The Basics Of Ninth 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 ninth grade kid some math over the summer, or whenever. It covers the key stuff in your local grade 9 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 feedback. Make some rules, offer rewards, and make it a game. If you can make practice fun and challenging, your child will thrive!
Mastered ninth-grade math? Check out our Grade 10 Math Curriculum resource page (coming soon).
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. Get the cracks fixed and you will build a beautiful house.
Grade 9 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.
- Exponent Laws: Product of Powers, Quotient of Powers, Power Of Powers/Quotients/Products.
- Exponent Identities: Zero Exponent Law, Negative Exponent.
- Algebra: Polynomials Definition, Like Terms, Degrees of a polynomial.
- Geometry: Trigonometric Identities, Special Triangles, Area Problems, Volume And Surface Area.
- Probability & Statistics: Basic Probability, Probability Models, Sample Spaces, Comparing Spaces.
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Grade 9 Math Curriculum Examples
Recall from Grade 8 that exponentiation is a operation involving a base and an exponent. There’s 7 kinds of “tricks” that you can use on exponents that will be a major part of your grade 9 math curriculum. Let’s look at them together.
Exponent Laws [1/7] Product Of Powers Rule
This makes sense because exponentiation is doing multiplication a bunch of times. If you have 2^2 * 2^3, that’s ( 2 * 2 ) * (2 *2 * 2), which is 2 * 2 * 2 * 2 * 2 or 2^5. Use the product of powers rule to figure out that faster.
Exponent Laws [2/7] Quotient Of Powers Rule
When there is a quotient of powers with the same base, you can subtract the bottom power from the top power.
This is a consequence of the definition of exponents and the fact that anything divided by itself is 1.
For example 2^3 / 2^2 means (2*2*2)/(2*2). Since 2/2 = 1 there is 2 cancelations:(2*
2*2)/( 2*2). That leave 2 as the simplified answer.
This rule comes in handy all the time. What you can do with it is simplify the question by canceling out factors. As long as the base is the same, you can use this rule.
Exponential Law [3/6]The Power Of A Power Law
This law comes from the definition of the exponent, and applications of Product Of Powers Law.
Let’s say we have (2^2)^5.
By the definition of exponentiation, we have (2^2)*(2^2)*(2^2)*(2^2)*(2^2). Now we apply the Product Of Powers Rule, and we get 2^(2+2+2+2+2). Add up all those 2 and we get: 2^10.
Instead of doing all that, we use the Power of a power rule.
Exponential Laws [4/7] Power Of A Quotient
Any quotient to a power x is equal to the numerator to the x over the denominator to the x.
This makes sense if we work backwards and make a little proof.
Let’s say there’s a number like a^x divided by b^x. It would look like this: a^x/b^x. We apply the definition of exponentiation to get a*a*a* … * a (x times)/ b*b*b*…*b (x times). Which is the same as a/b * a/b *… * a/b (x times). By the definition of exponentiation that makes (a/b)^x.
Exponent Law [5/7] – Power Of A Product Law
The Power Of A Product Law is (a*b)^x = a^x * b^x. This is because (ab)^x = ab * ab *… *ab (x-times). Order does not matter in multiplication (recall commutative property), so ab * ab *… * ab (x-times) = a * a * … * a (x-times) * b * b * … * b (x-times). Group the like terms. Now, recognize that it is a^x * b^x by the definition of exponentiation applied twice to the “a” terms and the “b” terms.
Exponent Law [6/7] – Zero Exponent Law
Any number raised to the power 0 must be 1. We can prove it using the Quotient Of Powers Rule. Suppose x^a/x^a. Then we know that x^a/x^a = 1 because anything divided by itself is 1. By the quotient rule, x^a/x^a = x^(a-a) = x^0. So that must mean that x^0 = 1. We know this because we showed x^a/x^a = 1 and also x^a/x^a = x^0.
Another way you can think of it is that exponentiation means multiplying 1 by the base over and over. The number of times to multiply is the exponent. If the exponent is 0, then that means you multiply 1 by the base zero times. Well, that’s like doing nothing at all, so the answer will always remain 1.
Exponent Law [7/7] – Negative Exponent Rule
Whenever you see a negative exponent, that means the reciprocal. When a number gets multiplied by its reciprocal its equal to 1. That’s what multiplicative inverse means.
For example, the reciprocal of 2^3 is 1/(2^3). So 2^(-3) = 1/(2^3).
What Is A Polynomial?
Degree Of A Polynomial
The degree of a polynomial is the highest sum of the powers of any term. For example, in the polynomial x^3 + x^2 + x + 1, the highest exponent is 3. That means the degree of the polynomial is degree 3. All polynomials of degree 3 will have similarities with each other. You will learn this in high school math when you study functions and calculus.
In the expression x^3*y^2 +x^2 + x*y^2 + 9, the highest sum of exponents is 5. Can you see why? It’s because x^3*y^2 has exponents 3 and 2 which makes 5 when added together.
A term is an expression in a polynomial. They are the “Lego blocks” of the equations. Two terms are identical if they have the same number, variable, and power. If you have two identical terms then you can group them together.
Ninth Grade Math Problem Worksheets
Are you looking for something you can hand to your kid to start learning? Check out our free 9th 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 9 math today! If you don’t have a printer, open it with the iPad/Tablet.