Lesson video

Hello, welcome to your maths lesson.

It's really good to have you here.

I hope you're ready for 20 minutes of focused learning, thinking about you, your maths and developing some new skills.

If you're not in a quiet space, if there are any distractions around you, press pause, take yourself off to somewhere where you are able to focus on your learning for around 20 minutes.

Press pause now, come back when you're ready.

In this lesson, we are learning to multiply and divide by 10 with decimals.

We'll start off with some partitioning work in a quick activity before we split our focus on multiplying by 10, then dividing by 10, and you'll be able to use those skills together in the independent task at the end.

Things that you're going to need: pen or pencil, a ruler, and something to write on, some paper lined, squared, a book, a pad, anything will do.

Press pause, fetch the items, come back and we'll start.

Okay, so a partitioning, oops, a partitioning activity to get started.

I'd like you to partition each number into any hundreds, tens, ones and tenths.

Record your solution as an addition equation, for example, 4.

29, you would record as 4.

29 is equal to.

Let's start with a partitioning activity.

I would like you to take each of the numbers and partition them into any hundreds, tens, ones and tenths.

Record your solution as an addition equation, for example, 4.

29 is equal to four, add 0.

2, add 0.

09.

Press pause, work through the rest, come back and we'll look at the solutions.

Ready to take a look? Okay, here we are.

So we're partitioning each number into any tens, ones and tenths.

And recording as an addition equation, making sure each part of the number is represented.

So that one had a 10, some ones, tenths and hundredths.

Whereas this one only had two parts, some ones and some hundredths.

Four parts here.

And although there are five digits in the final number, there are only four parts because there aren't any tens and there aren't any tenths.

How did you get on? Big happy smiles? Multiply by 10.

Tell me what you can see.

250, two tens, sorry.

Two hundreds, five tens.

250 multiplied by 10.

When we multiply by 10, each part of the number gets 10 times bigger.

Two hundreds, five tens, both need to become 10 times bigger.

250 multiplied by 10 is equal to 2,500.

Each part, take a look has become 10 times bigger.

Read the equation back to me, good.

Tell me what you can see now.

Two tens, five ones, 25.

25 multiplied by 10.

If I multiplied one 10 by 10, the answer is 100.

1 one 10 times bigger is 10.

So two tens, 10 times bigger and five ones, 10 times bigger.

Two hundreds, five tens, 250.

Read the equation, good.

How about this time? What do you see? Say it again.

2.

5, two ones and five tenths multiplied by 10.

Nice ideas, thank you for calling out what you think it's going to be.

Yes 25, two ones becomes two tens.

Five tenths becomes five ones.

Each part made 10 times bigger.

Let me read parts of the equation, you finish it off.

2.

5 multiplied by 10, good.

How about this one? What do you see? Two tenths, five hundredths, 25 hundredths as a decimal, 0.

25, multiplied by 10.

Each part made 10 times bigger.

What will happen to the tenths? And what will happen to the hundredths? Let's see, good.

The tenths become ones.

The hundredths become tenths.

You start the equation, stop after 10.

I'll finish it, go.

Is equal to 2.

5.

I think you're ready to have a little pause and a practise at multiplying by 10.

There are some numbers on the screen, pick one.

Represented with drawings of place value counters, and a place value chart.

Multiply the number you've picked by 10 and write the equation.

Use more drawings of place value counters to show how the number has changed.

Press pause, give this a go, come back when you're ready.

How did you get on? Did anyone pick 1.

1? You did, and what did the answer become? Or what did the number become when you multiplied it by 10? 11, good, who picked 2.

3? What did that become? 23, did anyone pick a number that became 530? Which number was it? 53, yes, and which number multiplied by 10 becomes 85? Good, 8.

5, well done.

Divide by 10.

What can you see? 1,000, one, two, three, four, five, 800, 1,800? Good, we're going to divide by 10.

Each part of the number will become 10 times smaller.

100 is 10 times smaller than 1,000.

One 10 is 10 times smaller than 100.

So 1,000 becomes 100 and 8 hundreds becomes eight tens.

When we divide by 10, what would the equation be? Yes, it is 1,800 divided by 10.

You finish it, good.

Is equal to 180.

Next number, what can you see? How many hundreds? How many tens? 180, good, divided by 10.

Each part becomes how much smaller? 10 times smaller.

The hundred becomes one 10 and the eight tens become, good, eight ones.

How do we say this number? One ten, eight ones, 18.

Can you read the equation with me? 180 divided by 10 is equal to 18.

Say what you can see.

How many tens? How many ones? 18, 18 divided by 10.

Each part becomes how much smaller? 10 times smaller.

One is 10 times more than 10.

One tenth is 10 times smaller than one 1.

1.

8, read the equation, very good.

Say what you can see.

1.

8, good, divided by 10.

Each part 10 times smaller.

0.

18, good, what will the equation be? Should we check? 1.

8 divided by 10 is equal to 0.

18.

So let's just compare those division equations with their multiplication equation.

Can you beat the division? I'll read the multiplication, you go.

180 multiplied by 10 is equal to 1,800.

My turn, your turn.

180 divided by 10 is equal to 18.

Good, your turn.

1.

8 multiplied by 10 is equal to 18.

Both at the same time.

1.

8 divided by 10 is equal to 0.

18.

0.

18 multiplied by 10 is equal to 1.

8.

Again, look at the connections within the division, within the multiplication and across the two.

Look at the changes to the numbers after making them 10 times smaller or 10 times bigger.

Time for your activity.

Can you spot and describe the pattern and use that to complete this grid.

All of the empty squares need a number to be filled in and you can find the number by spotting the pattern.

For example, I'm looking here.

I've noticed that on this side, the number in the bottom row is 10 times smaller than the number in the row above.

So a number 10 times smaller than 3.

4 is 0.

34.

I'm also noticing that between this side and this side, there has been an increase of one tenth, an increase of one.

So there's either an add or subtract or a multiply or divide by 10.

And that would help me to find this number 10 more and 10 times smaller than the one above 550.

Sorry, 540 is 10 times bigger than 54.

Again, 100 more and 10 times smaller than the one above.

And based on that pattern, I'm predicting that in the top row to the right is 1,000 more, to the left is 1,000 less.

I'd like you to pause and complete your copy.

It's different to the one that I've just shown you.

When you're finished, come back and I'll share with you the solutions.

Ready to look? So this is the copy that you had, two different numbers.

Were you able to spot the pattern and complete the chart? Now some of you may have been working straight onto a screen.

Some of you may have copied it onto paper.

If you've got anything you can hold up and show me, please do that now.

Good, really good effort, everyone.

And here are those missing numbers.

Can you compare? Have a look and notice bottom row increasing in tenths, increasing in ones, tens, hundreds, thousands, and within a column as you increase by one row, the number above is 10 times bigger.

The number below is 10 times smaller.

Let's finish with a quick activity together.

Four friends are sat around a table.

They are talking about the question.

How could you represent 2.

67? Let me share with you their thoughts.

It's your task to decide who is right.

It's the same as two ones and 67 tenths.

It's equivalent to 26 tenths and seven hundredths.

It's the same as 267 hundredths.

I could represent it using two ones, six tenths and seven hundredths.

Who is right? Press pause, have a think, write something down.

Try to match what they are saying with some drawings perhaps then come back and we'll find out.

Ready? So one of them said it's the same as two ones and 67 tenths.

Did you think that was right? So how would that look in the place value chart? Two ones and 67 tenths.

How many digits are we allowed in each column, one.

So if we've got 67 tenths, we need to regroup to the left.

So that's six, moves into the ones, which means we now have eight.

So what that person said would match 8.

7, not 2.

67, they're wrong.

How about this one? It's equivalent to 26 tenths and seven hundredths.

We put this one down as maybe right, okay.

26 tenths and seven hundredths.

What happens with those 26 tenths? Regroup to the left.

So it is equal 2.

67.

Next one, it's the same as 267 hundredths.

What do we think? Yeah, so looking like this.

267 hundredths, does that look right to you? What do we need to do? Regroup to the left.

We can only have one digit per column.

So we're regrouping to the left twice, 2.

67.

And the final one, I could represent it using two ones, six tenths, seven hundredths.

What did you think? Good, two ones, six tenths, seven hundreds.

So three of them were right.

And one of them, their thinking wasn't quite yet right.

If you would like to share your work with Oak National, please ask your parent or carer to share your work on Twitter tagging @OakNational.

Thank you for joining me for this lesson.

You have worked incredibly hard.

I'm really proud of all of you.

Thank you for engaging with the activities and holding things up for me to see against the camera.

If you've got any more lessons lined up for the day, I hope you enjoy them.

And I look forward to seeing you again soon for some more maths, bye.