Lesson video

Hello everyone, it's me Mr. C.

With your maths lesson for today.

Welcome, welcome, welcome, and great to see you all.

And hopefully we'll have some more fun reasoning with pattern and sequences.

So, let's take a look without any more time wasted.

We're going to be looking at again today at developing strategies to plan and solve problems. Well, before we get going, let's just play around with our maths words and brains a little bit more.

Have a look here, we've got some anagrams. Remember an anagram is when you take a word and jumble up the letters into a different order.

What maths words can you find here? And the words that we're looking at today, we've got HAGPR, GLANES, VIDDIE, NOTGAPEN and ROT FINAC.

Can you figure out what each of those words would be when you unscramble them? They're all maths words.

I'm sure you can do it.

Few seconds just to take a look.

Remember, some of those come up looking like two words, but they are in fact, just one word.

All of them are single words.

Take a look.

Have a look again.

10 seconds to go guys.

Five, four, three, two, one and time up.

Let's take a look then at what those words were.

So we had graph, angles, divide, pentagon and fraction.

If you got all of those, Fabo or great work from you.

Brilliant, brilliant, brilliant, brilliant as always.

So should we take a look at what it is that's coming up today? Let's do that.

Don't forget, you need to make sure that you've got your pencil, your ruler, the printouts or paper, or a book to work on.

Somewhere quiet with no distractions and a great, great sense of focus.

Okay.

So, key learning and vocabulary.

Then we've got our number puzzle warmup.

Moving on we're going to introduce the problem today of tables and chairs.

But the main activity is your investigation.

And then the challenge at the end and you'll see no final knowledge quiz, because we want to spend more time just looking through the investigation.

All right.

So, today.

To develop strategies to plan and solve a problem, That's our key learning.

And you know the score with our words.

We've got sequence, patterns, similarities, differences, increasing, decreasing, term and rule.

Fantastic.

Those are our key words.

Remember the rule is just what happens in between each of the terms. So what do I do from one number to get to the next? Similarities and differences are really important when it comes to looking for patterns.

Increasing means it's getting bigger.

Decreasing means it's getting smaller.

Okay.

So take a look here.

Here is our first number puzzle.

We have, a triangle that has some missing numbers around the outside.

Each of these sets of three numbers of these three, these three, and these three will all add to make 10.

And we're going to be using the numbers one, two, three, four, five, and six.

So what I'd be tempted to do is write one, two, three, four, five, six.

And I might decide I want to put number six in here.

And if that's true, then I'll cross it out to show I've used it.

So don't overuse any of those numbers and put them in there more than once.

The idea is then that when I add this number and the other two here, that all makes 10.

This number and the other two here will all make 10.

Then these three will make 10.

You can only use each number once.

So I can't put six, four, and six, four, six, four, six, four.

Can't do that, because you can only use each one once.

Cross it out when you have used it.

That by the way, doesn't mean that that's where it goes.

That was just my example.

So, can you make three sides all add up to 10 using the numbers one, two, three, four, five, and six? Warming up that brain.

Come back when you're ready guys.

Mm how did we do with that? Tricky? Or did you just fall upon the answer or did you have a strategy? Well, let's take a look.

This is one solution.

It doesn't mean that this is the only solution.

There may be other solutions.

Okay? I realised though, that one, really probably should have been in a corner because it's the lowest value and it's going to be used more than once.

So let me just check.

Four and one that gives me five.

Add the other five, that gives me 10.

So yeah.

Yup, yup.

One and three, that gives me four.

Knowing my number bonds, four and six is 10, so yeah.

And that means that I've only got the two left.

So three and two make five, five and five is 10.

Brilliant.

Did you have a different solution? If you did, photograph it, send it in.

Share with us your solutions.

Very well done now.

Doesn't mean it's the only way.

Okay.

So tables and chairs.

Now, I want you to imagine that it's coming up to a very special time in your life and you want to celebrate by throwing a party.

And you are working with your party planner to seat as many people as you possibly can.

Now here, we've got a couple of examples of how you might seat people.

So for example, this bit here, this shows my table and one, two, three, four chairs.

Okay? That's how I could seat four people.

You can see the chairs.

Imagine when looking at it from above looking down.

A bird's eye view.

I'm not drawing perfect pictures for you today I'm afraid.

So one table and four chairs.

Now that's for four people.

Let me just circle that key information.

Now here, I've squashed two tables together.

One, two tables, and I've got one, two, three, four, five, six people.

Now, if I then had three tables, what would the next bit in our sequence be? How many people would be sitting at our next seating arrangement? Hmm, Hmm, Hmm, Hmm, Hmm, Hmm,Hmm.

Any more? Well, we need to think about what's the same, what's different, what's changing each time? Now the number of tables is definitely changing.

Because that's come from one to two and now we've got three.

So the number of tables is, is it increasing or decreasing? Increasing or decreasing? Yeah, it's increasing it's going up.

What about the number of chairs? More tables more chairs, right? So that must also be increasing.

Does anything stay the same? Well, I would argue that yes, something does stay the same.

When we arrange our tables like this, there is always a chair at either end.

Look, here's my tables again.

There's a chair either end.

Well look, these are missing.

There's a chair either end.

So that doesn't change.

Those two chairs will always be there.

It's the number of chairs in between that changes.

All right.

So now that we've seen that, now that you've looked over that, let's take a look at the next step then.

So look, we've added a new table.

As you can see here, here's our new table, right there and we've added some new chairs.

So our original one, we had one table, four chairs.

We've still got one table and one, two, three, and there's the fourth chair.

But now we've added another table in and another two chairs.

So those chairs are new.

So brilliant, great.

That's a piece of information, fab.

But now what? Well, we can use that information to really help us by looking in the table yet again.

So, we can put it into our table just as we've been doing each time.

We're going to use our friend the table to help us.

So can you do that here? Okay, so term number one.

So one table.

I'm also going to put that there to help us.

That's going to remind us that the term we're looking at is the number of tables.

So one table, four chairs.

Two tables, six chairs.

Three tables.

And if you're unsure, diagrams okay? I'm going to draw the diagram in here for you just to remind you.

And try and keep it small and neat.

It's going well so far.

We've said the end, there are always two chairs at the end.

And then face partners opposite each other.

So there's three tables, one, two, three.

We've got one, two, three, four, five, six, seven, eight chairs.

Can you now figure out the rest and tell me what's happening each time? How can you explain using a sentence what's happening each time? Ready for it? Off you go.

Time is up.

How did you do? Did you manage? I'm sure you did.

Because you've been working through these sequences brilliantly up until now.

So let's take a look at what's been happening each time.

So we should then find that we've got four table, one table, four chairs, two tables, six chairs, three tables, eight.

Four is 10, Five is 12, six is 14, seven is 16, eight is 18.

So what did we notice? What is happening? What is our rule? Well, I've said in my sentence, the number of chairs increases by two each time.

I could also say the rule is add two each time.

And that's great because that then means that we can work out, going through our steps we can work out how many chairs I would need for nine tables, 10, 11, 12 tables.

We can work that out.

Nice and straightforward.

So, what I'd like you to do now though, is try and figure out how many that would be for 13, 15, 17, 19, 21, 23, 25 and 27 tables.

So just to help you, term number 13, that would mean that there were 13 tables.

But how many chairs around 13 tables? If you're not sure, look at what we left off on here.

We left on eight tables.

Can you work out, remembering that it increases by two each time? However, total chairs increases by two, but I'm not doing 13, 14, 15, 16, 17.

I've missed somehow.

Trying to make it trickier for you.

So total number of tables here would be 15 and so on.

But can you work out, how many chairs would be for each table? Tricky stuff.

Don't worry, we can do this.

You can do this.

I believe in you.

So off you go.

Welcome back.

Shall we see how close you were? I'm sure you were spot on.

So here we are.

Let's take a little look.

Because we're going to be using some little bits of tricky knowledge.

But it's not tricky, but we're going to use some simple knowledge to make something look tricky and work out.

Some numbers of chairs for random numbers of tables, because there is a rule that we can follow.

Okay? Now, I want you to just to take a very close look at these numbers.

Do you remember what I've said to you previously, when we've looked at sequences? What is it nearly? It's almost there, what is it nearly? 13 is almost hmm of 28.

15 is almost hmm of 32.

I wonder what's half of 28? To make it half I divide by mm hmm two.

Half of 28.

I'm going to just write half here.

Half of 28 would be, oh look, nearly the same number.

Half of 32 would be, almost the same number.

Half of 36 would be, huh, this is almost half.

That is a very interesting, very interesting and useful piece of information.

Let's see why.

Well, it helps us to work out the total number of chairs for any table.

So here's our challenge, okay? I know that for one table, I need four chairs.

For two tables, I need six chairs.

Now, half of four is not one.

So I can't just say let's multiply by two.

I need to do something to this number before I multiply by two.

What might I do to one to make it half of four? Half of four is two.

So what do I need to add to one? Yeah, this I add one.

And then times it by two to give me four.

So I'm saying we might add one and then times by two.

So let's see if that's right.

Two plus one is yeah, three.

Times two is, well, what do you know? So this is our formula to help us work out how many chairs I need each time.

It's really quite easy.

Whatever number is here, whatever number of tables, we add one and then double the answer.

So add one, double the answer.

Add one, double the answer.

Add one, double the answer.

And as an extra little challenge for you, how could I work out how many tables there were if I had 422 people? So let's do this one together.

I'm going to add one and multiply by two.

So 31, add one equals.

Yup.

And then times that by two equals.

And there's your answer.

Can you now work out the answer to those next ones? So how many chairs for 31, 47 and 130 people? You can do this.

I know you can do this.

So, off you go.

Add one, then times by two.

And we're back.

You did it, didn't you? You got it, right? Aargh I know you did.

Let's see if you got the correct answers.

So, let's just talk through it.

We've said that we add one and then times by two.

So 31 add one is 32, 32 times two is 64.

So that was 64.

Cheers.

47 add one is 48, 48 times two is 96.

And 130 add one is 131, 131 times two is 262.

And we would then just do the opposite, the inverse to work out how many tables.

Okay? So instead of doing times anything, I'm going to do the opposite of times the inverse, which is divide.

So instead of timesing by two, I'm going to divide by two.

422 divided by two is 211.

And then instead of adding one, I'm going to do the inverse I'm going to take it away.

211 takeaway one, means that there were 210 tables.

You just smashed it.

Well done, guys.

So proud of you.

Well, that's it.

I'm not going to be sending you off now to do your final knowledge quiz because you've done all the hard work.

What I would suggest is go back though, take a look at those sequences, those patterns and see what other general statements you can make.

You've had a fabulous session as always.

So well done for today and from me, Mr. C that's all.

And I'll see you next time.

Bye bye.