How to Learn Math

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How to Learn Math

Anyone can learn math whether they're in higher math at school or just looking to brush up on the

basics. After discussing ways to be a good math student, this article will teach you the basic

progression of math courses and will give you the basic elements that you'll need to learn in each

course. Then, the article will go through the basics of learning arithmetic, which will help both kids inelementary school and anyone else who needs to brush up on the fundamentals.

EditSteps

Part 1: Keys to Being a Good Math Student

1. 1Show up for class. When you miss class, you have to learn the concepts either from a classmate or

from your textbook. You'll never get as good of an overview from your friends or from the text as you

will from your teacher.

o Come to class on time. In fact, come a little early and open your notebook to theright place, open your textbook and take out your calculator so that you're ready to

start when your teacher is ready to start.

o Only skip class if you are sick. When you do miss class, talk to a classmate to find outwhat the teacher talked about and what homework was assigned.

2. 2Work along with your teacher. If your teacher works problems at the front of your class, then work

along with the teacher in your notebook.

o Make sure that your notes are clear and easy to read. Don't just write down theproblems. Also write down anything that the teacher says that increases your

understanding of the concepts.

o Work any sample problems that your teacher posts for you to do. When the teacherwalks around the classroom as you work, answer questions.

o Participate while the teacher is working a problem. Don't wait for your teacher to callon you. Volunteer to answer when you know the answer, and raise your hand to ask

questions when you're unsure of what's being taught.

3. 3Do your homework the same day as it's assigned. When you do the homework the same day, the

concepts are fresh on your mind. Sometimes, finishing your homework the same day isn't possible.

Just make sure that your homework is complete before you go to class.

4. 4Make an effort outside of class if you need help. Go to your teacher during his or her free period or

during office hours.

o If you have a Math Center at your school, then find out the hours that it's open andgo get some help.
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or on your investments. You can also use algebra to figure out how long you'll have

to travel based on the speed of your car.

o Work with exponents. When you start solving equations with polynomials(expressions containing both numbers and variables), you'll have to understand how

to use exponents. This may also include working with scientific notation. Once youhave exponents down, you can learn to add, subtract, multiply and divide polynomial

expressions.

o Solve squares and square roots. When you've mastered this topic, you'll have perfectsquares of many numbers memorized. You'll also be able to work with equations

containing square roots.

o Understand functions and graphs. In algebra, you'll really get into graphic equations.You'll learn how to calculate the slope of a line, how to put equations into point-

slope form, and how to calculate the x- and y-intercepts of a line using slope-

intercept form.

o Figure out systems of equations. Sometimes, you're given 2 separate equations withboth x and y variables, and you have to solve for x or y for both equations.

Fortunately, you'll learn many tricks for solving these equation including graphing,

substitution and addition.[2]

4. 4Get into geometry. In geometry, you'll learn about the properties of lines, segments, angles and

shapes.[3]

o You'll memorize a number of theorems and corollaries that will help you tounderstand the rules of geometry.

o You'll learn how to calculate the area of a circle, how to use the Pythagoreantheorem and how to figure out relationships between angles and sides of special

triangles.

o You'll see a lot of geometry on future standardized tests like the SAT, the ACT andthe GRE.

5. 5Take on Algebra II. Algebra II builds on the concepts that you learned in Algebra I but adds more

complex topics like quadratic equations and matrices.

6. 6Tackle trigonometry. You know the words of trig: sine, cosine, tangent, etc. Trigonometry will teach

you many practical ways to calculate angles and lengths of lines, and these skills will be invaluable for

people who go into construction, architecture, engineering or surveying.

7. 7Count on some calculus. Calculus may sound intimidating, but it's an amazing tool chest for

understanding both the behavior of numbers and the world around you.
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o Calculus will teach you about functions and about limits. You'll see the behavior or anumber of useful functions including e^x and logarithmic functions.

o You'll also learn how to calculate and work with derivatives. A first derivative givesyou information based on the slope of a tangent line to an equation. For instance, a

derivative tells you the rate at which something is changing in a non-linear situation.A second derivative will tell you whether a function is increasing or decreasing along

a certain interval so that you can determine the concavity of a function.

o Integrals will teach you how to calculate the area beneath a curve as well as volume.o High school calculus usually ends with sequences and series. Although students

won't see many applications for series, they are important to people who go on to

study differential equations.[4]

Part 3: Math Fundamentals--Ace Some Addition

1. 1Start with "+1" facts. Adding 1 to a number takes you to the next highest number on the number

line. For example, 2 + 1 = 3.

2. 2Understand zeroes. Any number added to zero equals the same number because "zero" is the same

as "nothing."
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3. 3Learn doubles. Doubles are problems that involve adding two of the same number. For example, 3 +

3 = 6 is an example of an equation involving doubles.

4. 4Use mapping to learn about other addition solutions. In the example below, you learn through

mapping what happens when you add 3 to 5, 2 and 1. Try the "add 2" problems on your own.
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5. 5Go beyond 10. Learn to add 3 numbers together to get a number larger than 10.

6. 6Add larger numbers. Learn about regrouping 1s into the 10s place, 10s into the 100s place, etc.

o Add the numbers in the right column first. 8 + 4 = 12, which means you have 1 10and 2 1s. Write down the 2 under the 1s column.
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o Write the 1 over the 10s column.

o Add the 10s column together.
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Part 4: Math Fundamentals--Strategies for Subtraction

1. 1Start with "backwards 1." Subtracting 1 from a number takes you backwards 1 number. For example,

4 - 1 = 3.

2. 2Learn doubles subtraction. For instance, you add the doubles 5 + 5 to get 10. Just write the equation

backward to get 10 - 5 = 5.

o If 5 + 5 = 10, then 10 - 5 = 5.o If 2 + 2 = 4, then 4 - 2 = 2.

3. 3Memorize fact families. For example:

o 3 + 1 = 4
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o 1 + 3 = 4o 4 - 1 = 3o 4 - 3 = 1

4.

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Find the missing numbers. For example, ___ + 1 = 6 (the answer is 5).

5. 5Memorize subtraction facts up to 20.

6. 6Practice subtracting 1-digit numbers from 2-digit numbers without borrowing. Subtract the

numbers in the 1s column and bring down the number in the 10s column.

7. 7Practice place value to prepare for subtracting with borrowing.

o 32 = 3 10s and 2 1s.o 64 = 6 10s and 4 1s.o 96 = __ 10s and __ 1s.

8. 8Subtract with borrowing.
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o You want to subtract 42 - 37. You start by trying to subtract 2 - 7 in the 1s column.However, that doesn't work!

o Borrow 10 from the 10s column and put it into the 1s column. Instead of 4 10s, younow have 3 10s. Instead of 2 1s, you now have 12 1s.

o Subtract your 1s column first: 12 - 7 = 5. Then, check the 10s column. Since 3 - 3 = 0,you don't have to write 0. Your answer is 5.

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Part 5: Math Fundamentals--Master Multiplication

1. 1Start with 1s and 0s. Any number times 1 is equal to itself. Any number times zero equals zero.

2. 2Memorize the multiplication table.
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3. 3Practice single-digit multiplication problems

4. 4Multiply 2-digit numbers times 1-digit numbers.

o Multiply the bottom right number by the top right number.o Multiply the bottom right number by the top left number.
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5. 5Multiply 2 2-digit numbers.

o Multiply the bottom right number by the top right and then the top left numbers.o Shift the second row one digit to the left.o Multiply the bottom left number by the top right and then the top left numbers.o Add the columns together.

6. 6Multiply and regroup the columns.

o You want to multiply 34 x 6. You start by multiplying the 1s column (4 x 6), but youcan't have 24 1s in the 1s column.
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o Keep 4 1s in the 1s column. Move the 2 10s over to the 10s column.
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o Multiply 6 x 3, which equals 18. Add the 2 that you carried over, which will equal20.

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Part 6: Math Fundamentals--Discover Division

1. 1Think of division as the opposite of multiplication. If 4 x 4 = 16, then 16 / 4 = 4.

2. 2Write out your division problem.

o Divide the number to the left of the division symbol, or the divisor, into the firstnumber under the division symbol. Since 6 / 2 = 3, you'll write 3 on top of the

division symbol.
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o Multiply the number on top of the division symbol by the divisor. Bring the productdown under the first number under the division symbol. Since 3 x 2 = 6, then you'll

bring a 6 down.

o Subtract the 2 numbers that you've written. 6 - 6 = 0. You can leave the 0 blank also,since you don't usually start a new number with 0.
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o Bring the second number that is under the division symbol down.

oDivide the number that you brought down by the divisor. In this case, 8 / 2 = 4. Write4 on top of the division symbol.
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o Multiply the top right number by the divisor and bring the number down. 4 x 2 = 8.

o Subtract the numbers. The final subtraction equals zero, which means that you havefinished the problem. 68 / 2 = 34.

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3. 3Account for remainders. Some divisors won't divide evenly into other numbers. When you've

finished your final subtraction, and you have no more numbers to bring down, then the final number

is your remainder.[8]
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How to Learn Math