# Lesson video

In progress...

Hi everyone.

I've been trying to keep up with my five a day, my five portions of fruits or vegetables.

This orange is proving very tricky to peel.

I wonder if it's not yet ripe enough.

I think I'll pop it to the side and keep my attention focused on this maths lesson instead and come back to that orange later on.

If you are not yet in a quiet space, then please pause in a moment, take yourself off somewhere that you're able to focus on your learning for about 20 minutes or so free of distractions.

Press pause if you need to do that and then come back when you're ready to get started.

In this lesson, we are mentally adding and subtracting numbers with one decimal place.

We'll start the lesson off with a partitioning activity, before we look separately at adding tenths, then subtracting tenths, both mentally.

Things that you'll need: pen, pencil, something to write on, a ruler if you have one.

Press pause if you need to go and get those things, then come back when you're ready to start.

Here's the partitioning activity.

I would like you to partition each of the numbers on the left into any numbers, sorry, not into any numbers but into any hundreds, tens, ones and tenths that there may be and you'll record that as an addition equation.

Let me show you what I mean.

So the number 3.

9, if you partition it into the ones and tenths, you'll record that then as 3.

9 is equal to three add 0.

9.

Three being the number of ones and nine being the number of tenths.

0.

9.

Press pause, work through the other numbers that are there, partitioning into them into any hundreds, tens, one or tenths.

How did you get on? Hold up your paper, let me have a look.

Good, I can see, oh, hold it steady.

Yes, I can see you've partitioned and you've recorded the partitioning with an addition equation.

Well done.

Check yours off against these.

So here we go.

20 plus eight plus 0.

1 is equal to 28.

1.

84.

4 partitioned into two parts.

There it is.

The next one partitioned into four parts, hundreds, tens, ones and tenths.

Eight plus 0.

2 for 8.

2.

Three parts because there aren't any ones, zero ones so three parts for 190.

9.

And four parts to finish.

How did you get on? Pardon, which one? 84.

4.

84.

4 is equal to 80 plus 0.

4.

Ah, I've missed out my ones.

80 plus four plus 0.

4.

Well done, for spotting that and thank you for grabbing my attention so that we can get that one sorted.

Good work, everyone.

0.

5.

What is the sum of those two numbers, of those two addends? If we're thinking part-whole, we know the parts, what is the whole? Let's think about this.

Using what we know about working with ones.

I'm going to use a sentence and you'll get the chance to use this sentence as well.

So if three ones add five ones is equal to eight ones, then three tenths add five tenths is equal to eight tenths.

There's the sentence I've just said.

Say it with me as well, on three.

One, two, three.

Is three ones and five ones is eight ones, then three tenths and five tenths is eight tenths.

On a number line, it would look like this.

If we were starting with the larger part, 0.

5, and we were increasing by three tenths, one tenth, two tenths, three tenths, the whole is 0.

8, eight tenths, which we record like that.

In our place value grid, if three ones, join in with me, if three ones plus five ones is equal to eight ones, then three tenths and five tenths is eight tenths.

Good start.

Let's think about it with subtraction.

So I'd like you to use that idea of ones and use that to help you explain, find out how many, when you're working with tenths, what the difference would be.

I say difference because we're now looking at subtraction but we can work from subtracting ones so saying what subtracting the tenths would equal to.

So we're looking for the difference between 0.

9 and 0.

7.

Nine tenths and seven tenths and in our part-whole diagram, that means we're looking for a missing part.

We know one of the parts, we're looking for the other one.

So using that language of ones then, if nine ones subtract good, seven ones is equal to two ones, then nine tenths subtract seven tenths is equal to two tenths.

There's the sentence.

You say it up until the comma and I'll finish it off.

One, two, three.

Then nine tenths subtract seven tenths is two tenths.

Good teamwork.

And we record that as 0.

2.

On a number line, I notice that 0.

7 and 0.

9, they're close together so it would be helpful, maybe more efficient to count up from seven tenths to nine tenths.

There's our two tenths.

That is the different between them.

And in the place-value grid, see if you can join in with the sentence.

If nine ones subtract seven ones is two ones, then nine tenths subtract seven tenths is equal to two tenths.

0.

2.

Okay, let me give you a chance to pause with this one.

Use that idea of ones and tenths to solve the problem.

How did you get on? Hold up for me anything that you've written down.

Oh wow, all drawn, good use of place value counters, everyone.

Fantastic.

Really showing your understanding of what's happening here.

Let's take a look then.

So we've got nine tenths and four tenths.

And we can use to help us find the whole, the sum of those two parts, we can use the idea of ones.

If nine, join in, ones, add four ones is equal to 13 ones, then nine tenths add four tenths is equal to 13 tenths.

There's the sentence that we've just said.

And we record 13 tenths as 1.

3.

Similar approach to last time but with subtraction now, please.

So again, we'll pause and give you a chance to solve it, have a go at drawing some place value counters.

If you didn't before, try it this time.

Press pause, come back when you're ready.

7, one and seven tenths subtract nine tenths.

Let's see, so we're looking for a missing part.

The difference between those two numbers is the missing part.

Let's think about it as ones.

Oh, quite a lot of ones now.

The numbers are getting larger, so there are more ones, more tenths when we're talking about them.

17.

If 17 ones subtract nine ones is equal to eight ones, then 17 tenths subtract nine tenths is equal to eight tenths.

Well done.

Record it as 0.

8.

I think it's time for you to have another pause and have a look at, we've got six addition or subtraction calculations to the left that I'd like you to solve.

Push yourself to use that sentence that we've used all the way through.

It's there on the screen.

And if you're ready for a challenge, choose a calculation, make a deliberate mistake.

Now write a sentence to explain how you would help someone who had really made that mistake.

So some options there for you.

Press pause, come back once you've had a go.

How did you get on? Give me a thumbs up if you managed all six.

Give me a wave if you tried the challenge.

Excellent, really like to see more and more of you.

I'm noticing more and more of you challenging yourself with the ready for a challenge tasks as these lessons have progressed.

Good work.

So here we go then.

I've added there or written the sums, the missing sums or missing differences.

For example, seven tenths and five tenths.

If seven ones and five ones is 12 ones, then seven tenths and five tenths is 12 tenths.

1.

2.

Or the last one, if 15 ones subtract nine ones is six ones, then 15 tenths subtract nine tenths is six tenths, 0.

6.

I really hope you could see how useful that sentence was.

We're just adding or subtracting ones or tenths.

It's the same idea.

We can make those connections across to help us solve the missing sum or missing difference.

Okay, the numbers are going to get bigger now.

And I will leave the sentence at the bottom.

It can still help but we might need to start using some drawings of those flats and sticks, the deans, the base 10 equipment, the flats and sticks to help us.

So I'll give you a chance to have a go at the next one but let me show you what I mean by those flats and sticks and drawings.

So 2.

7, yeah, two and seven tenths, add eight tenths.

There's a lot of tenths there now.

But I notice that if I add those tenths, the seven tenths, the eight tenths together, I'm going to end up with 15 tenths.

Look, as I move three of them across, see that again, watch carefully.

Three of them are moving across.

So we've got 10 tenths and five tenths, 15 tenths.

Well, those 10 tenths I can regroup for one flat, for one.

So I now have three flats, three ones, three and five tenths, 3.

5.

Here's one for you to try.

So you can pause, have a go at maybe drawing some flats and sticks to help represent that's happening when you add these two numbers.

And I've said it before, this is not art.

And I don't expect lots of time spent on the drawings.

So as long as they represent the maths, they represent the numbers we're working with and having a quick look, it's looking good.

Okay, so here's my drawings.

5.

2, five and two tenths add two and nine tenths.

We're going to deal with the tenths first.

I could deal with the ones first but I'm choosing to deal with the tenths.

The two tenths and the nine tenths.

Well, again, watch what happened.

I know that I can combine nine of those tenths and one of those tenths to make 10 tenths, one whole, one flat.

Look again.

So 10 of the tenths are disappearing, regrouped as one whole, as one flat.

So now, I've got seven, eight flats, eight wholes, eight and one tenth, 8.

1.

Give me a thumbs up if you got that too.

Well done.

Okay, subtraction.

Same, again let me show you how I'd approach this and I'll give you a go with the next one.

So the sentence is still there, it can still help us but these numbers are getting larger.

So we need to think about what they look like as well.

So five and three tenths.

Subtract seven tenths.

So I went a bit too fast there.

Let's slow it down.

Five and three tenths and I'm subtracting seven tenths.

I can see I've got three tenths there that I could subtract but I need to subtract seven.

Let me use what I know about those flats.

Each of those flats is 10 tenths.

I can exchange one flat, watch it go, for 10 tenths.

Now I've got 13 tenths.

I can subtract seven tenths, there they go, and I'm left with the difference between 5.

3 and 0.

7.

Four and six tenths.

4.

6.

Here's one for you.

So pause, have a go, use some drawings.

Maybe use the sentence.

See which you prefer as the numbers are getting bigger.

Come back when you're ready to share.

How did you get on? Let's compare, shall we? Five and three tenths.

Notice, I'm not including a drawing of the two tenths because I'm subtracting them.

Two and four tenths I need to subtract.

I've got three tenths.

Same again.

I'm going to need to exchange one flat for 10 tenths.

Did you see that happen? I'll show you again.

One of the flats, which we know is worth 10 tenths, it's worth one, I can exchange it for 10 sticks for 10 tenths.

Now I can subtract four of them.

Four tenths, watch them go.

And what I've got left.

No, what I've got left is not the difference because I've not yet subtracted two.

That's better.

Now I've got the difference between 5.

3 and 2.

4.

2.

9.

Give me a thumbs up if you managed that as well.

Brilliant.

So here's a cloud of numbers.

I would like you to choose any two of them to create an addition calculation or a subtraction calculation.

I haven't said how many to do.

At least six I would say.

If you're ready for a challenge, then I've got some rules for you.

5, more than five, equal to one, or equal to two? The sentence is there to help with your thinking but of course, you can use those drawings as well as we've just been doing for the flats and sticks, the ones and the tenths.

How did you get on? Can I have a look, hold them up? Hold your paper up, let me see the calculations you've written.

Oh and I can see, I think I can see but just so I know for sure, wave your paper gently if you tried the challenge as well.

Really good.

Fantastic.

Now, there are so many alternative addition and subtraction calculations that you could have come up with that we are not going to review this task.

Press pause, have a go at these four additions, use the sentence at the bottom to help.

Ready? Shall we take a look at the solutions.

So that sentence at the bottom with the first one, 0.

3, three tenths add 9/10 is 12 tenths, 1.

2.

It did help.

How about with the 8/10? 8/10 and 26 tenths is 34 tenths, 3.

4.

Seven and seven tenths, that's 77 tenths add 3/10.

77 and three, 80 tenths, eight.

And the last one, 7/10 and 15 tenths, seven and 15, 22, 22 tenths, 2.

2.

Really helpful sentence for working mentally, for adding mentally, subtracting mentally, connecting ones and tenths.

Another fantastic lesson.

Mental addition and subtraction of numbers with tenths.

Really, really pleased with how hard you've all been working.

Well deserved break now hopefully between anymore lessons that you've got lined up for the day.

I'm going to continue, ah ha, with more success, attempting successfully to peel this orange and I will enjoy this now that the lesson has finished.

See you again soon.

Bye.