Answer this calculation in Roman numerals: 4 + 4 =

To investigate Roman Numerals up to one hundred

Key Stage 2

Maths

Reasoning with patterns and sequences

﻿Hi, guys, it's me, Mr. C. How are we doing? Are we all well? Brilliant, I'm feeling great today and raring to go. I'm looking forward to what we're going to be doing in our session today. We're going to be continuing with reasoning with pattern sequences and we're going to move to looking at identifying Roman numerals. So let's move straight ahead, shall we? If you haven't done this already, make sure you've taken the knowledge quiz and then come on back and see us when you're ready. And welcome back. So let's get our thinking caps on. I've got a little riddle for you. I want you to try and figure out what the mystery number is. I'm going to give you some clues and you need to use those clues to help you deduce, to figure out the mystery number. So my mystery number has got four digits. It's smaller than 6,000 but bigger than 5,000. So it's somewhere in between. The hundreds digit is smaller than six but bigger than four. I know what that number is now. Smaller than six but bigger than four. That's the hundreds. The tens digits, that's an odd number. It's smaller than seven but bigger than three. And then the ones digit, it's in the three times table and it's bigger than six but smaller than 10. What could it be? Give yourself a little thinking time and see if you can work it out one clue at at time. Okay, five, four, three, two, one. And zero. Let's take a little look then at how we can use those clues to help us. I'm just going to make some little notes on the page here. So the number's got four digits. So it's got thousands, it's got hundreds, it's got tens and it's got ones. It's smaller than 6,000 but bigger than 5,000. So it's somewhere between here. I'm going to use those just to remind me. Now, the hundreds digit, so we're looking at this column is smaller than six, so that's five, four, three, two, one, or zero, but it's bigger than four. So what is the only number bigger than four, smaller than six that's a whole number? It's got to be five, hasn't it? The tens digit is an odd number, so we're looking now at this column. It's an odd number, smaller than seven but bigger than three. Well, let's just remind ourselves of the odd numbers. It's one, three, five, seven, nine. So between three and seven, what was that number? And then the ones digit is in the three times table and it's bigger than six but smaller than 10. Three, six, nine, 12, okay. Did you get it? Shall we see? Hopefully you got 5,559. If you did, amazing job. Well done, you are officially ready for maths today. All right, so make sure you've got your pencil and ruler, something to work on and somewhere that's quiet with no distractions. Now, today this is what we're going to be looking at for our agenda. We've done our knowledge quiz. And we're going to move onto our key vocab in a moment. And then our number trees warmup. We'll learn a little bit about what Roman numerals are and then putting Roman numerals into 100 square. Then we'll look at our main activity, which is sequences using Roman numerals. And a little challenge at the end and a final knowledge quiz. Okay, so it should be a quite nice lesson today. Almost like code breaking. So key learning is to identify Roman numerals up to 100. So here comes our key vocab. And you might be looking at it and thinking, those are just letters. It will make sense. So Roman. Numeral. Number system. I. V. X. L. C. And you'll notice that all of those letters are in uppercase, they're all capitals. That's really important. Well, here's our starter. You know how this works. So I'm going to not waste any time explaining it, other than the two numbers beneath added together give you the number above. Can you fill in those number trees so that you get all the way to the top? Give it a good go, come back when you're ready. And welcome back. Hopefully, you did a great job there. Let's see the answers, shall we? Taking a look over them and just seeing how you did. Brilliant. I'm sure you did an amazing job. So with that victory in your mouth, the taste of it there, let's move ahead, shall we? So Roman numerals. Well, what are they? Well, they've survived for thousands of years and we still, in fact, use them today. So today you might find them on things like clocks and you can see three really clear examples there. On a watch, on sundials, at the end of films or at the beginning of a film when they tell you when it was made. That's usually always done in Roman numerals. Book chapters quite often will have them at the header of the page. And numbering sometimes in books, page numbers in books, bullet points, the titles of kings and queens, like Henry VIII or even popes. All of those you would find Roman numerals being used. And they are around us all the time, especially if you look at older buildings in cities, you'll often see them somewhere on those buildings. Maybe it tells you when the building was built. Now, Roman numerals use a total of seven different letters to indicate different numbers. In Roman numerals, you don't have a letter that represents the value of zero. Okay? Now, all the numbers then are made by combining letters in different combinations. So you put them together in different ways to show numbers. Now, the single letters and the numbers they represent are all here. So I is worth one. V is worth five. X is worth is worth 10. So I, V, X. One, five, 10. L is worth 50, C represents 100 and I always remember that one in terms of things like century, 100 years. D is 500. And M is 1,000. Now, when I was younger, I used to always think that M must represent a million. But it doesn't. So I, one, V, five, X, 10, L, 50, C, 100, D, 500 and M, 1,000. Okay, so if I had XX, 10, 10, what would that be worth? 20. If I had III. One, one, one. That'll be worth three, yeah. So it's pretty logical actually and there's a couple of little set of rules that will make sense when you're looking at how these numbers go together and how the letters represent different numbers. So if the large number symbol is followed by a smaller one, so if the 10 is followed by a one, you just add them together. So XI, there's the larger one in front, the smaller one afterwards, 10 plus one, that's 11, yeah? VII. So five, one, one, five and two, seven. And so on, okay? Pretty straightforward, right? If the two symbols are the same, then you add them together. So just like here, I had the I and I. It's one and one, that's two. Now, if the smaller number symbol is followed by a larger one, then you take it away. So one is smaller than 10, so you'll do 10 take away one, that's nine. Okay? 10 is less than 50, because remember, L was 50 and X was 10, 50 take away 10 is 40. Simple as that really. So let's take a look here. Let's do a bit of deduction. I'm going to give you a clue. Somewhere for the number four, you'll need to use the letter I. And also, for the number six. Okay? See if you can figure out how you can work these out. Once you've done it, you should be able to do these calculations, okay? Give it a go and when you think you've got it, try the calculations and come back and check in. Okay, how what that? Now, some of them were really logical and it's just a bit confusing sometimes. If you have an analogue clock at home and you were looking at the dial, that would have been really useful as well. So shall we see what the answers were and we'll just talk through them, shall we? Here they are. So two is II. Three is III. And then four is IV. Remember, the smaller one in front of the larger one means you take it away. So five take away one is four. V is five and then VI, so five add one is six. VII, five add two is seven. VIII, five add three is eight. And then with nine, we'll do 10 take away one. So IX. So our calculations, V add V, that's five add five is 10 so that's X. I add I add V. So five add one add one, seven. Yeah. X and V. X and a V, 10 and a five, 15. And so on. If you of those, then all I can say is you made our gladiator smile. Nice job. All right, so let's move ahead. Now, here we've got our moving on and I'd love you to spend some time. So this is our 100 square. Now, please don't be terrified by this. It's not as hard as it looks and there are patterns, okay? Look for the patterns. So for example, it's like any normal 100 square that you might use in school. It goes one, two, three, four, five, six, seven, eight, nine, 10. And then down here, 11, 12, 13, 14, 15, 16, 17, 18 and so on. So we've got our 100 square as we would usually expect. One here and 100 down there. Now, look, there are patterns. Look what everything in this row seems to be starting with. Look at what everything in this row seems to be starting with. Look for similarities, look, these all seem to start with LXXX. LXXX. And look LXXX. So we can see the patterns. Okay? Have a real good go at that. See if you can fill in that 100 square. I have so much faith in you. I know you can do it. So spend a bit of time, look for logical patterns. You might also notice that not only going across will there be patterns but going down. Look, in this column, for example, everything ends in VII, VII, VII. Okay, so if you can work out one, two, three, four, five, six, seven, eight, nine, all the way up to 10, that helps you with everything else. Good luck, guys and I'll see you shortly. How's the brain? Fried yet? I'm sure you did a phenomenal job. And let's just take a look then at the answers and just have a quick look at the patterns that we can see in that 100 square. Here we go. Do you see the patterns? Do you see similarities? If we look, for example, in this column, what's the final letter in everything in this column? They all end in I. How about this one? What do they all end in and it's more than just X. Yeah, they all end in IX, which is nine. And it makes sense because this is the nine column. So you've got one, two, three, four, five, six, seven, eight, nine and 10. So it makes sense that everything would end in IX because they all end in nine. It makes sense that everything would end in VIII because VIII is eight. And this is the column where everything would end in eight. Yeah? And then again. This would make sense because everything in there would be 10s. 20 row. 30, 40, 50, 60, 70, oops. 80. 90. And then right at the end, 100. So it actually is very, very logical. Now, I suggest you write this out or have one of these in front of you to help you with the next activity. Now, the next activity is where you're going to put the skills in place now from using these, you're going to then start looking at applying some knowledge to them. So take a look. Here's your main task. You've got some number sequences here and you need to try and fill in the missing values. Now, what I would do first is rewrite them all in the numbers that you recognise. So for example, here I know that II is two. I know that IV is four, I know that VI is six. And now I can spot the rest of that pattern. What would come next? Two, four, six, yeah, eight and then? Yeah, 10 'cause I'm counting in twos. So you need to write the Roman numeral equivalent of both of these. And it's the same for the rest. You're all brilliant. And you're all complete brain boxes. And you're all amazing, so I know you can all do this. Write them in the script that you recognise first. Work out what the sequence is, what's happening to get you to the next number in that sequence. And then translate them into Roman numerals. That's your activity. Good luck. Okay, guys. Coming back in three, two, one. Shall we see how you did? Let's take a look at the answers, shall we? Here they are. I'll zoom in one those so you can see them and check them off. Now, I'm not satisfied that I've challenged you enough. I think you are up for even more of a challenge. So one final thing for you to take a look at. And that's this. Imagine we have a five-number sequence. And our middle number is XLIII. That's one of the terms in our sequence. Can you invent your own sequence where this would be in the middle? So for example, maybe you're adding two each time. So add two, add another two and if I'm going backwards, it would be take two, take another two. Can you invent your own sequence? That's your little takeaway for the day. See what you can do. And just be the brilliant you that you are. Now, with that in mind, you need to make sure that you have also taken our final knowledge quiz so that you're ready. Okay, great work today, guys. It can be tricky with the Roman numerals, getting that pattern right at first but keep going back to that 100 square and looking at the patterns going across and down. They make perfect sense. I know it's not anything that you can't cope with. So well done. Great session and I look froward to seeing you next time. So that's it from me, Mr. C. I'll see you again soon. Bye.

To investigate Roman Numerals up to one hundred

To investigate Roman Numerals up to one hundred

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UnitMaths / Reasoning with patterns and sequences

Maths