Which letter DOES have a line of symmetry?

How many lines of symmetry does the number 4 have?

I am a triangle. All sides are a different length. One angle is 90° degrees. What kind of triangle am I?

I am a quadrilateral. I have no right angles. Opposite sides are parallel. What shape could I be?

What do each of the angles in a rectangle measure?

To investigate a problem using symmetry (Part 2)

Key Stage 2

Maths

2-D Shape and Symmetry

A line of symmetry can also be called....

A regular pentagon has how many lines of symmetry?

How many lines of symmetry does this isosceles trapezium have?

Which of these numbers has 2 lines of symmetry?

﻿Hi, it's me Mr.C. We made it. We're here, we survived. We are in our last shape and symmetry session. Wow, how quickly time flies hey. But well done for getting this far and sticking through it, and we're really proud of you. So let's look at what's ahead today, shall we? First thing's first and you know what I'm going to say. Have you taken our knowledge quiz? If you haven't, why not, go and do it now. Show me your brilliance and come back when you're ready. So shall we take a look then? Have something pretty amazing for today. So did you know that the heaviest animal on earth, and on land, but on earth in general. So this isn't the sea as well, it's the blue whale. This blue whale can weigh up to 190,000 kilogrammes. That's mad. Now we've done a bit of work on weights. You can figure out what that might be in grammes, go in and see if you can figure that one out. That's a lot of grammes. That can be as long as 25 to 30 metres in length. That's longer than a bus. Just putting that one out there for you. They can swim at an average speed of about 12 kilometres now. It doesn't seem that fast, but definitely, probably faster than I can swim. And they can sprint 'cause obviously you can't sprint under water, but they can reach top speeds of up to 32 kilometres an hour. And they can live on average for between 80 to 90 years old. I didn't realise they lived as long as that. It's pretty amazing they are astonishing animals. And I would definitely urge you to go and have a read up about them or watch some footage of them, astonishing. Absolutely crazy. Weird animals on this earth. No, all of them are unique and impressive and interesting. Just like each of you. So making sure for today then, that you've got everything you're going to need. A pencil, a ruler, somewhere where you can work with no distractions. So probably not deep sea diving while you do today's work. And then some paper or a book to work in. You've done your knowledge quiz, but the rest of our agenda for today is as follows. I wonder if you can guess? Key vocabulary and key learning. Number fit warm up. Today, that doesn't mean that we're going to be counting and doing exercises. We'll be doing brain exercises, but not physical. And we've done a number fit before, so hopefully you remember how they work. Then we're going to recap on all the symmetry we've covered so far. Have a look at a variety of symmetry activities and then a final knowledge quiz to see what you've remembered. Now with the symmetry activities today, I'm going to really push you just to see how brilliant you are, 'cause I get a sense, I get a feeling that actually, what we've been doing so far, I can push you even more. So key learning. To investigate a problem using symmetry. And our key vocabulary, shocker, shocker, symmetry, symmetrical, mirror line, shape, grid, 2-D, two-dimensional and investigate. Excellent. So, shall we get straight on them with warming up our brains? You will hopefully remember our friend, the number fit. Number fit is basically a crossword wave of numbers, not letters. And you'll have a mixture of three digit numbers. You'll also have some four digit numbers, some five digit numbers and some six digit numbers. Always start where you have the least options left, crossing out numbers that have already been used. So if we look here, I've got all of my three digit numbers, all of my four digit numbers left and all of my five digit numbers left. So where might I start? Well, I would start with my six digit numbers because I've only got one, six digit number left to place. So I need to look at my grid and see if I can spot where the next six digit number would fit? So where can I see six white boxes side by side or on top of each other? I know then that that's when this number must go. So I'll look, one, two, three, four, five, six. So that must be my other six digit number. And what do you know, has a nine here in the first box and it starts with a nine. So this must be nine seven, one, three, zero, two. And you remember what I said I was going to do next? Cross out the number. And because I've used all the six digits, I'm going to do something that we wouldn't normally encourage, I'm going to scribble that out, so I don't try and use any of them again. So then I find some more that could fit. So let's look at this one. You've got how many digits? Three digits. I'm going to look at my three-digit column. How do I know which of these three digit numbers it must be? Do I have any of the digits? Yes, i do. My last digit has to be a three. So I'm going to look down my final column, do I see any three digit numbers that end in three? Yeah, here it is. One, four, three. One, four, three. Can cross it out, 'cause I've used it. Now, can you do the same with the rest? Have a real good go. I would say do your five digit number next. I'm going to give you a clue. Do this one next. It's a five digit and we've got a clue in there. Give it a go and see how you manage. I wonder how quickly you could do it. Remember, think clearly, be logical. Look for the easiest options you can first. Always go easy first. So pause it and come back when you're ready. All right, ladies and gentlemen, ladles and jelly spoons, boys and girls, everyone at home. How did you do? Shall we find out, let's. So here's where you should have placed those numbers. And look, here was the one that we've figured out. And we've also got the one for three. And hopefully when you went to your five digit number, you got this one here. That's a very well done. I really do quite like to spend a lot of times doing things like those, the dough cous. I just find, it keeps my old brain a little bit more active. And let's be honest, the more active I can make an old brain like this one, the better. Hopefully it is, I'll live out a little bit longer. All right, let's recap, shall we? Symmetry, you know this by heart now. It's when something is the same on both sides of a mirror line. You have your mirror line down the middle and either side would be an identical reflection of the one on the opposite side. So that when we folded them, they would overlap beautifully. They would sit perfectly on top of each other. That's a basic explanation of what symmetry is. But don't forget lots of shapes and images and patterns can have more than one line of symmetry. They can be horizontal. Let me just come back on your screen for this. They can be horizontal, vertical or diagonal. Each of those directions could be a line of symmetry. So take a look at this. We looked at lines of symmetry yesterday. We have a blocky picture there. And actually, when it's complete, I can't quite tell what it is. So If you know what it is, then brilliant. Please tell me because I don't know. Use the counting method if that works for you. Do you remember? Let's have a look at this column here. Always counting out from our mirror line. White, white, white, shade. White, white, white, shade. Shade, shade, shade. Shade, shade, shade and so on. So give it a go, complete the shape. See you soon. And just use whichever method works for you. Welcome back, my friends. Hopefully you have knocked that one out of the pack. So when I reveal my answers, you are going to see there is a mistake. Ad I've left one out on purpose to see if you can spot it. Iglie, I mean you. So there's still one square missing. Can you spot that missing square? I'm going to give you five seconds and then I'm going to do the big reveal. Five, four, three, two, one. And there it is. This one here is not in my answer. So if I just note that in, we now have a symmetrical picture. Want to say guitar or chicken drumstick, or I actually don't know. If you do know, please find a way of letting us know the secret, 'cause am I missing something? Not sure what it is. Maybe I just made a pattern and a got a bit confused, hey. So let's move on then to another activity. So you're going to investigate today. And I want you to think of regular shapes. Now remember a regular shape, is when all sides and all angles or vertices are equal. So if one side is five centimetres, all the sides are five centimetres. If one angle is 90 degrees, all the angles are 90 degrees. Think of the shape and then how many sides it has. Then can you find out, how many lines of symmetry it has? Because our friend here is saying, "I think that every regular shape "has the same number of lines of symmetry as it does sides." So basically what she's saying is, if a regular shape has five sides, her argument is that, it has five lines of symmetry. If a regular shape has 10 sides, her argument is that it has 10 lines of symmetry. If it has three sides, she's saying it has three lines of symmetry. So you need to figure out if she is right or wrong. Remember that these shapes we're looking at are regular shapes. So they must have all sides and all angles equal. So there are, for example, certain types of triangle we can't use. So we can't use an isosceles or a scalene or a right angled triangle, because they're not regular. Not all the angles will be the same and not all of the sides will measure the same. So think about regular shapes. What I would do to be systematic in this table here, I'd start with the least number of sides and work my way down. So I'm going to give you an easier start up. Little heads up here. Then I would start with one particular shape. And this one, equilateral triangle. I know it's a regular shape 'cause it's equilateral. How many sides? Yeah, three, it's a triangle. And then I would think, what four-sided, five-sided, six-sided and so on. And then I'll work out how many lines of symmetry they have. So I've got names and let's call them names down this column. How many sides do they have? How many sides, how many lines of symmetry and so on? So I would then say, be systematic. You've heard me use that word plenty of times. Systematic just means that you follow a logical way of doing something. So if I've started with the least number of sides, I'll keep going up in size. So three sides, four sides, five sides, and so on. Filling in that table then, it may help to go off onto the internet and find shapes. So you can look at those shapes. We've definitely looked at them in previous sessions here as well. Or you might want to be really careful and try and draw a few out. Then what I need to figure out is, is she right? If it is a regular shape and it has three sides, will it have three lines of symmetry? Give it a go, investigate, come back when you're ready, and I'll talk to you in a little bit. Good luck. And we're coming back in five, four, three, two, one. Here I am, much bigger than I was before. So how did you do it? I'm going to talk you through my thought process, and you'll notice that one of the shapes is going to stand out. So let's take a little look, shall we? So I started with my equilateral triangle and I figured out that my equilateral triangle did have three sides and also three lines of symmetry. If I think of my equilateral triangle, I'm going to do my best to draw a triangle here. Let's imagine it, perfectly equilateral. I would have a line of symmetry that goes through each of the vertices one, two, three. So yes, it does work. A square again, one, two, three and four. So yes, that does work. I haven't used an oblong, because remember we've said that a regular shape has to have all sides the same. Well, they're clearly not the same as those two. So no oblong. I've got a rhombus in there. For rhombus, let me just draw one for you. All the sides are the same length. Four sides, but only two lines of symmetry. One, two. Pentagon, five sides, just have five lines of symmetry. Hexagon, six sides, six lines of symmetry. And so on down that grid. So I could say that she's right, except for this rhombus. But I know that's what we might refer to as erroneous information, extra information, incorrect. I wonder if you can think, why? Why does the rhombus not fitting with the rest of this pattern? So remember we're talking about regular and irregular shapes. What's the difference between regular and irregular? Well, let's have a look here. Why does rhombus not fit in? This could help us. So this is a rhombus. What do we know about regular and irregular shapes? Are we right, if we call a rhombus a regular shape? Because look, they are actually all the same length. So it must be regular, right? I'm going to draw your attention to something else. Now, is it a regular shape? If you think yes, why? If you think no, why? Because if it isn't a regular shape, that throws off our entire argument from here. That means that she's wrong. But I can reveal that actually it is an irregular shape, because don't forget, not only do the sides all have to be equal, but so do the vertices. So do the angles. And these two are bigger than these two. So this is not a regular shape. I was trying to catch you out there. So if we now say, she made a mistake here, let's get rid of it. We can say that she is correct. Because however many sides it has, if it's regular, it also has the same number of lines of symmetry. So well done to her. Well done to you. If you manage to work your way through that, great job. Let's have a look at another activity, shall we? So don't forget pesky rhombus. You ain't regular, get out of here. So let's have a look at our challenge. I've got two challenges for you, because it's our last day. I thought it'd be double generous with our last day of symmetry. This shape has two lines of symmetry. Two mirror lines, one going down from top to bottom, and one going from left to right. Can you complete this shape and use the dots to help you. Again, so that counting. So look for mirror line to here, I've gone one dot, so one dot. From the mirror line to here, I've gone one, two, three dots. So one, two, three dots. I'm going to mark that in. And then I could with a ruler, look at that. Wibbly-wobbly, but you got the picture. Counting will really help. I wouldn't look, I can do the same here. One dot, one dot, two dots this time. So one, two. Join them up. And it does help. Give it a go. See if you can manage. See if you can do a better job than me. And also see if it is a challenge for you. When I was trying to draw the lines down and I was concentrating, this happened. Try not to do the tongue concentrating face, makes you look a bit strange, stranger than me. Shall we see how you did? It is time for the reveal of the final picture. Hopefully you had something that looks like this. All I did there was I counted my way around the dots and then joined them. So one final challenge, and this is the mother of all challenges. Dun dun dun dun. 'Can you complete this symmetrical image using those dots to help you? I will give you a little tip. That flag in the top corner, it's going to point the opposite way on the other side. Give it a go. See how you do. That was tough, right? And you'll see how to find it when I show you the next slide. Where's my answer? Well, I just wanted to really quickly show you how I would have started doing bits of this. Again, with my counting, I can see that I've gone one, two, three squares out. One, two, three. And I just kind of took it a shape at a time. I knew then this was my triangle. I'm dropping off the page. Sorry about that. Here's my triangle, so I would have joined up. Here and then here. You've done a much better job, I know. And then from here I counted my one dot to there. So one dot, there's my flag pole. I know it goes one dot up, one dot down. One dot up, one dot down. And then I've got my triangle on top, which goes one up. And then one, two, three up, one down. One, two, three up and one down, so on. That was a better line. Finally, I'm getting into practise. And that's how I would have gone through it. Just counting each time again. But I found the easier bits first. The dots is quite easy. From this dot I've got to go one out and one down. See, one out, one down. And then one, two dots down. And then I would have just joined up my pieces. One, two, three and so on. So hopefully you managed and you did this and you were better than me. Well, think about how much we have gone over in the last few sessions. Have a go at your knowledge quiz and then come back. Welcome back folks. Like I said before, your knowledge quiz. Think of all the things we have covered in our shape and symmetry topic, over the last few sessions. We've now spent 15 sessions on this, and you have done a huge amount. You've learned the names of shapes. We've looked at the properties of shapes. We've looked at what makes a shape regular or irregular. We've learned the correct vocabulary, vertices, sides, edges, faces, we'll come onto, when we look at 3-D later on. All of these things we've learned. We've learned about symmetry, about mirror lines. You've been phenomenal. And the work you've done in the last two sessions has been year five level. So a massive, massive, well done to you for that. You've been brilliant. So all I can say now is, well done for all your hard work. You should be so proud of yourselves. And from the end of this topic, until next time, that's it from me, Mr. C, so take care.

To investigate a problem using symmetry (Part 2)

To investigate a problem using symmetry (Part 2)

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UnitMaths / 2-D Shape and Symmetry

Maths