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Hello, everybody, welcome back.

This is the next lesson in the "Number, Addition and Subtraction" series of lessons.

I'm Mrs. Furlong, you might remember me from last week.

I'm going to be taking over for Mrs. Moe for the next two days.

So we're on to lesson three of "Deepening Understanding of Equivalents "and the Equal Sign In Addition and Subtraction." Yesterday, Mrs. Moe left you with these questions to practise.

And we're going to start today's lesson by reviewing those questions.

So in question one, you were asked to fill in the missing numbers.

I noticed a connection between 11,997 and 12,000, did you spot it? That's right, 11,997, if it's increased by three, will get us to 12,000.

So if one addend has been increased by three, the other addend has to be decreased by three, that's right? So our 64,036 becomes 64,033.

I think this is much easier to calculate than the original calculation.

So I'm saying that 64,033 plus 12,000 is easier to calculate, what do you think? That's right, we only need to pay attention to the thousands and tens of thousands columns to be able to do this using place value.

We really just need to look at the 64 in the 64,033 and the 12 in the 12,000.

And I know that 64,000 and 12,000 gives me 78,000.

I mustn't forget there's 33, they're very important.

So the next set of questions that Mrs. Moe left you was part two, which was to look at the calculations and decide which ones you would use redistribution for, and explain why.

Well, I was thinking about the purpose of redistribution in the previous lesson, and that was to make calculations easier, wasn't it? So let's take a look at A: 12,036 add 32,873.

I think to make these easier, Ideally I'd want to get them to either a multiple of a hundred or a multiple of a thousand.

So if I look at 12,036, I could decrease that by 36 to get me to 12,000, and I could increase 32,873 by 36.

But, this is meant to be a mental calculation method.

And I'm thinking by the time I've done all of that hard work, it might've been easier just to do a column calculation in the first place.

I equally, I could look at the 32,873 and think hmm, I could make it into 32,900.

But again, I would need to increase it by 27, and decrease the other number by 27.

And by the time I've done all of that redistributing, I still think I'd have been quicker to do a column calculation.

And this is meant to make a mental calculation easier.

And I think those numbers are just a little bit too much redistribution, what do you think? So let's take a look at part B: 504,992 add 11,008.

Hmm, take a close look at this, I wonder whether you noticed what I noticed.

I noticed that 504,992, it's actually really close to 505,000.

In fact, I only have to increase it by eight, and decrease the 11,008 by eight.

And then you can see, I've got myself a really easy calculation, 505,000 add 11,000 is 516,000.

That one's a really good one to redistribute.

I wonder if you thought the same.

Let's take a look at part C now.

25,317 add 22,997.

The second addend really jumped out at me.

22,997, that's almost 23,000, isn't it? In fact it's only three away.

So, if I increase that second addend by three, I must decrease the first addend by three to make sure that my sum remains the same.

I wonder if you did what I did.

SO look, here we are, we get 25,314, that's three less than 25,317.

And we get 23,000, which is three more than 22,997.

Now I've got an easy calculation, and I can find out that it is 48,314.

The final question, 99,164 add 8,419.

I took a really careful look at these numbers.

But I think both of them are quite far away from either helpful multiple of a hundred or multiple of a thousand.

So I decided not to use redistribution.

I don't know whether you did the same.

I wonder how you explained it.

So in the last set of questions, Mrs. Moe asked you to have a look at the equations and decide if they were correct.

And then explain how you know.

So let's have a look at A, we've got 7,644, add 21,996 is equal to 7,648 add 22,000.

So I had a look at the first addend, in A, that's 7,644, and notice that it has increased by four to get 7,648.

I then had to look at the second addend.

So the 21,996 had increased by four to get 22,000.

Hmm.

Our generalised statement was, if one addend is increased by an amount, and the other addend is decreased by the same amount, the sum remains the same.

Did you spot what had happened here? Yes, you're right, both addends have increased by four.

And if you think back to the first lesson Mrs. Moe did on this, with things like the water, where one jug increased by a little whilst the other decreased or with her sweets, one bowl of sweet got less, and the other bowl of sweets got more to get that sum to remain the same.

In this case, if we've increased both of those addends by four, we're going to have increased our sum, aren't we? Let's take a look at question B now.

123,017 add 4,999 gives us a total of 128,017.

Hmm.

Well, I've noticed that the 17 in the tens and the ones is the same in the first addend and in the sum.

Hmm.

And I'm not adding on a multiple of 10 or a hundred, so I'm wondering, can that remain the same? Let's a look at my thinking.

So my explanation was, that 123, 017 add 5,000 would give me 128,017.

So therefore, 123, 017 add 4,999, which is one smaller must give me a sum, that is one smaller, so 128,016.

So neither of those calculations were correct, were they? I wonder how you got them.

I hope you did well.

Okay, so now we're ready to start today's session.

You might need to get yourself some paper and a pencil.

And if you haven't already done that, pause the video now and go and find some.

Okay, so today's session, we are going to be again, looking at those addends and using our generalised statements of increasing one addend and decreasing the other addend by the same amount, to make sure that our sum remains the same.

But in our context today, we're going to be thinking about decimal numbers.

So I just wanted to do a quick reminder about those before we get started.

So in my presentation today in this lesson, you're going to see that this blue square is representing one, it's not representing 100 like you might've met before in other lessons and maybe at school, it's representing one.

So one large blue square represents one, okay? So just remember that.

All right.

Then, we need to think about this rod, okay? This rod in this session, 10 of those rods are going to make one, aren't they? If you imagine 10 of those green rod side-by-side, they would be the same size as the one.

So this rod is representing 0.

1 or one tenth.

And finally, this little yellow cube is going to represent one hundredth or 0.

01.

You need to remember that for today.

There's going to be a little bit more about this on the next slide, just to make sure you fully understand.

Okay, so just to make sure that everybody understands and everybody's clear, we're just going to spend a little bit longer looking at these rods.

Can you remember what this green rod is worth in today's session? That's right, it's one tenth or 0.

We're going to count in tens now.

I'd love it if you joined in with me.

One tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths and tenths.

What new about 10 tenths? That's right, you did a lot on this in the previous sessions when you were doing fractions.

10 tenths is equivalent to one, okay? So 10 tenths is the same as one.

So, we can also say that it's 10 multiplied by one tenth or 10 multiplied by 0.

1 is the same as one as well.

Can you remember what this small cube's worth in today's session? That's right, it's worth one hundredth.

Can you count with me? One hundredths, two hundredths, three hundredths, four hundredths, five hundredths, six hundredths, seven hundredths, eight hundredths, nine hundredths, 10 hundredths.

What is 10 hundredths the same as? Exactly, the same as my green rod, my one tenths.

So one hundredths equals one tenth or 10 lots of 0.

01, is also equal to add 0.

1, which we all know is the same as one tenth.

Just keep those in your head today 'cause it will really help you with some of your work.

So this is going to be our first calculation in today's session, 4.

5 add 2.

Have a look at the representations that I've done.

Can you see where the four is on the representation? That's right.

So, these four ones represent our four in our calculation here.

And, can you find where the 0.

5 is? Yup, that's right, you found them here our five tenths are here, aren't they? Brilliant.

And what do these over here represents? That's right, there are two ones.

And here? There are our nine tenths in this part.

Brilliant.

Okay, so we know that we can work out 4.

5 add 2.

And some of you might've been doing that whilst I was just explaining the representation.

In fact, I bet some of you did.

So we could work it out with a column, we could work it out using some kind of a mental method.

But, what if we consider our generalised statement? If one addend is increased by an amount, and the other addend is decreased by the same amount, the sum remains the same.

Hmm, have a look at the numbers, before using that redistribution property, which number would you increase? And which number would you decrease? And why? You might want to pull us the video for a moment here and have a think.

Did you make a decision? I wonder whether your decision was the same as mine, we'll find out in a moment.

I wonder, did any of you tried to increase the 4.

5, the first addend? If you did, did you decide that making the 4.

5 into five would make the calculation easier? Let's take a look.

So, oh, did you see what happened there? Did you see that from the 2.

9, five tenths moved over to the 4.

5 so that we have increased our 4.

5? What we increased it by? That's right, there's five tenths moved over so we've increased it by 0.

We've increased 4.

5 by 0.

5, and we've decreased 2.

9 by 0.

It's a bit like on that first session where Mrs. Moe moved those sweets in that bowl, isn't it? One bowl decreased and the other increased.

It was important that we focused on that 4.

5 then, and how much we needed to increase it by.

We increased it by five tenths to make it into five ones.

Can you see hear that we now have one tenths in those green strips that we looked at earlier, didn't we? We said 10 tenths is the same as one whole or one.

So we now have five one on the left hand side is our left-hand addend, and we now have 2.

4 on that right-hand side.

And I think that five add 2.

4 is quite an easy calculation.

I wonder if you agree.

Five add 2.

4, 7.

And because we have to know our increasing of one addend and decreasing the other by the same amount, our sum remains the same.

So that can help me now to answer 4.

5 add 2.

9, which is also 7.

I could also represent like the calculation at the bottom of the screen.

And you can see that they're side by side.

So 4.

5 add 2.

9 is equal to five add 2.

4, which is equal to 7.

Everything's balanced, our sums have remained the same so our equal sign is being used correctly.

Perhaps you didn't do that.

Perhaps you looked at these two numbers and you decided to focus on the 2.

I wonder why.

Oh, because 2.

9 is almost three, isn't it? How far away from three is 2.

9? That's right.

, it's just one tenth away.

So if I was to increase 2.

9 by one tenth, then I would make three.

And the only place I can get that one tenth from is from my 4.

So just have a look and look at the animation.

There we go.

One tenth went across from the 4.

5 and it landed on the 2.

9, it redistributed.

So can you see now that we decreased 4.

5 by one tenth, and we increased 2.

9 by one tenth.

And what did we get, if we swapped it? So, at this side here, we now have 10 tenths, don't we? And we neutrally.

And remember 10 tenths is equivalent to one whole, so at this side, we don't have 2.

9 anymore, we have three.

And at the other side, we don't 4.

5 anymore, that addend is now 4.

4 Aha, 4.

4 add three, I think that's quite easy, do you? Yeah, that's right, it's still 7.

And that means that our sums remain the same, and so 4.

5 add 2.

9, it's also 7.

And you can see again that the calculation at the bottom of the screen or the equation, 4.

5 add 2.

9 is equal to 4.

4 add 3, and both of those equal 7.

So we've balanced our equations, we've got that same sum all the way through.

Okay, so we've got a different calculation this time.

Have you spotted that we've now got hundredths in there? Remember those small yellow cubes are representing a hundredths, aren't they? Hmm, I can see a three in both of my addends.

I can see the three in 3.

08, and I can also see the three digit in the 4.

39.

Can you spot where they're represented in my base 10 equipment or in my deans? That right.

So the three ones is represented here by our three ones that we're using as per representation for today.

And my three tenths are represented over here, aren't they? By my three green rods.

That's right.

One of the time little confused by some people find a bit is why is my zero here represented? What's that's zero meaning? Yes, it's in the tenths column, it means we haven't got any tenths, there are zero tenths.

And as you can see over here in this representation, there are none of my green rods.

So we have zero tenths, okay? So this tenths are not represented as an absence I've left to little space just to show that.

Right.

Let's think about our calculation now.

So again, if we are going to be using that equivalent, sort of same sum rule, is one addend is increased by an amount and the other addend is decreased by the same amount, the sum remains the same.

So take a look at these two numbers now, the 3.

08 and the 4.

39.

What do you think you would do this time to redistribute those numbers, to make the calculation easier? Pause the video here and have a think.

I wonder whether in this calculation, you noticed what I noticed.

I spotted that 3.

08 is actually really close to three.

It's only eight hundredths away, which is a tiny amounts.

Hmm, so I wondered whether I could decrease 3.

08 by those eight hundredths and increase, therefore the 4.

39 by eight hundredths, have a look.

So, my hundredth have moved over, my eight hundredths have moved over to join 4.

39.

So 3.

08 has decreased by eight hundredths, and 4.

39 has increased by eight hundredths.

So now we get a new equivalent calculation.

But it's not that easy because if you start at this side, I've got eight hundredths here and I've got nine hundredths here.

I have to think quite carefully about recombining those, don't I? And if you imagine me stealing one of those hundredths or redistributing one of those hundredths and popping it on top of that, can you see that we get a new tenth? So therefore we would have four tenths and then we would have seven hundredths here.

I wonder if you can imagine that.

So, our new calculation or our equivalent calculation would be three add 4.

47.

But, I'm just wondering to myself, how's that really helped me, that redistribution? Because, merely couldn't I just have done three ones add four ones and then done the eight hundredths and the 39 hundredths, and partition the calculation.

I wonder whether this particular redistribution was very helpful.

I'm not so sure.

Sometimes redistributing the numbers doesn't help, or sometimes it doesn't help, because you might not have redistributed them in the best way.

Let's have a look at in the next example.

So with that, with those last same calculations is 3.

08 add the 4.

39, maybe you chose to redistribute the numbers in a different way.

Maybe you spotted that the 4.

39 is very close to 4.

4, and that that might help us.

So if I increase the 4.

39 by one hundredths, if you watch it happen, it should happen now, there we go,.

Increased it by one hundredth, you can see now that we have not got 4.

39 anymore, we've got four and one, two, three, four tenths, because remember 10 hundredths is the same as one 10th, isn't it? So, we increase 4.

39 by one hundredth, so we had to decrease the other addend, the 3.

08 by one hundredth, which happened a moment ago in my animation.

And we've now got 3.

07 add 4.

We could use place value to help us to work this out now.

And we would get 7.

47.

Perhaps that redistribution was a little better than the other, but you may still be stuck there thinking that you didn't really need to do it, that actually I could just have added eight hundredths onto the 39 hundredths.

In which case, if that is quicker, there's no point in redistributing the numbers at all, is there? So let's look at this example now.

Saidi decided to make this equivalent calculation to help her to solve this more easily.

So let's have a look for that equivalent calculation first.

Who is the big here and have a careful look at what did Saidi do to make the calculations equivalent? Did you spot it? She decreased the first addend, hasn't she? And she's increased the second addend.

I wonder which one she focused on first.

I think she focused on 3.

982.

Because 3.

98 is very close to four.

And we've already discovered that calculating with integers or whole numbers is much easier than calculating with decimals.

So 3.

98 has increased by what to get to four? It's got 98 hundredths.

How many hundredths do we need to make that next one, that whole one? That's right, we need a hundred hundredths to make a whole one so we need two more hundredths.

So it's increased by two hundredths.

And that first addend has decreased by the hundredth.

Hmm.

How do we know that 5.

3 decreasing by two hundredths gives us 5.

28? What do we know about 0.

3? We do know it's three tenths, it's brilliant.

How many hundredths make a tenth? That's right, it's was ten hundredths.

Do you remember at the start of the video where we saw those 10 little yellow cubes make the same size as that one green rod that tenths rod? Brilliant.

So if you imagine that we had three tenths rods, how many of those little yellow cubes would we need? That's right, 30 hundredths.

So is 5.

3 is also the same as five and 30 hundredths.

And if we decrease those 30 hundredths by two, we'd get 28 hundredths, so it's 5.

28.

And 5.

28 add four is 9.

28.

So we've now got that equivalent calculation.

I think Saidi has made it quite easy.

So Sanjay decided to complete the calculation in this way.

What decisions do you think Sanjay made to create his equivalent calculation or his same sum? Have careful look, you might want to pause the video just whilst you do that.

Did you spot it? That's right, there was a bit of a clue, wasn't there? In the 5.

3 and the five.

The 5.

3 must have decreased by three tenths to get it to five.

So to make sure it's that equivalent, same sum, we must increase the other addend by 0.

Let's take a little bit of a careful look at 3.

98 and increasing it by 0.

What do we know about 0.

3? That's right, it's three tenths.

And what do we know about three tenths? How many hundredths are there in three tenths? Yes, we did this on the previous slide.

there's 30 hundredths, aren't there? So we're increasing this by 30 hundredths.

So I was thinking, how about if we take our 3.

98, increased it by two hundredths to get to four ones, and then I need to increase it by a further 28 hundredths, it will get me to 4.

28.

And he's created another equivalent calculation.

And you can see that we have that same sum, the 9.

28.

So five add 4.

28 is 9.

28.

I think that's a little easier than the original calculation.

Let's just compare Saidi in Sunjay's methods now side by side.

Which one do you prefer and why? If you could pause the video here and have a careful look at them side by side, and we'll speak about it again in a moment.

I wonder which one you chose.

Well, both of them are absolutely fine, aren't they? Because both of them give us that same sum and that equivalent calculation.

I think, as long as you followed the rule, if one addend is increased by an amount and the other identity is decreased by the same amount, and the sum remains the same, then you could use either, because I think both Sunjay and Saidi have created easier calculations.

I think really this decision on which one's easier probably comes down to your own number sense and which one you think would work for you.

In the last few calculations, we discovered that you can alter either addend, but now I want you to make some careful decisions about which addend to increase or decrease to make these two calculations easier to solve.

So have a look at the two calculations carefully and pause the video to consider the equivalent calculations you could use to make these as easy as possible to solve.

Have you done that? Let's have a look at what I thought.

You might have a different decision to make.

So I had a look at the 7.

8 add 1.

68, and I thought 7.

8 is close to eight.

So I'm going to increase it by two tenths to make it into that whole number.

So 7.

8 becomes eight, so I'm going to decrease the other addend by 0.

2 or two tenths to make it 1.

48.

And now I've got quite an easy calculation to solve, eight add 1.

48 is? That's right, 9.

48.

And so therefore 7.

8 add 1.

68 is also 9.

48.

What about in example two? Did you spot that 3.

96? It's close to four, isn't it? How far away is it from four? Yes, it's only four hundredths.

So I decided that I would increase 3.

96 by four hundredths.

Did you do the same? And decrease the 7.

31 by four hundredths.

So our equivalent calculation is 7.

27, add four.

And now we've got a much easier calculation because I can do seven add four in the ones, and then I just need to remember that 0.

27 at the end, don't I? So we'd get a total or a sum of 11.

27, which means that both 7.

27 add four is 11.

27, and so is 7.

31 add 3.

96.

Personally, I think redistributed numbers are definitely easier to solve, what do you think? Okay, so now it's your turn to do some work.

And I've left you with some practise for today.

in part A, I just want you to fill in the missing numbers, and you'll notice there was a connection between the ones in the box there.

So make sure you pay attention to the connection between this calculation and the equation underneath, okay? Thinking about that redistribution.

And that's the same in each of those boxes.

I've put on that generalised statement for you just to remind you.

And then part B says "Ready for a challenge? "Salvo says that the best way to solve these calculations "is to use the same sum." Or an equivalent calculation, it means the same thing to make them easier.

"Mia disagrees and says that it is easier and quicker "to use a written method.

"who is right." I wonder whether you could compete with someone in your household and help you find out who's is quicker.

Remember, our equivalent calculations, you don't have to write down all the steps we've written down today, they're just there to help you understand.

Eventually, it'd be great if you can imagine that one addend increasing and the other addend decreasing, and then it's a bit like turning your sum into a magical new calculation that you can do really quickly, and maybe keep it secret from your parents or whoever you compete against about what you did, and show them what an absolute wiz you are.

I hope you've enjoyed today's session.

I'm back again tomorrow, so I'll see you then.

I've finished the video