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# 8th Grade Math

Some students entering eighth grade are ready to begin algebra while others are not. The way to tell is to consider a student’s current math abilities.

In order to be successful in algebra, students should already have a strong foundation in basic math facts, including place value, fractions, decimals, and percentages. They should understand positive and negative numbers and be able to add, subtract, multiply, and divide them. Students should be familiar with roots and radicals, additive and multiplicative inverses, order of operations, and the associative, commutative, and distributive properties.

If your eighth grade student has not mastered these topics, instead of moving into algebra, consider these alternative eighth grade math programs:

## Eighth Grade Math Curriculum

Math for 8th graders is not a subject where you'll want to wing it. You’ll want a trusted curriculum to guide the way, cover everything your child needs, and teach math in a logically sequential order.

Each option below has everything that you need for an entire school year of eighth grade math instruction.

### Worksheets for Eighth Grade Math

Whether your student uses worksheets, workbooks, written practice problems, or online app exercises, practice is essential at any level of math learning. Eighth grade is no exception!

These two workbooks provide exercise worksheets on math for 8th graders.

#### Worksheets in Eighth Grade Math Curriculum

- Math-U-See includes a student workbook with both practice and review/application worksheets for each lesson. Students complete only as many problems as necessary to prove mastery of the lesson. See pages 7-10 here for eighth grade math worksheets.
- Saxon uses a textbook only. So a Saxon student copies problems to notebook paper and works them there instead of in a workbook. Basically, the student creates their own eighth grade math worksheets.

### 8th Grade Math Lessons

Math-U-See includes video lessons (both DVD and streamable), so you know exactly how to teach each lesson. Also there is a printed Instruction Manual with more help for teaching the math lessons.

- Download a lesson from Math-U-See Algebra 1 here.
- Watch the video below for a demonstration of a Math-U-See Algebra 1 lesson.

Saxon Math Homeschool has lessons in the text and are designed to be used independently by the student. There are video lessons available on the DIVE into Math CDs which walk your student through the math.

### 8th Grade Math Charts of Formulas for Reference

Download, save, and print the 8th Grade Mathematics Reference Sheet to keep these key formulas handy.

#### 8th Grade Geometric Formulas

Perimeter of rectangle 2l + 2w = P

Perimeter of square 4s = P

Circumference of circle 2πr = C or πd = C

Area of rectangle lw = A

Area of square s2 = A

Area of triangle ½ bh = A

Area of circle πr^2 = A

Area of trapezoid ½ h(b1 + b2) = A

Surface Area of rectangular prism 2B + Ph = SA

Surface Area of right cylinder 2πrh+2πr^2= SA

Surface Area of right pyramid ½ l P + 2B = SA

Pythagorean Theorem a2 + b2 = c2

To calculate distance traveled d = rt

Volume of rectangular prism lwh = V

Volume of right pyramid 1/3Bh = V

Volume of right cylinder πr^2 h = V

Volume of cone 1/3 πr^2 h = V

Volume of sphere 4/3 πr^3=V

##### Perimeter of rectangle

2*l* + 2*w* = P

##### Perimeter of square

4*s *= P

##### Circumference of circle

2*πr* = C or *πd* = C

##### Area of rectangle

*lw* = A

##### Area of square

s^{2} = A

##### Area of triangle

½ bh = A

##### Area of circle

*πr*^{2} = A

##### Area of trapezoid

½ h(b_{1} + b_{2}) = A

##### Surface Area of rectangular prism

2B + Ph = SA

##### Surface Area of right cylinder

2*πrh *+ 2*πr ^{2 }*= SA

##### Surface Area of right pyramid

½ ℓ P + B = SA

##### Pythagorean Theorem

a^{2} + b^{2} = c^{2}

##### Volume of rectangular prism

*lwh* = V

##### Volume of right pyramid

1/3B*h* = V

##### Volume of right cylinder

*πr ^{2} h* = V

##### Volume of cone

1/3 *πr ^{2} h* = V

##### Volume of sphere

4/3 *πr ^{3 }*= V

##### To calculate distance traveled

*d *= *rt*

#### 8th Grade Imperial Measurement Conversion Factors

##### Units

12 inches = 1 foot

3 feet = 1 yard

5,280 feet = 1 mile

8 fl oz = 1 cup

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

16 oz = 1 pound

2,000 pounds = 1 ton

##### Units of Time

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

52 weeks = 1 year = 365 days

#### 8th Grade Metric Measurement Conversion Factors

## Metric Conversions |
||
---|---|---|

10 millimeters = 1 centimeter | 10 milliliters = 1 centiliter | 10 milligrams = 1 centigram |

100 centimeteres = 1 meter | 100 centiliters = 1 liter | 100 centigrams = 1 gram |

1,000 meters = 1 kilometer | 1,000 liters = 1 kiloliter | 1,000 grams = 1 kilogram |

### 8th Grade Math Problems & Equations

For algebra 1, eighth grade students will learn to work these kinds of problems and equations:

- solving equations and inequalities in one and two variables
- solving literal equations
- working with ratios and proportions
- graphing linear equations and quadratic equations
- factoring polynomials and trinomials

#### Numbers & Operations for Eighth Grade Math

Eighth graders will study these kinds of numbers:

- square roots
- cube roots
- rational and irrational numbers
- exponents

The 4 essential operations are

- addition
- subtraction
- multiplication
- division

In eighth grade, students learn how to **order **these operations using the mnemonic **PEMDAS**: Please excuse my dear Aunt Sally. A fun math activity is to ask your child to create an *original *mnemonic for PEMDAS. The goofier the better because it will be more memorable.

P | parentheses |

E | exponent |

M | multiplication |

D | division |

A | addition |

S | subtraction |

### Pre-Algebra for Eighth Grade Math

While the necessity of algebra 2 and higher math is debated among educators, there’s strong consensus that algebra 1 is the minimum floor of math proficiency for most jobs and trades. Because math is incredibly sequential, the path to algebra 1 always passes through** pre-algebra** which is commonly studied in the eighth grade.

#### Math-U-See Pre-Algebra

Math-U-See offers pre-algebra in a convenient set that includes everything you’ll need for a full year of math instruction.

#### Saxon Pre-Algebra

Although Saxon Math Homeschool does not have a level called pre-algebra, two levels cover pre-algebra topics: Saxon 8/7 and Saxon Algebra ½. A student doesn’t need to use both of these though. Start with Saxon 8/7 and if successful, move directly to Algebra 1. If more practice is needed, then opt for Algebra ½ for additional review.

#### Life of Fred Pre-Algebra

Life of Fred has five books in their pre-algebra series for middle schoolers which can be done any time during grades 5-9. These titles take a quirky approach to math that can resonate with teens who typically dislike math. So they make a great option for remediation or filling gaps.

Although the publisher claims they can be a stand alone math program, Sonlight considers Life of Fred books a *supplement* to enrich a more comprehensive math curriculum (such as Math-U-See or Saxon below). A student without a good foundation in fractions, decimals, percents, and pre-algebra can use Life of Fred to build the skills they will need in algebra.

## Eighth Grade Math Standards

Math standards are set by state departments of education. But they are typically easy to find online. Simply search *[state] 8th grade math standards* to find your state’s particular guidance.

41 states have opted to use Common Core Standards for math. You can read the Common Core Grade 8 Standards here. In grade 8, the focus is linear algebra and linear functions.

For math curriculum that meets Common Core standards, opt for one of these programs:

- Math-U-See (K-12th grade)
- Saxon Math Homeschool (K-12th grade)

Please note that while these programs cover the standards, they are presented in a slightly different *order* than prescribed in Common Core. So a certain topic may be assigned to 2nd grade in Common Core but is covered in 3rd or 1st grade in a certain curriculum. If Common Core Standards are important to you, simply remember that as long as you stick with the same program over many years, your child *will* eventually cover all of the concepts.

## Eighth Grade Math State Tests

The Every Student Succeeds Act (ESSA) was signed into law on December 10, 2015 as an updated version of the 2002 No Child Left Behind (NCLB) Act. This act requires states to test students in grades 3-8 annually in math and language arts.

States can set their own standards for these tests, but they are required to be “challenging.” Many states have opted to use Common Core standards. Since each state is different, it’s best to go directly to the particular state department of education website for information about your state’s eighth grade math test. Begin your search here at the U.S. Department of Education’s map.

Achieve.org offers data about the various state mandated tests to measure math mastery. Read their math policy report here. Algebra 1 is a key math marker, and thus many states give students an end of course test in high school on that particular topic.

## Eighth Grade Math Vocabulary

Here’s a list of key vocabulary for eighth grade math. Any good eighth grade math curriculum will teach students the meanings and applications of these terms.

- cartesian coordinates
- linear equation
- quadratic equation
- substitution
- factoring
- balancing
- substitution
- exponents
- scientific notation
- polynomials
- trinomials
- coefficient
- rational numbers
- irrational numbers
- commutative property
- associative property
- distributive property
- order of operations
- slope-intercept
- square root
- base (for example, base 10)
- ellipse
- parabola
- hyperbola
- probability
- statistics