Lesson video

Hi guys, it's me, Mr. C.

Here for another math session with you and your wonderful math brains.

So let's move straight on shall we, with our number sequencing, and reasoning with sequencing patterns.

Well, I'm going to start us off with a Maths puzzle.

Here's a little, code breaker I guess we could call it.

So take a look.

Here's an image with some numbers and a question mark.

Now the question mark shows us that something is missing.

What I need you to do is try and figure out, what should take the place of the question mark? So let's just look, shall we? We've got one, two, then we've got three, four, five.

What comes next? What do you think takes the place of the question mark? Few seconds to have a think, 10 seconds.

Three, two, one.

Here's a hint for you.

What takes the place of the question mark? Well, it isn't a number.

Why is that picture there? Alright, five seconds.

Two, one, and that's it guys.

Would you like me to put you out of your misery? It's another one of those tricky ones.

Some of you are probably either, no you don't.

So let's take a look.

Have a look here, then I put on a picture of a, well, what looks like a motorway, and I told you that the number isn't a number.

The missing information is not a number.

You ready? Drum roll, please.

Here it is.

It's an R, an R is missing, because it's actually the top of a gearstick from a car.

It's gears one, two, three, four, five, and then R for reverse.

Sorry, I tricked you again.

Alright, I'm a dreadful person.

So let's move straight on, and see what we're going to need.

You're going to need a pencil, a ruler, and something to work on.

So whether that'd be printouts, paper, or just a book that you're working in, that's fine, and some where quiet with no distractions.

Probably not in the middle of a motorway, I would suggest.

So, key learning of vocabulary is coming up in just one moment.

And then we're going to look at our speedy tables warm-up.

Then we've got a matchstick triangles problem.

How do we spot what's happening? And then our main activity is to investigate the sequence with a challenge at the end, and then a knowledge quiz to see us all off into the next session.

Key learning then.

To develop strategies, to plan and solve a problem.

In our key vocab, we know these words really well, super quick.

Let's go from the bottom to the top today.

Rule, term, decreasing, increasing, differences, similarities, patterns and sequence, well done.

Remember the similarities and differences are really important we'll be looking at it.

In then the last few times we've looked at sequences and patterns together, looking at blocks and shapes and pictures, we've spotted the differences, that's the key part, spotting the difference.

So here's your speedy tables grid, can you fill that in as quick as possible? I'm going to stop talking.

You're going to start showing off your amazing math skills.

On your marks, now get set, go.

Mega stars, did you beat your last time? Do you think you did? Did you finish quicker? Let's see if you manage to finish quickly with all the correct answers, which I'm sure you did, here they are.

Let me zoom on in so you can see them really clearly.

Amazing, I bet you got them all, because you're all just wonderful.

Good job.

Okay, let's move ahead.

Let's meet our new problem.

This is a Matchstick triangle right here.

And this is the next step in our Matchstick triangle sequence.

So I wonder what our next step after that would look like.

Now, just to make this really clear, they are matchsticks, I promise you.

Each side of this triangle is a Matchstick.

So that's one, two, three, that's three matchsticks and there's one triangle.

Here we've got one, two, three, four triangles, and one, two, three, four, five, six, seven, eight, nine matchsticks.

So what would come next? But what's changed between step one and step two, what's changed? How many more matchsticks did we add? How many more triangles appeared? Have a look, see if you can spot that information.

Let me zoom into it a bit closer for you.

One triangle and then we added another one, two, and this one in the middle, three.

So add one triangle, then we had three triangles.

We had three matchsticks and then we had three, six, nine matchsticks.

Okay.

So something's happening , is it getting bigger or smaller? What's changing? I wonder what the next step would look like.

The next step would look something like this fella here.

So the original term was here, then we had these new ones.

So two new triangles, but they also formed a third in the middle.

So we added these two new green ones, but they formed a third.

And then imagine this one has been transferred to here, we then got one, two, three, four, five more triangles.

So, we could do this in a table.

Let's just quickly do it here, so M is the Matches, number.

So triangle one, two and three, matches and triangles.

Okay? In number one, we had three matches and one triangle.

In number two we had, three, six, nine matches, and one, two, three, four triangles.

In number three we had three, six, nine.

Can you do this? Can you tell? Listen, three, six, nine, 12, 15, 18.

So 18 matches and one, two, three, four, five, six, seven, eight, nine triangles, check again.

One, two, three, four, five, six, seven, eight, nine triangles, okay.

That's one way of doing it, putting it into a table like so.

The Matches has gone from three, to nine, to 18.

Triangles has gone one, to four, to nine, it's increasing.

Hopefully that's making sense, putting in a table helps my old brain.

So taking a look then.

Take a look at triangle one, triangle two and so on.

We've kind of done this, what's the same? What's different? Yeah? How many more matchsticks to add each time? We quickly pop that into a table just here.

Now you're going to do the same.

Can you work out what would come next? Just looking at the number of triangles to start with, okay? One triangle, four triangles, what comes next? Drawing it helps.

So one triangle and then our next one was one, two, three, with the extra one in the middle and so on.

Can you work them out? Looking at the gap in between.

Okay? Looking at the gap in between.

And also, these diagrams help.

So one, two, three, four, five, six, seven, eight, nine would be our next one.

What's the gap in between? So what do I add to one to make four? Yeah, what do I add to four to make nine? Yeah, three, five.

What would come next? This looks familiar.

Could it be seven? Can you fill in the missing information? Got your little diagram down at the bottom to help you.

Can you go up to the sixth term? See if you can fill in what's missing, and come back when you're ready.

Great stuff, how have we done? Shall we take a look? Okay.

Got it? And look, we're coming back to squared numbers again.

Hopefully you recognise that from the last time we looked at squared numbers.

A squared number don't forget is, when you multiply a number by itself.

So for example, step three, it could be three times three or, three squared.

And that will give you the number of triangles, which was nine.

Okay? But that's just the number of triangles.

What if we wanted to work out more? And let's just look, shall we.

The differences between, we've got three, you've added three here.

Five, seven, nine, 11, and so on.

Now, as I say, is just the total number of triangles.

But what if we wanted to know the number of matches as well? That's what we'd have to look at it slightly differently.

And that's why something like this, is really going to help.

So, we're going to look at, the matches and the triangles.

So in step one, here's step one, we had three new matches, three matches in total and one triangle, okay? In step two, if I scribble out the matches we already had, we then had one, two, three, four, five, six, new matches, and nine matches in total.

One, two, three, four, five, six, seven, eight, nine.

And that gave us a total of four triangles.

What about step three? How many new matches, how many total matches and how many triangles in total? So we've got these three, let's cross these out.

These were the matches we already had.

So now I've got one, two, three, four, five, six, seven, eight, nine new matches.

Matches in total.

So that's nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, how many triangles and so on.

And what do we notice is happening as we look down the columns? See if you can fill in the rest of the information there, and then come back when you're ready.

Are you done? Tricky? Did any of you sketch it? 'Cause the sketching I find really helps.

I've had to do that several times, just the sketching for me makes it seem so much clearer, so much more real.

Well, let's take a look at those answers, let me zoom in there so you can see them real clear.

Now there are patterns happening all the time.

For example, let's have a look at our new matches.

Three, six, nine, 12, 15, 18, 21, 24, what can you see is happening each time? Yeah, our new matches is increasing by three.

Our total number of matches, what's that increasing by? Is it the same each time? It's not, is it? Three to nine, that's adding six.

What do I add to there? So nine to 18.

That's adding nine.

And here, yeah, 12.

And here.

So, we're adding multiples of three, that increase by three each time, and our total number of triangles, and so on.

So for each part of this pattern, something slightly different is happening.

That can make it really tricky to figure out what comes next but, it's not even hard.

Because here's something I noticed.

If I, add the total matches, from before, to the new number of matches, that gives us the new total.

So three add six is nine.

Nine add nine is 18.

18 add 12 is 30.

30 add 15 is 45 and so on, so that makes sense, doesn't it? So you have a tiny bit of a pattern there, a little formula we can see, and it's just about playing with it, and seeing what we can spot.

So have a look at this, we've just mentioned it already, but what three things, think back to here.

Tell me three things that you notice at all about those figures.

So remember we're looking for the similarities and the differences.

What's the same? What's different? What's staying the same? What's changing? So just have a look, see if you can tell me three things that you notice about anything on there at all.

Write them in, if you think you got it, it can be anything.

I'm going to write some in as well as you do.

So we're doing this together, same time.

So first thing I noticed is, that, the number of triangles, is the, step number, squared.

That's number one, that's the first thing I spot.

Number two, new matches, increase, by, each, time.

What do they increase by each time? Yeah, three.

And point three, I'm going to say.

Ooh, what can I say here? I mean, look at the total number of matches.

Total matches, go up, in steps, of odd, numbers.

You may have others that you spotted there.

Not everyone will spot the same when they look at a pattern or a sequence, we'll all see something slightly different in there.

So what I would suggest now is, take a look at the bigger picture that we were looking at before, use that to help you spot other things, write a list of as many things as you can spot about that.

Here are just three, what else do you notice? That's your takeaway for today, your homework if you like.

What else can you find? Now, tricky stuff, but you've done well.

So go and take our final Knowledge Quiz, and then come back when you're ready.

Well done today everybody, tricky stuff, lots of spotting, being detectives and really looking out for those things that we could see today.

Well done, great job.

And from me Mr. C, that's all.

And I'll see you again in our next session.

Okay, bye guys.