[Music] [Music] hey guys welcome everyone how we all going today guys comment down below if you are super excited if you're feeling ready to go guys because today we've got a really really exciting lesson we will be looking at perimeter area and volume for maths and then we'll follow that theme and we'll look at some spatial reasoning for thinking skills so today maths and thinking skills like really go hand in hand if you do well in spatial reasoning you'll do well in perimeter area and volume and same thing goes for the other way around if you do really well in perimeter area and volume you guys are going to find spatial reasoning so much more easier so today's lesson is super important like those two things as i said they really go hand in hand okay so comment down below if you've already seen these concepts before have you seen perimeter before have you seen area before volume spatial reasoning in general have you seen this before or is this brand new for you guys like if you already know that's great but if you don't that's okay because i'm going to be explaining everything right from the beginning just to make sure we've all got it but as i said guys yeah comment down below if you know even like a tiny bit of it just let me know okay even a tiny bit of it just tell me and say oh i've done like the tiniest bit of perimeter and that's fine okay so as i said guys today's lesson is super super exciting this stuff is really cool but today we've really got to put our thinking caps on okay because a little this stuff we have to actually imagine things in three dimensions we have to imagine them in our heads so it does get a little bit tricky okay it might be a bit tricky but we've got this guys we've got to work together we're going to work hard we've got this now a quick thing before we start just wanted to remind you guys um last thursday so what two days ago i did the scholarly podcast so go have a watch of that if you haven't seen it already and comment down below if you watched it because it was super exciting and next week there's going to be another really really exciting guest on the podcast so don't forget guys that's on every single thursday at 7 30. i'll write that down thursday 7 30. make sure you're watching that it's really really good really useful great tips and tricks for you guys okay so that being said let's get started let's do it let's look at perimeter area volume and of course some spatial reasoning for thinking skills okay you guys are all ready let's go so number one our first question for the day is what is perimeter perimeter this is the distance around a two dimensional shape the key thing here is most the time we're looking at two d shapes two dimensional 2d that means something flat so for example a square oh this isn't probably a perfect square let's say this is a rhombus right my drawings didn't come out very nicely but this is a rhombus this is a 2d shape a two-dimensional shape what is the difference between something that is two-dimensional and three-dimensional guys who knows the difference of something that is two-dimensional versus something that is three-dimensional who can tell me who can tell me the difference between those two things what is 2d and what's 3d what's the difference and how can we tell if something's 2d how can we tell if something's 3d what is the difference guys 2d two-dimensional versus 3d three-dimensional what is the difference 2d versus 3d i want someone to tell me what do you think the difference is even if you don't know just take a little bit of a guess let's all work together today guys i want every single person here to participate okay because that's how we get our best lessons done we all gonna give our ideas and we're gonna work together okay so what do we think 2d versus 3d what's the difference so 2d as i said earlier 2d is something that is flat okay so a rhombus a square a rectangle even a circle i'll change the color of the rhombus guy so that they're all red anything that is flat is 2d okay that's what it is anything that is flat is 2d something that is 3d though is not flat okay something that is 3d is something that's actually real in our world like something that i can actually touch so yes 3d objects use 2d shapes so for example if i take a square right a square is 2d i can make it 3d sort of like this i'm going to draw you guys a cube and i'm going to do the best drawing that i can in three dimensions as you guys can see right i'll zoom in so you guys can see a little bit better as you can see this is three-dimensional it's got the flat square shape but it extends backwards it's got three different dimensions so we say it's got a length a width and a height these are the three dimensions we call these these things dimensions whereas something that is 2d it only really has a length and a width we sometimes use these words interchangeably but the key thing is it only has two dimensions see how it's got one two where something that's 3d has one two three different dimensions so here's how i like to think of it in my head if i can touch it in real life then that's 3d right i can touch a sphere i can hold a sphere in my hand i can't really hold a circle in my hand like sure i could print out a photo of a circle or cut out a circle but it's still going to have some sort of height in there so it's actually 3d okay that would be like technically a cylinder right a cylinder has a circle a circle it sort of looks like that let me draw it a little bit better sort of looks like that so are we all clear uh with these differences between 2d and 3d shapes comment down below if you're all clear with this and you understand it and i also want you to tell me some examples of 2d and 3d shapes so what examples do you know off the top of your head i've given you guys some examples here i've told you we've got a rhombus is 2d we've got a square is 2d a rectangle and circle these are all 2d shapes two dimensional shapes but things like cubes and cylinders are three dimensional so any more examples that i haven't mentioned here that you guys can think of i want every single person to give me an example and i'll give you some more too but i'm going to give you guys a chance for you to tell me first and then i'll go through some more examples of these with you guys we'll be looking at a lot of these today as well we're going to be calculating the perimeter of the 2d shapes the area the volume we're going to be doing all these cool things with them perfect an example that we've got is a square pyramid right so that one's a little bit difficult to draw but i'll try my best it's got a square base right and it's got a pyramid sort of shape like that so imagine that in 3d it's got a base of a square and it's got these triangular faces going upwards that would be a square pyramid and this is 3d we could also have a triangular base pyramid which is also called a tetrahedron and that one's also a little bit tricky to draw but i'll sort of try my best oh that's a pretty horrible drawing but all it is right is it's the same thing as this with a triangle at the bottom instead of a square we can also have things like rectangular prisms right same thing as squares um becoming cubes this time it's a rectangle let me fix that drawing a bit this time it's a rectangle actually becoming a 3d shape it's a rectangular prism we can have triangular prisms we can have spheres right we have spheres we can have cylinders all these different shapes now in terms of 2d shapes we've got all these ones that i just mentioned squares as well of course we've also got things like parallelograms right which look a bit like this we've got things like trapeziums that's a 2d shape we've got triangles of course right triangles are like probably one of the most basic 2d shapes so these are all really good examples that i want you guys to keep in the back of your minds okay so now let's return back to our idea of perimeter we said perimeter is that distance around a two-dimensional shape which means that it is the continuous line forming the boundary of a closed geometric figure key thing here is closed we can have closed shapes and open shapes if i draw a square this is a closed shape all the lines are connected there's no gaps if i draw this this is an open shape because there's nothing here guys there's no line in there right it's actually an open shape so really we usually deal with closed shapes when we're looking at perimeter okay so now let's look at how to actually find perimeter how can we calculate the perimeter the perimeter is just the sum of all the different side lengths so let's have a look at some examples and let's figure this out guys okay our first shape the simplest one that we're going to be looking at is of course the triangle a triangle is a plane figure with three straight sides and three angles okay three straight sides and three angles do we all know what a side is do we all know what an angle is because these are our key words over here so are we all clear with sides and angles guys or do you guys want me to go through that are we all clear with what that means or are we not so clear let me know what you think guys in the meantime more you guys let me know about that i'm going to quickly run through this formula remember the perimeter is just that distance around a shape so the perimeter of a triangle is going to be this side plus this side plus this side okay so if i name these sides a b and c doesn't matter what order i name them in the perimeter is just going to be a plus b plus c we're just going to add all these different side lengths together okay so since you guys want me to quickly go over it the sides are just these lines that form our shapes so this here is a side of a triangle as i said a b and c are all sides and if i draw two of these sides together guys an angle is this little gap between these lines this here is an angle and we measure it in degrees degrees have just this little symbol so we can say that angle might be 60 degrees now really quick i'm also going to run you guys through the three different types of triangles that we see okay our first type is i'll do my best drawing that i can here guys our first type is of course this triangle which is called equilateral and what this means is that all sides are equal in length so i'll say all sides equal and all angles are equal so let's say this side is a then this side is also a besides also a they all have the same length and one way we can indicate that is with these little lines they tell us that all the lines have the same length and the angles are all the same all these angles are actually going to be 60 degrees okay now the next type of triangle that we've got we've just gone over this first one equilateral i want everyone to comment this one down below okay our next one is an isosceles triangle so we might have something like this this here is isosceles and what this means is that two sides are equal and two angles they're equal so as you guys can see those two sides that i've indicated have the same length but this side is much much smaller so not all of the sides are the same okay and this means only two of the angles are going to be the same as you guys can see these two are the same but this one is slightly different okay now the size of these angles depends on the triangle like i could stretch it out i could put it back down etc etc so there's no like one special number like there is with equilateral triangles but it's still important to remember okay so can everyone comment these two things down can we comment down the word equilateral and the word isosceles and the next one the last type of triangle is this this is a scalene triangle and as you guys can see no sides are equal and no angles are equal they're all different i'm going to move this up a little bit none of this is the same all the sides are different lengths or the angles are different lengths so really really key ideas here are we all crystal clear with this okay because if we can understand the different types of triangles it makes finding the perimeter a lot easier okay are we all clear guys comment down below if you are crystal clear with this okay then let's keep going let's look at an example let's find the perimeter of this triangle who can tell me what type of triangle this is what type of triangle is this triangle that we're looking at in this example guys what type is it equilateral is it isosceles or is it scaling what is it and how do we find its area well oh sorry no it's area it's perimeter in this case so the perimeter of this shape is just all the side lengths added together so it's going to be 5 plus 8 plus 12 which is the same as 13 plus 12 which is equal to 25 okay so yes guys this triangle is scaling we need to do some addition to find its perimeter because all its sides are different lengths all these angles are different and that is how we find the area of the triangle nice and simple to start off with okay now let's jump into squares let's jump into squares a square is a plane figure with 4 equal straight sides and four right angles these angles instead of indicating them like with little curves like within our triangles we use this little half square shape to indicate that they are right angles okay we call these angles right angles and so the perimeter of this shape is just four times one of the side lengths so remember guys if each if one of the side lengths is a in a square all the side lengths have to be a because they're all the same so this the perimeter is the same as a plus a plus a plus a which of course if we just put our thinking caps on and we think about some multiplication that is literally just 4 plus a or 4 times a sorry so a plus a plus a plus a is 4 times a and that is how we get this formula here for the perimeter of a square four times the side length remember squares have the same size right four equal sides and four right angles we call these angles over here right angles that is a right angle okay so let's have a look at an example if i've got this square over here when one of its sides is three centimeters i mean this is three this is three this is three this is three how can we find the perimeter guys i mean i've got the solution right there for you but i still want you guys to just give it a go in the comments this is just going to be 4 times 3 which is of course 12 centimeters that's why it's really important to know all our times tables right and if you don't know your times tables yet i really suggest that after this class you go and revise them okay because they're super useful like we really need to know at times tables otherwise we're just gonna be wasting our time going three plus three plus three plus three and that just takes too long if you know that four times three is 12 that makes your life so much easier okay all right next up our next shape is a rectangle it is a plain figure again with four straight sides and four right angles but it has one it has unequal adjacent sides adjacent just means next to each other so these two sides are equal and these two sides are equal can you guys see how i've drawn the lines that sort of match them just like i did with the triangles so the adjacent sides this side over here and this side over here are not the same they are unequal so the adjacent sides aren't equal so if i let this side here be a and this side at the top down the bottom here be b the perimeter is just going to be a plus b plus a plus b which is the same as 2a plus 2b what i can do is i can just do 2 times a plus b which works out really really nicely okay so the perimeter of a rectangle is going to be 2 times the sum of the adjacent sides a plus b over here i'm going to write it out here this is the sum of the adjacent sides okay adjacent just means next to each other really nice fancy word there to describe a concept that we use all the time so it's really important to know what adjacent means so i want you guys to be keeping a note of these formulas okay these are so so important so remember the perimeter of a rectangle is going to be two times that sum of the adjacent sides two times a plus b two times that sum of a plus b we first have to work out what's in the brackets then we can times the whole thing by two okay two times a plus b so who can help me with this example i'm just going to quickly rub out the solution i know you guys have already seen it probably um but that's okay let's work through it together first and i'll spoil the answer okay so given this shape here this is of course a rectangle how can we find its perimeter well the perimeter is going to be two times the sum of the adjacent sides two times three plus seven now work this work through this with me guys what is three plus seven 3 plus 7 is of course 10 and 2 times 10 is 20. now remember guys you can't forget your brackets brackets are super important i'm gonna write a really important statement here okay if i have 2 times a plus b that is not the same as 2 times a plus b we always do what's in the brackets first so we have to be really really careful with how we write it we have to do brackets for this we need to use brackets because what this second statement is saying is it's just saying oh do two times one of the sides a and just leave b by itself so they're actually two different things we have to be really careful with our brackets brackets are like really really key over here okay so as you guys saw i did two times brackets three plus seven which is two times ten which is twenty if i just did two times three plus seven that's the same as six plus seven which is not 20. so it doesn't actually work both ways you've got to be careful with your brackets okay careful with your brackets i want everyone to write down that word brackets super important we're going to be really careful okay guys now we're going to look at some more general shapes which are quadrilaterals in this case a quadrilateral is a closed two-dimensional figures that has four sides four angles okay and a few examples of quadrilaterals are of course squares rectangles trapeziums rhombuses uh parallelograms anything that has four sides and of course four angles falls under this nice little umbrella of quadrilaterals and always uh of course it's just gonna be this side plus this side plus this side plus this side okay we're just gonna add up all our sides to find the perimeter so let's look at another example this time we have this shape which is a trapezium and i still want you guys to help me out with these questions so how do we do how do we find the perimeter of a trapezium we just have to add all the sides so we're going to have 12 plus 9 plus 10 plus 14 and let's do the addition together guys i can just split it up i can do these two what's 12 plus 9 what is this i can even do this the long way but i'm sure you guys can do this without the long way like we all know how to do 12 plus 9 9 plus 2 is 11 so we get 21 10 plus 14 is of course 24 and now we have 21 plus 24 which is going to give me 45. so yes the answer is of course 45 centimeters remember we are just adding everything together all these different sides we add them to find the perimeter now we are getting into some tricky things this thing here is circumference circumference is just a really special word that gives us the perimeter of a circle okay so circumference is just like a type of perimeter but we only use this word for circles okay and we've got this formula over here which tells us that the circumference is equal to two times a special number pi times the radius which is really it's a really special number this thing called pi right as you guys can see it's approximately equal pi is around 3.14 but pi actually goes on forever it's a crazy number guys if you search up i think there's like thousands of digits of pi that people have found even like hundreds of thousands but pi goes on forever it's a really special number okay it's a very very special number it goes on forever pi 3.141592 or something something something and it just keeps going and going and going and going and going and there's actually no pattern in its decimals that's the crazy thing about pi there's no pattern in its decimals but if you do ever put pi into a calculator it can do that calculation for you you can also leave your answer in terms of pi so i'm going to show you guys that in a second okay well i'm just going to show you here real quick you don't need you don't need to know too much about this circumference stuff yet because you will do it later on as well but if the radius of this circle which is the distance from the center to any sort of point on the outside that's the radius okay if my radius let's say radius is 8 then my circumference is going to be 2 pi times 8 which is 16 pi okay and if you put pi in the calculator it will give you like an approximate sort of number for the circumference okay so does everyone understand this concept of circumference because it's quite tricky pi as i said is a really cool number and it's so so so useful and you guys will do it uh we'll look do plenty of things with pi as you keep going through school you even do it like in high school okay so you never stop learning about pi it's so useful so we all clear with all our perimeter stuff that we just looked at because we're now going to move on to area okay are we all clear with perimeter all clear with circumference all clear with everything that we just looked at okay perfect guys let's keep going let's now move on to area area is our next concept of the day it is the quantity that expresses the extent of a two-dimensional region and shape in the plane it is basically the size of a surface of a two d surface so we only deal with area for two d shapes if we have 3d shapes we can find their volume or we can also find this thing called surface area which we won't look at today okay but now we're going to be looking at area remember guys i want you guys to all write this area is only 2d okay area is only two dimensional we are not going to be looking at areas for 3d shapes we can look at things like surface area the area of different surfaces on a 3d shape but if we just look at area area is for two d shapes okay so if we look at the area of a square that's just going to be the side length squared squared just means times by itself it just means the same number multiplied twice so area is going to be equal to the side length times the side length which we can also write as squared have you guys seen this notation before have we seen this before do we know our square numbers have we seen square numbers before because it's really good to know our square numbers okay so have we seen square numbers before at all or have we not seen that yet now square numbers i'm going to write some of them down for you guys okay 1 squared is just 1 times 1 which is 1 2 squared 2 times 2 is 4. then we get 3 squared is 9 4 squared is 16 5 squared 25 6 squared 36 and we could just keep and keep it keep on going okay so as i said this is 1 squared 2 squared 3 squared 4 squared 5 squared 6 squared so all you need to do to find your square numbers is just multiply a number by itself so if i square a number that means i multiply it by itself okay so 2 squared is 2 times 2 which is 4. and this lets us find the area of squares so the area of this shape over here just the square is going to be let's say that this is 4 and this is four it's going to be four squared which is of course four times four and four times four is sixteen so are we all clear with this idea of square numbers you know they do get a bit tricky but it's really good to practice writing down sort of like a list of squared numbers they're just like a special part of our times tables it's all out they're technically just times tables but they're just like a special little subset of our times tables okay so that lets us find the area of a square it is just the side length multiplied by the side length and because the two side lengths are the same it's just going to be that side length squared now what about a rectangle where the side length is not the same and we can't square anything but we still got to multiply together so the area of this is going to be b h right we might call this breadth and we might call this height sometimes you also see this written as length times width so you might see the area written as this length times width it means the exact same thing remember it is just the adjacent sides adjacent sides multiplied together the adjacent sides multiplied together so really important stuff there again okay the area of a rectangle is going to be the base times the height so if i have a rectangle that has a base of 7 and a height of three that is going to be remember this can also be base that is just going to be 7 times 3 which is 21 centimeters squared another difference there perimeter we measure in centimeters area is two dimensional so it's measured in centimeters squared centimeters multiplied by centimeters okay does everyone remember this formula b h area is bh base times height all right now what about triangles guys triangles are a little bit special okay triangles are actually half the area of a rectangle there are half times the base times the height so for example guys if the base is 10 and the vertical height is 5 then the area of the triangle will be half times 10 times 5 which is a half times 50 which is 25 centimeters squared so write this down guys area of a triangle is a half times base times height really really important formula as well okay a half times base times height and if i draw a rectangle you guys can actually see where this comes from right it's literally just half the area of a rectangle if this is a rectangle this is one triangle and the other side is the other triangle right and if we if these triangles are actually half of the rectangle then the area has to be half of the rectangle so the area is of course half times base times height that is where the formula comes from write this down for me guys super important and let's look at some more things next up we've got parallelograms the area of a parallelogram is the same as the area of a rectangle but you've got to be careful the height is now this distance over here it's no longer the side length the height has to be vertical okay it has to go up and down it can't be sort of like slanted on an angle the height must be straight up and down it needs to be vertical so in this case if i have a parallelogram with these dimensions then the area is going to be 5 times 10 which is 50 centimeters square another really important formula for you guys there and now we're going to move on to the idea of volume okay volume is the measure of a 3 dimensional space remember volume is 3 d everyone write that down for me volume is 3 d see the difference guys area was 2d but now volume is 3 d so definitely a bit of a difference there it's very very important to recognize this difference so it's that measure of three-dimensional space occupied by matter or enclosed by a surface and it's measured in cubic units remember guys how we had for area we had centimeters times centimeters which is centimeters squared for volume we have centimeters times centimeters times centimeters which we call centimeters cubed so anything cubed that means we times a number three times by itself okay see the difference there so 2 squared is two times two times oh times two sorry which is four two cubed is two times two times two three times which is eight so this is only two times whereas this is three times so there's the difference so volume has cubic units because we are measuring we've got three dimensions that we multiply together so the volume of a rectangular prism a rectangular prism is a polyhedron it's just a very fancy name here it has two pairs of concrete and parallel bases congruent same same basis it has six faces twelve sides and eight vertices faces are just these things here faces are actual surfaces right faces are the same as surfaces on our shape okay so for example this top part here is a is a face another face another face and then we've got this face at the back we've got this face at the back and we've got this face down the bottom this gives us six faces sides are the exact same things that we looked at before so this is a side this aside okay aside is just these little lengths here that make up our shape and vertices are where sides meet so points vertices are just points they are just corners so it's a vertex vertex vertex vertex vertex vertex vertex vertex okay oop not there sorry there you go we've got one vertex many vertices so i want everyone to write this we've got face we've got a side and we have of course a vertex these are like our three key thing with 3d shapes so from here we can find the volume of a rectangular prism that's just going to be length times width times height so if this is 5 three and four then the volume is going to be five times three times four which is five times twelve which is sixty okay so everyone write those terms down for me because as i said they're so so important okay it's really important to understand faces size and vertices and of course we want to know that for a rectangular prism the volume is the length times the width times the height length times width times height okay perfect now spheres are a little bit special we've got that really crazy number pi again pi this is how we write pi pi remember it's that three point one four one number that crazy number like goes on forever so we can find the volume of a sphere using this special formula four thirds pi times the radius cubed so the radius remember the radius is just the distance from the center to any point on the outside okay and so cube just means we times it three times so the volume of a sphere is four over three pi r cubed so yes pi really crazy number it comes in everywhere we've got to do with circles pi we use just we use pi all the time okay yeah be careful guys it's not like a pie that we eat it doesn't have an e at the end it's just a greek letter that's that's where it comes from so pi is a greek letter and it's just a very special number and in this case it can give us the volume of a sphere and the volume of a cylinder also we have to use pi anything that has circles we're basically using pi in it so we've got pi r squared h in this case where h is the height and of course r is still the radius so we're going to have pi r squared h pi times 4 squared in this case times 6 and if you put pi to the calculator you would get this number approximately over here so after we finished class guys i have a bit of a suggestion for you go up and just see how many digits of pie you can find i think there's a song i don't remember if it's a song but one of my friends memorized 100 digits of pie which is crazy so yeah pi super cool number and it's c as you can see it's very useful it even helps us find the volume of a cylinder it is pi right so pi is the number pi is like an actual pie with pieces right so if i've got like a like let's say a pumpkin pie or somewhere sort of pie it's got all these random things in it so not the pie without the e is the number and pi helps us get to the volume of cylinder so now guys let's do some examples of this stuff okay then we're gonna do some thinking skills arnold has a vegetable garden that is 12 meters long and three meters wide he's planning to set up a second vegetable garden that is twice as wide as the first garden but has the same area how long should the second vegetable garden be guys i need you all to help me with this question just like we do every single week i need everyone to help me so if i draw the original one okay if i draw a rectangle oh that's a horrible rectangle if i draw this over here this is 12 and this is 3. 12 meters long 3 meters wide now we want twice as wide okay we want twice as wide but same area so if what's 3 times 2 6 the width is going to be 6 but we don't know what this side is going to be we want to have the same area so let's name this side x you can name it any letter you like but i'm just going to name it x okay the area of our first shape is 12 times 3 and guys what is 12 times 3 everyone comment down below what is 12 times 3 12 times 3 is 36 and in our second shape we want the area to be the same so we can have 36 is 6 times x so what i can do to solve this guy is i can actually divide both sides by 6 and i get that x is equal to 36 divided by six which is of course six so the second vegetable garden if we want to actually keep the same area it has to be six meters long okay so see how we've done this question guys it can be a little bit tricky but with these i always like to draw them out for myself just makes it a lot easier in your head if you can just have it on paper and draw it out all right perfect now um this is the exact same question that we did so i'm not going to do it again not sure why it's there twice don't know why that happened but that's okay all right now let's move on to some thinking skills okay we can we might have time to do some more questions at the end i'm not sure what these quiz points are about so i'm just going to ignore that for now okay but i'll be all clear with those ideas guys are we all clear with these ideas of perimeter area and volume are we all clear with these because they are quite tricky like they're quite tricky but do you understand this how are we all feeling with it and if you are still a little bit iffy with it of course you can always re-watch this video you can watch it as many times as you like you can comment on it again when you re-watch it that's completely fine and you've got some really good questions here for homework that you can go through as well okay and we might have a chance to go through some of them all right perfect you guys have been absolutely amazing today let's keep that amazing streak going while we look at some thinking skills okay let's look at some thinking skills let's do it spatial reasoning now i have a question for you guys okay i want you to use your imagination like this spatial reasoning stuff is all about imagination so use your imagination even close your eyes for a second if you need to and try to imagine in your head a cube that is sort of spinning around okay so if you can imagine this i'm going to give you guys a couple seconds imagine this cube spinning around in your head spinning around in your head that what you're actually doing there what you're using is called spatial reasoning spatial reasoning is a really really cool concept now i think i've got like a bit of a fidget cube here that my little sister uses right if you can imagine this thing spinning around in your head without me actually doing it in real life if you can imagine this in your head you are using spatial reasoning okay that cube that is spinning that if you can think about in your head you're using spatial reasoning so spatial reasoning is the ability to imagine things in three dimensions in 3d you really got to use your imagination here guys comment down below if you have a really good imagination because i think all you guys have absolutely amazing imaginations but comment down below if you've got a really really good imagination if you're really strong at imagining things so because spatial reasoning is all about imagining 3d objects it includes that ability to move around objects like if i've got this cube as i said we can spin around we can also have it moving around we can have it rotating we can have all sorts of things happening to these 3d objects we have to be able to imagine them in our heads okay so if you're really good with imagination comment down below if you're really good at it because i need everyone to work on their imagination skills to work on their spatial reasoning ability okay and be really good at it so let's look at this let's look at this first shape over here which i've just outlined in red we can rotate this shape to look like this second shape i want you guys to try and picture this in your head it's really tricky to do but i want you to try and imagine this so imagine rotating the top left shape to look like the right shape so if i try to quickly outline this shape for you guys it's not going to be perfect but i'll try draw it out real quick and outline it for you and what i'm going to do is i'm actually going to rotate it okay i'm going to play around with it so here's my shape can we all see this i am actually going to rotate this shape i've got that shape up there i can actually rotate it around and i can get all these different views of it as you guys can see you need to be able to imagine it in your head because you don't have like an ipad in an exam to do this rotation for you you need to actually imagine this rotation okay you need to be able to imagine all these different rotations in your head see how i'm spinning it around guys you need to be able to do this in your head as well okay so that's what we're doing that is what we are doing and if you don't have a good imagination yet that's okay we gotta we just gotta work on it these questions you're only get going to get better at with practice all right so how would this look imagine rotating this gray shape now the same way how can we actually which which image is it going to give us is it going to give us a b or c guys if we rotate it the same way a b or c if we rotate it the same way as we did with those two shapes up there so imagine that rotation okay imagine that rotation you have to rotate it this way and then flip it a little bit so it's really cool so which shape would it actually be rotated to would be a b or c again these questions are tricky guys they're actually quite tricky so i really need you guys to try to imagine this in your head the best that you can what i used to do in these exams i would actually like pretend i'm holding the shape and sort of like move around like this and all the teachers would look at me like anastasia what are you doing but it just helped me sort of imagine if i went like this and i would go up flip flip flip it help me sort of use my hands in my head so would it be a b c or d it's a really tricky question this one a b c or d let's look at our original shapes again because we're going to rotate it the same way so how do we rotate it how do we rotate it let's have a look the answer guys is actually b really really tricky so you gotta rotate it this way sort of gonna go around that way and then you're gonna like flip it around the other way so it's quite tricky but the only way you're gonna get better at these questions is if you practice practice practice you gotta really try to sit down imagine these in your head what i would even do after this lesson is i would get a piece of paper start cutting out some different shapes see if i can rotate them around okay so yeah guys the answer is b and don't worry if you didn't get it right the first time because these take a lot of practice these are like one of the hardest things about thinking skills but yes the answer for this one is b now we can also look at things like two two-dimensional shapes we can fold two-dimensional shapes to make 3d shapes so if i fold this shape guys what shape am i going to get in the end am i going to get a 2d shape or am i going to get a 3 well of course i'm going to get a 3d shape but what shape am i going to get if i fold this what do we think what do we think we're going to get which shape are we going to get if i fold this thing here we can call this a net with 3d shape uh what do we get we get a cube we actually get a cube so if we fold all those sides we get this cube shape over here okay so imagine this will be this and this are going to meet up these two things are going to be upright and we can keep folding all this up so we also call this the orthographic view orthographic views are two-dimensional depictions used to describe three-dimensional objects so of course on paper i can't draw something like sticking out of people but i can draw it like it's sticking out of paper again remember how i drew my cube before guys i can draw like these little dotted lines to imagine what the back of it looks like and this gives me like a really nice indication of this shape so yes this is an orthographic view it's a 2d depiction like i've drawn it on a page on a screen in this case but it's actually representing a 3d shape so let's look at an example guys if i've got this shape over here i could draw this as the top view of it i could draw this as the front view and i can draw this as the side view because if i look at it from the side i'm gonna see this this and this so i'm gonna see just three squares okay if i look at it from the top i'm gonna see this thing over here which gives me this shape over here and if i look at it from the front i'm gonna get this shape where does this shape come from it comes from over here really really important guys okay so orthographic view we also call this multi-view we call these multi-view drawings as well really really important there okay so let's look at some more examples of this we could have this shape over here we can have again a top view if you imagine yourself looking at it from the top like this you might end up looking at it from the side and if you imagine yourself looking at it from the front it's three completely different views okay really really important to remember these three different views let's stay focused guys we've only got a couple minutes left so we really want to get through this we want to stay focused for this last little bit of the lesson remember you guys have been so good today so let's keep it up let's keep it going okay now let's try to visualize this let's try to draw these views in order from top front and side okay then you can draw lines where these edges are these are changes in plane and you can use these dotted lines over here and all these dotted lines to show hidden edges okay now of course solid lines are actually trunk outer lines remember just like i did with our cube i'm going to draw the cube one more time because it's nice and it's just an easy shape to think about oh that's horrible let me draw it again there you go we've got this sort of shape and i can draw the hidden sides using dotted lines so we use solid lines for like our main bits dotted lines for our hidden edges and this lets us convert between different views okay really important to remember this let's try visualize this shape as well this is a really trippy shape to think about okay let's look at all the different parts of this shape let's look at the top view the front view the side view and we get these three different views right i can get this little shape over here giving me this i could get the top of course i can get this we can get all these different parts of the shape which are super super super important all right really important to have a play around with these shapes cut these out on paper that's what i used to do when i was young i would cut out shapes on paper play around with them you really just gotta try to improve your imagination as much as you can and these are really hard okay these are hard like they're really tricky but you really have to pay lots of attention to them to really get it so if i've got this shape guys what do you think it would look like try to sort of imagine this in your head what would it actually look like it's got this top view this front view and this side view so what it would actually look like i know you can't really draw in the comments but what i'm going to do i'm going to show you it would look a little bit like this remember that's the front view over here right the side view is sort of like this let me try to draw it nicely for you guys it's this and this shape and this shape and the top view is just going to be this and this and this see how it matches really nicely you've got to actually remember that these things have to match so of course in an exam you'd get like a multiple choice type of question where they'd give you options and you've got to select which one you agree with you wouldn't have to draw it yourself but it's still really good to know how to draw these do we all see this again i know it's really hard but i want you to try to use your imagination as much as you can if you don't use your imagination these questions are like so so difficult okay use your imagination for these questions guys now if i'm given that this first shape is rotated to the second shape okay let's have a good look at this that first shape is rotated to this second shape let's see how we'd rotate the second shape look at this first picture really carefully now let's have a look now down the bottom here how we would rotate this shape would it be a b or c look at the first rotation down here look at the first rotation and is it a b or c guys let's give this one a quick go a b or c what are we thinking is it a is it b or is it c last example for today guys let's put our thinking caps on let's get to it a b or c for this one if i rotate it have a really close think about this one guys a b or c remember we want the same rotation as those white shapes for the gray shapes a b or c let's all try this question and then we're going to end there a b or c guys let's go quick quick quick quick quick so we're running out of time hey but you'll see it seems like you guys have definitely improved because you guys are correct the answer is a give yourselves a really big clap guys that was really hard but you guys all got that rotation perfect and that's it guys that is it for today that is amazing you guys did so so so well today thank you so much for paying attention like you guys did and for contributing as always again i definitely recommend you guys three watches because today's lesson like was pretty jam-packed we had lots of tricky things that we looked at but you guys did so well okay everyone deserves a big clap a big pat on the back today because you guys did so so so well so of course you guys got to practice this i've said it like 50 times today so we've got as i said some really good maths homework on volume perimeter area okay and of course you've got some thinking skills homework on spatial reasoning when you go to practice these skills that we learned today spatial reasoning for thinking skills and of course we've got some area volume perimeter questions so comment down below if you found this class really useful thank you guys so so so much for being as amazing as you were today i had lots of fun it was super exciting teaching you guys and i'll see you guys all next week for our last week of the term so again if you found this difficult have a look at this video again practice those homework questions don't be discouraged you've got this i know you do and i i'm gonna see you guys next week bye everyone [Music]