Learn How to Master Number in GCSE Maths with Jolene Moon!

Welcome back to gcsc Minecraft and chill I’m Jolene Moon and today’s Math’s revision topic we’re starting at the very beginning and talking all about number what it is what it’s useful how to improve your understanding to take that into your exams and probably I’ll

End up going on a few tangents so grab a drink get your revision notes so whatever you’re going to do while I entertain myself and maybe you with some Minecraft and let’s get going so I am carrying on from where I left off in my videos last time I’m building my house

Um let me know if you recognize it uh yet or Point see if you know where I’m going with this um but anyway let’s talk about some maths while I do that so most people think of number as the the basic rules of Math’s topic right it’s the it’s the arithmetic the the

Adding the subtracting the multiplying the dividing and of course they would be completely correct that is what it’s about however it’s to me it’s a lot more than that it’s the foundation for understanding why we even use maps in the first place like what what the underpinning crucial logic behind the

Whole thing is and and why that’s useful and why that’s important and and and I just think it’s unappreciated or underappreciated so that’s what I’m going to talk about um so number is about relating quantities that’s fundamentally how it it arose um particularly by um African and Islamic scholars and when when you

Realize that you want to relate quantities to one another you you then and you know as Humanity expanded Agriculture and ly and everything else that humans were doing we had to process a lot of quantities and investigating or discovering depending on where you land philosophically with ma um

I I like to think of it as discovering that these these natural rules and Logics seem to naturally uncover themselves um when someone studies math and appreciates how it all works um but what we needed to do when we started to really process a lot of quantities was

Use definitions we had to specifically Define things and and develop a system of rules or a syntax like grammar in language um to have a a sort of universal logic uh to shorthand all of the explanation and all of the calculation and instead of writing everything out you know writing out our

Working millions and millions of times when we were adding lots of numbers together we needed to we needed to Shand all of that adding and and so we got multiplication you know and then in the same way taking something to the power of something is a shorthand for a

Specific type of advanced multiplication right so you don’t have to write it out over and over again so 2^ 2 is 2 * 2 and 2 * 2 is 2 + 2 right but if I take that example to the 3es 3^ 2 is 3 * 3 and 3 *

3 is 3 + 3 + 3 um three times right so we get 3 squ doing that three times uh we have to do 3 + 3 + 3 + 3 + 3 + 3 time just plus three + three + three and clearly writing that Shand is um

Three three Cub sorry what I was talking about then um not s um that’s clearly a lot quicker right so lots and lots of writing and explanation can be very quickly communicated um and since we start with number where we’re only ever combining quantities of taking them away when when

You start learning your arithmetic um there are lots of invisible instructions that make that easier um and if you’re one of my students and you’re listening to this hey hello um you’ll be familiar with me using that phrase invisible instructions um especially because that’s what bid mass is all about so brackets indices

Division multiplication addition and subtraction bid mass is about telling us the order in which to do those calculations or th those operations um which operations is just another word for the instructions telling you what to do with the quantities so the invisible instructions are all about what is being

Communicated based on what is written on the page um and and what is not written on the page that you’re supposed to naturally understand from that so as an example of what I’m talking about here consider any number so I’ve got seven levels of experience at the moment so

Seven um there’s an invisible implied POS positive there I’m level positive s I’m not negative s um it’s also divided by one to tell us that it’s a whole part I’m not it’s not it doesn’t say 7.4 or 7.5 you know it’s seven it’s a whole number it’s not divided um equally it

Has no point zero to communicate that it’s a whole number we don’t write the point zero for for most numbers unless you’re specifically required to based on the context of the problem right so um another one it’s got an invisible power of one that’s not that doesn’t

Represent s squar or 7 cubed we’re not in we’re not counting in base seven here it’s just seven we’re just counting seven once right so it’s kind of the when we just write a number like that the kind of default settings of a number we understand all of these things um

Intuitively and it just kind of becomes confusing when you don’t appreciate that in your learning number and it suddenly suddenly you have X to the^ 1 and then your teacher says oh but don’t write the power one and you’re like what um you know things like that so we have these

Kinds of blank boxes surrounding the number where all of the invisible rules and instructions around that number that make maths easier to understand they’re just we don’t write them you don’t appreciate them until you’re studying and and discovering more about all of the systems that we have that relate quantities to one another

And that allows you to then process these facts and rules and logic into even bigger ideas that help you start to understand and uncover rules about the Universe um you know when you take that into science or into statistics or you know anything like that and and that’s

Hugely powerful and that’s and that’s why I think it’s severely unappreciated as kind of the foundation for all your math skills uh because it leads on to some pretty powerful um understanding but uh anyway I digress so make sure you’re never taking for granted what you’re learning within this topic um and

I think when I when I say that I think it’s because students and teachers provided very very Rush timetables very stress very limited amount of lessons um and you’ve got a limited amount of revision time so you’re not going to be revising the basic for months the basics for months on end but

Um I yeah I I want you to never take for granted what you’re learning with number and to really think about what it’s actually teaching you because I don’t just mean adding dividing or putting something to the power of two or three I I mean that there are underlying

Patterns that of of understanding that you’re developing that can be applied to bigger and more complex problems when we go beyond just adding dividing multiplying subtracting right so um for example one of the things you you first learn once you’ve got your basic number skills down the next thing you learn is

That um the the existence of subtraction when we’re learning about addition and the existence of positive numbers implies the existence of negative numbers so you learn about how negative numbers exist and what rules govern what we do with negative numbers and how we write them down and how we notate them

Uh sort of in the same way that when you first learn adding that then would imply to you that subtracting exists and when you learn multiplying that kind of naturally implies that you can divide because if we’re doing an operation and I’m I’m gesturing with my hands and you

Can’t see me but um you know in in our culture in I’m in England um we conceptualize number and adding and subtracting as um a left to right situation that left or right is a positive direction and that’s the direction we’re going in but of course that’s you know we’re not talking about

The dimension of time which only ever marches onwards we can turn around and go backwards in the opposite direction you know other cultures visualize this vertically on an up and down scale up for adding and down for subtracting so we have these like this inherent directionality with these operations and

We can just easily reverse and go backwards um so that’s what I mean by inverse operation and so you can see how they’re just mirror images of one another so positive numbers are kind of the mirror image of their negative number um and I I recently explained this to one of my

Students say like in uh stranger things where you have you know the the normal inverted commas um above ground world and then you have the um the upside down and positive and negative numbers are kind kind of like that they’re kind of the same but different um different

Sides of the same coin and when you understand what that means you might start to ask bigger and better questions about what number even really is like what do we mean and what what is a binary system of logic how do they work why do they work and that’s even more

Fascinating and and you can’t begin to ask those questions or even like get towards an answer for those questions until you understand this um because if you can conceptualize subtracting as the reverse or inverse of adding just the different direction depending on your starting point or your frame of

Reference you can see that they’re really the same thing in their in their Essence they’re not they’re not opposites the the directionality might be reversed or in or inversed but they’re not really opposite operations right um like you might say that the the opposite of of adding or subtracting is is not to

Change the quantity of number at all right um and to just stay where you are like the opposite of motion isn’t going in the opposite direction it’s to not be in motion so that’s kind of what I mean with that and and the same thing goes for multiplication um or squaring and

Square rooting or any other pairs of operations in maths like differentiation and integration for example if any calculus students are listening the same thing over and over again right so there’s lots of these binary Concepts in maths and one particularly interesting one that I want to draw people’s

Attention to um or possibly tangent off about is uh zero and one because yeah this is really going to be a little bit of a tangent but let me explain what I mean so how I was saying um directionality and frame of reference and um the opposite motion is is not the

Opposite direction is to not move at all right think about zero and one which we see as this ultimate binary difference especially in in our culture in in Britain and in America too um we see Zero as often one is on um zero is nothing and one is something they they

Could not possibly more be more opposite um they could not be more you know that is that is the binary you know even in binary encoding we see Zer and one switches off on and off um but I I would I would question that I would say that

When you understand what number is and you come back to questioning what all of this invisible communication around how we notate number how that’s working and all of these operations and Concepts that you take for granted when you’re learning arithmetic you might ask you know it kind of naturally to me at least

Lends itself to the question of what is the oper that gets me nothing as the result or equally what is the operation that gets me one as the result because they’re really they’re really specific quantities aren’t they zero and one um you know we think of zero or or one as

Just like the starting point in the number line but they are also these bigger Concepts that they are these fundamental uh quantity differences to us in in a very material way um but also logically and philosophically and conceptually zero can represent uh balance um the wholeness of of quantity nothing was added and

Nothing was lost you are in the same place that you started or you’re at the same quantity that you started nothing changed the opposite of motion is to not move um the opposite of some amount of quantity change is no amount of quantity change Zero but equally one

Represents a whole thing a whole part one um you know the concept of of unity of Oneness um it is an entire amount the full picture um when you have six slices of cake that were cut into six pieces um 6 over six would be the fraction there which means you have one

Cake right one full thing but it depends on your frame of reference because you if you zoom out a little bit you added plus one that’s what one means you had one more thing than when you started you had one more cake in your life whereas you had no

Cake before zero cake right that is the nature of not being able to create or destroy matter or energy in our limited Dimension where we exist so if you simply zoom out your frame of reference in this case in terms of time um you you actually had one cake shifted from the

Baker to your home to share with your friends so overall zero cakes were added or lost from the universe what how can you buy a cake and then there was Zero cake um but then you might say oh but I’ll eat the cake and then there’ll be no cake so actually

There might be minus one cake in the universe and I would say well the balance is still zero cuz think about it if you zoomed out the the time scale forwards like that you can also stretch out the time scale backwards and zoom it out that way and equally the cake didn’t

Exist as a cake until the baker baked it so one cake came into being one cake left the shop one cake entered your home and one cake was eaten so all of these exchanges of ones happened but overall the result was zero so one was just zero in a specific zoomed in

Instant in time so they’re not that different and everything I probably just said probably sounds like a lot of nonsense to a lot of people and that’s completely fine it’s just a concept to play around with and to consider and question what you’re actually learning when you learn about numbers and to to

Think about what these systems of of logic are teaching you and ultimately they are just tools to understand the world around us to communicate and to connect with people historically through understanding our population and the world around us and in gifts and trade and you know that eventually you became

The modern uh Financial hellscape that is capitalism but also in the Sciences in in statistics in understanding the shapes and form of things in in Engineering in architecture to build and create things that are useful for us for Humanity um and if you’ve if you’ve ever tried to make something and just like

Went straight from um having the material to cutting it up or chopping it uh without any measuring like me you’re probably pretty impatient or just not very good at crafting things or you’re otherwise very very lucky and very good at crafting things you other wise probably gained an experiential

Appreciation for the usefulness of measuring something right because you probably made mistakes if you just went straight to cutting up a piece of fabric without measuring it first but anyway another example to make that a bit clearer is let’s go back to our theoretical Baker right the smallness of

Ratio and quantity and and proportion and number becomes quite clear here so some people I have a friend in my life for example um shout out to Ren who is an exceedingly gifted Kitchen Witch uh they don’t measure anything they just have this inherent intuitive knowledge

Of what ratios and quantities need to go in a recipe in what proportions that would make the tastiest meal for me with my ungreen thumb and my un blessedness by the goddess of home and Heth I need the specific quantities of how much water in sunlight a plant needs or how

Many herbs perfectly seasoned a dish or how many grams of something will go into a recipe I can’t just in it or just guess or know the amounts I need each ingredient listed to get a cake just right so for me in that instance the the

Math the number is a tool that helps me bridge the gap between that intuitive inherent understanding of the universe of cakes into a grounded defined system of measurement where everyone is following the exact same agreed upon rules that allow us to check the balances and to make sure that everyone

Is arriving at the same conclusions of exactly how much flour versus how much butter or eggs or sugar or whatever that make a a perfectly fluffy cake no matter how big or small I need the cake to be for a given event so if that makes sense all of that are

Given how on Earth is any of this useful in your exams you ask well I’ll tell you um if you’re thinking about what Logic underpins the rules that you’re learning a number and you can apply that like I just did in a real life example and understand why that system of number

Logic that system of arithmetic was useful by the time you get to those annoying exam questions that have entire walls of text um to understand and comprehend before you start calculating any answers you’ll find it much easier to know what’s going on and what you’re

Supposed to do and how to apply that in those really tricky questions so ultimately learning number trains your logical brain to think about what rules and patterns are governing the systems of quantity and how to apply those rules as Tools in in problem solving and that skill itself self is then crucial to

Developing critical thinking lateral thinking or being an a totally excellent creative and skilled Problem Solver in not just maths in anywhere right and it also in terms of the gcsc on your exam provides the foundation to build your skills in algebra which really levels up your problem solving because then we

Take our specific quantity rules and logic and apply it broadly or generally or every single time no matter what the quantity is and that is incredibly powerful and that’s why I love algebra it’s kind of like the rules and systems of number on hyper High powerered rationality mode um and then

Investigating where those systems break down and the logic doesn’t logic is incredible and I and I love that um but that’s kind of like the difference between a kid at school learning their arithmetic and that’s fine versus a matured mathematician who can apply this logic iic to any numeric problem who

Then would become an expert mathematician who can apply this algebraic logic to any problem at all and I will talk about that more next week and and how that relates to coding and um all sorts of scientific principles um but yeah so I think that’ll do for today thank you for

Watching if you made it this far and if you enjoy these chatty revision videos give me a like or let me know in the comments what was useful about about this for you um because I’m thinking about concluding this series once I’ve gone through each of the sort of major

GCS topics uh but if people like it I will keep it going um either way whatever you do um check out my other videos for today I’m also doing a physics and chemistry one every week um don’t forget to be kind to yourself because our words of spells have a

Lovely rest of your week and I shall see you next time y bye