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## Algebra 1

### Course: Algebra 1 > Unit 16

Lesson 1: Creativity in algebra# Creativity in algebra

Hear from professionals as they talk about creativity in algebra and mathematics. Created by Khan Academy.

## Want to join the conversation?

- how is algebra creative?(6 votes)
- It does not say algebra is creative, it says there is creativity in algebra. There are a lot of number sense tricks based on algebra. For example, the difference of perfect squares (x-a)(x+a)=x^2-a^2. We can thus multiply 43*37 and get 40^2-3^3=1591. It makes the times table make more sense, if 5^2=25, then 6*4=25-1=24, 7*3=25-4=21, 8*2=25-9=16. 8^2=64, so 7*9=64-1=63. You can prove that 35^2=(30*40)+25=1225. The video talks about Algebra is not just Math, but has practical purposes in the real world that allows for all sorts of creativity.(7 votes)

- Algebra saves chickens(7 votes)
- This is a fantastic addition to your program. Often times, we skip over the depth, beauty and complexity of the design of Algebra. I look forward to more of this because a lot of students want to know how this will help them in life and although I give them many reasons from daily life, more examples and explanation is most welcome!(7 votes)
- I'm so confused. None of the questions in each sections of the video was answered directly by the speakers. It's almost like there is zero connection(1 vote)
- This video isn't about solving problems. It is about the creativity in Algebra.(3 votes)

- I have always understood that i would require the use of algebra throughout my life, but my critical thinking and creativity in algebra seems to be a lot less than average. can somebody help me with my dilemma?(1 vote)
- whats 23 x 3? whats (6+9)(6)(9)(1 vote)

## Video transcript

(upbeat music) - Hi folks, Sal Khan here. And all I have to say is
that algebra is perhaps the most pure way of
expressing human thought. And like everything
dealing with human thought, it's incredibly creative. But you don't have to take my word for it. We have some of my good friends
to better draw that link between algebra and creativity. (upbeat music) - It's all out solving problems. It's not about like,
maybe in previous years, you've done multiplication
table memorization. It's not like memorizing
how to solve problems. It's learning the tools
of how to solve problems and then using them, and building
them up in creative ways. So it's kind of like, it
really does remind me of art, because if you are doing
like a painting or something, you have like a specific tools
about maybe paint brushes or different techniques you can use to create something bigger. So I feel like algebra is really
all about combining things that you already know how
to do into something bigger. - So the word algebra comes
from the Arabic word al-jabr, that literally translates
to reunion of broken parts. This breaking apart of
mathematic representations and putting it back together in the form of balanced equations, is the essence of algebra. And the beautiful thing is that this balancing and solving of equations can be done in many different ways, which is where creativity comes in. (upbeat music) - So if you're trying to
communicate a complex topic, such as mathematics or
a mathematical problem to the general public
who might not be familiar with the specifics behind that problem, there are many different ways to help you get that concept across. And one of the ways that
we do this in mathematicals is to use videos and things that are visually appealing to people. So by using lots of visual aids, so bright colors and cartoons, and word prompts on your screen, you can engage and capture the audience in different ways that you
might not be able to do if you're just speaking in terms of equations and mathematics. - When we're more creative
about how we present, and how we talk about math, it makes it more relatable to people from a variety of backgrounds
and cultures and experiences. When we are creative in how we explain, or how we relate mathematical concepts, we can use things from sports,
entertainment, or real world to help really ground the
principles that we're learning, and the theories that we're
learning to something relatable. So the more creative we can
be in explaining how math is related to the world around us, how it's related to things
that we are invested in, the more likely it is to resonate
with the people around us. - As soon as a problem is posed, our instinct is to find the solution. But remember, often there's
more than one solution. And usually there's more
than one path to it. (keyboard tapping) - One day my family
was building this fence around my chicken coop 'cause there were problems with raccoons. And we wanted to make sure that, like the the perimeter
of the fence was like, twice the the length of the width. And I remember thinking, this is exactly like my algebra class. Like, I'm actually doing
things that are useful. And actually, like algebra
wasn't just something that you do on paper, it's something that like, it
was actually like protecting the lives of my chickens. So I felt like that was a moment for me where like math is useful to the worlds, and we're solving real problems with it, and it's really powerful. - So I realized that I first liked algebra and just math in general. My first year in college, I was a little bit of a late bloomer in realizing the importance of math. I was taking an early statistics course for my psychology degree, and I really began to
understand how the concepts that I were learning
could help me understand the world around me
better in a more concrete, fluid and rich way. And so being able to make that connection from these things that I'm
learning in the classroom, out into the real world, so I can understand different phenomenon, I can understand how various things in our culture work and progress, really helped me and made me feel like I had a deeper understanding for the importance of math and algebra. And from that point,
I've really been in love. (upbeat music) - In order to get more creative, I would encourage young
people to be not afraid of making mistakes. It's okay to fail while
exploring a new trail of thought. Know that usually there
is more than one solution to the problem. Math is as much about posing
problems as problem solving. And at that point, creativity is noticing where there is something
worthwhile investigating. - As a student in math, I think
it's important to remember that math isn't just like
random symbols on paper. Like, math can mean something,
and it's pretty powerful that you as a student, can
build something that uses math. Creativity in math isn't
just about being able to pluck numbers from the air and like, oh yes, I know the solution. It's about being able to use problems that help with your daily life.