If I asked you to think

of a really tough problem what is the first thing

that comes to mind? Well, if you’re anything like me you probably thought of some big complex math equation, right? For most people, math

seems like one of the most difficult subjects out there. It’s abstract, it’s

complex, and unfortunately for those reasons a lot of people adopt the belief that

they’re just not math people. Which is patently untrue because math is a skill that can be learned just like any other. But since you clicked on this video hopefully you are not one of those people. Hopefully you have at least some degree of belief that you can

become better at math and you have the motivation to do so. And if you do, the obvious question is how do you get better at math? Well, fortunately, this is one of those questions that has a pretty simple answer. If you want to get better at math you have to do lots and lots of math. And the tougher the

problems are, the better. Because tough problems will

stretch your understanding and lead you to new breakthroughs. But, in the course of studying math and working through these tough problems you are eventually going

to come to problems that just stump you, that

you get completely stuck on. And when you get to these points it’s important to know how to eventually solve these problems, because these are the ones that are

really going to stretch and build your skill set. So that is what I want to

focus on in this video. I want to give you practical techniques for working through,

and eventually solving those problems that seem

insurmountable at first. To start, I want to focus on a piece of advice the Hungarian mathematician George Polya shared in his

1945 book “How to Solve It.” It goes: This is, in my opinion, the most important technique to understand

and put into practice when you’re trying to

solve tough math problems. Because math builds upon itself. More complex concepts are

built upon simpler concepts. And if you don’t have a strong grasp on the fundamental principles, then a more complex problem is going

to likely stump you. So, if you come across a problem that you can’t solve, first,

identify the components or the operations that it

wants you to carry out. A lot of times, complex

problems will have multiple. Now, what you can do in this case is split the problem

into multiple problems that isolate just one of those components or operations. I want to show you this concept in action so let’s work through a quick example. Now, I did have one example picked out that would be pretty easy but it ended up being a little bit too easy, so let’s do something a little

bit more complicated. So, this is a summation problem which uses the Greek symbol, sigma. And it essentially says that we’re going to add up a series of expressions that use a variable starting

at one and ending at four. But, if you notice, this summation problem also has a fractional exponent in it. Now, maybe some of you

math wizards out there could do this kind of

a problem in your sleep but it’s also possibly the case that you don’t have a really firm grasp on either summation or

fractional exponents. So, when you’re working a problem that combines the two of

them, you might get stuck. So, assuming that’s the case, let’s break this problem into two simpler problems that each focus on just one

of the underlying concepts. First, let’s create a

simpler summation problem that just gets rid of that

fractional exponent altogether. Now, all we have to do is

evaluate that expression four times and then add up the answers which gets us to a final answer of 66. And now let’s move on to

the fractional exponent. Now, I’m going to go pretty quick here because this is not a lesson

on fractional exponents but essentially you can rewrite this as four to the power of three times the power of one half. And then you can rewrite that again to the square root of four

to the power of three. And once you evaluate that,

you get an answer of eight. Now, the whole point of

working these simpler single concept problems is to master the underlying concept or operation that you’re working on here. So, if you solve a few

and you still don’t feel really confident on that concept keep working it until you do. Remember, mastery means not

being able to get it wrong. Not just getting it right once. Anyway, once you’ve

mastered those underlying components in an isolated setting now you can come back

to the more complicated problem that combines them. At this point, you should be able to work those isolated concepts in your sleep which means that all of

your mental processing power can go towards the new and novel problem of how they work in tandem. Now, there is one additional

way of simplifying tough problems that I want to talk about and you might have already guessed it if you paid really close

attention to the examples. I didn’t use really complex numbers. I didn’t use long numbers. I didn’t use decimal points. I didn’t use big fractions. And I stuck to a low limit

on my summation problem. Really complex, big numbers

with lots of decimal points can distract your attention

away from the concepts and the operations that you’re

supposed to be practicing. So, if you’re stuck on a tough problem that has these kinds of numbers go work a similar

problem with really small whole numbers that are easy to add or operate in your head, that way you can really zero in

on the actual concepts. Of course, sometimes you have too shaky of an understanding of the concepts and operations themselves

for you to actually work with them and solve that problem. And in that case, it’s time

to go do some learning. Go dig into your book,

look through your notes, or find example problems online that you can follow

along with step-by-step so you can see how people are getting to the solutions, using these concepts. And, if you need to, you can actually get a step-by-step solution

to the exact problem you’re working on as well. There are several tools out there that you can use to do this. The two that I want to

focus on in this video which are the best ones

I’ve been able to find are WolframAlpha and Symbolab. Both of these websites will allow you to type in an equation and get an answer and also gypha and Symbolabs that you can follow along with. The difference between the two is that WolframAlpha,

while being much more power and capable, does require you to be part of their paid plan if you want to get those step-by-step solutions. By contrast, while I found that typing in equations into Symbolab

was a little bit slower and less intuitive than

it is with WolframAlpha their step-by-step solutions are free. Regardless of the tool

that you choose to use here the underlying point is that sometimes it can be useful to see

a step-by-step solution for a problem you’re stuck on. But, there are two very

important caveats here. First and foremost,

before you go running off to find a solution, ask yourself “Honestly, have I pushed my brain to the limit trying to

solve this problem first?” Expending the mental effort required to solve the problem yourself is going to stretch your capabilities. It’s going to make you

a better mathematician in a way that just looking

through solutions won’t. Now, if you do need to look

up a solution, that’s fine. Look it up, follow the steps and make sure that you understand how the answer was arrived at. But, once you’ve done

that, challenge yourself to go back and rework the problem without looking at that reference. It is really important to

stay vigilant about this. Because if you want to get better at math the whole point is to master the concepts that you’re working with. The danger that comes

with looking up solutions is that with math it’s really easy to follow along with a

step-by-step solution and comprehend what’s going on. But that is very different than being able to do it on your own. And that brings me to

my final tip for you. And this is especially

important for anybody in a math class working

through assigned homework. Don’t rush when you work

through math problems. I know it’s really tempting to try to work through homework as fast as you can and heck, I even made a video

about it pretty recently. But, with math and science and any sort of really

complex subject especially rushing is only going to

hurt you down the road. Because when you rush, you

don’t master the concepts. You just brute force your way to answers or you look things up, or you otherwise kind of cheaty-face your way to a completed homework assignment. And later on, when you’re sitting in a testing room, or you have to apply what you’ve learned in the real world you are going to get a harsh lesson about exactly what it is you don’t know. So let’s recap here. If you want to get better at math and you want to improve your ability to solve those really tough problems first, identify the

combination of concepts or operations being used in a problem and then isolate them. Work simpler problems that use just one and then master each concept. You can also simplify the problem by leaving the combination

of concepts intact but swapping in smaller,

easier to handle numbers. If you need help with

the concepts themselves go to your book or an

explainer article online look up sample problems, or use a tool like WolframAlpha or Symbolab

to get step-by-step solutions to the problem you’re working on. And finally, don’t rush through

your homework assignments. Make sure that you’re focusing intently on mastering the concepts,

not just finishing. Hopefully these tips will

give you the confidence to tackle some really tough math problems and to expand your math skill set. And on that note, I want

to leave you with a quote from the great physicist,

Richard Feynman, who said, The bottom line is this: Ultimately, your ability

to get good at math and anything else for that matter starts with having the

confidence to approach it. And as you solve problems

and make mental breakthroughs your confidence is going

to naturally increase. It becomes a self-sustaining cycle. If you’re interested in starting the cycle of learning now, a great place to begin your journey is at Brilliant. A learning platform that uses hands-on problem solving as a basis to help you learn math, science and computer science, really effectively. I’m actually taking their computer science fundamentals course

right now, and as I was going through the first

section on algorithms the quiz questions they gave me forced me to learn new math I had

never learned before. I had to dig into wikis

and example problems. And eventually I had to get out a sheet of notebook paper and literally draw out algorithms step-by-step so I could understand what was going on. This process provided me

with a much more intense and effective learning

experience than I got sitting through most

of my college lectures. And these types of challenges that really force you to dig in, form the foundation for all of their courses. Which include probability, logic, calculus astronomy, computer memory and more. In addition to the structured courses Brilliant also has weekly challenges that you can use to improve your skills and has a community where you can talk with other learners and

it has a fantastically detailed and helpful wiki with lots of explanations and examples. So, if you want to give Brilliant a try click the link the description down below and sign up for free to start learning. And, as a bonus, if you’re among the first 200 people to sign up, you’ll also get 20% off your annual premium subscription. I want to give a huge thanks to Brilliant for sponsoring this video and helping to support this channel. And, as always guys, thank

you so much for watching. If you found this video helpful you can give it a like

to support this channel and maybe you can consider sharing it with a friend who could

benefit from it as well. Otherwise, you can subscribe right there and maybe hit that bell icon if you want to be the first to

know when new videos drop or click right there to get a free copy of my book on how

to earn better grades. Alternatively, you can click right there to listen to our latest podcast episode on how to crush job interviews or if nothing else, you

can click right there to get one more video on

this channel right now. Thanks for watching and I will

see you in the next video.

Whoops – looks like my computer had a bit of a rendering hiccup around the 5:00 mark. In case it wasn't clear, that part just said that both sites provide step-by-step solutions that you can follow along with.

Man i dont even know where to start

I'm a 6 grader and i stumbled here…. Nvm goodbye

1+1=?

Math is good but our math teacher doesn't even know how to explain and do the solutions.

Why does not it always appear when I activate the Portuguese caption? So it gets a bit complicated to fully understand.

Fcvk I'm grade 7th in we will now road on algebra I adv read algebra a lot and do algebra math but I'm now stuck somewhere i dont know

wow guilty of doing everything that wasn't recommended + thank you this was helpful

Thanks for this video. This inspired me a lot more coz' I kinda regretted slacking off and wasting time on my highschool days.

School: 2+2=4 8+8=16

I'm good at math I just clicked because your cute.

Okay mr big-brain

Are we going to ignore the Monty Python and the Holy Grail reference?

What is this maths I'm in 9th grade and I'm scared

All of my sibling are geniuses when it comes to math… I’m 54 I’ve never been good at math I don’t know maybe because I had such a hard time at school…. I’m dying to be good with maths as I need to get out of my negative job , my bosses are so negative …. don’t even know my Times tables

Maths will be my gateway I know that

How do I go about it …. plus I have terrible concentration

Je looks like alisson the liverpool goal keeper hhhhhh

Great video but you wasting a lot of pages

MATH IS EASY.

So… practice makes perfect?

÷

Is hard

Youtube knows me well

Thank you. This video boosts my confidence, although I am not that good at Maths, but I will try. It is a challenge and I am not going to give up this easily. It is all hard works.

If you don't find math inherently enjoyable, it's important to look for interesting uses of math so you can see how math applies to that particular usage.

My point is that math can seem rather detached from the real world, but it isn't. It's just involved in everything, and when something is in everything, it seems less special without a narrow identity.

You can narrow it though. Just find a topic you're interested in like warfare, criminology, etc, and do some research on what is done there and how math is utilized. You can give yourself a large goal so that you have an objective when building up your skill set.

After 12 years of studying Math, you'd think that that the general population would be amazing at it.. but they're not. "Practice" is not enough..

"最重要 所有的符号我都看得懂” from someone who sees patterns everywhere

Enrique ????

What about photomath

i went here to prepare for exam and ehem distracted….

I'm not a math person ¯(°_o)/¯

M-MENTAL

A-ABUSE

T-TO

H-HUMANS

Brain.exe is not responding

|-Close Program-|-Check for solution-|-Wait for app to respond-|

Practice!!!

H=half

O=of

M=my

E=energy

W=wasted

O=on

R=random

K=kuestion

M= MENTAL

A= ABUSE

T= TO

H= HUMANS

Sorry😂

I was in LD and teachers just didn't want to teach math. I had an 8th grade teacher that said f it let's do algebra. It wasn't part of his original curriculum but he wanted to see how we did.

Now being in LD doesn't mean we have low IQs because if we did we'd be in the special education class. We were smart kids that just had some kind of learning disability. Schools and teachers a lot of the time just fail to teaching us. Having a dozen kids who have unique needs and problems can can make it hard to write a particular curriculum.

Back to my 8th grade math class. He started teaching us the basics of algebra and I was loving it. To me it wasn't hard at all and it was fun. I wanted to learn more but his experiment ended and he decided to teach us the original humdrum basic simple math. I was doing great and got everything right but most of the kids couldn't do it. Since then I haven't learned anything more.

My learning disability wasn't that big of a deal. Just a little dyslexia but mostly an anxiety disorder. When I was in large classes I couldn't think or do my work. And the LD classes didn't individualize a learning curriculum. We where giving work that the slowest kid could do so what that meant for me was doing the same work year in and year out. Only a few teachers taught me anything and they were 3 teachers in middle school. Other than that I learned everything on my own and after highschool.

What I really want to do now is teach myself math. Even though I don't know much I think I'm capable.

Math is very important, so thank you.

I want to make games when I get older but that involves math so I'm afraid I won't be good at it…

Mathematics is very easy for me but hard In grade1

i just want a gaming pc i hate asian parents

The thing is i dont know where to start

How to get better at literally anything in life:

You practice. Do the thing more/end

How i really wish i could understand math

i finally know the answer for 9+10

21.I seem to forgot about the easy math formulas and most of the multiplication table and I can't remember it all now

Shut up and do lots and lots of maths.Just do it…….

I'm here because I'm one of the four out of three people who are bad at math.

I'm so bad at math that I don't even know my 3x tables well. Seriously im embarrassed at my self like if you ask me what's 2×8 I'm gonna have to think and count since I can't say it immediately.

what if ur in preschool and dont even understand what ur talking about yet？

Whoever created math should be executed

Never even seen this type of math and I'm 22🤨

Math,

Mental

Abuse

To

Humans

School,

Six

Cruel

Hours

Of

Our

Lives

My brain on first day of school: this is gonna be the best day ever!

After mathBrain: F!$? MATH I QUIT

slams doorMy brain after watching this vid:

DED NOT BIG SURPRISEE=mc2

Don't mind me, I'm just flexin' with my math abilities.

1:10 that is definitely not a word, or you pronounced it wrong lol.

I have a C+ in math and I want to be a brain surgeon 😞 oof

Tried out the mobile app of Symbolab and it doesn't show the steps unless I subscribe. Maybe it was free when you made this but I guess we have to pay now. Sad.

I love math but I really wanna go pro

I don’t understand

M-Mental

A-Abuse

T-To

H-Human

I nevered learned that math yet ………

1+1 11

2+2 12

4+4 44

19+19 1919

20+30+20 203020

Am i good?

I will marry maths ❤❤❤😍💯

You have to study every day and stop playing with phone and Xbox

Btw i know i won't do that

He looks like Tyler Hoechlin a little bit

I wish this video was available 40 years ago.

I need to practice mastering concepts before the actual test. I’d get half the concept right and bomb a quiz. On my own right after I got my quiz back I’d work through and solve all problems- helped me improve my test scores. I just need to pay more attention 😂

You're just so hot! Your eyes are beautiful!

you are watching this video instead of actually doing mathPractice

I’m ok in math but I want to be better

Fractions subtracting and division Suck

I am not good at math I can't do ✖️➗

BiOloGy Is A ScieNCe

Math isn't hard at all don't expect the answer of an equation to pop into your head when you look at it although this video is helpful you need to change your mind set first

I was literally crying while watching this lol. I have a tutor and I pay attention so much but it doesn’t work and I’m gonna fail school

I got a math ad,

Im scaredWhy was this recommended now.

I'm good at math , why am I here 😅😅😅

How to get better at math:

first question : You're dumb and you will never understand this.

You talk toooooo much

You know that I'm here coz I'm dEsPeRaTe

I have always have hard time whit math. Now im in the 6th grade and STILL " can't math"

My parents just thinks im a failure

im watching this vid cuz this subject do really piss me off AL THE TIMEEEEE..

Thank you for your sharing. That is useful for my study

I am struggle in math ever since middle school!

Thomas frank :

math stuffmy brain :

Me AnD THe bOYsWhat i only know is math is killing students

it didnt work ive been doing what you said before I even watched this video. I lost all motivation to study and ill just stick with computers atleast I know how to program and shite. I am dissapointed in myself.

Hey hey hey!!! I’m a mathematics tutor for all ages all level!! I have tons of experience and can help anyone understand the math class they are In! Leave a message or reply for more details. Also I work with ALL ages, ALL levels, and all learning types.. I hold a bachelors in math from UCLA and I’m getting my masters currently.

contact studybay1(atgmail . com) for best assignment help services, you will get help in all subjects, they are a group of Writers offering writing services WhatsApp +254 701 540 201

I love to do math

فدوة ال هل الاستاذ

اكو عرب بل طيارة

2nd day of school, and my teacher hands us homework with “Fill in the blank” numbers. Its technically easy, but really confusing and stressful, and I couldn’t find it out. So, I looked for the cheat sheet, and guess what, I found it. 😂

I'm about to be in linear algebra, calculus 4, and differential equations. I'm gonna be gg this semester.

School:If h(t)=1.85x(2.3)^t, find, correct to 4 decimal places, the value of h(4).

Exams:T(t)=24+4cos(pie,t over 8),0<x<24

The equivalent or greater than version of <, so < if a line underneath it.

Thomas : this of the most difficult math question

Me( who’s still on summer break) : 6×6

I got high grades on exam

Since my formula is so complicated

My teacher didnt have to check it so he just checks it