Imagine being such a good teacher that your students literally gasp and shout out in excitement at the insight you gift to them. Talk about inspiring. Mr Woo is a legend.
absolutely blew my mind, great explanation. I feel that understanding the logic behind what I'm learning really helps me grasp the concept, instead of just memorising rules
The amount of sheer glee Eddie Woo derives by just showing them these concepts is infectious. It's incredible how much he loves the subject, and even more so that he can communicate and share where that love comes from with his students.
Eddie's a different kind of math teacher because he was a different math student (in comparison to traditional ones). Eddie, like a lot of people, grew up excelling at the humanities and social sciences but struggling with math. However, while he was in college, he met professors and such that helped him to shift the way he thought about math. Plus, he was able to figure out how he learned it. Unfortunately, most of us weren't that lucky. Kids today are lucky -- because they have access to a lot more resources and such.
I'm 32 years old, and this is the first time I've ever seen the completing the square rule being shown geometrically! I learnt the rule in school and understood it in terms of the coordinates of the turning point of the parabola on a Cartesian plane. My mind was as blown as those kids in your class when I saw the rule visually represented!
actually, if you look at some old books, they show it this way. Lots of work was done in ancient Persia with quadratics and completing the square with using area for farmland, thus the area model. I didn't learn the area model until I became a Math teacher.
That's why we start by teaching multiplication of two binomials with algebra tiles and the box method. It's so beautiful to see the conceptual diagram continues to work. But to hear this group get so excited about seeing the "why" behind the algorithm they know is awesome!
Absolutely blew my mind! This is why I love math so much. A lot of people hate it because they think it's all just about numbers, but when you put tangible context to it, it becomes something entirely different and meaningful.
You are the most insightful teacher I have ever had the pleasure to watch. I have even caught myself watching you teach subject matter I thought I already knew, mostly because your approach is so uniquely eye-opening (and entertaining). And then BAMM! You hit me with an idea I never saw coming...like you did in this video (eg, completing the squares). I'm all smiles. Thanks.
Great video! Are these high school students? They seem very enthusiastic, excited, and engaged in learning math. I wish my community college students would get this excited about learning math…
These are high school students. This is just like my class was in HS. It's worth noting that maths is not compulsory in years 11 and 12 in NSW(Aus) so these kids chose the class and want to be there.
twistedblktrekie Think about how our generation was taught. Teachers today are basically in new territory and its a difficult thing. Also on the new scheduling some students will go as much as 9 months without having a math class. Also teachers are left with no extra time to review basics. You have to have very motivated students.
@@milly4543 It is sad that math is not compulsory in years 11 and 12 in Australia. Math is something that is so fundamentally important to developing a sense of logic, especially as an early adult. I think policy makers of the future should keep this in mind.... math is very useful, the most important thing you will ever learn.
Roon Station You have to keep in mind that some people, even successful people won’t need trigonometry, calculus, complex numbers, or even geometry to get through most of life’s problems. In fact, math is entirely useless without being able to apply it. We always apply math in physics and economics (because what else is there other than physics and economics). Algebra is one of the most useful concepts there is and is easy to apply. Want to know how much wood you’re going to need for a month? Construct a function of demand. Now higher levels of math are almost always used in the stock market, physics, and other really complicated stuff, but only a small minority deal with this stuff.
I love your charisma and expertise. I'm showing this video to my students since this made me get so excited about solving quadratic equations by completing the square.
THIS is tge teacher i aspire to be if i ever really become one. Energetic, passionate, logical, and names my students gasp in excitement!! Im in grade 11 and my class is so dead. They hate math but next year, its not compulsory to take it so hopefully my class is a lot more happy and willing to learn. Its hard to feel motivated when the people around you hate that room so much
Great video Eddie. This is from al-Khwarizmi, circa 820 AD. If he had understood Brahmagupta as well as Euclid he could have solved this problem with a circle to solve for both positive and negative solutions.
I actually cried at the kids gasping! I am a teacher (not maths) trying to home educate my autistic son. We are learning complete the square just now and this video made me quite emotional.
I used the geometric representation in my credentials interview today!! I did it algebraic representation first and when the professor asked me where did the (b/2)^2 came from, I demonstrated it geometrically.
As I've dived into math on my own I've learned that we are taught things out of order so all the formulas we learn just seem like tricks rather than the obvious conclusion to something we were taught. We should've been taught the geometry of this formula before the algebra
Late night browsing on the tube; I studied math at a top tier university, I never knew why it was ever called completing the square. I never did bother to ask. Lol. BUT, I completely get it now. awesome. lol. Algebra is nice, and efficient, but this is pretty amazing. lol. Get this man to 100 mil subs!! The future depends on it. lol. make people like math again. Because it is beautiful
This is great stuff and the more ways we can explain things, the greater the likelihood that (a) we find at least one way that works for us and (b) those explanations can combine to deepen understanding. There does need to be caution of course in that geometrical proofs might not always tell us the *whole* story. We live in a physical world where the distance between two points is positive, and an area is positive, and negative distances and areas don't really make sense. So we can neatly see here, for example, that a solution is x = 3, because we make up the side length of (x + 5) = 8 and therefore get an area of 64. However, this might lead us to easily ignore or discard the other solution x = -13, because (-13 + 5) is -8, (-8)² is also 64, and therefore -13 is also a solution to the original equation. It might be possible to somehow geometrically represent that solution by working in terms of displacement and saying "well if we treat moving to the right as positive, and we move x units right, we can then move 13 units left, and do the same in the up/down direction, and construct some other square that might show the relationship, but to be honest, I haven't thought it through fully and to be honest, don't want to, because it seems like more work than is necessary. I'm taking nothing away from an excellent visualisation and if it gets you further than you would otherwise be, that's fantastic, I'm merely saying depending on level, one has to be mindful of the limitations of a particular explanation.
I agree with you. I'm no math genius but he is converting between 1D and 2D to his convenience which is kinda breaking the essence of it... I think its just a cool coincidence, geometrically speaking...
Both of the math teachers I've had this year were awesome- 1st dude was super chill and clearly and efficiently explained every concept to us. Miss that guy. Second teacher that I just got recently is enthusiastic and incredibly helpful. She makes sure we don't ever have any unanswered questions and clearly loves her job. Now I want this dude too. How much is a plane ticket to Australia? I'm gonna be completely honest- I hate math. it just isn't for me. I'm actually pretty good at math once I know the formulas (I mean duh, that's kinda how math and math classes work) but I don't get any joy from it. And yet somehow the teachers keep me thoroughly engaged. Pay these people more please
Imagine being such a good teacher that your students literally gasp and shout out in excitement at the insight you gift to them. Talk about inspiring. Mr Woo is a legend.
AGREE !!!!!!!!!!🏅
The moment a concept clicks in mathematics, is pure bliss.
ItsThatMilkshake I can't tell you how right you are. One of the reasons maths is my favourite class
Makes the week long struggle feel so worth it
Eurekaaaa!
I love seeing your name at the top of a comments section on a video my teacher sent
nice name
the students are so excited to have it click. awesome.
absolutely blew my mind, great explanation. I feel that understanding the logic behind what I'm learning really helps me grasp the concept, instead of just memorising rules
That understanding is the essence of math. Memorizing rules is just computation and calculation, and machines are better at that.
That is so true! Most minds can memorise but enquiring minds need to know why!
So, "completing the square" is about literally completing the square. I have never seen such an explanation ! Mind blown !
Me too. I did not know why they call this way. I wish i had a teacher like him.
@@sergiodongala should be in your algebra textbook though
The amount of sheer glee Eddie Woo derives by just showing them these concepts is infectious. It's incredible how much he loves the subject, and even more so that he can communicate and share where that love comes from with his students.
Eddie's a different kind of math teacher because he was a different math student (in comparison to traditional ones). Eddie, like a lot of people, grew up excelling at the humanities and social sciences but struggling with math. However, while he was in college, he met professors and such that helped him to shift the way he thought about math. Plus, he was able to figure out how he learned it. Unfortunately, most of us weren't that lucky. Kids today are lucky -- because they have access to a lot more resources and such.
I'm 32 years old, and this is the first time I've ever seen the completing the square rule being shown geometrically! I learnt the rule in school and understood it in terms of the coordinates of the turning point of the parabola on a Cartesian plane. My mind was as blown as those kids in your class when I saw the rule visually represented!
actually, if you look at some old books, they show it this way. Lots of work was done in ancient Persia with quadratics and completing the square with using area for farmland, thus the area model. I didn't learn the area model until I became a Math teacher.
@@eugene188 In that case! plz try teaching your students like this. They'd thank you for life.
Just two words........
Absolutely brilliant!
I have gone my whole life hearing the expression 'completing the square', and never knew what it was about. What lousy maths teachers I had!
Mrs Brady has a lot to answer for.
Maybe they did, maybe you weren't present.
@@fredd298 and maybe not, like what most teachers do in my country, sad..
That's why we start by teaching multiplication of two binomials with algebra tiles and the box method. It's so beautiful to see the conceptual diagram continues to work. But to hear this group get so excited about seeing the "why" behind the algorithm they know is awesome!
Absolutely blew my mind! This is why I love math so much. A lot of people hate it because they think it's all just about numbers, but when you put tangible context to it, it becomes something entirely different and meaningful.
and majority of students are in debt while never even knowing these type of beauty in math. really sad!
This makes so much sense and it is so awesome. I wish I could just watch RUclips videos all day to learn instead of going to college
i think you can...
This is absolutely brilliant for visual learners ! Thank you so much....this is fabulous for helping my son to understand. You are awesome.
You are the most insightful teacher I have ever had the pleasure to watch. I have even caught myself watching you teach subject matter I thought I already knew, mostly because your approach is so uniquely eye-opening (and entertaining).
And then BAMM! You hit me with an idea I never saw coming...like you did in this video (eg, completing the squares).
I'm all smiles. Thanks.
Great video! Are these high school students? They seem very enthusiastic, excited, and engaged in learning math. I wish my community college students would get this excited about learning math…
Joshua Britt
This is just like my maths class
These are high school students. This is just like my class was in HS. It's worth noting that maths is not compulsory in years 11 and 12 in NSW(Aus) so these kids chose the class and want to be there.
twistedblktrekie Think about how our generation was taught. Teachers today are basically in new territory and its a difficult thing. Also on the new scheduling some students will go as much as 9 months without having a math class. Also teachers are left with no extra time to review basics. You have to have very motivated students.
@@milly4543 It is sad that math is not compulsory in years 11 and 12 in Australia. Math is something that is so fundamentally important to developing a sense of logic, especially as an early adult. I think policy makers of the future should keep this in mind.... math is very useful, the most important thing you will ever learn.
Roon Station You have to keep in mind that some people, even successful people won’t need trigonometry, calculus, complex numbers, or even geometry to get through most of life’s problems.
In fact, math is entirely useless without being able to apply it. We always apply math in physics and economics (because what else is there other than physics and economics).
Algebra is one of the most useful concepts there is and is easy to apply. Want to know how much wood you’re going to need for a month? Construct a function of demand.
Now higher levels of math are almost always used in the stock market, physics, and other really complicated stuff, but only a small minority deal with this stuff.
I love the energy and enthusiasm with which concepts are made clear!
You sir is the best teacher ever.. the students should consider themselves really really lucky to have a teacher like you
I love your charisma and expertise. I'm showing this video to my students since this made me get so excited about solving quadratic equations by completing the square.
Bloody brilliant!! What a fabulous and inspiring teacher!👏🏻👏🏻👏🏻
Omg that MathGasm I had was the most mind blowing one I've ever had :D
The best video and representation of the applied information I have seen on the subject. You have blessed me today, thank you Mr. Woo.
THIS is tge teacher i aspire to be if i ever really become one. Energetic, passionate, logical, and names my students gasp in excitement!! Im in grade 11 and my class is so dead. They hate math but next year, its not compulsory to take it so hopefully my class is a lot more happy and willing to learn. Its hard to feel motivated when the people around you hate that room so much
MINDBLOWN!!! I was literally screaming with the students as if I was in the class. Thanks for the explanation.🙌👍
This is a beautiful representation of completing the square. Thanks man, now I can’t forget how the process
Simply the best..thank you!!
THIS MAKES SO MUCH MORE SENSE THANK YOU EDDIE
the reactions of your students are so wholesome ❤
What a great Match Teacher, this is so enlightening.
Wow, U are a very enthusiastic teacher.
God bless Sir.
Brilliant! Love the enthusiasm as well 😊
Wow, that's what I am exactly looking for. the practical meaning of "completing the square". Thank you.
One of the finest teachers in the world!
The sound of students getting it is the most rewarding feeling ever.
2:08 The beautiful lightbulb moment that every teacher loves to experience!
It's trivial math, but I LOVE your method of teaching! You're awesome ;) ;) I wish I had this kind of teacher at my school :-(
Rudolf Klusal I know it was a year ago lol but it’s not trivial mate, can be used to find the roots of the equation
it all suddenly made sense! thank you!!!
Pure genius. Everyone needs a math teacher like this.
Pure genius, man. May need to find another word to describe you soon.
WOW !!!! I'm going to point my daughter to your lessons !!!!
If only I could get my students to get excited about learning like you have here.
This man just made Algebra so much easier for me! *Give this man an award!*
Great video Eddie. This is from al-Khwarizmi, circa 820 AD. If he had understood Brahmagupta as well as Euclid he could have solved this problem with a circle to solve for both positive and negative solutions.
Very nice. I will use that with my students this term when solving quadratic equations. Thanks.
Just amazing. Thank you. 20years after failing my GCSE math I'm retaking.
Good luck!
simple and logic thanks from Algeria.
Really impressive sir....I wish if every maths teacher could teach like you...
Love the reactions!!
Awesome! Thank you!
I will never forget this video! (:
Dislikes are from the triangle people. Thank you for the visual Eddie. You're a great teacher.
I wish you were my teacher. No one make us learn this way or explained this way. When i see your videos, i feel my maths teachers were seriously dumb.
I actually cried at the kids gasping! I am a teacher (not maths) trying to home educate my autistic son. We are learning complete the square just now and this video made me quite emotional.
I used the geometric representation in my credentials interview today!! I did it algebraic representation first and when the professor asked me where did the (b/2)^2 came from, I demonstrated it geometrically.
Oh man ! You rocked.
As I've dived into math on my own I've learned that we are taught things out of order so all the formulas we learn just seem like tricks rather than the obvious conclusion to something we were taught. We should've been taught the geometry of this formula before the algebra
very good teacher. thanks
This has saved my GCSE mock today in two hours
Beautiful
thank you for making maths interesting! keep going professor!!
You are the best one i ever had..
Woah that's some really good explanation bro! Doing great!
Eddie Woo is the man!
2:08 is the climax
2:20 second one
mathgasm, they came twice, he's definitely professional 👏👏👏👏👏
Comparing maths to sex now are we?
yes, since they're mathing
mind blown!!!!!! if only the teacher we had actually explained it like this I wouldn't be searching the web for hours on how to do these problems. >_
Eddy Woo is a math guru.. he's beautiful!
oh my god! this is so cool!! Thanks for sharing this.
He has been nominated for global top prize teacher
Thank you
That's an amazing math teacher.
I can relate to the euphoria the students are experienced because I experienced the same while the math unfolded ❤.
loved this video
Late night browsing on the tube; I studied math at a top tier university, I never knew why it was ever called completing the square. I never did bother to ask. Lol. BUT, I completely get it now. awesome. lol. Algebra is nice, and efficient, but this is pretty amazing. lol. Get this man to 100 mil subs!! The future depends on it. lol. make people like math again. Because it is beautiful
I wish I had a teacher like him.
This is great stuff and the more ways we can explain things, the greater the likelihood that (a) we find at least one way that works for us and (b) those explanations can combine to deepen understanding.
There does need to be caution of course in that geometrical proofs might not always tell us the *whole* story. We live in a physical world where the distance between two points is positive, and an area is positive, and negative distances and areas don't really make sense. So we can neatly see here, for example, that a solution is x = 3, because we make up the side length of (x + 5) = 8 and therefore get an area of 64. However, this might lead us to easily ignore or discard the other solution x = -13, because (-13 + 5) is -8, (-8)² is also 64, and therefore -13 is also a solution to the original equation.
It might be possible to somehow geometrically represent that solution by working in terms of displacement and saying "well if we treat moving to the right as positive, and we move x units right, we can then move 13 units left, and do the same in the up/down direction, and construct some other square that might show the relationship, but to be honest, I haven't thought it through fully and to be honest, don't want to, because it seems like more work than is necessary.
I'm taking nothing away from an excellent visualisation and if it gets you further than you would otherwise be, that's fantastic, I'm merely saying depending on level, one has to be mindful of the limitations of a particular explanation.
I agree with you. I'm no math genius but he is converting between 1D and 2D to his convenience which is kinda breaking the essence of it... I think its just a cool coincidence, geometrically speaking...
Awesome Sir.
Brilliant! The reason we come to RUclips for maths!
It was too awesome.
Both of the math teachers I've had this year were awesome- 1st dude was super chill and clearly and efficiently explained every concept to us. Miss that guy. Second teacher that I just got recently is enthusiastic and incredibly helpful. She makes sure we don't ever have any unanswered questions and clearly loves her job. Now I want this dude too. How much is a plane ticket to Australia? I'm gonna be completely honest- I hate math. it just isn't for me. I'm actually pretty good at math once I know the formulas (I mean duh, that's kinda how math and math classes work) but I don't get any joy from it. And yet somehow the teachers keep me thoroughly engaged. Pay these people more please
Didn't I see you in itf's videos lol
Do we always add to both sides..? sometimes we subtract.. when do we subtract on the right side?
Awesome!
i love his dress code
i need this man as my teacher istg
worth watching...
love your website name!
Great this really helps a very thick, dyslexic person like myself LOL! But for some reason I have taken an interest in maths because its a challenge!
Ohh, mann... Wish i got a teacher like him..... 😢😢😢😢😢
Somebody nominate this guy for a Nobel prize
Eddie's 1 million subscriber video lead me here
i wish i had this teacher as my maths teacher
Amazing
Awesome.........
he's like the teacher I never had
i need a video of their reactions :')
This was also shown in Edexcel International GCSE Mathematics B
Magical
Mind=Blown
Your acc blessed Eddie Woo
big math very big maths 👍🏿 thank you mr woo
SO SATISFYING
Do we always add to both sides..? sometimes we subtract.. when do we subtract on the right side?
2:11 That's the Mind=Blown moment