hey guys welcome to Angels and Acid where we learn things maths and science
and today's topic is the importance of showing full working out
whenever you're doing a maths problem, chemistry problem, or a physics problem,
or any sort of mathematical thing you've got to do
whether it's for school or if you're doing this in real life for...
you know; everyday stuff.
And I know, I know is such a drag to do all this extra sort of working on paper, and writing and scribbling
it slows you down and you might think that it's much better if you take some
shortcuts here so you can get more practice done within the hour you can
get through your exam faster
and you might think that's better,
but you're kind of shooting yourself in the foot
because you are ... there are a lot of consequences to doing things by cutting corners
and I'm hoping that I can convince you in this video
about 4 reasons why you should do things in full working out
I'm also gonna then talk about at the end of this video about how sometimes
especially this is the first time you're doing high school mathematics
sometimes the ways you did things in primary school
it might have been okay for the kinds of maths work that you did then
but I I'm having to bring you some bad news is that you
you may need to adopt a new way of setting out because the primary school way may not be able to scale
as you go through grade 7, grade 8, grade 9, grade 10, and 11 mathematics
as the problems require more work ...
the way you do it at primary school is probably not going to work so
I'll show you what I would like my year 7's to start off with and then I'm
also going to show you what I don't want to see and I'm also going to show you
what things look like when you're sort of much further up the road in mathematics
Alright so my 4 reasons why you should do things in full working on the page
1. Is that you can check yourself much more effectively
especially if you've done a problem that requires in multiple steps it's so much
easier than trying to do it all in your head several times over
2nd: Other people can check your work and that's SUPER important for multiple reasons but I'll get to them later.
Next is that your teacher or whoever's grading your exam or assignment
they can actually see you're working and thinking and like
'Oh yes they can they can do multiplication they can do division they
can do the the things in the right order they're applying the rule because I can
see it on the page.' If they don't see anything on the page besides the final
result they can't tick all the boxes which means you don't get the full
grades last one is that as you get older the math problems that you do tend to
require a few more steps and also the the the problems that you do are much
more important like it can be life and death whether you get the answer right
or not. You kind of want to make sure it's right, and you... you kind
of want other people to be able to tell (that you're right) like to check your work especially if
there's a lot of money involved or people's lives are at stake so let's say,
let's say you're you're an engineer you're gonna build a bridge if you did
the math wrong and your bridge isn't as strong as you said it was, then people
could that thing could break people could die... Argh! Such a mess! Lawsuits
everything. If you're a business owner and you can't calculate how to pay your
employees properly let's say you pay them too much that costs you money let's
say you don't pay them enough that that's gonna make them angry let's say
you are also a business owner and you need to get some supplies in and you did
the math wrong and you didn't get enough your business is screwed if you're an
employee and your boss says I want you to do this and this and this and you did
some calculations and say 'yep this is the answer' and you're wrong... your boss is going to
be mad so you want to make sure that you're able to do maths in such a way
there that is it's it's easy as possible for other people to be able to
collaborate and check your work so that you have the best chances of things not
going wrong. All right so I'm now gonna move on to showing you the kind of
setting out that I'm looking for particularly for my year 7's as you
go to grade 8, and grade 9, and 10, and so on obviously you're not gonna
have to do a lot of this sort of you know rigid structure but for now you
7's we want to go with the whole bells and whistles of structure only
when you get further in life can you sort of take them off
think of it like training wheels when you're riding a bike okay I've got a
problem from the book I set up the question I like to put them in a
different color or I like to sort of section it off, you know sort of signpost
that this is the problem I'm working on, this side here I'm gonna do my working
if I have to do any sort of side calculations and the kinds can sort of
neatly tuck it away from the from the the main line by line solving. Alright
here we go I'm gonna do some rules I'm gonna use
the BOMDAS rule which means have to do division first I'm going to tackle
this bit of the of the problem here first so division so I want to find out
60 divided by 3 which means how many times does 3 fit into 60?
Well 3 fits into 6 twice, 3 fits into 0, zero times, so the answer
is 20 so this new line is 18 divided by 9 plus 20 now I do the BOMDAS rule
again and that means I've to do 18 divided by 9 so that means how many
times does 9 fit into 18 so if you know your 9 times tables that
answer is going to be 2, so now the the problem becomes 2 plus 20 and then I can
just simplify that down to the answer of 22. That's the sort of do you know I step
line by line by line work and I'm looking for you can see I did the
problem in three stages this is what makes the system I'm trying to advocate here
- the thing I'm trying to convince you of - if you do things this way as the
problem requires more steps you just take more lines. Okay, it's nice
and neat yes it feels like you're doing a lot more pointless extra writing but
trust me it saves yo,u especially where things get really hard. Now what I don't
want to see (so I'm going to show you an example what I don't want to see) I don't
want you to give me an exam or an assignment where I have: 'question equals
22'. Really? You could have guessed that. Lucky guess. Zero marks. Well, I don't know
if it's zero marks but if your teacher's looking for: are you applying the rule,
can you multiply, are you doing them the right order... I
lots of these sort of things. There's no evidence on this page right now that you
know what you're doing. No evidence that you did the problem in the right order.
No evidence whether you guessed that luckily or not. You need to convey as much as you
can on paper when you're applying a rule. Write the rule, and then you can keep
going. Try and make it as literal as possible so that there's no question
(for the person who comes to read this) there's no question about: 'what is that???'
'Where is he going with that?' 'Where does that number come from?'. There should be no
question about what you're thinking and what you're doing. Okay
that sets you up for success. Now I'm going to show you (I hope
I don't freak you out too much) I'm now going to show you what it looks like when you get
older. So here's a math problem that I would encounter; I think I did stuff like
this in grade probably grade 12 Maths B... I definitely encountered it again
at University, so I did a chemistry and mathematics degree, so this is the type
of problem that's way into the future. Now I don't want to it overwhelm you
don't worry about the fancy symbols, and the numbers that go in the different
corners, all the letters... don't worry. Okay? Just push it out of your mind. What you
should be focusing on as I do this problem is I want you to take note of
how many steps, how complicated the thing is meaning it requires lots of
little steps to do it. Okay? And each step is not that (if you know what the rules
are) the steps aren't that hard but it does take quite a few steps sometimes
and there's no way you can solve this in your head. And I'm going to show you here we go.
Oh I've done the problem before in advance; not because I don't know how to do the problem,
it's just that I don't want to waste your time on video by going:
(mumbling, thinking)
that's reason why I've got it here just in case if I sort of need to double check.
Alright so the answer is equal to integral of ... (mumble, mumble)
okay there I'm done so here you can see that it actually took me
quite a number of sort of little steps for me to finally come to my answer
and this is why the system that I showed you just previously;
this is what makes it so scalable.
So I did the same sort of presentation as I did in this problem
where I had line by line as I go through lots of steps
when you get to stuff that requires a few more steps-
you just add more lines down below now this looks hard (but) it's not that bad
you'll be taught how to do this in grade 11 or 12
if you choose to take maths to a more advanced level but it's not that bad
So I hope that doesn't freak you out. That's not the point. The point is that it scales.
I hope at the end of this video now that I've convinced you that
you should be doing full working out
and the setting out you use is super important
because it can either get in your way or it can allow you to get
more advanced in maths in years to come.
I think that's it for this video and I will catch you in the next one.
If you liked the video I'd love to hear some feedback
so thumbs up is wonderful, comments down below is great,
if something's confusing you can leave a comment down below
I'll see you guys later. Bye.
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