The Basics Of Eighth Grade Math On One Page
Don’t know what’s going on with your kid’s math? Let’s make this easy on you. Here’s a resource for parents who want to teach their eighth grade kid some math over the summer, or whenever. It covers the key stuff in your local grade 8 curriculum. Read through the sections and download the workbooks. Try to have as much fun with it as you can because the key to learning is to make it a game. Make some rules, offer rewards, and make it fun. If you can make make practice fun and challenging, your child will thrive!
Mastered eighth-grade math? Check out our Grade 9 Math Curriculum resource page.
Introduction To Math Education
Like building a house, there are no shortcuts to learning math. All new math is build on top of an existing math foundation. Sir Isaac Newton, the inventor of calculus once wrote: “If I have seen further, it is by standing on the shoulders of giants.”. We discover new things by building on previous things. It is important that our the foundation is strong. This makes learning advanced math easier. Knowing the prerequisite knowledge unlocks paths and makes learning the new stuff easier. Without a strong foundation anyone will find it difficult to follow the new material. This causes stress and confusion in later years. Like building a house, we should aim to have the most complete foundation we can.
Grade 8 Math Curriculum
It is very important for parents to be aware of what their child is learning in school.
Your school gets its direction from a governing body. The school board issues a curriculum (or math standards) for schools to follow. The curriculum varies across the world. For example. in Russia, the multiplication table starts in Grade 1, while in Ontario it starts in Grade 3. That means your school’s curriculum differs from what you may find online. In this article we cover an estimation of what you can expect from your school’s curriculum.
- Numbers and operations: Converting fractions and decimals, Square roots, Exponentials
- Solving equations: Equations with one unknowns
- Linear equations and functions: Coordinate plane, Slopes, Proportional Relationships,
- Systems of equations: Solving with graphing, Solving with substitutions
- Geometry: Pythagorean thoerem, Angles, Parallel and Perpendicular Lines
- Geometric transformations: Rigid Transformations, Translations, Reflections, Rotations
- Data and modeling: Scatter plots, Lines of best fit
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Grade 8 Math Curriculum Examples
Converting Fractions To Decimal Numbers
Converting Repeating Decimals To Fractions
To get rid of the repeating decimals there’s a trick. The trick is to subtract that number from 10-times of itself. The first step is to write this: 10x – x = 9x. The second step is to replace “x” with the decimal number to convert. This process can be repeated with any number. To summarize:
1). Let x be the decimal number you want to convert
2). Multiply by 10, represent it like 10x
3). Subtract x from 10x.
4). Solve for x
Let’s convert 0.333… (repeating forever decimal number) into a fraction. Let x = 0.333… Then 10x =3.333…. because when you multiply by 10, you move the decimal over to the right by one. 10x – x = 9x. We calculate that 10x – x = (3.333… – 0.333…) = 3. See now we have nice whole numbers. Did you see how that algebra worked? The final step is solve for x. We have 9x = 3. All we’ve got to do is to divide both sides by 9. We then get x = 3/9. We simplify by dividing 3 and 9 by 3 to get x = 1/3. which is equal to 0.333…
What Is A “Square Root” Of A Number
Think the area of a square. The area is a number. Call that number “x”. The area of any rectangle is its length times its width. A square is a rectangle that has equal length and width. So, the area is the “square of” its length. The “square root of x” is the length of a side of that square.
What if the area of the square is negative? You can not find the square root of a negative number without complex numbers. For fun, recall that a negative times a negative equals a positive. So, no negative number will be negative when it gets squared. A number getting squared means a number getting multiplied by itself. Is there a positive number that when squared it equals a negative number? No there isn’t. To find a number that is negative when squared you need to learn “i” the imaginary number. It’s a Complex number, defined as i^2 = 1. In Grade 8, you don’t gotta worry about that on your test.
Introduction To Square Roots Of Perfect Squares
Recall the multiplication table. The diagonals are called perfect squares.
The Inverse Of The Square Root
Recall that the square root of a number is the side of a square with that number as the area. To undo a square root, you can multiply it by itself, or in other words “square it”. That can be shown a couple of ways. Either with an exponent of 2, or by literally writing the square root times the square root. It means the same thing.
Cube Root Of A Number
A cube root is a lot like a square root, except extend the idea of the length of a side to the length of an edge on a cube.
Similarly to a square root, the inverse of a cube root is the “cube” of it. That means take the cube root and put it to the power of 3 to get the volume of the cube.
The Difference Between Rational And Irrational Numbers
A rational number is a number that is as a ratio of two whole numbers. Recall that a ratio is a rate of two of the same type of numbers. A ratio like 1/3 can bet written as 0.333… (repeating). An irrational number cannot be a ratio of whole numbers, and it is not a repeating decimal either. An irrational number always has infinite digits to the right of the decimal. The difference is that there is no pattern that repeats itself.
Pi is a number that represents the ratio of a circles circumference to its diameter. It cannot be a ratio of two whole numbers, so it is irrational. When written out in decimal form, pi continues forever without any pattern.
Exponential Numbers With A Positive Base
Exponential Numbers With A Negative Base
When a negative number (base) has an odd number exponent, then the result is negative. When a negative base has an even number exponent, then the result is positive. This happens because the product of two negative numbers is positive.
Scientific Notation Numbers
Number can be very big. They can be so big that it is bothersome to write down all the zeros! Number in science tend to be very big or very small. That is why there is scientific notation.
Scientific notation uses exponentiation and decimal numbers together to make very large or small numbers easy to read. For example instead of writing 123, 000, 000, 000, 000, 000 grains of sand, you can write 1.23 x 10^17.
Eighth Grade Math Problem Worksheets
Are you looking for something you can hand to your kid to start learning? Check out our free 8th grade math worksheets. You can download or try out our math problem generator to learn online. You can make a copy, download, and print these problems. Make it an exciting game and start learning Grade 8 math today! If you don’t have a printer, open it with the iPad/Tablet.