
• State the rule of reflection when given a preimage and an image.
• Graph the rotation of a pre-image on a coordinate plane.
• State the coordinates of a figure that has been rotated.
• State the rule of rotation when given a preimage and an image.
• Graph the dilation of a pre-image on a coordinate plane.
• State the coordinates of a figure that has been dilated.
• State the rule of dilation when given a preimage and an image.

Lessons:

• Translations
• Reflections
• Rotations
• Dilations

Section 2 – Congruence and Similarity

Objectives:

• Verify experimentally the properties of rotations, reflections, and translations.
• Describe the effect of dilations, translations, rotations, and reflections on two dimensional
• figures using coordinates.
• Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
• Given two congruent figures, describe a sequence that exhibits the congruence between them.
• Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
• Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Lessons:

• GeoGebra Transformations
• Sequences of Transformations
• Congruence Transformations
• Similarity and Transformations

Section 3 – Parallel Lines and Triangles 

Objectives:

• Explore the relationships between the angles created by cutting parallel lines by a transversal.
• Find the measure of unknown angles in a triangle.
• Prove the Pythagorean Theorem.
• Apply the Pythagorean Theorem to solve problems.
• Use the Pythagorean Theorem to find distance between points in the coordinate plane.

Lessons:

• Parallel Lines
• Angles in Triangles
• Pythagorean Theorem
• Distance in the Coordinate Plane

Section 4– Volume

Objectives:

• Know and use the formula for finding the volume of cylinders.
• Know and use the formula for finding the volume of cones.
• Know and use the formula for finding the volume of spheres.
• Apply finding volumes to real world situations.

Lessons:

• Volume of a cylinder
• Volume of a cone
• Volume of a sphere
• Applications of volume

Section 5– Data Analysis 

Objectives:

• Construct and interpret scatter plots.
• Describe patterns in scatter plots such as clusters and outliers.
• Find the lines of best fit for linear data.
• Use lines of best fit to analyze data.
• Construct two-way frequency tables.
• Create relative frequency tables to analyze categorical data.

Lessons:

• Analyze Bivariate Data
• Applications of Linear Regressions
• Two-Way Frequency Tables
• Relative Frequency Tables