Lesson video

Hello.

I'm Dr.

Claire Shorrock.

And welcome to lesson number five in our series of lessons on number, addition or subtraction for Upper Key Stage 2.

Let's start by reviewing the practise activity that Mrs. Furlong set for you yesterday.

Did you notice something? Did you notice, that we added 0.

24 to this addend? So what did it mean we had to do to the other addend? That's right.

We had to subtract 0.

24.

Now I'm interested in how you did this calculation to fill in this missing box here.

Did you notice that you've got two tenths and eight tenths? In which case we can use our number bonds.

Two tenths at eight tenths is? I'm sorry.

I didn't hear you.

Two tenths add eight tenths is that's right.

10 tenths and 10 tenths is equivalent to one whole.

So that means we have five wholes and another whole.

And then these 400 left over.

So we have 6.

04.

We can then write out our balanced equation.

If we have a look at the next question, what did you notice? That's right.

We added 0.

57 to one addend.

So what did we have to do to the other addend to make the sum the same? That's right.

We had to subtract 0.

57.

So then how did you do this calculation here is to fill in this missing box.

Did you notice there were five tenths here and five tenths here.

Five tenths add five tenths is? that's right.

10 tens and 10 tens.

Is the same as one whole.

So we had seven wholes in total and these seven hundreds left.

So 7.

07.

We can then complete our balanced equation where the left-hand side and the right-hand side had the same sum.

And that sum was 10.

You will also set a challenge to have a go at it.

If you wanted, about using the same original addends and this structure to redistribute a different amount from one other end to the other and form some other balanced equations.

I wonder what you did.

I'm sure they were fantastic.

So really well done.

If you had to go at the challenge before sys.

excuse me, before we start, today's learning.

I just like to quickly review the learning from yesterday where you redistributed 340 grammes from one addend to the other addend, you subtracted 340 from one addend.

So you needed to add 340 to the other addend.

So you could keep the sum the same from that you took the original amount and the re-distributed amount, and you formed a balanced equation.

In today's learning, we're going to show you a different representation for balancing equations, and we're going to use that to work out some missing numbers in some missing number problems. So have a look at this, pause the video.

If you want to tell me what you notice that's right.

This is just another representation of our bags of potatoes.

We've got the two bags here and the total mass was 10,000 grammes.

We can tell, this is a balanced equation because my balance is level and we've got the equal sign here, which tells us that the total value of the left-hand side must be equal to the total value on the right hand side.

And we're going to use this representation now to solve some problems. But before we look at some problems, what do you notice here? Hmm, that's right here.

I've shown the re-distribution.

I've shown the subtraction of 340 from one addend.

And i've shown the addition of 340 from the other addend, the balance has stayed level, which means the sum of this side is going to be equal to the value of the number.

On this side, I have subtracted 340 from one addend.

So I need to add 340 to the other addend so I can keep the sum the same I wonder what might be under, wonder what the values of the numbers is.

that might be under these orange boxes pause the video If you want, have a go at saying the calculation out loud and staying the same sentence out loud, when you're ready and you've had to practise, press play again.

Okay.

Did you spot? We subtracted 270 from one addend.

So we had to add 270.

The other addend, the balance has remained level, which means the sum of these numbers here must be equivalent to 10,000.

I have subtracted 270 from one other addend.

So I need to add 270 to the other addend to keep the sum the same, keeping the sum the same shows that the balance is level.

Hey, what about this one? Pause the video.

Have a go, say the calculation out loud and the STEM sentence.

Did you notice? We added 690 to one addend.

So therefore we must've subtracted 690 from the other addend so that we could keep the balance level and the sum the same, say the STEM sentence with me.

I have added 690, to one addend So we need to subtract 690 from the other addend to keep the sum the same.

What do you notice about this? There's another different representation.

Oh yes.

Look on the left-hand side here.

We have the original, massive bag of potatoes, which the total some of which was 10,000 on the right hand side, we've got the re-distributed amount of the bag of potatoes.

But again, the sum was 10,000.

So the scale remains balanced because we have the same sum on the left-hand side as the right hand side.

Let's look at this in the context of a problem now there's the same number of children in year five, as there is in year six in year five, there were 28 boys and 32 girls, in year six.

There were 29 boys.

How many girls are there in year six? So I'd like to pause the video, read the question for a second time.

So you've got all the information that you need and have a go, give you a hint? You should be able to do this with very little calculating and maybe use that balance representation that I've left there for you.

When you've had a go start the video again.

Okay.

I wonder if anyone else used the balanced representation like I did.

I've got my year five children on one side and my year six children on the other side, the balances level, because I know there are the same amount of children in year five as they are in year six.

But how does this representation help me solve the problem? How, how does it help me work out? How many girls there are in year six? Well, I could represent it using a bar model.

I know the total is going to be, the 28 plus 32, which is 60.

That's the total number of children in year five.

And in year six, I've got one part here.

So I can use this information to calculate the missing part by doing 60 take away 29.

But that seems an awful lot of work.

I wonder if there's a more efficient way.

And usually when teachers say that, they mean, yes, there is a more efficient way.

And we like you using efficient ways.

When we use an efficient way, a method there's less steps and there's less chances for anyone to make mistakes.

So let's take a look, now lets take a look at these addends.

What do you notice about 28 and 29? That's right.

29 is one more than 28.

So if I add one to my addend, what do I need to do to the other addend? We should be getting good at this by now.

That's right.

If I add one 12, addend, I've got to subtract one from the other addend 32 subtract one is 31.

So that means there are the 31 girls in the year group.

Now, before we move to our next word problem, what I'd like to do is to just have a chat about these addends.

I chose to redistribute the 28.

Could I have redistributed the 32? What do you think here? We distributed a number of boy to boy.

Could I have looked at the number of girls and then gone to the boys? Hmm, yes.

That would be absolutely fine.

When we represent these imbalanced equations.

I'm not so worried about if it's a boy or a girl, it's the numbers that we're interested in.

And because addition is competitive, we can do to either order.

It doesn't matter which number I redistribute from.

As long as I redistribute the correct amount, let's have a look.

So this is what we did.

We looked at the 28.

We added one.

We noticed we could add one to get 29, which means we could just subtract one from the 32 to give us 31.

But could we have looked at the 32 instead? Let's have a look.

What did you notice about 32 and 29.

That's right.

29 is three less than 32.

So if I subtract three from 32, I get 29.

So if I subtracted three, what do we need to do to the other addend to the 28? That's right.

I'm going to need to add three, 28 add three.

Well, I know 28, add two is 30 so 28 add three must be 31.

So it doesn't matter whether we redistribute from the 28 or the 32, we both ended up with 31, year six girls, and that's a lot of, a much simpler method.

Just one set method compared to representing the bar model and doing that more difficult subtraction.

Okay.

Should we have a look at another problem? Sally plans to buy 30 bottles of Cola and 25 bottles of juice for a party? Yeah.

Sounds like a good party.

doesn't it my kind of party.

When she gets to the shop, they only have 15 bottles of juice.

Oh, no disaster.

She can't buy what she wanted to buy.

She does however want to buy the same number of bottles of drinking total.

If she buys all 15 bottles of juice, how many bottles of Cola will she need to buy? So that she ends up with the same amount of bottles.

you don't want her guests being thirsty.

Do we? no So pause the video, read the question again.

First, it's really valuable in math to read questions more than once you get all the information, then have a go.

Maybe use the balance scales represented there for you and see if you can do it by as little calculating as possible.

Okay.

When you've had a go press play on the video again.

Okay.

I wonder if anyone represented the problem like I've done on my balance scales.

So I've got the total number of bottles that Sally wants to buy that she planned to buy.

And then I've got here, the actual, what actually happened when she went to the shops.

So how can we use this information to work out what we need to work out the number of bottles of Cola that she's going to have to buy? Again, we could represent this in a bar model.

We know the total amount of bottles that Sally planned to buy 55.

And we know we've got this part here, the number of bottles of juice that she can buy.

So we could do a subtraction 15 55.

So excuse me, take away 15 and find this part here.

Or we could use that more efficient method.

So let's have a look at the addend here.

What do you notice about 25 and 15? That's right.

15 is 10 less than 25.

So I have subtracted 10 from one addend.

So what does that mean? I need to do to the other addend.

That's right.

I need to add 10 to 30.

Add 10 is 40.

So that means she had to buy 40 bottles of Cola.

So the, in total, she planned to buy 55 bottles and she actually bought 55 bottles.

It just wasn't quite the same as her plan again should we have a look at the other addend? Would it have mattered? if instead of redistribution from the 25 we'ed we distributed from the 30 would that matter? Let's have a look.

So what do you notice about the 30 and 15? Hopefully you're all shouting out at me now.

15 is half of 30.

Good.

Glad to hear it.

Okay.

So what we notice, we notice that 15 is 15, less than 30.

So if I have subtracted 15 from one addend, what do I need to do? That's right.

You know this by now that you've got this, we need to add 15 to our other addend 25 add 15 is 40.

So we re-distributed them from the other addend.

It doesn't matter which addend you choose to re-distribute from.

As long as you're re-distributing the correct amount, Okay,I'm going to fantastic work.

You guys really worked really hard, really impressed, really well done.

I'm going to leave you with a practise activity that we will pick up again tomorrow.

So I've got a scenario for you here.

I've got dad on the balancing scales and one end of the balancing scale holding his cat.

And on the other end, is the daughter holding a dog.

Okay.

We've got some questions for you based on that scenario.

How is it possible that this scale is balanced? I wonder if you can have a think about what the masses might have to be and whether or not you can find the possibility that you'll think no one else will think of if the mass of the pets is the same as each other.

So that means maybe a bigger cat and a smaller dog.

What does this tell you about the mass, the dad and the daughter? Here's a, here's a thing to wonder.

I wonder, do you know roughly what the mass of a cat might be? What about the mass a dog, what of, a dad or a daughter, that maybe a little bit of extra practise for you, maybe go away and do a little bit of research and come back tomorrow.

Ready to be able to tell me the rough, mass of a cat and a dog and a dad and a daughter.

But anyway, if the mass of the pet is about the same, what does this tell you about the mass of the dad and the daughter? If the dad weighs two kilogrammes more than the daughter, what does that tell us about the mass of the cat and the dog with this in mind, if I tell you the mass of the dad is 90 kilogrammes, what has the mass the daughter got to be? And then what might the massive the pets be? And there's a challenge.

I wonder if you can have a go writing your own problem based on this scenario.

So think of something like this and then go and ask somebody else in your family to see if they can solve your questions.

Okay.

So I will catch you again tomorrow really enjoyed today.

Worked really hard, really impressed.

Thank you for all your hard work.

See you all tomorrow.

Bye-bye.