Grade 8 Mathematics

Required Materials:

• Paper
• Pencil
• Ruler
• Cutout rectangles
• Cardstock
• Glue or tape
• 5-10 classmates
• Online calculator

Syllabus:

Unit 1 - Real Numbers, Exponents, and Radicals

Objectives:

• Understand the relationship between sets of real numbers.
• Convert fractions to decimals.
• Convert decimals to fractions.
• Recognize rational and irrational numbers.
• Find the square root of rational numbers.
• Locate rational approximations of irrational numbers on a number line.
• Use approximations to compare and order real numbers.
• Understand scientific notation.
• Convert numbers between standard decimal notation and scientific notation.
• Apply scientific notation to real-world problems.

Lessons:

• Working With Real Numbers
• Evaluating and Approximating Square Roots
• Comparing and Ordering Real Numbers
• Scientific Notation
• Scientific Notation Applications

Unit 2 - Working With One-Variable Equations

Objectives:

• Simplify and evaluate algebraic expressions.
• Solve one-variable, two-step equations.
• Solve and graph one-variable, two-step inequalities.
• Write one variable equations or inequalities with variables on both sides from real-world situations.
• Write real-world problems from one-variable equations or inequalities with variables on both sides.
• Model solving one-variable, two-step equations using concrete and pictorial representations.
• Solve one-variable equations with variables on both sides mathematically.
• Recognize solutions to equations having no solution and equations having an infinite number of solutions.
• Write and solve real-world problems modeled by one-variable equations with variables on both sides.
• Understand and use a problem-solving model.

Lessons:

• Variable Expressions and Two-Step Equations
• Two-Step Inequalities
• Writing Equations and Inequalities With Variables on Both Sides
• Writing Problems From Equations and Inequalities
• Modeling Equations With Variables on Both Sides
• Solving One-Variable Equations With Variables on Both Sides
• Applying One-Variable Equations With Variables on Both Sides

Unit 3 - Functions and Linear Relationships

Objectives:

• Recognize independent and dependent variable quantities in mathematical relationships.
• Identify functions using sets of ordered pairs, tables, mappings, and graphs.
• Determine and calculate the rate of change or slope from equations, tables, and verbal situations.
• Compare properties of functions from different representations.
• Determine and calculate the rate of change or slope from graphs.
• Use similar right triangles on the same graphed line to develop an understanding of slope.
• Develop the slope formula from the slope of a line.
• Use the slope formula to calculate the slope of a line passing through two points.
• Represent linear proportional situations using tables and equations.
• Determine and calculate the rate of change or slope from equations, tables, graphs, and verbal situations.
• Represent linear proportional situations using tables, equations, and graphs.
• Graph proportional relationships using the unit rate as the slope of the line.
• Describe slope as the steepness of the function line.
• Describe slope as the direction of the function line’s slant.
• Describe and recognize increasing and decreasing functions from tables, graphs, and verbal situations.
• Solve problems involving direct variation.

Lessons:

• Variable Quantities and Two-Variable Equations
• Functions
• Linear Functions and Slope
• Determining Slope From a Graph
• The Slope Formula
• Linear Proportional Functions
• Graphs of Linear Proportional Functions
• Working With Linear Proportional Functions
• Solving Direct Variation Problems

 

Unit 4 - Linear Relationships and Linear Systems

Objectives:

• Determine and calculate the slope and y-intercept from equations, tables, graphs, and verbal situations.
• Use similar right triangles on the same graph line to model the slope of a function.
• Write equations in the form of y=mx+b using verbal and numerical situations, graphs, and tables.
• Distinguish between proportional and non-proportional functions using tables, graphs, equations, and verbal situations.
• Represent linear proportional and non-proportional situations using tables, graphs and equations.
• Identify proportional and non-proportional linear functions in mathematical and real-world situations.
• Compare linear functions to non-linear functions.
• Solve systems of linear equations in two variables by locating the intersection of the two graph lines.
• Understand why the point of intersection is the solution to a system of linear equations in two variables.
• Solve real-world and mathematical problems leading to two linear equations in two variables.
• Solve systems of linear equations in two variables algebraically.
• Use a graphing calculator to solve a system of two linear equations in two variables and in slope-intercept form.

Lessons:

• Linear Non-Proportional Functions
• Graphs of Linear Non-Proportional Functions
• Comparing Proportional and Non-Proportional Linear Functions
• Applying Linear Functions
• Writing Linear Equations, Part 1
• Writing Linear Equations, Part 2
• Solving Systems of Linear Equations Using Graphs

Unit 5 - Working With Triangles

Objectives:

• Identify planes, points, lines, types of lines, line segments, rays, and angles.
• Classify and measure angles.
• Find unknown angle measures in geometric figures.
• Solve equations for unknown angle measures with numerical and algebraic expressions.
• Classify triangles.
• Understand the rules of triangles and use them to find unknown angle measurements.
• Solve equations for unknown angle measures of triangles with numerical and algebraic expressions.
• Recognize exterior angles in a triangle.
• Know and understand geometric properties relating to the exterior angles of triangles.
• Use geometric properties relating to the exterior angles of triangles to find unknown interior and exterior angle measurements.
• Know and identify the angles created when parallel lines are cut by a transversal.
• Understand the relationships between the angles created when parallel lines are cut by a transversal.
• Find the unknown measurements of the angles created when parallel lines are cut by a transversal.
• Confirm and validate that triangles are similar by comparing the corresponding parts.
• Solve problems involving similar figures.
• Demonstrate triangles are similar using AA, SAS, and SSS.
• Demonstrate that triangles formed by two transversals crossing parallel lines are similar.
• Solve problems using triangles formed by two transversals crossing parallel lines.

Lessons:

• Geometry Review
• Solving for Unknown Angle Measures
• Review of Triangles
• Exterior Angles of Triangles
• Parallel Lines and Transversals
• Similarity

Unit 6 - Geometric Transformations

Objectives:

• Know and recognize similarity and congruence between two-dimensional shapes.
• Know that a geometric transformation changes the location, orientation, or size of a two-dimensional shape.
• Know that a dilation is a geometric transformation that results in similar shapes.
• Calculate the scale factor between similar figures.
• Know and recognize dilations, translations, reflections, and rotations.
• Know which geometric transformations remain congruent and which do not.
• Know and recognize the properties of orientation and congruence of translations, reflections, rotations, and dilations of two-dimensional shapes on the coordinate plane.
• Explain the effect of translations applied to two-dimensional shapes on the coordinate plane using algebraic notation, verbal descriptions, and tables.
• Explain the effect of reflections applied to two-dimensional shapes on the coordinate plane using algebraic notation, verbal descriptions, and tables.
• Explain the effect of rotations applied to two-dimensional shapes on the coordinate plane using algebraic notation, verbal descriptions, and tables.
• Explain the effect of dilations applied to two-dimensional shapes on the coordinate plane using algebraic notation, verbal descriptions, and tables.
• Compare and contrast the attributes of a shape and its dilation on the coordinate plane.
• Use algebraic notation to explain the effect of a scale factor on a shape drawn on the coordinate plane.
• Explain the effect of dilations and translations as applied to circles.
• Identify and explain the effect of multiple transformations applied to two-dimensional shapes on the coordinate plane using algebraic notation and verbal descriptions.

Lessons:

• Similarity and Congruence
• Introduction to Geometric Transformations
• Properties of Congruence and Orientation
• Translations
• Reflections
• Rotations
• Dilations
• Working With Geometric Transformations

Unit 7 - Surface Area and Volume of Solids

Objectives:

• Review area and formulas for area and perimeter.
• Solve problems involving area.
• Understand the effect of dilations on the area of two-dimensional shapes.
• Solve problems involving the effect of dilations on the area of two-dimensional shapes.
• Know the formulas for the surface area of rectangular prisms.
• Solve mathematical and real-world problems involving the surface area of rectangular prisms.
• Know the formulas for the surface area of triangular prisms.
• Solve mathematical and real-world problems involving the surface area of triangular prisms.
• Know the formulas for the surface area of cylinders.
• Solve mathematical and real-world problems involving the surface area of cylinders.
• Compare the volume formula of a cylinder to the volume formula of a prism.
• Describe the volume formula of a cylinder in terms of its base area and its height.
• Learn the volume formulas for prisms and cylinders.
• Solve mathematical and real-world problems involving the volume of prisms and cylinders.
• Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights, and connect that relationship to the formulas.
• Learn the volume formulas for cones.
• Solve mathematical and real-world problems involving the volume of cones.
• Learn the volume formula for spheres.
• Solve mathematical and real-world problems involving the volume of spheres.

Lessons:

• Working with Area
• Lateral and Total Surface Area of Rectangular Prisms
• Lateral and Total Surface Area of Triangular Prisms
• Lateral and Total Surface Area of Cylinders
• Volume of Rectangular Prisms and Cylinders
• Volume of Cones and Cylinders
• Volume of Spheres

Unit 8 - The Pythagorean Theorem

Objectives:

• Recognize the types of right triangles.
• Learn the parts of a right triangle.
• Solve problems involving right triangles.
• Understand the Pythagorean theorem.
• Use models or diagrams to explain the Pythagorean theorem.
• Determine if a triangle is a right triangle by satisfying the Pythagorean formula.
• Determine if a triangle is a right triangle using the converse of the Pythagorean theorem.
• Use the Pythagorean theorem to solve real-world and mathematical problems.
• Use the converse of the Pythagorean theorem to solve real-world and mathematical problems.
• Use the Pythagorean theorem to find the distance between two points on the coordinate plane.

Lessons:

• Right Triangles and the Pythagorean Theorem
• The Converse of the Pythagorean Theorem
• Solving Problems Using the Pythagorean Theorem, Part 1
• Solving Problems Using the Pythagorean Theorem, Part 2
• Distance Between Two Points on the Coordinate Plane

 

Unit 9 - Working With Statistics

Objectives:

• Know and recognize various types of data, including bivariate, continuous, and discrete data.
• Construct scatterplots from discrete, bivariate data sets using tables and ordered pairs.
• Recognize graph breaks and add them appropriately to scatterplots.
• Analyze and interpret scatterplots that include clustering, outliers, and trends.
• Know and determine types of bivariate associations.
• Know and recognize trend lines for linear associations.
• Draw the trend line on scatterplots of linear associations.
• Use the trend line for a linear relationship to solve problems and make predictions about data sets.
• Know what correlations are in the context of linear relationships.
• Interpret the sign of the correlation for a linear relationship.
• Write the equation of a trend line from a scatterplot.
• Use the equation of a trend line to solve problems and make predictions about data sets.
• Select appropriate simulations for generating random samples.
• Generate random samples from populations by using simulations.
• Review how to calculate the mean, median, and interquartile range of a numerical data set.
• Interpret the interquartile range for a numerical data set from real-world situations.
• Understand and calculate the mean absolute deviation for a numerical set of data.
• Calculate and interpret the mean absolute deviation from a set of real-world numerical data

Lessons:

• Scatter Plots and Data
• Analyzing Scatter Plots
• Linear Associations and Trend Lines
• Working With Linear Relationships
• The Equation of a Trend Line
• Variability and Measures of Central Tendency
• Mean Absolute Deviation

Unit 10 - Personal Finance

Objectives:

• Solve problems that involve simple interest and compound interest.
• Explore loans and investments that compare simple interest and compound interest.
• Know what credit is in terms of personal finances.
• Solve real-world problems that compare how interest rates and loan length affect the cost of credit.
• Know the different types of personal finance loans.
• Calculate the APR given a monthly interest rate.
• Compare the total cost for different types of easy-access loans.
• Calculate the total cost of repaying different types of personal loans using an online calculator.
• Identify and explain the advantages and disadvantages of different payment methods.
• Know the difference between financially responsible and irresponsible decisions.
• Analyze personal finance situations and determine if they represent financially responsible decisions.
• Identify the benefits of financial responsibility and the costs of financial irresponsibility in personal finance situations.
• Estimate the costs for attending two-year and four-year colleges and universities.
• Develop periodic savings plans for saving the money needed to attend college.

Lessons:

• Simple Interest and Compound Interest
• The Cost of Credit
• Repaying Loans
• Payment Methods
• Making Financially Responsible Decisions
• Planning and Saving for a College Education