Lesson video

Hi everyone.

It's me, Mr. C.

How are you? Hope you've had a great time since we were last together.

Hope you've done some fantastic things, and you've done something educational, something fun, something healthy, and something kind.

Well, let's take a look at our final session at the moment on reasoning about patterns and sequences.

We are going to continue to look at developing strategies to plan and solve problems. And it's kind of going to be less talk from me, and more over to you guys today.

Take a look here, I have a little maths riddle for you, and it's all about deciphering codes.

These codes here to be particular.

Now, I've got a mixture of numbers and letters that you really need to think around, to help you work out what each of them stand for.

So let us just take a little look, at the very first one that I've got on here, that I want to share with you.

It says, here at the top, 365 d in a y, and we need to figure out what that actually stands for.

When I think of the number 365, there's only really one thing I can think of that links to that.

And that's how many days there are in one year, and what do you know? The d, and the y are there, So this must mean 365 d, days, in a y, year.

Can you work out the rest of these? I'll give you a clue, two of them are sport related.

Have a go, and see how well you can do.

So the next one, 11 p on a f t.

So you've got to find three words.

One starts with p, one starts with f, and one starts with t, do you think you know? Well, have a go, and come back as soon as you've tried it.

Whenever you see those numbers on there, just think to yourself, what do I associate these numbers with? Now when you're thinking about what you associate them with, do any of the letters correspond? We're all going to move on shortly, so you might want to pause now, just to give yourself a little more time.

All right folks, well, how did you do? Shall we see what the answers are? I wonder if you managed to get them.

Let's check, shall we? Here are the answers.

So the 11 p in a f t, was 11 players in a football team.

The four y between, o g, that's four years between Olympic Games.

We've got six s on a d, six sides on a dice.

52 w in a y, 52 weeks in a year, and 60 s in a m, 60 seconds in a minute.

I wonder if you got them.

I want you to think of any more of your own that you could try out on people at home.

So it was quite a nice little thing there and I had quite good fun, thinking of those to share with you.

Alright, let's have a look then at what's coming up today.

Before we do, make sure you've got a pencil, a ruler, either print out of the slides, or a paper or a book to work in, and somewhere quiet with no distractions.

So our agenda to key learning in a few seconds, then we're going to do our number fit warmup, which we've been practising and they've been gradually getting harder this week, this one is even trickier.

And then we've got sequence tasks one, two, and three with a sequence challenge at the end, and no final quiz, cause I just want you to spend time today, if you need to, going back over previous lessons that we've looked at, especially with the problem solving and just recapping there where you need to.

Brilliant.

So our key learning then is to develop strategies, to plan and solve a problem.

And I wonder if you can guess what our key vocabulary is? It's not that we've seen it several times recently, but it's all important stuff nonetheless, we've got sequence, patterns, similarities, differences, increasing, decreasing, term, and rule.

Well done.

Another word that we might want to add in there because we've looked at these a couple of times recently, is formula.

Do you remember we've looked at it before where we're looking at the next term is, the number of, I dunno we say the number of, tables plus one, and then times it by two.

The formula is just the rule that we follow, a little quick rule to help us work anything out.

Okay? Brilliant.

All right, so let's move on then just having a look then at our first activity, and that is our number fit.

We've done many, many, many of these, my top tips will always remain the same when you've used a number, cross it out to make sure you don't get confused about it again.

Always look to start somewhere where you've got your least options and in this case, we've already gotten rid of two of our five digit numbers, it might be worth starting with that, but also look at starting somewhere where you've already got some digits given to you.

Okay? Now, for example, I'm going to start with a simple one to start with, I'm going to look at our three digits here, we've got something, nine, something.

So I'm going to look down my three digit columns, something, nine, something so I'm looking for nine in that middle column, nine in the tens column.

And now here I found one, it's the only one.

So 796, I think, goes here.

What do I do once I've used that number? Correct, cross it out.

I've then got one, two, three, four, a five digit, and my second digit is seven.

So then I'm going to go to my five digits and have a look.

Second digit is here, so going down.

Oh, well that was a seven, but that's already been used.

Here's one, that's got a seven in it.

Oh, but there's two with seven, in that space.

So I'm actually going to leave that for now because I'm not a 100% sure.

So let's have a look, what other options I've got.

I've got a three digit number here.

One, two, three, four, five digit number here and a six digit number here, all of them, have at least one of the numbers in them.

So let's have a look at my, oh, I'm going to go to my six digit, look cause I've only got two of those.

So my six digit, one, two, three, four, five, six, I need a six digit number, where the second digit is zero, is four, sorry, second digit is four.

So let's have a look, this one is zero, this one up is four.

So this must be eight, four, three, eight, four, three, nine, two, five, and I'm going to cross that out.

Now you can find the other six digit number that's on here somewhere and fill that in and cross out all of your six digit numbers cause you've done them.

So I think I've given you a little head start there.

I can already see which three digit number is going to go in here, and I can already see which three digit numbers could go in here, it's more than one that could go here, but I know that definite one that goes there.

So I would say do this three digit number next, have a go at that task and when you're done, come back and let's share where those numbers would go.

Okay.

Welcome back, we are almost there.

So let's come back here first and then I'll share with you the full set of answers.

If you remember, I said I think I could already tell which one's going to go in here, it's a three digit number ending in nine.

Well, here are my three digit numbers, can we see one that has a nine in the ones column? Mm-hmm, it's the very first one and it's the only one with a nine in that column.

So I can now write it in one, four, nine, and cross that out.

Now I've got this number here, it's a one, two, three, four, five digit number two, something, one, something, something.

Look here go, two, something, one, something, something, two eight, one, three, six, two, eight, one, three, six, cross that pesky one out.

And let's have a look here, one, two, three, four, five, six, oh it's a seven digit number, that ends in three.

I've only got one left, that ends in three, so it must be seven, two, six, five, seven, one, three.

Cross that out.

Now I can find my other seven digit number which would be, oh let's check, one, two, three, four, five, six, seven, there, so two, three, nine, four, six, zero, eight, cross it out, cross them all out so I don't use any of those again.

And I'm not going to sit and go through all of them, cause hopefully that's something that you've already done, so I'm going to reveal to you, right now, those answers.

Best of luck guys, I'm sure you got them all right.

Here it goes, here are the answers.

Okay.

Well done folks.

I'm sure you did a fantastic job in that anyway so big old thumbs up and a well done from me, to you.

Okay, let's move ahead.

Thinking about sequences, patterns and problem solving.

Have a look here, I'm asking you to try and work out what the rule is, for each of these sequences.

Remember the rule is, what to have I done, to get from one number to the next.

So if I went, two, four, six, eight, 10, and that one would be, add two each time.

We're also going to be asking you now to find any increasing sequences.

Two words that we've looked at were increase and decrease.

Increase, if you remember means it gets, you got it, bigger.

Decrease means it gets, ahah, smaller.

So all you need to do then, is once you've worked out the rule, tick the ones that are increasing, so we know that you've spotted that, the enlarging numbers.

So for the first one, if you think on this first one, I'm adding 50 each time I would say, the rule is add 50 each time.

Have a go, see what you think those rules are, and then we'll come back and share our answers.

I'm sure it won't take you very long so, I'm not going to keep you much longer.

Go for it.

Just about to come back so let's take a look at those answers, shall we? Now you'll notice that the first one, we've added 25 each time, 25, 50, 75, a hundred.

We're counting in steps of 25, so that just means we're adding 25, you could have just written, add 25, that's fine.

Okay? It's better if you say each time because sometimes, we might not be adding the same amount each step.

So if you say each time that makes it really clear.

This, to figure it out if our sequence is getting bigger or smaller, if you remember, I say, we look at the first number and the last number.

If the last number is a larger number, then it's increasing.

So we can tick it, 200 is definitely larger than 25, right? Okay now, we had, minus five, minus 10, minus 15, minus 20, minus 25, minus 30.

We're not adding, even though numbers look like they're getting bigger, five, 10, 15, 20, they're not.

They're actually getting smaller because we've got the minus a negative number.

So they're actually getting smaller.

So this time we've subtracted five each time, or you could have just said take away five each time or use the subtract sign.

Here, we're finding half every time so we've halved each time, you could also say divided by two each time that would work.

Looking at the first number and looking at the last number, is it getting bigger or smaller? It is, it's getting smaller so it's a, decreasing pattern, well done.

Here, were adding 16 each time.

So look at the first number, look at the last number, is it getting bigger or smaller? it's getting, bigger, so it's an increasing pattern.

Here we've subtracted 70 each time, and here we're dividing by five each time.

If I'd have divided by five here, I could have kept it going, but I wouldn't have had whole numbers anymore.

Okay? But I wanted to stick to whole number, so I stopped at eight.

Well done.

All right.

Let's take a look at the next activity I have for you then.

Task number two.

Now, we've seen some of this before, I'm asking you to write the first six terms in each sequence, the first six numbers, follow the rule and also pay close attention to the number that you're starting on so the start number is mentioned at the end.

And I'm going to make those really clear for you, I'm going to just underline the start number, so that would be your first term each time.

So what I'm tempted to do, is write the start numbers for each on the line, so I know what's coming.

And then you just need to do the next five numbers, cause we're looking at the first six terms. I've got one, I need to know the next five.

So on the first one, you're adding 11 each time, if you find that tricky just 10 each time and then, add on the extra one.

The next one, you're going to be adding 25 each time, then you're going to be adding, oh no, you're not, you're going to be taking away.

Ooh! See this is where it's careful, is it? Important to read them carefully, I nearly made a mistake there, so subtract 23, So another word for subtract? Minus, another way of saying subtract, take away.

You starting on 29 this time.

On the next one, the rule is subtract nine, so your start number will be 15.

And then finally the rule will be at 104 and your start number will be minus 94, that's the trickiest one of them all.

Okay, I think I've talked enough.

Let's get your brains engaged.

Next six terms in each sequence.

Off you go.

Now coming back in five, four, three, two, one, and zero.

Here we are, take a look then at these answers, and I've given you your starting number on each of them.

The one I think would have been the trickiest would have been this last one here.

I wonder if any of you went from minus 94, and then got, you added the other a hundred and in front of it, so you had 194, and the other four, so I wonder if any of you said minus 198 and went the wrong way.

You're actually going the opposite direction, you're getting bigger, don't forget.

And also in this one, you also have to remember that zero will count when you're going across from negative to positive numbers.

So we've got 17, 28, 39, 50, 61, 72.

Brilliant.

Then we've got 37, 62, 87, 112, 137, 162, what do you notice about this pattern? Is there anything you can say, general statement, I'm going to just help you out by popping a little dot over the bit I want to draw your attention to.

Yeah, the ones column goes seven, two, seven, two, seven, two, and we'll probably keep going, seven, two, seven, two, seven, two.

I wonder if you know, why, what does this have in common with another times table that we know that does exactly the same? Mm-hmm.

The five times table we'll alternate between five, zero, five, zero, five, zero, the 25 times table does the same.

I wonder if that's the same with any times table that ends in a five, something you could check out, but here we've got the alternating ending digit in the ones column.

Subtracting 23, while we're starting at 29, we've got 29, six, remembering to use zero as a number in this case, minus 17, minus 40, minus 63, minus 86.

And then we're subtracting nine so we've got 15, six, minus three, minus 12, minus 21 and minus 30.

And then finally minus 94, 10, 114, 218, three, two, two, 322 and 426.

Fantastic, well done.

Hopefully you remembered to count zero as a number in those patterns.

So now, we're putting the two last tasks together.

Can you work out the rule? And then can you work out the missing terms in each sequence? You've got enough there to help you work out the rule, all you need to do is look at two numbers next to each other, so here to here, what have I done to get from 150 to 190? Start with adding and subtracting first, that's the easiest way to do it.

So what would I add to this to make this? And is it the same as what I add here to get to there? And that's all you're doing.

You're looking for what's happening in between the numbers and apply that.

I think you're going to do fabulously on this.

So again, I'm going to stop talking.

I'm going to let your brain start to do the working.

Can you work out the rule? I would say, do the rule first, for each one, and then the missing numbers.

What are the missing terms in each sequence, best of luck, people and I will see you very, very soon.

Go for it.

Welcome back, let's just take a look then a brief look at this first one.

See how we would work that out.

So I'm saying to you, the best thing to do is find what's happening between the numbers.

So what would I add to 150 to get to 190? If I'm not sure, I could say, what would I add to 15 to get to 19 and then just make my answer 10 times bigger.

So 15, 16, 17, 18, 19, that's four, but what's four, 10 times bigger, 40, so here, I'm adding 40 each time.

And then we can work out the rest.

Let's see how you did with those answers.

Here they come.

Take a good close look at those, I'm sure you've got a fantastic result.

I was hoping on the 9.

9, the 8.

7 and the 7.

5 was really trying to catch you out on that.

And I bet, well, not I bet, I know that I probably didn't catch many of you guys out.

I wonder how many of you looked at it and imagined that number without the decimal point first, that's how I checked it afterwards, I imagined it without the decimal point and I imagined it as 99, 87, 75 and so on, and then made everything 10 times smaller.

That helped for me.

Okay so we've done a lot of work recently, looking then at sequences and patterns and how to spot them.

So, what I really wanted to do now was, challenge you, okay.

I'm going to give you some slightly longer worded questions, and I want you to have a look through those questions and see if you can work out the answers.

Okay? Let me show you some of those questions.

Take a look at this.

There are two questions for you on here, it says, the first one, the numbers in the sequence increase by 75 each time, so what I'm going to do, find the key information and then I'm just going to circle it.

75 and, increase, if it's increasing is it getting bigger or smaller? It's getting bigger.

So, which of these operations would make a number get larger? If I divide one number by another, is the answer going to be bigger or smaller? Yeah, it's going to be smaller.

So let's get rid of that cause that's decreasing.

If I add two numbers, will the number I end up with be bigger or smaller than what I started with? It's going to be bigger, isn't it? So it could be adding.

If I subtract, is my answer going to be bigger or smaller, smaller, so it's not that.

So it could also be times, but in this case, I'm increasing by 75, I can see that I'm not multiplying by 75 each time.

So I must be adding 75.

So to get from here to here, I've added 75, to get from here to here, I've added 75 and so on.

Can you fill in the missing numbers? This one the numbers in the sequence increase by 14 each time.

So what would I do? So think to yourself, if I've got the numbers going forwards, for example, like on the top one here, I can see that to go from this one to there I've added 75.

So to go from here to there, I'm adding 75, I'm adding 75.

What happens when I go the opposite way? What do I have to do if I go the opposite way? I'm going to say a really important word to you, and that word is inverse, okay? Inverse, what's the inverse of adding? That's all I'm going to say, have a go at these and come back, as soon as you're ready.

Almost there, nearly made it, we are on the home stretch guys let's take a look at those answers, I'm sure you did a wonderful job.

Now don't forget, if we were going this way, we were adding 75 each time, but if we had to go backwards, we would do the inverse, which would be subtracting 75.

So we added 75 go that way, we subtracted to go that way.

Exactly the same on this one, if we're going this way, we're adding 14, if we go this way, we are subtracting 14.

Okay? Check in those answers.

Got it? Oh, I'm sure you did a phenomenal job there.

Well, we are almost there.

Final thing for us to do.

I want us to look at one more problem.

You ready? I know you are.

Here.

It is, this one here.

It says, the numbers in this sequence increase, by 30 each time.

Now the sequence is going to continue, in exactly the same way.

So every single time, add 30, add 30.

Oh look, add 30, add 30.

It's going to keep going, keep going.

Look at all this space over here to work it out.

What I want you to do is work out which number in the sequence, when we add 30 each time, which number will be closest to 300? So, I would say keep going until you get just past 300 and then see which number in that sequence is closest to it.

Okay? So basically, you're going to have to add 30 again and again and again, until you get as close to 300, as you can.

Ready to investigate? I'm sure you are.

Okay folks.

On your marks, get set, investigate.

Whoa! We're back.

All right, this is it.

Let's take a look at that last bit from today.

Let's have a look at those answers, here they come.

If I continued this sequence, if I continued adding, 30 each time, I would get 140, 170 and then 200, 230, 260, 290, 320.

Now these two, were the closest to 300, but 290 is 10 nearer, than 320 was.

So the number that's closest to 300 in this sequence would be 290.

Guys, you can breathe, we have no final quiz today, that's it, that was some heavy going.

You, have blown me away because you have worked your way through that, so fantastically and I'll let you in a lot of secrets.

Some of that stuff we were doing at the end, was way beyond what I would normally do, so well done, you have really impressed me.

It's been great to working on this with you.

So take care of yourselves, stay happy, stay healthy, and keep learning and, from me, Mr. C, goodbye.

Have a good day.

See you guys.