Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher.

I teach all of the different subjects, but the one that I enjoy teaching the most is definitely maths, so it's a real pleasure to be here with you today.

If you're ready to begin, let's begin the lesson.

The outcome of today's lesson is I can scale known multiplication facts by 100.

Hopefully, you know lots of times tables facts off by heart and automatically.

If so, that's going to really help you today.

We've got some keywords.

If I say them, will you say them back? Are you ready? My turn.

Scaling.

Your turn.

My turn.

Factor.

Your turn.

And my turn.

Product.

Your turn.

What do those words mean? Do you know? Would you like a little reminder? Scaling is when a given quantity is made mm times the size, so it might be five times the size, or 10 times the size, or one 10th times the size.

A factor is a number which exactly divides another whole number, so for example, three and four are both factors of 12, and a product is a result of two or more numbers being multiplied together, so for example, three multiplied by four is equal to 12, and 12 is the product.

We've got two cycles in this lesson.

The first will be times table knowledge and scaling by 100, and the second will be reasoning and problem solving, so let's begin by focusing on times table knowledge and scaling by 100.

In this lesson, you're going to meet Sofia and Jun.

Have you met them before? They're here today to give us a helping hand with the maths and very good they are too.

Jun and Sofia use Base 10 to show scaling up by 100.

If you've got some Base 10 in front of you, you might want to join in.

Let's start with two ones and make them 100 times the size.

Let's multiply each block by 100 to make it 100 times the size, so one multiplied by 100, and that's what we get.

We can exchange that one for a 100 block, and the same again.

We've taken two one blocks and scaled them up by 100, so we now have two 100 blocks.

We've made them 100 times the size.

To scale up a value by 100, you multiply it by 100.

This time, Jun and Sofia use place value counters.

Have you got place value counters in front of you? You could use them here.

Jun says, "Let's start with two ones counters with a value of two." And then Sofia says, "Let's scale up the value by 100 to make it 100 times the size." How could we represent that? How could we show that? It wouldn't be two ones, would it? It would be two one hundreds.

We've taken two ones counters and made their value 100 times the size, leaving two hundreds counters.

Let's do a little check.

Use Base 10 or place value counters, or maybe both, to model scaling up three by 300.

What would that become? Pause the video.

So we need to make each of these one blocks 100 times the size.

There won't be one blocks anymore, they'll be 100 blocks, and we need to make these one counters 100 times the size, so they won't be ones anymore, they will be one hundreds, and it will look like this.

So well done if you either drew or represented that physically just like this.

Jun and Sofia create an array using ones counters, what times tables fact can you see here? And there's a couple of answers you could give here.

This shows four groups of three as an equation.

That's four multiplied by three is equal to 12.

Did you see that? Did you spot that? Four multiplied by three is equal to 12.

That's four groups of three.

Four lots of three.

Now you might have seen it differently and Sofia did.

She says, "It also shows three groups of four, which, as an equation, is three multiplied by four is equal to 12." Let's see that.

Can you see that now? Three groups of four.

Three lots of four is equal to 12.

The products are the same for both multiplications.

What does that tell you? That's because multiplication is commutative.

You can swap over your two factors and still end up with the same product.

Jun and Sofia scale up by 100, so four multiplied by three is equal to 12.

Three multiplied by four is equal to 12.

Let's scale them up.

What would it look like? How could we represent that number scaled up by 100? Let's change the value of the ones counters to 100 counters to scale up.

Here we go.

This changes the equations too.

The group size scales up by 100 too, so it would be four multiplied by three equals 12 and it would be three multiplied by four is equal to 12.

Now we have four groups of 300, which is four multiplied by 300 equals 1,200 or 1,200.

Here we go.

Or we have three groups of 400, which is three multiplied by 400 is equal to 1,200 or 1,200.

So there we go.

"Multiplication is commutative, so we could write more equations." "I agree.

We could switch the positions of the factors." Yes we could.

So what could we do with the first one? It's four multiplied by 300.

Could we swap those over? Yes.

300 multiplied by four is equal to 1,200.

And what about the second one? Three multiplied by 400.

Could we swap those over? Yes, we could.

400 multiplied by three is equal to 1,200.

"If I multiply one factor by 100," says Sofia, "I must multiply the product by 100", says Jun.

And you might have learned that before in a previous recent lesson.

Let's do a little check.

Write down the four multiplication equations being shown by this array of one hundreds counters.

Remember to use the commutative law where you can swap them over.

Okay? Pause the video and away you go.

Did you manage to get four different equations outta that? Let's have a look.

Well, we've got this one.

You might have seen four multiplied by 500.

Four lots of 500, which is equal to 2,000, and then using the comm commutative law, swap those factors over.

We've got 500 multiplied by four is equal to 2,000.

And then we've got five multiplied by 400 is equal to 2,000, and using that commutative law, swapping it over, 400 multiplied by five is equal to 2,000.

Jun and Sofia look at the three times table.

Hopefully you're very familiar with the three times table.

Hopefully you know them off by heart.

For each of these equations, we could scale up by 100.

Hmm.

"That would give us four other equations.

Let's try it." So we're going to choose one of them.

We're going to choose this one.

Could have been any but we're going to choose six multiplied by three is equal to 18, so let's think about scaling that up.

Can we get four multiplication for those? So what are the four equations? We'll get two different ones depending on which factor we choose to scale up by 100, so if we chose the second one, the three, that becomes six multiplied by 300 is equal to 1,800, and if we chose the other factor to scale up, that gives us 600 multiplied by three is equal to 1,800.

Now let's use our commutativity.

300 multiplied by six, we can swap those two factors over, is equal to 1,800, and three multiplied by 600, again, swapping those two factors over from the previous example is equal to 1,800, so that's four facts.

It is time for some practise.

Number one, for each times table, write four more equations by scaling up each factor in turn by 100 and then use commutativity, So pick one of the factors, scale it up by 100, pick the other factor, scale it up by 100.

Number two, find the missing numbers.

Number three, find the missing numbers.

And this time you might see it's not the product that's missing, it's one of the factors.

Okay, good luck with that and I will see you very shortly for some feedback.

Pause the video.

Welcome back.

How did you get on with that? Are you feeling confident? Do you feel like you're getting good at this? Let's see.

So number one, we're going to scale up each factor in turn by 100 and then use commutativity, so three multiplied by four is equal to 12.

That's a known times tables factor, I hope.

So if we pick the four, the factor four, we could say three multiplied by 400 is equal to 1,200.

If we pick the three, the factor three, that becomes 300 multiplied by four is equal to 1,200, and then we swap them over.

We use the commutative law.

400 multiplied by three is equal to 1,200, and 4 multiplied by 300 is equal to 1,200.

B, eight multiplied by seven is equal to 56, our known times tables fact.

Well, starting with the seven as the factor that we're scaling up, that's eight multiplied by 700 is equal to 5,600, and then scaling up the other factor, we've got 800 multiplied by seven is equal to 5,600.

Using our commutative law, 700 multiplied by eight is equal to 5,600, and then seven multiplied by 800 is equal to 5,600, and here are the answers to C.

Again, we've started by picking one of the factors and scaling up by 100 and then the other, and then use the commutative law.

And the missing numbers.

Well, we can start with our known times tables fact, that's six multiplied by eight, and then we can scale up, so that gives us 4,800, and again, nine times seven could be our starting point.

Scale it up, make it 100 times the size.

That's 6,300.

C is 1,500, D is 5,500, E is 8,100, F is 7,200, G is 3,600, and H is 6,000, and in all of those cases we started by taking a known times tables fact and scaling up.

And the missing numbers, this time we are missing one of the factors, so six multiplied by something is equal to 6,600.

Well, I could use a times tables fact, a known times tables fact.

I know six multiplied by 11 is equal to 66, so therefore six multiplied by 1,100 is equal to 6,600, so 1,100 is the answer, and for B, 800 multiplied by something is equal to 7,200.

Well, eight multiplied by nine is equal to 72, so 800 multiplied by nine is equal to 7,200.

And for C, 1,200 multiplied by five is equal to 6,000.

For D, 600 multiplied by nine is equal to 5,400.

For E, nine multiplied by 600 is equal to 5,400.

For F, 700 multiplied by four is equal to 2,800.

For G, 1,200 multiplied by seven is equal to 8,400, and for H, 1,200 multiplied by eight is equal to 9,600, and in all of those cases we can work those out by starting with a known multiplication fact.

Well you're doing really well and I hope you're rearing to go for the second cycle and that's reasoning and problem solving.

There are six multiplication expressions.

They need to be arranged into three pairs which have the same product.

What do you think? So we've got four multiplied by 600, 800 multiplied by six, 400 multiplied by 12, 800 multiplied by three, 1,200 multiplied by six, and 800 multiplied by nine.

Now would it be easier, I wonder, if we started by thinking of the known times tables fact that you can see within there? So let's do that.

"We need to examine the digits for that and I'll write the facts underneath", says Sofia.

So here we go.

Here are the known times tables facts.

The related facts.

Now let's see which related times tables facts do have the same product.

We've got these ones, so four multiplied by six is equal to 24 and so is eight multiplied by three.

That's also equal to 24, so therefore four multiplied by 600 is equal to 800 multiplied by three, and these two have the same product as well, so their related facts have the same product, and these two have the same product, therefore their related multiplications also have the same product.

Let's have a check.

Match the multiplication equations with their related times tables fact by drawing a line between the equations.

Have a good think about that.

Pause the video and away you go.

So let's see.

We've got 1,200 multiplied by three is equal to 3,600 and that's related to 12 multiplied by three is equal to 36.

Seven multiplied by 500 is equal to 3,500, and that relates to seven multiplied by five is equal to 35, and then six multiplied by 400 is equal to 2,400 resembles and is related to six multiplied by four is equal to 24.

Well then if you've got that, you're ready for the next step in the learning.

Jun jogs every day around a running track.

If he completes six laps, how many metres did he jog? Hmm.

We need to work out what's being asked.

I don't think we have enough information.

No, I agree with you, Jun, there.

What could we do with knowing? What information is missing? We need to know how many metres long the running track is so that we can multiply.

Yes.

Well then, Sophia, that would help.

How about this? The running track is 400 metres long.

Now we can do it.

So he's going to complete six laps.

How many metres will he jog? Let's use a known times tables fact to help us to solve the problem.

Which times table should we use? Can you see it? What do you think? It's this one.

Six multiplied by four is equal to 24.

We can use that.

If I jogged six laps of four metres, I'd have jogged 24 metres in total.

That's not very far, but that's going to help us.

Each lap was 400 metres, which is 100 times as many as four, so we can exchange those one counters for 100 counters, 'cause the product will be 100 times as many.

So can you see that factor? That factor of four has been scaled up.

It's now 100 times the size, so we need to do the same to the product, which is also going to be 100 times the size.

24 multiplied by 100 is equal to 2,400, so Jun jogged 2,400 metres altogether.

It's time for some final practise.

Number one, match up the pairs of multiplication expressions with equal value by placing them in the boxes.

Remember, just like we did before, look for that multiplication fact, that known fact, within each one.

And the same for B.

And number two, solve the following worded problems. I will leave you to read those.

Make sure you've read them very carefully and that you've understood them before you attempt them.

Right here, we pause the video, and away you go.

Welcome back.

How are you getting on with this? Are you feeling confident? Let's see how you did.

So number one, match up the pairs of multiplication expressions with equal value.

So eight multiplied by two is equal to four multiplied by four.

That's 16, so therefore 800 multiplied by two is equal to 400 multiplied by four.

Five multiplied by eight is 40 and so is 10 multiplied by four, so therefore these two belong together.

They're equal.

And then six multiplied by 10 is 60 and 12 multiplied by five is equal to 60, so therefore 600 multiplied by 10 is equal to 1,200 or 1,200 multiplied by five.

And then here, 200 multiplied by nine is equal to six multiplied by 300 because two multiplied by nine is equal to six multiplied by three.

10 multiplied by 300 is equal to 600 multiplied by five, and we know that because 10 multiplied by three is equal to six multiplied by five.

And then 1,200 or 1,200 multiplied by four is equal to 600 multiplied by eight, and we know that because 12 multiplied by four is equal to 48 and so is six multiplied by eight.

And then the worded problems. A, Sofia is carrying sacks of potatoes into the school kitchen and each sack contains 200 potatoes.

She carries in 12 sacks.

How many potatoes is that in total? Did you first start by looking at the known multiplication fact? Two multiplied by 12 or 12 multiplied by two, which equals 24, and we're going to scale up that two, that factor.

We're going to make it 100 times the size, so that becomes 200, so we then have to do the same with the product.

The product's going to be 100 times the size.

That's 2,400.

2,400 potatoes.

And B, Jun is making a mixed fruit juice drink for the summer fair.

He uses four bottles of orange juice and three bottles of pineapple juice.

How many bottles is that? Each bottle contains 600 millilitres of juice.

How many millilitres of mixed juice are there altogether? So we've got four bottles and three bottles make seven bottles.

so seven bottles, each have 600 millilitres.

Seven multiplied by six is equal to 42.

We're gonna use that as our known fact and we're going to build on that.

We're going to make the six 100 times the size.

We're going to scale it up.

That's 600.

So the 42 is going to become 100 times the size as well.

We're going to scale that up by the same amount, so that's 4,200.

That's 4,200 millilitres of mixed fruit juice drink.

And C, Jun runs around a 400 metre track five times.

Sofia runs around a 300 metre track seven times.

Who's run the furthest? Well, let's find that multiplication.

Five multiplied by four is equal to 20, and we can use that as our starting point.

We're going to scale up that factor 100 times.

That's 400, and we're going to scale up this factor 100 times.

That's 2,000.

So he's run 2,000 metres.

And Sofia, we're going to take the seven multiplied by three is equal to 21 as our known starting point.

We've scaled up that factor, the three, that's become 300, so we scale up the 21 as well.

That's going to become 2,100, so very, very slightly, it's Sofia.

Sofia ran the furthest.

We've come to the end of the lesson.

You've been very impressive today.

Well done.

Today we've been scaling known multiplication facts by 100.

Scaling up by 100 requires multiplication by 100.

It's the same thing.

If one factor in a multiplication equation is made 100 times the size, the product will also be 100 times the size, and you've done lots and lots of examples of that today.

This can be applied to different contexts in combination with known times tables facts.

Well you have been fantastic.

Give yourself a pat on the back.

It's very well deserved.

I hope I get the chance to spend another maths lesson with you at some point in the very near future, but until then, have a wonderful day.

Be the best version of you that you can possibly be.

Take care and goodbye.