Question

How to Learn (Math)

Answer 1

Like any other skill, math expertise can be gained with practice. You don't have to LOVE it but I guarantee that other subjects become easier with a good math foundation. If you don't build a good foundation you will find it harder and harder to progress as the math becomes more complex.

Answer 2

Math is a language, sometimes called "the universal language" because it can be understood by people regardless of nationality, language, or culture. Humans have invented a universal system to describe quantities and patterns that exist in nature.

The most prevalent system is the Arabic numeral system. We use the digits 0,1,2,3,4,5,6,7,8, and 9, combined with things such as decimals, fractions, exponents, to represent a variety of physical quantities.

Answer 3

A key component of mathematics is being able to translate a literal situation to numbers. Certain key phrases in English translate (roughly) into mathematical expressions.

"Sally had 3 apples. Billy has 5 more apples than Sally. Cindy has half as many apples as Billy. Dylan has 2 less apples than Sally. Emily has twice as many apples as Cindy." How many apples do they have all together?"

phrases such as "more than" "all together" mean add. "less than" means subtract. "half as many as" means divide by 2. "twice as many" means multiply by 2.

Answer 4

we can write an "equation" which states that certain quantities are equal to each other.

Sally has 3 apples so:

sally's apples = 3 (later we will find a way to write this in a more concise way)

Answer 5

Billy has 5 more apples than Sally.
billy's apples = sally's apples + 5

Cindy has half as many apples as Billy.
cindy's apples = (1/2) * billy's apples

Dylan has 2 less apples than Sally.
dylan's apples = sally's apples - 2

Emily has twice as many apples as Cindy.
emily's apples = 2 * cindy's apples

Answer 6

addition, subtraction, multiplication, and division are the four basic operators

+ (addition)
- (subtraction)
* (multiplication. this is sometimes written as x or ⋅)
÷ (division. this is sometimes written as / or with a horizontal fraction bar)

I cannot cover everything in this tutorial but I would strongly suggest practicing these operations with 1 to 3 digit numbers.

Answer 7

You should also be able to make estimations. For example, you may not be able to calculate 78.5 * 40 in your head but you know it must be less than (80)*40 = 3200 but greater than (75)*(40) = 3000. This will help you judge when you have made a mistake in your calculation (for example, if you have calculated 78.5 * 40 to be greater than 3200 or less than 3000 you know you have messed up somewhere!)

Answer 8

Math follows rules. For example, fractions, decimals, and percents (ways we can express numbers that aren't whole numbers) follow a system for the four basic operations. Learn the rules and practice them until they become second nature.

Answer 9

Pattern recognition will help you GREATLY in math.

If you are given:
f(x) = x + 1
f(2) = ???

even if you don't understand what all of these letters mean, you can make a good guess as to what they want as an answer. see how the "x" inside the parentheses is re-written on the right side and added to 1? perhaps they want us to do the same thing to the 2 since it is inside the parentheses.

f(x) = x + 1
f(2) = 2 + 1?

Answer 10

A rule that describes a relationship between quantities is called a "formula". For example, the formula for the area of a circle is A = 2*pi*r^2. Take what you are given and use the formula to find what the question is asking for.

For example, if you are given r, you can "plug in" r into the equation to find A. If you are given A, you can find r.

Answer 11

Formulas and equations can use letters called "variables" to represent some quantity that is unknown. In the Area equation, r represents the radius of a circle. If the problem tells you that

radius = r = 2 cm

then you take the formula, replace "r" with 2 cm, and simply multiply 2 * pi * 2^2 to get the area.

Answer 12

When we write equations or formulas, we refer to the sides of the equal sign as the "left side" and "right side".

if A = B, then A is "the left side" and B is "the right side"

Answer 13

In order for both sides of the equation to stay equal, we must perform the same operations on both sides. If we add 3 to one side, we must also add 3 to the other side.

Answer 14

Going back to our area equation, if we are given "A = 100" we can plug this in to the equation to get:

100 = 2 * pi * r^2

and solve for r.

Since we want "r" by itself we can do the exact opposite of what's being done to r on the right side.

opposite of multiplication? division

opposite of multiplying by 2? dividing by 2!
opposite of multiplying by pi? dividing by pi!
opposite of taking a square? taking the square root!

Answer 15

you must take these operations and apply them to both sides

100 = 2 * pi * r^2

100/2 = pi * r^2

100/(2pi) = r^2

sqrt(100/2pi) = r = your answer

Answer 16

one last fundamental skill before I close with some general tips: drawing a picture based on a question! the goal is to produce a simple, accurate depiction of what is going on in the problem. the goal isn't to be artistic or fancy.

Answer 17

"If Sally walks 3 miles east and 4 miles north, draw the shortest path she can take to get back to the starting point."

Answer 18

If you have graph paper, you could try to make each grid line represent one mile. But if not, then you can try to make it roughly proportional using estimation.

Answer 19

make sure your drawing is labelled with meaningful information + units.

Answer 20

the shortest line between the start point and the end point looks like this:

Answer 21

let's label it to make our answer clear.

Answer 22

I hope this tutorial has helped you grasp the fundamentals of math. These skills are purposefully broad and show up in ALL forms of mathematics, and in turn, other subjects involving mathematics (chem, physics, bio, stat, etc.)

Answer 23

Some parting advice:

1. GO TO CLASS and PAY ATTENTION. Your future employers/admissions officers will not care about trivial things like social media, gossip, and entertainment. They will care about what you learned, how well you learned it, and how you applied it. Save non-academic stuff for after class.
2. When you take notes, make sure you actually understand what you are writing down. If something is unclear write a star next to it, and later consult your teacher/textbook/reputable sites on the internet (KhanAcademy is a life-saver).
3. Do practice problems, even ones that aren't assigned. Check the answers yourself if they are available, or ask someone to check for you. There's no point in doing drills over and over if you don't check yourself and correct errors before they become habits.
4. Learn from exams/quizzes/graded activities. Re-do the ones you got wrong.
5. Don't be afraid to go back to the basics if you need to. Everyone forgets things after a while.