The HACK to ACE MATH no matter what - Caltech study tip

has this ever happened to you in math class the teacher gives you a paper of problems to solve you look around and all of your peers are breezing through the assignment you're still stuck on problem one all the numbers and letters blur together in your mind and you feel dumb this is exactly my experience in sixth grade I was working on problems with three classmates and they just seemed to get it while to me the math was like a foreign language I was embarrassed that I was so confused so I just nodded along pretending like

I was keeping up with them while slowly dying inside like man this is hopeless I'm just dumb I suppose later that year my dad taught me the magic secret of being good at math and starting from eighth grade I went on to win math competitions eventually winning a gold medal state level I was in advanced math classes taking both AP calc BC and AP stats my sophomore year now I would rather solve 100 math problems than write one essay so what click for me math tends to be the hardest subject for many students but then

the best or easiest for other students why is the difference so extreme there must be a magic secret that the good students know well there is so today you'll finally learn the truth behind why you struggle in math and of course the solution warning you might begin to like math let's go we'll start with quick magic in an example the question is what is a ratio of the area of the Red Square over the area of the Blue Square basically the area of this divided by the area of everything in these blue borders now I'll

give you a moment to think about it see if you can solve it real quick that's the fun try it all right maybe you tried it maybe you didn't you might have been thinking uh I'm gonna assume you know this side length is one and then do some circle diameter Square relationships to then get the side length of this big square and then once I get the areas of both squares I'm just going to do one area divided by the other area now either you thought that or you're like man I'm not seeing a problem

like this anywhere before I don't know how to solve it here comes the trick I'm gonna redraw this shape now what if I simply turned the inside Square 45 degrees like [Music] whoa do you see anything special do you see anything that makes the problem really easy yes indeed if we cut it up like this you can see that in each of these four quadrants the red area is actually half of the blue circle area so the answer is really easy you don't need to do any calculations at all it is simply one half whoa

it's just like magic magic drop a like right now if you thought that was cool come on guys that's that's really awesome right that's an instance showing that if you have problem solving skills and you're creative in math and understand the relationships between shapes you can do one little adjustment or one little flip of the shape and get the answer so much more easily now I know your schoolwork probably doesn't look like this question but here is the headline it doesn't matter how many formulas you know to solve that area problem and other math problems

it's about math sense and problem solving skills the better your understanding of what math truly is the easier the solutions will be for you I'm a private tutor right now for the ACT SAT and for the math section I can always get my students up to make that one of their easiest sections significantly increasing their scores because of these tricks that I show them that flip of the mindset I hear all the time I can't remember the formulas I can't solve it because I've never seen a problem like that before that that was my students

struggle and probably yours as well you think that adding math is just adding more formulas to your brain more tools to your toolbox but let me ask you this if you were a construction worker who wanted to improve what would be more helpful relying on adding more tools to your toolbox or increasing your actual skills as a construction worker if you add more tools Without Really knowing how to use them you're just going to get more and more overwhelmed as the construction worker like you won't be able to get anything done you'll just be piled

under this accumulating weight of all these new things you have to remember and use just like in math if you're not improving your real math skills you'll fall more and more behind because there's so much more and more to memorize but when you really learn and understand you solve more problems with less effort like no wonder those math students find it their best subject using your math toolkit becomes easy when you don't have to think hard about what to use when and how to use it and at the end it is like magic like check

out these comments from students who watched my ACT SAT Math tricks video I didn't have to try and remember those tricks from all those years since I took the act and sat so long ago I just had that math sense that's always there that's going to help me solve any problem that comes my way the truth is it's not your fault I'm sorry but there are many subpar teachers out there I've seen it with my own eyes one of my students right now tells me that his teacher just writes some things on the board sits

back and goes learn it and then gives him the test that is not math guys so really don't feel bad if you have been living your life so far not knowing that this is the real way to get good at math another quick example before we go into the solution think about square roots if you were just trying to memorize square roots like you learned that square root of 25 is five then if someone asks you what is the square root of 36 you wouldn't know because you never learned it it's not in your memory

on the flip side if you knew what the square root actually means as the inverse of squaring a number then you know what the square root of 36 is imagine the next time you take your math test and all the solutions just come to you here's how to make that happen this is the three-part solution you should do this while practicing math number one take your math problem and break it into Parts often we don't even realize that we don't actually understand the little foundations behind the bigger more complex math problem so for example if

you have a big geometry problem and using the unit circle is part of it then the concept unit circle would be a piece of that math problem so you would break that math problem into unit circle then maybe algebra operations whatever other tools that you would need to solve that math problem number two once you have your math problem broken into those foundational parts and you know the tool you need for each part then review the tool you use for each part so in that unit circle example the tool or concepts you might need are

what the X Y coordinates are all around that Circle and what the radians are around that Circle ask yourself do I know this because I'm memorizing it or do I know it because I understand it if it is the former and you don't actually understand it then watch videos on that concept and the origin the reason behind why all of those numbers are around the unit circle Khan Academy and YouTube both have excellent resources so just watch as many as you need to understand it maybe even do some practice problems repeat this process for each

foundational part of your original problem so that you actually understand and have the fundamentals good again if you don't feel confident and strong in the little Concepts that make up a big problem then every big problem and the bigger and bigger problems that come after that will be even harder this works for basically any math problem and I know I used the unit circle but the reason I bring that up is because me after like eight many years of not using the unit circle or even seeing it in front of me if you gave me

a blank unit circle I would be able to fill in all of those numbers right now That's The Power of understanding and not memorizing and that's also why I can take the ACT Math Live and get a 36 on it even without any preparation right now number three solving that initial big math problem try to solve it on your own from scratch without looking at the answer key even when you do get to a problem and feel stuck don't look at the answer key yet I know it's really tempting because the solution's right there in

the back of the book but don't do it stop stop it first write down everything you know about the problem in front of you if like an act problem it asks you how do you make this number even the term there is even so think back to everything you know about even numbers when I did this with my student and my student said an even number is divisible by two he immediately knew how to solve the problem at first my student was stuck then I simply asked him what do you know about even numbers he

told me and then he knew how to solve it on his own after you think about everything you know about that one problem try and draw connections between those things I encourage you to write that down this is like your attempt at a solution think about it for a few more minutes and then if you're still stuck yes now go into the answer key now when you're looking at the solution compare it to your initial thinking and see how similar or how different it might be this is where the learning and problem solving ability gets

built over time this last step is so so important because if you only look at the solutions instead of trying the problem yourself as much as you can first you won't build problem solving skills the real world doesn't just hand you Solutions on a silver platter you'll have to figure them out on the job otherwise your boss is going to hate you man that's why this approach of understanding an attitude of wanting to build your math skills will set you up for success in the real world too foreign to flip the switch at the beginning

when I was getting taught by my dad I was like this is taking so long why are you explaining all these things I just need to get the problem done all that upfront effort will pay off so much in the long run trust me from my experience you can see from my math Awards now that just having this flipped switch and going back to the foundations and understanding things will make a huge difference a magical difference and just think about it it might be hard to flip the switch right now but it's going to be

even harder to catch up if you fall farther and farther behind I stress this again because so many students think that this is what math is math is not memorizing repeat after me math is not memorizing it's really not good to read the solution and just try to memorize it you will automatically yourself go down the right path if you understand we should go back and take a shot every time I say understand in this video knowing how math Works will make you the master of any map class no matter what get excited about trying

this new approach and I'm really excited too to see your progress so keep me updated in the comments let me know how your math grades are going yeah ask me any other questions you have how else can I help you Ace school and life let me know and give me a thumbs up thank you so much I'm using an accent randomly thank you bye foreign [Music]