Lesson video

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Hi there, my name is Miss Darwish and for masses in today we are going to be investigating some properties of number.

So before we get started, if I could just ask you to take yourself somewhere peaceful, we can get some work done.

Okay, for the lesson, we are going to be first of all looking at some calculations, and then moving on to look at palindromic numbers and iterations.

Don't worry if you think they're big words we'll explain later.

And then at the end of the session, of course, there will be a quiz for you to go and complete based on today's learning.

So, for the lesson, if I could just push to grab yourself a sheet of paper, pencil and a ruler so we can stop.

So, how would you go about calculating these? What I want you to do is quickly jot down on your sheets of paper and your pencil, calculate them, but after you've calculated them, have a think about how you went about calculating them.

Okay, it could be 10 more seconds.

Okay, and stop.

So did you use any formal written methods for these? If he did, why, if he didn't, why not? So 100 plus nine squared, What I did is I know that nine squared is equal to 81 181 is 181.

So I wouldn't really need a formal written method.

I could just sort of, that's quick math.

I can do my head, right.

So what about 83 at four at three, which two numbers did you add first? Might be easier to add maybe four or three is equal to seven, I know that seven and three number bonds to 10, or 83 at three is 86, and then 86 at four, again, six and four number bonds to 10.

And then eight squared, four squared if you know eight square to 64, four square to 16.

So you've got four and a six in the ones column again.

Thinking about those number bonds to 10 sometimes helps with calculations.

So well done if you did those mentally.

When we do work out calculations, it's always best to ask yourself, what's the most efficient way of doing this? Is it a long written quantum method? Or actually, could there be a way I could do it in my head? so now it's time for a game, are you ready? I'm excited about this.

I would like you to choose a number.

Let's say a three digit number? Write down a three digit number for me.

I'm going to do the same.

So I'm going to give you five seconds just write down any three digit number, a number with three digits.

Okay, finished, done pencil down.

So, my three digit number is 234.

Doesn't matter if it's the same or different to yours.

That's my three digit number.

What's your three digit number? Now what I'd like you to teach your three digit number is right, the digits in reverse.

But wait, let me show you what I mean by that.

And then you can go ahead and do it to yours.

Okay, so my three digit number, that's why I chose is 234.

Now I need to write the digits in reverse.

So the two would go in the ones column, and the four would go in the hundreds column, And the three would stay in the 10s column.

So now I've written my number in reverse.

Does that make sense? Now I would like you to go and do the same.

So you've written your three digit number.

And then the next step is to write the digits in reverse, but don't cross out or rub anything out.

Okay, ready for the next step.

Okay, now, I would like you to add them.

Again, stop, wait, let me show you my example.

So my three digit number that I chose was 234.

And then I had to reverse the digits, which is 432.

Now I'm going to add 234 and I'm going to add that to 432.

Now go ahead and add your two numbers and let Know what your total was? Okay, how did you get on finished? What total did you get? Now I'm going to choose a different three digit number.

So my next three digit number is 513.

After this round I'll explain why we are doing this, I promise.

So my next number is 513.

I would like you to also choose a different number.

different from mine as well, not just different from your first one.

Okay, and then I'd like you to complete the next step, write the digits in reverse.

Finished, and then guess what I'm going to ask you to do next, add them together.

So add your two numbers together and let me know what you get.

Okay, what total did you get? Interesting, so now I'm going to explain why we have been doing this.

So Oh, before we have a look at another example, I've got 234, when I reverse the digits, I got 432.

And my total was 666.

We would call 666 a palindromic number, because if I wrote it the other way, it would still say 666, does that make sense? And then my second example, 513, adds 315 is equal to 828 if I wrote 828 and reverse the digits, what would it say? It would still say 828.

So 666 and 828 are palindromic numbers.

So, actually, when you when you pick a number, any number, and you reverse the digits, and you add these two numbers together, you should most of the time get a palindromic number.

Now, I'm going to guess either you did, or you didn't, because either you do or you don't.

And if you don't, I'm going to go on to explaining why not and how we can turn it into palindromic number you with me so far? Here is another example you don't need to read.

You don't need to write sorry, another example.

I just want you to watch and listen look at this example that I've got.

So I chose a different three digit number and that number 694.

And then the next step I will say did which is I wrote the digits in reverse 694 then became 496.

And as we have been doing, I added the two numbers together, and I got a total and then I got a total of can you add them up? Did I get a total of a palindromic number? No, because we've had to regroup here, haven't we? Let's go back.

Now, I don't always get a palindromic numbers.

Sometimes I do and sometimes I don't.

Now, I'm going to explain in a bit when we don't, why is that? So, palindromic numbers first of all, they are the same when the digits are reversed.

So for example, 1441 for reverse the digits is still 1441 you choose a number from the ones listed? Read it out loud and then read it in reverse.

It's the same, right? Did you notice the number six there? Six is a palindromic number.

So is seven, so it's three.

In fact, any one digit number is considered a palindromic number.

Now, so, our answers to those first two examples are palindromic number 666.

If I was to read it in reverse, it's still 666.

828, if I was to read it in reverse, it would still say 828.

Now let's go back to that third example that we had, Now, this is similar to that example, if I have the number 67, when I reverse it, it becomes 76 and then if I add them together, what do I get? 143, is 143 a palindromic number? No, it is not, if I read 143 in reverse, what would it say? 341 that is not the same as 143.

So, that is not a palindromic number.

What I could do though, is take 143 take that answer and have that as my three digit number, and then I'm going to reverse it.

So, 143 becomes 341 and then I'm going to add them and my answer is 484.

Is 484 a palindromic number? If I read in reverse, it's still 484 484 is a palindromic number.

Now, the number 67, the first time we did it, we call that the first iteration, can you say that for me? The first iteration that's right.

It did not work, we did not get a palindromic number.

It took two iterations for it to become a palindromic number.

Did you see that? So first we did 67, add 76, and we got 143.

So that was the first iteration.

And then the second iteration was 143, add 341.

And we got 484, and that was a palindromic number.

Some numbers just take one iteration, like those first two examples we saw and some numbers, like this example takes two iterations.

Sometimes a number can take three, four, five, six even up to 20 iterations for it to be a palindromic number.

Crazy, right? Okay, so two iterations there.

Now, I want you to have a think and jot down for me 421 625 2751, How many iterations does it take to get those numbers palindromic numbers? Give me some thinking time and again, if you want to drop anything down, go for it before we reveal.

Okay, should we have a look together now? So 421 add 124, that would give us an answer of 545.

That is a palindromic number.

So that just took one iteration if it completes it straight away, that's one iteration.

625 what did you notice? Couldn't do it after the first time when usually when we have to regroup when we adding together and it goes over 10 then it usually takes two or more iterations.

And 2751 did you have a go at that one? That takes three iterations, so when we added it, and then again, and then again three times.

Okay, what about 67 152 or 443? Do you want to have a go at these three? Tell me how many iterations Okay, how did she go? She goes through the answers together, but not together.

So 67 at 76 it would not be one iteration, would it? Two iterations, 152 would all say take two iterations, and 443 also takes two iterations.

Whereas over here we had 123.

So can a number contain the digit six or more and just have one iteration? What do you think? So is it possible for a number to have the digit six or more and just have one iteration? What do you think? Should we explore this together? Let's have a look The number 1616, add 61 is equal to 77.

Yes, it is possible.

What about 46? Be 46 at 64 no, that wouldn't work.

But 16 definitely work.

So can a number contain the digit six or more and just have one iteration? Yes, it can.

well done, now it's time for you to pause the video and have a go at the independent task.

Once you've had it go and you've checked over, then come back and we'll check the answers together.

Good luck.

Okay, welcome back, how did you find that? Should we look go through the answers together now? So, is that how many iterations of the numbers below have I gave you three numbers? That's for 146 and 76.

So 34, you would have done 34 add 43, well done.

And that would have given you an answer of 77.

That's just one iteration.

What about 146? What would you have added to that to check 641 and that would have given you an answer of 787 completed.

So that's just one iteration.

And then what about 76? What would you have added to 76 to check? 67 and what answer would you have got? And that's not a palindromic number, is it? So then we've had to, we'd have had to add it again, and then we'd get a palindromic number.

I'm going to ask you a question about something that you might notice isn't necessarily true that the larger the number, the more iterations there are? No, definitely not, because we can see in this example 146 is actually a larger number than 76 but it has less iterations than 76.

Okay, well done.

If you would like to share your work with us here at Oak National then please do ask your parent or carer to share your work for you on Twitter, tagging @OakNational and the hashtag LearnwithOak Well done on the brilliant learning that you have completed today.

Now it's time for you to go and complete today's quiz.

Good luck.