# Lesson video

In progress...

Hi everyone.

I've just been doing some tidying.

A bit of cleaning in my house and I came across this bear.

It was a gift from a little girl in a class that I taught a few years ago.

And she told me that it caught her eye in the shop because of the tie that he's wearing.

I'm not wearing a tie today, but I normally wear one in school.

I struggle to find one to match this shirt actually.

Anyway, finding the bear reminded me of that class that I taught, and I have lots of happy memories from being their teacher.

So I'm really pleased to have come across this bear on my shelf at home.

I'm going to pop him down while we start this lesson.

If you've got anything in your hands, that is going to cause a distraction as well, pop it down or move into another space, so that you can focus on your learning with me for your math lesson over the next 20 minutes.

Press pause and come back when you're ready to start.

In this lesson, we are multiplying and dividing by 10 with decimals.

We'll make a start with some mental addition before we spend time looking at multiplying by 10, then dividing by 10.

And then your independent tasks, you'll have the chance to apply your skills of both multiplying and dividing by 10.

The things you'll need.

A pen or pencil, rubber, ruler and some paper or a book.

Press pause while you collect the items, come back and we'll start.

Let's get going with some mental addition.

Press pause, have a go finding the sum of each of these pairs of numbers.

Come back and we'll look at the answers together.

4.

Then if nine ones and two ones is equal to 11 ones, then nine tenths and ten tens is equal to 11 tenths 1.

1.

Next, good 1.

8.

Next or 2.

5.

that two and four add nine tenths four and nine tenths 4.

9.

We're doubling 0.

6, but I know double six is 12.

So double six tenths is 12 tenths, 1.

2.

Next 2.

4.

Next, what? It's not correct.

1.

9 13 ones and nine ones is equal to, ah good spot.

22 ones 2.

2.

Thank you.

And the last one, good 4.

4.

Good start everyone well done.

Multiplying by 10.

Let's take a look.

Tell me the number you can see.

Good, 300.

We're going to multiply 300 by 10.

When you multiply by 10, all parts of the number become 10 times bigger.

100 multiplied by 10 will be 1,000.

So three hundreds multiplied by 10 will be, good 3,000.

300 multiplied by 10 is equal to 3,000.

You say it.

Good.

Here is the next number.

Tell me what you can see.

Good three tens 30.

30 multiplied by 10.

Each part of the number will be 10 times bigger.

One tens multiplied by 10 will be 100.

So three tens multiply by 10 will be good, 300.

Say the equation.

one, two, three, 30 multiplied by 10 is equal to 300.

Next, what can you say? Three ones.

Three multiplied by 10.

Well, one multiply by 10 will be 10.

So three ones multiplied by 10 will be good 30, three tens.

Let's say the equation.

I'll see the first part, you say the second part.

Let's split after I have said 10.

Three multiplied by 10, good.

Let's do it the other way round.

You start I'll finish one, two three, is equal to 30.

Next number, what do you see? Good 0.

3, three tenths.

Three tenths multiplied by 10.

One 10th multiplied by 10 will be one.

So three tenths multiplied by 10 will be three ones.

we have made each part 10 times bigger.

Let's say the equation together one, two three.

0.

3 multiplied by 10 is equal to three.

Last one, what do you see? Three hundredths, 0.

03 multiplied by 10.

Each part made 10 times bigger.

One hundredths multiplied by 10 will be one tenths.

So three hundredths multiplied by 10 will be three tenths 0.

3.

Equation, let me listen to you one, two, three.

Very good, well done.

Now I wonder particularly when those decimals multiplied by 10.

What does that look like? What's actually happening there? I wonder if you could on your paper with some drawings of some sticks represent 0.

3 multiplied by 10 is equal to three.

Press pause and have a go, then come back and we'll share.

Ready? Here is how I've represented it.

0.

3, ten times.

0.

3 multiplied by 10.

That's a lot of sticks isn't it? That's a lot of tenths.

Well, we know that ten tenths is equal to one.

So we can regroup ten tenths for one flat and there are three ones.

0.

3 multiplied by 10 is equal to three.

How would you represent 0.

03 multiplied by 10 is equal to 0.

3.

Remembering the flat down here is made up of 100 hundredths.

100 small cubes.

I wonder, press pause and have a go then come back and we'll share.

Let me see how you've represented it.

Oh I can see some really smart thinking.

so neat, mathematically neat.

Not looking for artists, but I'm looking for mathematically neat drawings to represent this equation good.

Have a look at how I've done it.

So 0.

3 three hundredths 10 times and they can six times, seven times, eight times, nine times, ten times.

0.

3 ten times.

Oh, I mean 0.

03 tens times.

Now we know that how many hundredths make one tenth.

10 hundredths is equal to one tenth? Another 10 hundredths another tenth and then we've got 10 hundredths there to regroup as one tenth.

How many tens do we have? Good, 30 hundredths, three tenths.

0.

03 multiplied by 10 is equal to three tenths.

I think it's time for you to have a pause and have a go at using the skills we've just been learning about multiplying by 10.

There is a start card and an end card.

But all of those other cards in between need to be ordered from start to end.

Have a go at working out based on the start question 0.

2 multiplied by 10.

Where's the answer? Which question is attached? Where's the answer that matches that and so on until you get to an answer of eight at the end.

Press pause, have a go.

Come back and share when you're ready.

How did you get on? So here's the order you ready? From start to end working across.

0.

2 multiplied by 10 is equal two.

A question eight multiplied by 10 equal to 80 and so on, all the way through.

Quickly check off working from left to right.

Did you manage that for your order? Good.

So you've had a chance to practise multiplying by 10.

Let's have a think about dividing by 10.

What do you see? Four thousands.

When we divide by 10, each part of the number is made 10 times smaller.

100 is 10 times smaller than 1,000.

So four hundreds is 10 times smaller than 4,000.

4,000 divided by 10 is equal to 400.

See what you say.

Good four hundreds.

400 divided by 10, each part made 10 times smaller.

What would the answer be? Good, four tens.

100 made 10 times smaller is one ten.

So four hundreds 10 times smaller is four tens, 40.

Say the equation.

Good, well done.

See what you say.

Four tens, 40.

Good.

Let's make it 10 times smaller.

Let's divide by 10.

One ten 10 times smaller is one.

So four tens 10 times smaller.

Good, four ones.

Let's say the equation together.

40 divided by 10 is equal to four.

What do you see? Four ones made 10 times smaller.

four divided by 10, pardon you think it's going to be four tenths? Well, one may 10 times smaller.

One divided by 10 is one tenth.

So four divided by 10, four tenths 0.

4.

Let's whisper the equation.

Four divided by 10 is equal to 0.

4 Last one.

What do you see? Four tenths? 0.

4 divided by 10? Good four hundredths, 0.

04.

Can you say the equation in a loud voice, but not so loud that you disturb anyone nearby to you? So you choose an appropriate volume.

Are you ready, I'm going to listen out one, two, three.

Wow, that's loud, a little bit quieter.

Okay, much better.

My ears aren't hurting as much that time.

Let's have a think again about the two equations where we're working with decimals.

Four divided by 10.

Four ones divided by 10.

How many tens is each one made up of? Good 10 tens.

Let's exchange one one for 10 tens.

So our four ones, and now how many tens? Good, 40.

40 tens divided by 10.

Let's equally share 40 tenths.

I'm going to move my face over to here.

Sharing 10 at a time until we're able to look at one of those equal shares.

What is that equal share worth? 0.

4 four tenths.

How about with this one? Let me move again.

0.

4 divided by 10.

How can we divide four tenths by 10? What do you know about each tenth? Each tenth is worth ten hundredths.

So four tenths or 40 hundreds.

40 hundreds divided by 10.

Can we divide and share equally 40 hundreds by 10.

We can share out 10 at a time, another 10, another 10, and another 10 and then look closely at one of those equal shares.

What's it worth? Four hundreds, 0.

04.

Finally, before a chance for you to have a go at your task, let's look at those connections between dividing and multiplying.

4,000 divided by 10 is equal to 400.

You say the multiplication.

Good.

You say the division.

40 multiplied by 10 is equal to 400.

Whisper the division and shout not too loudly, the multiplication.

My turn four divided by 10 is equal to 0.

4.

My turn 0.

04 multiplied by 10 is equal to 0.

4.

Look at those patterns.

Can you see the connections within the division and across the division and multiplication? Look at the digits.

Look at the police's those digits are in and the changes that are happening.

As we divide by 10, we make our number 10 times smaller.

As we multiply by 10, we make our number 10 times bigger.

Here is a chart.

I struggle with the name of the chart.

It looks like it should say Gattegno.

I've heard lots of people call it Gattegno.

I've called it Gattegno as well, but I'm not too sure if that's correct.

We can call it a chart at least.

In this chart, I'm going to read out some instructions and I want you to follow across the chart from start to finish.

I add two going to the right.

I multiply by 10 up, I add 30 to the right, I divide by 10 down, what number have landed on? Good, eight.

In your activity, I've left my example instruction.

I would like you to use the chart to make up five sets of instructions of your own.

There are some rules.

You can use addition, subtraction, and multiplication or division by 10.

Through your instructions, you're only allowed to move up or down, left or right, no diagonal movements.

Press pause while you complete the task and come back with your five sets of instructions.

How did you get on? Do you have your five sets of instructions? Maybe you can test them out on a parent or carer, a brother, or sister or even a teddy bear at some point and see how they get on.

Let's finish up by having a look at these two children and what they have to say.

What numbers are they thinking of? Press pause, have a read, see if you can work out the numbers and come back and share.

Are you ready? So let's look at the chart on the left, I divide a number by 10 and my answer is three tenths.

What is my number? I can use some connections here although I'm dividing.

Let me connect back to multiplication.

So if the answer is three tenths, three tenths multiplied by 10 instead of dividing will give me a number three.

Use that strategy if you can, or a different one of your own for the boy.

I divide a number by 10 and my answer is three hundredths.

What is my number? What did you get? Good.

Three hundredths multiplied by 10 is equal to three tenths, 0.

3.

Fantastic work again, plenty to share I'm sure.