Course Overview:
In grade 8, students extend their knowledge of expressions and equations, including modeling bivariate data with linear equations and solving equations. Students will also solve systems of equations using a variety of methods. Students are introduced to the concept of functions and use functions to describe quantitative relationships. Their previous study of geometric concepts is extended to include analyzing two- and three-dimensional figures and calculating volumes of solids. Transformational geometry is used to present the concepts of similarity and congruence. Students will know and apply the Pythagorean Theorem to real world problems.
Semester 1 provides an opportunity for students to explore algebraic concepts that will prepare them for high school math courses. Students will study the Real Number System, solve one variable equations, and be introduced to functions. Students will explore and analyze linear functions in detail. They will solve systems of linear equations. Mathematical concepts explored will be applied to real world concepts.
Semester 2 explores geometric concepts. Students will experiment with transformations and their relationships to congruent and similar geometric figures. Students also are introduced to the relationships between parallel lines, angles in a triangle and use the Pythagorean Theorem to solve problems. Students use the Pythagorean Theorem to find distance in the coordinate plane. Formulas for finding the volume of cones, spheres and cylinders are applied to real-world problems. Students analyze bivariate data by creating linear regression equations and using two-way frequency tables.
Prerequisites:
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
