Lesson video

In progress...

Hi, my name's Mr. Peters, and today we're going to be thinking about column addition and column subtraction and how we can use this to help us when working with decimal numbers.

I'm really looking forward to our lesson today.

Hopefully you are too.

If you're ready, let's get going.

By the end of this lesson today, you should be able to use both column addition and column subtraction when looking to calculate with decimal numbers.

Throughout this lesson, we're going to need some keywords.

Let's have a go at saying them.

I'll say them first and then you can repeat them afterwards.

My turn, decimal number.

Your turn.

My turn, regrouping, your turn.

My turn, place value, your turn.

Let's have a think about what these mean in a little bit more detail.

So a decimal number is a number that has a decimal point within it, and this decimal point separates the whole numbers from the fractional parts.

A decimal number will have digits after the decimal point, which represent these fractional parts.

When we think about regrouping, we're talking about a process, and in this process we think about unitizing and exchanging place values for another place value.

For example, we could regroup 10 ones for one 10, or we could regroup one 10 for 10 ones.

And finally, place value.

We think about place value with regards to where a digit is placed within a number, and therefore that defines the value that that digit has within the number.

Okay, so let's think about our lesson for today then.

We're gonna break this lesson down to three parts.

The first part of our lesson is thinking about using column addition when working with decimal numbers.

In the second part, we're gonna be thinking about subtracting using column subtraction with decimal numbers.

And then finally, in the last part, we're gonna look to solve a range of problems using both column addition and column subtraction.

Let's get going with the first part.

In this lesson today, you'll also meet Jacob and Alex.

Okay, so we start this lesson today with a problem.

On Monday, a gardener digs up 2.

5 kilogrammes of potatoes.

On Tuesday, she digs up another 1.

3 kilogrammes of potatoes.

How many kilogrammes of potatoes has she dug up altogether? Hmm, Jacob's having a think.

He's wondering, how can I solve this problem? Take a moment for yourself.

How do you think you would have a go at solving this problem? Jacob's gonna draw a bar model to help him.

He's drawn a bar here with 2.

5 kilogrammes in it.

And he says this blue bar represents the potatoes that were dug up on Monday.

He's now drawn a second bar, it has 1.

3 kilogrammes there.

He says that this represents the potatoes that were dug up on the Tuesday.

And then finally at the top he has the whole.

So far we've had two parts.

We've had Monday's potatoes, which acts as the first part, and we've had Tuesday's potatoes, which act as the second part.

And now we need to think about combining both of those parts to find our whole.

And that is what the question mark is in our bar at the top.

So as Alex has pointed out, we need to add these values together and the bar model helps us to see that we need to use addition to help us here.

Jacob feels that we could do this mentally, and we don't need to write this down.

We could do 0.

5 kilogrammes plus 0.

3 kilogrammes.

Hmm, well that's five tenths of a kilogramme plus three tenths of a kilogramme, which would be equal to eight tenths of a kilogramme.

We could then add the whole kilogrammes together.

So we've got two kilogrammes plus one kilogramme, which would be equal to three kilogrammes.

And then we need to combine both of them together.

We need to add the wholes with the fractional parts.

So we had three kilogrammes and then we also had the eight tenths of a kilogramme.

So, all together the gardener would've dug up 3.

8 kilogrammes of potatoes.

Now, whilst we did that mentally, we could also represent it in a column addition.

In order to do so, we need to lay this out correctly.

First of all, we're going to line up our ones.

The first number was 2.

5, so that had two ones and the second number was 1.

3, so that had one one.

Then we need to place our decimal points within our column addition.

What do you notice about them? That's right, they've been placed between the two numbers that we're writing so far, but there's also an additional one that's been placed in our answer within the equal sign.

And that's really important that we don't forget that one, because our answer is also going to need a decimal point.

Now we're gonna line up our tenths.

The first number was 2.

5, so we had five tenths.

The second number was 1.

3, so we had three tenths.

And then finally, it's really important that we also place our units.

So our column addition now reads 2.

5 kilogrammes plus 1.

3 kilogrammes is equal to something point something kilogrammes.

We can now work through this together.

Let's start with the smallest place value, which in this case would be the tenths.

Five tenths plus three tenths is equal to eight tenths.

Now we move to the next place value.

Two ones plus one one is equal to three ones.

The gardener altogether dug up 3.

8 kilogrammes, which is exactly what we said when we worked it out mentally.

Now our problems changed slightly.

Have a look at this one.

The next week a gardener dug up 3.

6 kilogrammes of carrots.

Her neighbour next door dug up 1.

8 kilogrammes of carrots.

How many kilogrammes of carrots did they dig up altogether? Jacob's drawn a bar model again.

He said that the blue bar represents the carrots that were dug up by the gardener.

He's then used a yellow bar to represent the carrots that were dug up by her neighbour.

And we are trying to find the total amount of carrots.

Therefore, we are looking to find out what the whole is.

So it looks like we're going to need to add again, aren't we? Alex is saying that he thinks he could do this calculation mentally as well.

He starts off with naught 0.

6 kilogrammes plus 0.

8 kilogrammes is equal to 1.

4 kilogrammes.

At six tenths of a kilogramme plus eight tenths of a kilogramme is equal to 14 tenths of a kilogramme.

And we can write that as 1.

4 kilogrammes, can't we? He then adds the ones, three kilogrammes plus one kilogramme is equal to four kilogrammes.

And then altogether he would add the tenths and the ones.

So we've got 1.

4 kilogrammes plus four kilogrammes is equal to 5.

4 kilogrammes.

Jacob is saying that whilst he feels that he might have been able to do that mentally, actually he had quite a bit to remember.

He had to remember what he regrouped those tens for and how many tenths were left each time.

Maybe he feels that he could go and write it in a column addition instead.

Let's have a look how that would be represented.

Six tenths plus eight tenths is equal to 14 tenths.

And now we're going to need to regroup 10 tenths for one whole.

Let's have a look at that.

Here we have six tenths, and then here is an additional eight tenths.

You can see that my tens frame is now full.

That represents 10 tenths, which is the same as saying one whole.

And then I've also got four tenths remaining.

When we record this in our column addition in can see now that we've placed the four remaining tenths in the tenths column and then the one whole or the 10 tenths that we regrouped to make that one whole has been placed in the ones column underneath the equal sign.

Now we need to add the ones, three ones plus one one is four ones, but hang on, we've got that additional one underneath the equal sign as well, haven't we? And we need to bring that back into play.

So actually it would be three ones plus one one plus another one, which would equal to five ones.

So altogether the gardeners had 5.

4 kilogrammes of carrots that they dug up.

Here's one more for us to have a look at.

In October, the gardener dug up 12.

3 kilogrammes of carrots altogether.

Throughout the whole month of October her neighbour dug up only 4.

8 kilogrammes of carrots.

And again, we're asking how many kilogrammes did they manage to dig up altogether? Jacob is asking, Hmm, what'd you notice about the numbers this time? That's right, one number actually has three digits in it doesn't it? And the other number only has two digits in it.

I wonder how we'd represent this in a column addition? Jacob was saying it's gonna be really important to make sure that we line up our place values correctly.

Let's give this a go.

So first of all, we're gonna start with the tens this time.

The first number was 12.

3 and 12.

3 has one 10.

So we placed the one 10 in our column addition like so.

The other number 4.

8 didn't have any tens.

So we leave that blank.

We then start thinking about the ones, well the first number was 12.

So again, this has two additional ones.

We placed the two next to the 10, and then our second number 4.

8 had four ones.

So we placed that underneath the two ones from the 12.

Then we start thinking about our decimal points again.

And remember we placed them all the way through our column position here, including in the equal sign.

As this is where it's gonna separate our whole numbers from our fractional parts.

Then we start thinking about those fractional parts Our tenths, here 12.

3 has three tenths and the 4.

8 has eight tenths.

So we place the three next to the 12 to make 12.

And we place the eight next to the four to make 4.

We also need to include our units, don't we? As always, we're gonna start working with the tenths first.

Three tenths plus eight tenths is equal to 11 tenths.

Hmm, 11 tenths.

We're gonna have to regroup again, aren't we? 10 tenths are going to need to be regrouped for one one.

And that would leave us with one remaining tenth.

Now we need to add our ones, two ones plus four ones is equal to six ones.

But don't forget we've also got the additional one underneath, which was from the regrouping.

So now we have seven ones.

And then finally we work with the tens.

Well 12.

3 has one 10, but 4.

8 doesn't have any 10.

So one 10 plus zero 10 is equal to one 10.

And then we can say altogether that the gardeners dug up 17.

1 kilogrammes of carrots over the whole month of October.

Okay, time for you to check your understanding now.

Which column addition has been correctly drawn out? Take a moment to have a think.

That's right, it was C, C has been drawn correctly.

Alex is asking for us to have a look at A and B and start to unpick well why A and B have been drawn incorrectly.

Well in A, we can see that our place value columns haven't been lined up correctly and neither have our decimal points.

The decimal points are not in one straight vertical line, which are separating the ones from the fractional parts.

And let's have a look at B.

What did you notice? Ah, I see there's a decimal point missing between our ones and our tenths in our answer isn't there? Within the equals sign.

So we would need to make sure that the decimal point was placed in there, 'cause our answer is not 57, it's 5.

Here's another opportunity for us to check our understanding and to have a little bit of practise as well.

I'm gonna have a go at laying out the equation on the left hand side first and then you are gonna have a go at laying out the equation on the right hand side.

Let's go through mine first.

So first of all, we're gonna write in our ones, two ones and three ones, and we line them up in the same column.

We then need to place in our decimal points remembering that goes into the equal sign as well.

And then we're gonna line up our tenths.

And you can see here that we've got five tenths and seven tenths.

Then having a go at solving this, well five tenths plus seven tenths is equal to 12 tenths.

And I know that 'cause five and seven is equal to 12, but five tenths plus seven tenths equaling 12 tenths means that we need to regroup, don't we? We've got 10 tenths which would be equal to one whole.

And then we've got an additional two tenths.

So we place the 10 tenths or the one additional whole underneath the ones column.

And then we place the two additional tenths that are remaining in the tenths column.

Now we can calculate our ones.

Two ones plus three ones would be equal to five ones.

But then we've also got the additional one underneath.

So that would make six ones, so the answer would be 6.

Okay, now is your turn.

Have a look on the right hand side here.

Can you have a go at laying out your column addition correctly and then solving it too? Have a go.

I'll see you in a second.

Okay, let's have a look.

Let's start off by lining up the ones of course.

Then we're gonna place the tenths.

Now we can see that our column addition is saying 4.

6 plus 1.

Let's have a go at solving it.

Six tenths plus nine tenths is equal to 15 tenths.

We're going to need to regroup 10 of those tenths for one whole.

Then we move on to adding the ones four ones plus one one and the extra one is going to equal to six ones.

So altogether our calculation would equal 6.

Well done if you managed to get that.

Okay, now we're on to our first opportunity for you to practise.

Here I've left you three calculations.

I wonder if you could have a go at using column addition as it's laid out to solve each of these.

Once you've done that, here's another task.

I've given you three more calculations but I haven't laid it out correctly in column addition for you.

So your task is not only to lay it out correctly but then also to solve it.

And finally, a little opportunity for you to really deepen your understanding of column addition here.

I've given you a column addition laid out and I've given you the sum of our column addition of 7.

5, but I haven't given you the two add-ins that you need to add together.

So using the digits zero to nine only once, I want you to have a go at finding two add-ones that would add together to make 7.

And then think how many different ways could I solve this as well? Can I find more than one solution? Jacob's just reminding us on the left hand side that although that there has been a seven and a five already used, you can use those numbers once more as well.

Once you found plenty of solutions, have a think about this.

What do you notice now? Ah, well actually I've given you a regrouped one here, haven't I? I wonder if that would fit with any of the solutions that you might find.

Maybe it might give you some more solutions to find.

Good luck and I'll see you again shortly.

Okay, welcome back.

Here are the answers to our first task.

Okay, let's line up our calculations correctly here.

So we can see now we've got 2.

6 plus 3.

3 lined up.

Six tenths plus three tenths equal to nine tenths.

And two ones plus three ones is equal to five ones.

So our total would be 5.

Three tenths plus six tenths equal to nine tenths and four ones plus two ones is equal to six ones.

So our total would be 6.

And then the last one, what did you notice here? One of the numbers has three digits and the other one has two.

So you have to think carefully about lining up these place value columns.

First we line up the tens, there's only one of those.

Then we line up the ones, the four and the two.

Then we line up our decimal points.

And then we line up our tenths, the three and the six.

Three tenths plus six tenths is equal to nine tenths.

Four ones plus two ones is equal to six ones.

And then one 10 plus zero tens is equal to one 10.

So that would be 16.

Okay, I wonder how many different solutions you found for this.

Alex has given us one solution here.

I wonder how many you found? If you're able to, maybe compare your solutions with somebody nearby to you.

Were there any that you missed? Did you manage to find all of the solutions? How do you know you found them all? Well done if you managed to get all of those.

Okay, let's move on to the second part of our lesson then.

Subtracting decimal numbers using column subtraction.

We've got another problem here.

Alex has to travel 3.

7 kilometres to get to school.

He travels by car for 2.

3 of those kilometres and then he travels the rest of the way using his bike.

How far does he have to cycle? Alex is gonna represent this as a bar model.

He says the whole distance that I travel is 3.

7 kilometres.

He says a part of the way that I travel is represented by the blue bar and the blue bar is how far he goes by car.

And then the yellow bar this time represents the remaining part how far he needs to travel by bike.

We can see from our bar model here, we need to find the difference between the whole and the blue bar, which would be the yellow bar.

So we're going to do 3.

7 kilometres minus 2.

3 kilometres and that should give us the remaining part.

Alex again thinks he could probably do this mentally.

Let's have a look.

Seven tenths of a kilometre minus three tenths of a kilometre is equal to four tenths of a kilometre.

And then three kilometres minus two kilometres is equal to one kilometre.

We then need to bring those back together.

So one kilometre plus the 0.

4 kilometres would be equal to 1.

4 kilometres.

So we've worked out that Alex would need to ride his bike for 1.

4 kilometres to make sure he got to school.

Again, Jacob is saying we could also represent this as a column subtraction.

We're gonna work very similarly to how we did with the column addition in terms of how we line up our columns.

First we're gonna line up our ones, then we line up our decimal points and again that goes all the way through into the equal sign and then we line up our tenths.

So now our equation reads 3.

7 kilometres minus 2.

3 kilometres is equal to something kilometres.

Okay, let's recalculate this.

Starting with the smallest place value, which is our tenths.

Seven tenths minus three tenths is equal to four tenths.

And then we work with the ones, three ones minus two ones is equal to one one.

One Alex has to ride 1.

4 kilometres by bike.

Our problems changed again here, have a look carefully.

On Friday, Alex travelled his usual 3.

7 kilometres to go to school.

However this time he travelled 2.

9 kilometres by car.

How much further did he have to travel by bike this time? Well have a look at our bar model.

What do you think might need to change from our bar model this time compared to the previous one? That's right.

He travelled further by car this time, didn't he? So the size of our blue bar is going to increase and the size our yellow bar is going to decrease.

Let's have a look at that.

Actually we know now that the missing part that we are looking for is gonna be smaller than the missing part that we had before because the whole stayed the same didn't it? Alex is now looking at the tenths digit.

He says the whole has seven tenths and the part that he's subtracting has nine tenths.

That means he's going to need to regroup again.

'Cause he is not gonna have enough tenths.

So initially to subtract the nine tenths.

So Jacob's suggesting it might be quite practical to record this as a column subtraction.

Let's work through this.

First we start with the tenths don't we? Seven tenths minus nine tenths.

So we don't have enough tenths in the tenths column to subtract the nine tenths, do we? So we're going to need to regroup one one for 10 tenths.

Let's have a look at how we can do that.

So at the moment we have three ones.

If we take one of those ones, we'll now be left with two ones and we regroup that one one for 10 tenths and we place that now in the tenths column.

So the little one next to the seven represents 10 tenths, and the seven represents seven tenths, so altogether we have 17 tenths.

Now we can subtract the nine tenths.

17 tenths minus nine tenths is equal to eight tenths.

Now we can work with the ones.

So two ones minus two ones is equal to zero ones and therefore the difference, the amount he needed to travel by bike was 0.

8 kilometres.

Have a look at this problem as well.

In total over one week, Alex needs to travel 18.

5 kilometres to get to school.

If he travelled 6.

8 kilometres by bike, how far would he need to travel by car? Hmm? What would you notice this time about the numbers? That's right again, one of our numbers has three digits and one of our numbers has two digits.

And I wonder how we can line this up in a column subtraction? Well there we go.

It's really important that we line up the place values correctly within their columns.

I wonder if we could calculate this together.

We start with the tenths.

The smallest place value, five tenths minus eight tenths.

Do we have enough tenths at the moment in this column to subtract these eight tenths? We don't do we? So we're going to need to regroup again from the ones.

At the moment there are eight ones.

And we're going to regroup one of those ones for 10 tenths.

So that would leave us with seven ones.

And now we can place that regrouped one, which now acts as 10 tenths in the tenths column.

15 tenths minus eight tenths is equal to seven tenths.

Now we work with the ones.

Seven ones minus six ones is equal to one one.

And finally the tens, one 10 minus zero tens is equal to one 10.

So the total distance that Alex needs to travel by car for this week altogether would be 11.

7 kilometres.

Not forgetting those units that are placed next to each row in the column subtraction.

Time again for you to check your understanding.

Have a look at the column subtraction that Alex has laid out, there is a mistake.

Can you spot it? I'll give you a moment to have a think.

Yes, well spotted, he hasn't lined up his decimal points correctly again, has he? which hasn't then helped him to line up his place values correctly.

So the 3.

6 needed to be moved one column to the right in the second row.

As Jacob was pointing out, lining up the decimal points is really helpful to make sure that you get your place values in the correct columns.

And there we go.

That's how it should have been represented.

Three tenths minus six tenths.

Again, we don't have enough tenths in this column, so it's gonna require a regrouping.

So we regroup one one for 10 tenths.

Now we have 13 tenths minus six tenths equal to seven tenths.

Six ones minus three ones is equal to three ones.

And five tens minus zero tens is equal to five tens.

Have another check for your understanding.

Which calculation might be the best one to use for column subtraction? That's correct.

It's B.

Why option B? Well, if we look at the digits, it starts in the tenths column doesn't it? And we need three tenths minus seven tenths.

And again, we don't have enough tenths here, so we require a regrouping and where we need to regroup with column subtraction, it can be a good idea to record it written down.

Okay, an opportunity for you to practise now.

For task one, I'd like to have a go at writing out these calculations and putting them into column subtraction for me and then solving them as well.

And for task two, I'd like you to have a go at completing the calculations which I've already laid out for you.

And when you're doing that, I want you to think about what is it that you notice each time and why is this happening? Good luck and I'll see you again shortly.

Okay, welcome back.

How did you get on? Let's have a look through these then shall we? The first one, 5.

6 minus 2.

That left us with 3.

15.

6 minus 2.

Well again, that left us with five in the tenths.

That left us with three in the ones.

And this time we had a 10 didn't we? So one 10 minus zero 10 is equal to one 10.

So that leaves us with 13.

And then finally the last one, again leaves us with five in the tenths.

This time it leaves us with three in the ones again.

Ah, but here we've got one 10 minus one 10 is equal to zero tens.

And I've placed a zero here.

Do we need to place a zero here? No, you're right.

We don't need to place a zero here before the first whole number.

And the second task.

Let's have a look at these, shall we? Hmm? Well we don't have enough tenths do we to start off with to subtract the five tenths that we need to.

So we're going to need to regroup.

So we regroup here.

That leaves us with 14 tenths now because we've regrouped one one for 10 tenths, 14 tenths minus five tenths is nine tenths, two ones minus two ones equal to zero ones.

And the second one, 3.

5 minus 2.

This time we've got five tenths that need to subtract six tenths.

That means we don't have enough tenths again.

So we're going to do another regrouping.

Now we've got 15 tenths minus six tenths, which is equal to nine tenths.

And again, two ones minus two ones is equal to zero ones.

Hmm.

Are you're starting to notice something here? The final calculation, this time we've got seven tenths and we're minusing eight tenths.

Again, we don't have enough tenths at the moment, so we need to regroup, now we have 17 tenths minus eight tenths, which is equal to nine tenths.

And then finally two ones minus two ones again equal to zero ones.

Hmm.

Look at our answers.

What is it that you noticed? Alex is saying that he noticed that all of our answers were 0.

Well why was that? Well if you have a look at the numbers in our calculations, the initial numbers we had were 3.

4 and 2.

Then this next set of numbers were 3.

5 and 2.

What did you notice has changed there? That's right, they've both increased by one 10th.

Then let's have a look at the last two calculations.

We've got 3.

5 and 2.

6 and then the last one is 3.

7 and 2.

What did you notice this time? Oh yeah, actually those numbers increased by two tenths each time.

So I wonder, have we got a bit of a generalisation coming here? Alex is saying it's because the number of tenths that I've started with and subtracted increased by the same amount each time.

So building towards the generalisation here, where we increase the size of the whole and we increase the size of the number that we're subtracting by the same amount, then the difference will always remain the same.

While I've done a few managed to spot that.

Okay, now we're into the last part of our lesson.

We're thinking about solving additive problems. So either addition or subtraction problems now with our decimal numbers that we've been working with.

Here's our first problem.

Sydney the snake was 3.

6 metres long, after one year he was 1.

1 metre longer.

And one more year on after that he was another 0.

3 metres longer.

So how long is Sydney the snake now? Now Alex has drawn this as a bar model.

He's now asking what do each of his bars represent? Well the blue bar, the 3.

6 metres represents how long Sydney the snake was initially.

Then the yellow bar, the 1.

1 metres represents how much he grew the year after.

And the 0.

3 metres in the red bar represents how much he grew the year after that.

And therefore it looks like we're going to need to add all of these bars together to find the total amount that Sydney grew altogether.

Alex is saying that he feels that he might be able to do this mentally, but he's going to write it in a column addition to help us see how we would represent this.

Working through this then we're gonna start with the smallest place value.

Six tenths plus one tenth is equal to seven tenths plus another three tenths is equal to 10 tenths.

Hmm, 10 tenths means we can continue to regroup it, aren't we? We're gonna regroup 10 tenths for one one.

And we're gonna place that underneath the ones column.

We don't have any additional tenths remaining.

So we place a zero in the tenths column.

Now we work with the ones three ones plus one one is equal to four ones plus an additional one would be equal to five ones.

So altogether sitting the snake was 5.

0 metres long or we could just say five metres, can't we? Okay, here's another problem for us to think about.

A dress maker has 5.

2 metres of blue ribbon and 2.

6 metres of red ribbon.

How much more blue ribbon does she have then red ribbon? Have a look at Alex's bar model.

What does each part represent? Well that's right, the 5.

2 metres in the blue bar represents the blue ribbon.

And the 2.

6 metres in the red bar represents the red ribbon.

The green line represents the difference between the blue ribbon and the red ribbon.

And this is what we're trying to find out, how much more blue ribbon is there than red ribbon.

Alex has represented this for us now in a column subtraction, let's work through that starting with the smallest place value as always.

Two tenths minus six tenths.

Hmm, we don't have enough tenths do we? So we're going to require a regrouping.

So we're gonna regroup one one for 10 tenths, which will leave us with four ones.

And those 10 tenths will now be placed in the tenths column to make 12 tenths.

12 tenths minus six tenths is equal to six tenths.

And four ones minus two ones is equal to two ones.

That means we have 2.

6 metres of blue ribbon extra compared to the red ribbon.

If you feel really confident with your column addition and column subtraction, then solving missing number problems is a really good way to deepen our understanding even more so.

Let's have a look at these examples here and work through these.

Starting on the left with the column subtraction, seven point something minus something 0.

6 is equal to 2.

Hmm, so as always, I'm gonna work through this from right to left starting with the smallest place value.

Something tenths minus six tenths is equal to two tenths.

Well Jacob knows that six and two is eight, so therefore eight must be the missing number.

Eight tenths minus six tenths is equal to two tenths.

Let's look at the ones, seven ones minus something ones is equal to two ones.

Do you know a number fact that can help you with that? Seven minus something is equal to two? Hmm.

Oh it must be five, seven ones minus five ones is equal to two ones.

So therefore the second number must be five that was missing.

Let's look at the second one.

Three tenths plus eight tenths, well that's 11 tenths.

If that's 11 tenths, that means we need a regrouping.

So that means I'm gonna need to place 10 of those tenths underneath the ones column 'cause I've regrouped that now for a one one.

And that would leave me with an additional one tenth.

Now we can work out the ones hopefully.

Two ones plus something ones is equal to six ones.

Hmm, well is that four? Two ones plus four ones equal to six ones it would be, but oh, don't forget we've got the one underneath that we would've had as well.

So we've got two ones plus one one and we need to add three ones with something now to make six ones.

So actually the missing number would be three wouldn't it? That's made us think even harder, hasn't it? Okay, and moving on to our last set of tasks for today's learning.

Question number one is asking you to solve these worded problems. There are four of these, A, B, C, and D.

Question number two is asking you to have a go at some of those missing box problems. And question number three, I've given you a little pyramid here where two boxes are next to each other.

Both of those boxes need to add together to make the number that would go in the box above it.

So for example, if I have 2.

8 in the bottom left hand corner of the box and I placed a one in the middle box in the bottom row, 2.

8 plus one would be equal to 3.

8 and I therefore need to write 3.

8 in the box above both of those.

Have a go and see if you can find a way to solve the pyramid.

Good luck and I'll see you again shortly.

Okay, so let's work through these then.

Alex and Laura and the first one were picking cherries, weren't they? Alex picked 0.

5 kilogrammes and Laura picked 1.

2 kilogrammes and it asked us how many they picked altogether.

Well we needed addition for that, and the answer would've been 1.

7 kilogrammes.

It then goes on to say that Laura picks another 1.

4 kilogrammes.

So we need to add the amount that we just had, with the additional 1.

4 kilogrammes that Laura has picked.

Andy had a 1.

5 litre bottle of water and he drunk 0.

7 litres of it.

So the question then became how much did he have left? So we needed subtraction for this, and that left us with 0.

8 litres of water.

And finally Sophia cycled 2.

4 kilometres at the weekend and Jacob cycled 1.

5 kilometres at the weekend.

And the question was asking us what was the difference between the amount that Sophia cycled compared to Jacob.

So 2.

4 minus 1.

5 and that's left us with 0.

9 kilometres.

Okay task two then, we had to fill in the missing numbers here, didn't we? Let's have a look, see if you managed to get the same ones.

The first one, the missing number was two in the tenths column and the missing number was three in the ones column.

In the second one we needed to regroup, didn't we? So the first missing number was a two, which was a part of 12 tenths.

We then had to place the additional regrouped tenths underneath the ones column to make an additional one.

Therefore the five is required here, there's five ones and three ones which would give us eight ones plus the additional one one which would be nine ones.

And then the last one, this one was a little bit trickier 'cause we started with seven tenths and we finished with eight tenths.

But we're subtracting, which means actually that's not going to be possible unless we regroup.

So we need to regroup straight away, and make it into 17 tenths.

17 tenths minus something was equal to eight tenths where we know that could now be nine.

Then we've got a regrouping and we don't know what number we had originally to start off with.

So we have something and then we minus three ones which ended us up with zero.

Well, three ones minus three ones would be equal to zero ones.

But remember we'd already regrouped, didn't we? So the starting number wasn't a three, the starting number would've been a four.

Okay, and the last one here was the solution.

Alex said here that 2.

8 and 2.

4 in the bottom row were then nearly 2.

5 and if you add that with another 2.

5, that would make roughly five.

And if the numbers above in the second row were both fives and they would then therefore both make a 10.

So he knew that the number at the bottom in the middle needed to be roughly two point something to get the numbers in the second row close to being fives.

As you can see, they're not exactly five, but they were close to, they were 5.

2 and 4.

8 that gave us our 10.

Okay, well done for taking part in this lesson today.

Hopefully you've been able to extend your understanding of column addition and subtraction and now feel confident in applying this when working with decimal numbers.

So to summarise our lesson today, you should have been able to use column addition and column subtraction to solve problems with decimal numbers.

When working with column methods, we need to make sure that we line up our columns correctly into the correct place values, including making sure our decimal points are all lined up correctly.

And finally, whilst we felt we could work out some of these calculations today mentally, where one or more regroup might be required it's probably worthwhile writing it as a column method to help you record your thinking.

Thanks for learning with me today.

Hopefully you've enjoyed yourself and I've got something new to take away from it.

Take care and I'll see you again soon.

I've finished the video