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).

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    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.

    Think of educational learning as a pyramid. The foundation is Elementary School Math and the Pinnacle being a pHD. A knowledge gap at he base affects your ability to learn at the top.
    Think of educational learning as a pyramid. The foundation is Elementary School Math and the Pinnacle being a pHD. A knowledge gap at the base affects your ability to learn at the top.
    This is a 1-page summary of the grade 9 math curriculum
    This is a 1-page summary of the grade 9 math curriculum

    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. 

    This graph shows how exponentiation acts with different bases around the origin.
    This graph shows how exponentiation acts with different bases around the origin. Base 10 is for scientific notation. Base e (Euler’s number) is common in mathematics. Base 2 is common for Computer Science (Binary). Base (1/2) is an example of modeling something that is reducing, like drug concentration in the blood.

    Exponent Laws [1/7] Product Of Powers Rule

    There’s 2 main things you need to know to apply the product of powers rule:
     
    1). That the base is the same for both numbers
     
    2). How to add positive or negative numbers together.
     
    These numbers tend to be very big or small, so you can leave them in the Standard Form. 

    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.
     
     
     
    This video explains how the product of powers law of exponents can be applied to negative bases, positive bases , negative exponents or positive exponents.

    Exponent Laws [2/7] Quotient Of Powers Rule

    This video explains how the quotient of powers works. When you have a numerator and denominator in exponential form with the same base then you can cancel out powers. It works by the quotient 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.

    This video explains the 3rd exponent law called the pwoer of a quotient and shows how it is useful by factoring the denominator and cancelling factors.

    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.

    This video covers the exponent law of when you take a power of a product.
    This video covers the exponent identity of when some base it taken to the 0 power

    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).

     

    This video shows what a negative exponent is and how it makes sense in grade 9 math
    This video covers the definition of a polynomial for grade 9 math

    What Is A Polynomial? 

    A polynomial is an expression of numbers and variables. The only operations are addition/subtraction, multiplication, and powers with positive exponents. There’s no division. There can be one variable (x) or many variables(x, y, z, … ). In your high school education, you will study polynomials in depth. You will see many polynomial equations and functions. You will learn how to study them by graphing them and analyzing them with Calculus. You will learn about the characteristic of a polynomial. What’s the degree, the roots, the critical points, the inflection points, and more.   
     
     

    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.

     
    This video explains what the degree of a polynomial is. It is the highest sum of the powers of variables.

    Like Terms

    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. 

    We also love to write blogs about learning. check out our blog on 6 free back to school math activities to get to the next level.

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