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## 8th Grade Math (Prealgebra) Online Course

## Thinkwell's 8th Grade Math (Prealgebra) with Professor Edward Burger

Buy now, start anytime. start anywhere, go as fast as you like. are you ready free placement test ..

## Video Lessons

- 12-month, online subscription to our complete 8th Grade Math (Prealgebra) course
- 36-week, day-by-day course lesson plan
- 90+ course lessons with 300+ streaming videos
- Automatically graded drill-and-practice exercises with step-by-step answer feedback
- Downloadable, printable course worksheets & answer keys
- Automatically graded section quizzes
- Chapter & Practice tests, a Midterm & Final Exam
- Animated interactivities....and more!

## How It Works

- Purchase Thinkwell's 8th Grade Math (Prealgebra) through our online store
- Create an account username and password which will give you access to the online 8th-grade Math (Prealgebra) course section
- Activate your 12-month subscription when you're ready
- Login to the course website to access the online course materials, including streaming video lessons, exercises, quizzes, tests and more
- Access your course anytime, anywhere, from any device
- Your work is automatically tracked and updated in real-time
- Grade reports and certificates of completion are available at request

Learn from award-winning mathematician Dr. Edward Burger

It's like having a world-class college professor right by your side.

- "Global Hero in Education" by Microsoft Corporation
- "America's Best Math Teacher" by Reader's Digest
- Robert Foster Cherry Award Winner for Great Teaching
- Author of The 5 Elements of Effective Thinking and Making Up Your Own Mind: Thinking Effectively Through Creative Problem Solving
- A leader on thinking, innovation, and creativity

## 1 Principles of Algebra

Office Hours are offered every

## 8th Grade Math Quizzes and Answer Keys

## 8th Grade Math Worksheets and Answer Keys

## 8th Grade Math/Prealgebra Printed Notes

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## Eighth grade math

## A. Number theory

- 2 Divisibility rules
- 3 Prime or composite
- 4 Prime factorization
- 5 Greatest common factor
- 6 Least common multiple
- 7 GCF and LCM: word problems
- 8 Sort factors of numerical expressions

## B. Integers

- 1 Integers on number lines
- 2 Graph integers on horizontal and vertical number lines
- 3 Absolute value and opposite integers
- 4 Compare and order integers
- 5 Integer inequalities with absolute values

## C. Operations with integers

- 1 Integer addition and subtraction rules
- 2 Add and subtract integers using counters
- 3 Add and subtract integers
- 4 Add and subtract three or more integers
- 5 Add and subtract integers: word problems
- 6 Integer multiplication and division rules
- 7 Multiply and divide integers
- 8 Evaluate numerical expressions involving integers

## D. Exponents

- 1 Understanding exponents
- 2 Evaluate exponents
- 3 Solve equations with variable exponents
- 4 Exponents with negative bases
- 5 Exponents with decimal and fractional bases
- 6 Understanding negative exponents
- 7 Evaluate negative exponents
- 8 Evaluate negative and zero exponents
- 9 Multiplication with exponents
- 10 Division with exponents
- 11 Multiplication and division with exponents
- 12 Power rule
- 13 Evaluate expressions using properties of exponents
- 14 Identify equivalent expressions involving exponents I
- 15 Identify equivalent expressions involving exponents II

## E. Scientific notation

- 1 Convert between standard and scientific notation
- 2 Scientific notation on calculators
- 3 Compare numbers written in scientific notation
- 4 Add and subtract numbers written in scientific notation
- 5 Multiply numbers written in scientific notation
- 6 Divide numbers written in scientific notation

## F. Square roots and cube roots

- 1 Square roots of perfect squares
- 2 Estimate positive square roots
- 3 Positive and negative square roots
- 4 Estimate positive and negative square roots
- 5 Relationship between squares and square roots
- 6 Solve equations using square roots
- 7 Cube roots of positive perfect cubes
- 8 Cube roots of positive and negative perfect cubes
- 9 Solve equations using cube roots
- 10 Estimate cube roots

## G. Rational numbers

- 1 Write fractions in lowest terms
- 2 Least common denominator
- 3 Round decimals and mixed numbers
- 4 Convert between repeating decimals and fractions
- 5 Convert between decimals and fractions or mixed numbers
- 6 Absolute value of rational numbers
- 7 Compare rational numbers
- 8 Put rational numbers in order

## H. Operations with rational numbers

- 1 Reciprocals and multiplicative inverses
- 2 Add and subtract rational numbers
- 3 Add and subtract rational numbers: word problems
- 4 Apply addition and subtraction rules
- 5 Multiply and divide rational numbers
- 6 Multiply and divide rational numbers: word problems
- 7 Apply multiplication and division rules
- 8 Apply addition, subtraction, multiplication, and division rules
- 9 Evaluate numerical expressions involving rational numbers

## I. Rational and irrational numbers

- 1 Identify rational and irrational square roots
- 2 Identify rational and irrational numbers
- 3 Classify numbers
- 4 Irrational numbers on number lines

## J. Ratios, rates, and proportions

- 1 Understanding ratios
- 2 Identify equivalent ratios
- 3 Write an equivalent ratio
- 4 Equivalent ratios: word problems
- 5 Unit rates
- 6 Word problems involving ratios
- 7 Do the ratios form a proportion?
- 8 Do the ratios form a proportion: word problems
- 9 Solve proportions
- 10 Solve proportions: word problems
- 11 Estimate population size using proportions
- 12 Scale drawings: word problems
- 13 Scale drawings: scale factor word problems

## K. Proportional relationships

- 1 Find the constant of proportionality from a table
- 2 Write equations for proportional relationships from tables
- 3 Identify proportional relationships by graphing
- 4 Find the constant of proportionality from a graph
- 5 Write equations for proportional relationships from graphs
- 6 Identify proportional relationships from graphs and equations
- 7 Identify proportional relationships from tables
- 8 Identify proportional relationships: word problems
- 9 Graph proportional relationships and find the slope
- 10 Interpret graphs of proportional relationships
- 11 Write and solve equations for proportional relationships
- 12 Find the constant of variation
- 13 Identify direct variation
- 14 Write direct variation equations
- 15 Write and solve direct variation equations

## L. Percents

- 1 Convert between percents, fractions, and decimals
- 2 Compare percents to fractions and decimals
- 3 Find what percent one number is of another
- 4 Find what percent one number is of another: word problems
- 5 Estimate percents of numbers
- 6 Percents of numbers and money amounts
- 7 Percents of numbers: word problems
- 8 Compare percents of numbers
- 9 Solve percent equations
- 10 Percent of change
- 11 Percent of change: word problems
- 12 Percent of change: find the original amount word problems

## M. Consumer math

- 1 Price lists
- 2 Unit prices
- 3 Unit prices with unit conversions
- 4 Unit prices: find the total price
- 5 Percent of a number: tax, discount, and more
- 6 Find the percent: tax, discount, and more
- 7 Sale prices: find the original price
- 8 Multi-step problems with percents
- 9 Estimate tips
- 10 Simple interest
- 11 Compound interest

## N. Units of measurement

- 1 Convert rates and measurements: customary units
- 2 Convert rates and measurements: metric units
- 3 Mixed customary units
- 4 Convert between customary and metric systems
- 5 Precision
- 6 Convert between Celsius and Fahrenheit

## O. Problem solving

- 1 Multi-step word problems
- 2 Guess-and-check word problems
- 3 Use Venn diagrams to solve problems
- 4 Elapsed time word problems

## P. Coordinate plane

- 1 Coordinate plane review
- 2 Quadrants and axes
- 3 Follow directions on a coordinate plane
- 4 Find the distance between two points

## Q. Two-dimensional figures

- 1 Identify and classify polygons
- 2 Classify triangles
- 3 Identify trapezoids
- 4 Classify quadrilaterals I
- 5 Classify quadrilaterals II
- 6 Graph triangles and quadrilaterals
- 7 Find missing angles in triangles
- 8 Find missing angles in triangles using ratios
- 9 Triangle Angle-Sum Theorem
- 10 Find missing angles in quadrilaterals I
- 11 Find missing angles in quadrilaterals II
- 12 Exterior Angle Theorem
- 13 Interior angles of polygons
- 14 Identify complementary, supplementary, vertical, adjacent, and congruent angles
- 15 Find measures of complementary, supplementary, vertical, and adjacent angles
- • New! Write and solve equations using angle relationships
- 16 Identify alternate interior and alternate exterior angles
- 17 Transversals of parallel lines: name angle pairs
- 18 Transversals of parallel lines: find angle measures
- 19 Transversals of parallel lines: solve for x
- 20 Find lengths and measures of bisected line segments and angles
- 21 Parts of a circle

## R. Transformations and congruence

- 1 Line symmetry
- 2 Rotational symmetry
- 3 Rotational symmetry: amount of rotation
- 4 Identify reflections, rotations, and translations
- 5 Describe a sequence of transformations
- 6 Translations: graph the image
- 7 Translations: find the coordinates
- 8 Translations: write the rule
- 9 Reflections over the x- and y-axes: graph the image
- 10 Reflections over the x- and y-axes: find the coordinates
- 11 Reflections: graph the image
- 12 Reflections: find the coordinates
- 13 Rotations: graph the image
- 14 Rotations: find the coordinates
- • New! Reflections and rotations: write the rule
- • New! Describe transformations
- 15 Sequences of congruence transformations: graph the image
- 16 Identify congruent figures
- 17 Congruence statements and corresponding parts
- 18 Side lengths and angle measures of congruent figures
- 19 Congruent triangles: SSS, SAS, and ASA

## S. Transformations and similarity

- 1 Similar and congruent figures
- 2 Dilations: graph the image
- 3 Dilations: find the coordinates
- 4 Dilations: find the scale factor
- 5 Identify similar triangles
- 6 Angle-angle criterion for similar triangles
- 7 Side lengths and angle measures of similar triangles
- 8 Side lengths and angle measures of similar figures
- 9 Find missing side lengths in proportional triangles

## T. Pythagorean theorem

- 1 Pythagorean theorem: find the length of the hypotenuse
- 2 Pythagorean theorem: find the missing leg length
- 3 Pythagorean theorem: find the missing leg or hypotenuse length
- 4 Pythagorean theorem: find the perimeter
- 5 Pythagorean theorem: word problems
- 6 Converse of the Pythagorean theorem: is it a right triangle?

## U. Three-dimensional figures

- 1 Parts of three-dimensional figures
- 2 Nets of three-dimensional figures
- 3 Front, side, and top view
- 4 Base plans
- 5 Similar solids

## V. Geometric measurement

- 1 Perimeter
- 3 Area and perimeter: word problems
- 4 Area and circumference of circles
- 5 Circles: word problems
- 6 Area and perimeter of semicircles and quarter circles
- 7 Area between two shapes
- 8 Volume of cubes, prisms, and pyramids
- 9 Surface area of cubes, prisms, and pyramids
- 10 Volume of cylinders
- 11 Volume of cones
- 12 Surface area of cylinders
- 13 Surface area of cones
- 14 Volume of spheres
- 15 Surface area of spheres
- 16 Volume and surface area of similar solids
- 17 Perimeter and area: changes in scale

## W. Number sequences

- 1 Identify arithmetic and geometric sequences
- 2 Arithmetic sequences
- 3 Geometric sequences
- 4 Number sequences: mixed review
- 5 Number sequences: word problems
- 6 Evaluate variable expressions for number sequences
- 7 Write variable expressions for arithmetic sequences

## X. Expressions and properties

- 1 Write variable expressions: one operation
- 2 Write variable expressions: two or three operations
- 3 Write variable expressions from diagrams
- 4 Write variable expressions: word problems
- 5 Evaluate one-variable expressions
- 6 Evaluate multi-variable expressions
- 7 Evaluate absolute value expressions
- 8 Evaluate radical expressions
- 9 Evaluate rational expressions
- 10 Identify terms and coefficients
- 11 Sort factors of variable expressions
- 12 Properties of addition and multiplication
- 13 Multiply using the distributive property
- 14 Write equivalent expressions using properties
- 15 Add and subtract like terms
- 16 Add and subtract linear expressions
- 17 Factors of linear expressions
- 18 Identify equivalent linear expressions I
- 19 Identify equivalent linear expressions II
- 20 Identify equivalent linear expressions: word problems

## Y. One-variable equations

- 1 Which x satisfies an equation?
- 2 Write an equation from words
- 3 Model and solve equations using algebra tiles
- 4 Write and solve equations that represent diagrams
- 5 Properties of equality
- 6 Identify equivalent equations
- 7 Solve one-step equations
- 8 Solve two-step equations
- 9 Solve two-step equations: complete the solution
- 10 Solve one-step and two-step equations: word problems
- 11 Solve equations involving like terms
- 12 Solve equations with variables on both sides
- 13 Solve equations with variables on both sides: fractional coefficients
- • New! Solve equations with variables on both sides: word problems
- 14 Solve equations with the distributive property
- 15 Solve multi-step equations
- 16 Solve multi-step equations with fractional coefficients
- 17 Solve equations: mixed review
- 18 Solve multi-step equations: complete the solution
- 19 Find the number of solutions
- 20 Create equations with no solutions or infinitely many solutions

## Z. One-variable inequalities

- 1 Solutions to inequalities
- 2 Graph inequalities on number lines
- 3 Write inequalities from number lines
- 4 Solve one-step inequalities
- 5 Graph solutions to one-step inequalities
- 6 Solve two-step inequalities
- 7 Graph solutions to two-step inequalities
- 8 Solve multi-step inequalities
- 9 Graph solutions to multi-step inequalities
- 10 Solve inequalities with integers: variables on both sides
- 11 Solve inequalities with decimals: variables on both sides

## AA. Linear equations

- 1 Find the slope of a graph
- 2 Find the slope from two points
- 3 Find a missing coordinate using slope
- 4 Slope-intercept form: find the slope and y-intercept
- 5 Graph a line using slope
- 6 Graph a line from an equation in slope-intercept form
- 7 Graph a line from an equation in point-slope form
- 8 Write a linear equation from a slope and y-intercept
- 9 Write a linear equation from a graph
- 10 Write a linear equation from a slope and a point
- 11 Write a linear equation from two points
- 12 Convert a linear equation in standard form to slope-intercept form
- 13 Graph a line from an equation in standard form
- 14 Graph a horizontal or vertical line
- 15 Equations of horizontal and vertical lines
- 16 Slopes of parallel and perpendicular lines

## BB. Functions

- 1 Identify functions
- 2 Identify functions: graphs
- 3 Does (x, y) satisfy the linear function?
- 4 Relate the graph of an equation to its solutions
- 5 Identify independent and dependent variables
- 6 Rate of change: tables
- 7 Rate of change: graphs
- 8 Constant rate of change
- 9 Evaluate a linear function
- 10 Complete a table for a linear function
- 11 Complete a table and graph a linear function
- 12 Interpret points on the graph of a linear function
- 13 Interpret the slope and y-intercept of a linear function
- 14 Write a linear function from a table
- 15 Compare linear functions: graphs and equations
- 16 Compare linear functions: tables, graphs, and equations
- 17 Write linear functions: word problems
- 18 Evaluate a linear function: word problems
- 19 Identify linear and nonlinear functions: graphs and equations
- 20 Identify linear and nonlinear functions: tables
- 21 Does (x, y) satisfy the nonlinear function?
- 22 Evaluate a nonlinear function
- 23 Find values using function graphs
- 24 Complete a table for a function graph
- 25 Domain and range of functions
- • New! Identify graphs: word problems

## CC. Systems of linear equations

- 1 Is (x, y) a solution to the system of equations?
- 2 Solve a system of equations by graphing
- 3 Solve a system of equations by graphing: word problems
- 4 Find the number of solutions to a system of equations by graphing
- 5 Find the number of solutions to a system of equations
- 6 Classify a system of equations by graphing
- 7 Classify a system of equations
- 8 Solve a system of equations using substitution
- 9 Solve a system of equations using substitution: word problems
- 10 Solve a system of equations using elimination
- 11 Solve a system of equations using elimination: word problems
- 12 Solve a system of equations using any method
- 13 Solve a system of equations using any method: word problems

## DD. Monomials and polynomials

- 1 Identify monomials
- 2 Model polynomials with algebra tiles
- 3 Add and subtract polynomials using algebra tiles
- 4 Add and subtract polynomials
- 5 Add polynomials to find perimeter
- 6 Multiply monomials
- 7 Divide monomials
- 8 Multiply and divide monomials
- 9 Powers of monomials
- 10 Square and cube roots of monomials
- 11 Multiply binomials using algebra tiles
- 12 Multiply polynomials
- 13 Multiply polynomials to find area

## EE. Data and graphs

- 1 Interpret tables
- 2 Interpret bar graphs
- 3 Create bar graphs
- 4 Interpret line graphs
- 5 Create line graphs
- 6 Interpret line plots
- 7 Create line plots
- 8 Create and interpret line plots with fractions
- 9 Interpret stem-and-leaf plots
- 10 Create stem-and-leaf plots
- 11 Interpret histograms
- 12 Create histograms
- 13 Create frequency charts
- 14 Box plots
- 15 Interpret scatter plots
- 16 Create scatter plots
- 17 Identify trends with scatter plots
- 18 Make predictions with scatter plots
- 19 Interpret circle graphs
- 20 Circle graphs and central angles

## FF. Statistics

- 1 Calculate mean, median, mode, and range
- 2 Interpret charts and graphs to find mean, median, mode, and range
- 3 Mean, median, mode, and range: find the missing number
- 4 Changes in mean, median, mode, and range
- 5 Calculate mean absolute deviation
- 6 Calculate quartiles and interquartile range
- 7 Identify an outlier
- 8 Identify an outlier and describe the effect of removing it
- 9 Outliers in scatter plots
- 10 Identify lines of best fit
- 11 Write equations for lines of best fit
- 12 Identify representative, random, and biased samples

## GG. Probability

- 1 Probability of simple events
- 2 Probability of opposite, mutually exclusive, and overlapping events
- 3 Experimental probability
- 4 Find probabilities using two-way frequency tables
- 5 Make predictions
- 6 Compound events: find the number of outcomes
- 7 Compound events: find the number of sums
- 8 Identify independent and dependent events
- 9 Probability of independent and dependent events
- 10 Factorials
- 11 Permutations
- 12 Counting principle
- 13 Combination and permutation notation

## Eighth grade lessons

## Rational and irrational numbers

- Rational numbers
- Adding and subtracting rational numbers
- Multiplying and dividing rational numbers
- Irrational numbers

## Exponents, scientific notation, and roots

- Properties of exponents
- Scientific notation
- Adding and subtracting numbers in scientific notation
- Multiplying and dividing numbers in scientific notation
- Square roots
- Proportional relationships
- Constant of proportionality
- Simple interest
- Percent change

## Two-dimensional figures

- Parts of a circle
- Area of circles
- Circumference of circles
- Complementary angles
- Supplementary angles
- Adjacent angles
- Vertical angles
- Transversals of parallel lines
- Interior angles of triangles
- Exterior angles of triangles
- The Pythagorean theorem
- The converse of the Pythagorean theorem
- Distance formula

## Transformations, congruence, and similarity

## Three-dimensional figures

- Surface area formulas
- Volume formulas
- Volume of prisms
- Volume of cylinders
- Volume of pyramids
- Volume of cones
- Volume of spheres

## Expressions

- Writing algebraic expressions
- Evaluating expressions
- Simplifying expressions
- The distributive property
- Expanding expressions
- Factoring expressions

## Equations and inequalities

- Solving equations
- Multi-step equations
- Equations with infinitely many or no solutions
- Solving inequalities
- Linear equations
- Slope-intercept form
- Point-slope form
- Standard form of linear equations
- Equations of parallel and perpendicular lines
- Systems of equations
- Relations and functions
- Independent and dependent variables
- Linear functions
- Domain and range

## Data and graphs

- Teachers go over definitions along with multiple problems for the skills so that students fully grasp the concepts.
- Skills available for statistics, time, ratios, and other eighth grade skills.
- Students learn how to use the scracthpad to better understand how to tackle the problems.

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## Summit Math 8, Semester 1 (MTH08A)

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## Online Programs

Group Session meeting times (optional): Wednesdays 7 – 8 p.m. ET

By the end of this course, you will be able to:

- Classify numbers as rational or irrational
- Work with radicals and integer exponents in expressions, operations, and equations
- Model relationships with linear equations and lines
- Solve linear equations and 2x2 linear systems
- Evaluate and compare functions
- Create functions that model relationships between quantities
- Determine if two figures are congruent or similar using transformations
- Apply the Pythagorean Theorem in problem solving
- Calculate angle measures and volumes in geometric figures
- Investigate patterns of association in bivariate data

## Testing and Prerequisites

## Course Prerequisites

Successful completion of Grade 7 Mathematics or equivalent

## Cost and Financial Aid

- Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
- Nonrefundable International Fee - $20 (outside US only)

## Earning School Credit

Recommended school credit: One academic year

## Technical Requirements

## Terms & Conditions

Virtual class meetings may be recorded for students to review.

After a you complete a course, your projects may be used to illustrate work for future students.

## About Mathematics at CTY

## New math enrichment courses available!

## Join the exciting world of competitive math

## Meet our Mathematics Instructors

I love that through CTY, I get the chance to work with gifted students from all over the world. I consider it an honor to be part of their journey!

## Amanda Broton

I love helping students understand difficult topics and make connections between them. Understanding Calculus is what makes advanced engineering applications possible, so it is extremely relevant to today's world and to the inventions of tomorrow.

## Donna Miller

I am so excited when students are able to persevere and decode a very challenging cipher in the course! I love that Cryptology teaches patience and dedication, and that mathematics is so much more than just the study of numbers and equations.

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